Mathematics - Grade 2 (2026-2027)

基本问题

• How does the value of a digit change based on its place?
• How can counting patterns help us understand number relationships?

标准

1. 1 Hundreds, Tens, Ones: Building 3-Digit Numbers with Base-Ten Models 完整课程 Hundreds, Tens, Ones: Building 3-Digit Numbers with Base-Ten Models

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group mini-lesson; partner talk; independent practice; optional small-group reteach/enrichment during independent practice

   学习目标

   • I can build a three-digit number with base-ten blocks and tell how many hundreds, tens, and ones it has. Apply

     成功标准:

     • I correctly use hundreds flats, tens rods, and ones cubes to build a number my teacher says (e.g., 348).
     • I say the number as “___ hundreds, ___ tens, ___ ones” and my model matches.
     • I write the number using digits to match my model.

   • I can write a three-digit number in expanded form to show hundreds, tens, and ones. Apply

     成功标准:

     • Given a base-ten model or a three-digit number, I write the standard form correctly (e.g., 348).
     • I write the expanded form correctly (e.g., 300 + 40 + 8).
     • My expanded form matches the hundreds, tens, and ones in the model/place value chart.

   • I can explain what each digit means in a three-digit number. Analyze

     成功标准:

     • I point to each digit and name its place (hundreds, tens, ones).
     • I state the value of each digit (e.g., in 348, the 3 means 300).
     • I use a complete sentence to explain (e.g., “The 4 is in the tens place, so it means 40.”).

   • I can compare two three-digit numbers using >, =, or < and explain my thinking using hundreds, tens, and ones. Analyze

     成功标准:

     • I compare the hundreds digits first; if they are the same, I compare the tens digits; if they are the same, I compare the ones digits.
     • I use >, =, or < to record the comparison correctly.
     • I explain in words why one number is greater/less based on place value (e.g., “392 > 329 because both have 3 hundreds, but 9 tens is greater than 2 tens.”).

   标准

   • CCSS.MATH.CONTENT.2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
   • CCSS.MATH.CONTENT.2.NBT.A.1.A 100 can be thought of as a bundle of ten tens — called a “hundred.”
   • CCSS.MATH.CONTENT.2.NBT.A.1.B The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
   • CCSS.MATH.CONTENT.2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
   • CCSS.MATH.CONTENT.2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

   材料

   • Base-ten blocks (hundreds flats, tens rods, ones cubes) · 1 student set per pair (minimum: 6 hundreds, 12 tens, 20 ones per pair)Pre-bag sets in zip bags; include a few extra tens/ones for swapping mistakes.
   • Student place value chart (Hundreds | Tens | Ones) · 1 per studentLaminated optional; if laminated, provide dry-erase markers and erasers/socks.
   • Document camera or projector · 1To model building numbers and to display quick visuals for the number talk.
   • Teacher place value chart (large) · 1Chart paper or magnetic chart for whole-group modeling.
   • Whiteboard/chart paper and markers · 1 setPost learning targets, vocabulary, and worked examples.
   • Recording sheet or math notebook page for independent practice · 1 per studentIncludes sections for: draw model, write H/T/O, write standard form, expanded form, and one explanation sentence.
   • Exit tickets (half-sheet) · 1 per studentCollect for quick scoring (0-1-2 rubric).
   • Optional: base-ten picture cards and number/expanded form cards · 1 class set (8–12 cards per type)Use for matching center or fast-finisher extension.

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Facilitate a quick number talk using 3 visuals. Keep pace brisk; prompt multiple strategies; record student language using H/T/O terms.

   学生操作: Look at each visual, think quietly, show a silent thumb when ready, then share the number and reasoning using place-value language.

   教师脚本（完整）

   “Eyes on the screen. I’m going to show a model for just a few seconds. Your job is to figure out the number and be ready to explain how you know. Here’s the first model.” (Show 2 tens and 7 ones.) “Think… What number is it? Give me a silent thumbs-up when you know.” “Turn and tell your partner: ‘I think it’s __ because I see __ tens and __ ones.’ Go.” (10 seconds) “Who can share? Use the words tens and ones.” (Repeat with: 1 hundred; 9 tens.) “Today we’re going to build and read three-digit numbers using hundreds, tens, and ones. When I show a model, you will tell me how many hundreds, tens, and ones you see, and then say the number.”

   Direct Instruction10 min

   教师行动: Explicitly model base-ten block values; connect blocks to a place value chart; model translating among model → H/T/O → standard form → expanded form; check for understanding with targeted questions and partner talk.

   学生操作: Watch, listen, answer choral questions, use partner talk to explain digit value, and track with finger on a place value chart.

   教师脚本（完整）

   “Watch me closely. These blocks help us *see* place value. This flat is 100—one hundred. Say it with me: ‘one hundred.’ This rod is 10—one ten. Say it: ‘one ten.’ This little cube is 1—one. Say it: ‘one.’ Now I’m going to build a number: 3 hundreds, 4 tens, and 8 ones.” (Build under document camera.) “Let’s connect it to our place value chart. In the hundreds column I write 3, in the tens column I write 4, in the ones column I write 8.” (Write 348.) “I read 348 as ‘three hundred forty-eight.’ I can also write it in expanded form to show the value of each digit: 300 + 40 + 8.” “Now I’m going to cover the ones with my hand.” (Cover the ones blocks.) “If I cover the ones, what place is left on the right side of the chart?” “Turn and tell your partner: What does the digit 4 mean in 348? Use this sentence frame: ‘The 4 is in the ___ place, so it means ___.’ Go.”

   理解检查: Use 3 quick checks: (1) Choral response: “In 348, what place is the 3 in?” (2) Cold call: “What is the value of the 3?” expecting “300.” (3) Mini-whiteboard check: students write expanded form for 348; teacher scans for 300 + 40 + 8.

   Guided Practice15 min

   教师行动: Lead a structured We Do sequence building numbers together; monitor manipulatives use; correct misconceptions in the moment; incorporate brief comparison routine if time allows.

   学生操作: Build numbers with base-ten blocks, say H/T/O aloud, record on place value chart, and write standard/expanded form; participate in comparisons using place-value reasoning.

   教师脚本（完整）

   “Now we will build numbers together. Keep your blocks in the middle of your desk so I can see them. Ready? We are building 215. Step 1: Show me 2 hundreds. Hold your hands up when you have 2 hundreds. Step 2: Now add 1 ten. Step 3: Now add 5 ones. “Point to your model as you say it with me: ‘2 hundreds, 1 ten, 5 ones.’ What number did we build?” (Choral: “215.”) “Now write it on your place value chart: 2 in hundreds, 1 in tens, 5 in ones. Write the standard form: 215. Write the expanded form: 200 + 10 + 5.” “Let’s do one more, and this time I’ll choose a helper to lead the steps.” (Choose student.) (Student leads for 420.) Teacher: “Class, check: Do we have 4 hundreds, 2 tens, and 0 ones? If there are 0 ones, what do we do?” Optional compare (if time): “Look at these two numbers: 392 and 329. Which is greater? Start with the hundreds. If the hundreds are the same, what do we compare next?”

   支架提示: “Where do hundreds flats go on the chart—hundreds, tens, or ones?” | “Count the flats first. How many hundreds do you have?” | “If you have 0 tens, what should you *see* in your model? What should you *write* in the tens place?” | “Say it in order: hundreds, tens, ones. What do you have?” | “Point to the digit you are talking about. What is its value?” | “How do you know 4 tens is 40 and not 4?” | “If two numbers have the same hundreds, what place do we compare next? Why?”

   Independent Practice15 min

   教师行动: Release students to independent work; circulate with a checklist; pull a quick small group for reteach if needed; confer with individuals using brief prompts; collect evidence of explanations.

   学生操作: Complete task set: draw quick base-ten sketches, label H/T/O, write standard and expanded form, and write one sentence explaining a digit’s value; ask for help using agreed-upon routine (e.g., raise hand, ask partner, then teacher).

   教师脚本（完整）

   “Now you will work on your own. Your goal is to make your drawing match the number, then prove it by writing the hundreds, tens, ones, and the expanded form. Remember: Flats are hundreds, rods are tens, cubes are ones. If you finish early, double-check: Does your expanded form match your drawing?”

   监控清单: Student draws or builds the correct number of hundreds flats for the given number. | Student draws or builds the correct number of tens rods for the given number. | Student draws or builds the correct number of ones cubes for the given number. | Student labels or writes the correct H/T/O counts (e.g., “1 hundred, 3 tens, 7 ones”). | Student writes the correct standard form matching the model. | Student writes the correct expanded form (e.g., 500 + 0 + 6 or 500 + 6, per class expectation). | Student explanation sentence correctly names the place and value of a digit using a complete sentence.

   Closure5 min

   教师行动: Administer and collect exit ticket; prompt students to self-check using place value language; select 1–2 students to share reasoning if time; preview next lesson.

   学生操作: Complete exit ticket independently; use self-check strategy (match H/T/O to expanded form); hand in ticket; listen to brief wrap-up.

   教师脚本（完整）

   “Before we leave, show what you know. Write the number, then write ‘___ hundreds, ___ tens, ___ ones’ and the expanded form. If you’re stuck, ask yourself: What does each block stand for? Hundreds are 100, tens are 10, ones are 1.” “Today you used models to build numbers and explain what each digit means. Tomorrow we will practice reading and writing more numbers to 1,000 and we’ll get faster at switching between forms.”

   退出票: Exit Ticket: The number is 604. 1) Write it as: ___ hundreds, ___ tens, ___ ones. 2) Write the expanded form. 3) Write one sentence explaining what the digit 6 means in 604.

   hundreds place

   It tells how many groups of 100 are in the number.

   tens place

   It tells how many groups of 10 are in the number.

   ones place

   It tells how many leftover ones are in the number.

   base-ten blocks

   Math blocks that help us build numbers with 100s, 10s, and 1s.

   expanded form

   We “stretch out” the number to show hundreds, tens, and ones.

   English Language Learners

   • I can use the sentence frame “___ hundreds, ___ tens, ___ ones” to describe a three-digit number.
   • I can use the sentence frame “The ___ is in the ___ place, so it means ___.” to explain digit value.
   • I can correctly read three-digit numbers aloud using place-value language (hundreds, tens, ones).
   • Pre-teach vocabulary with real blocks and picture cards; gesture: hold up flat/rod/cube while naming hundred/ten/one.
   • Provide bilingual glossary or home-language support when available (e.g., translated key terms on a small card).
   • Use sentence frames on desk strip and board; require oral rehearsal with partner before sharing out.
   • Use visuals consistently: labeled place value chart (H/T/O) + color-coding (hundreds=blue, tens=green, ones=yellow).
   • Allow students to respond by pointing to blocks/digits first, then saying the sentence; accept approximate grammar if mathematical meaning is correct.
   • Strategic pairing: ELL with supportive peer; assign roles (Builder, Recorder, Speaker) to structure talk.

   Struggling Learners

   • Start with smaller, friendlier numbers that still include hundreds (e.g., 101, 110, 205) before moving to 3 non-zero digits.
   • Chunk tasks: (1) build/draw model, (2) say H/T/O, (3) write digits, (4) write expanded form; check each chunk before moving on.
   • Provide a guided recording sheet with prompts: ‘Hundreds: __’ ‘Tens: __’ ‘Ones: __’ and expanded form template ‘__00 + __0 + __’.
   • Use physical place value mat where blocks must be placed in labeled columns to prevent swapping tens/ones.
   • Offer reduced set during independent practice (complete 2 numbers instead of 4) with expectation of high accuracy and a verbal explanation.
   • Peer support: partner check using a “match test” (Does the model match the chart? Does the chart match the number?).
   • Frequent micro-checks: teacher asks student to point and name each place before writing expanded form.

   IEP / 504 Accommodations

   • Preferential seating near teacher/modeling area; minimize visual distractions during modeling.
   • Provide extra processing time and allow oral responses in place of some written responses (especially for the explanation sentence).
   • Use large-print place value charts and enlarged exit ticket if needed.
   • Allow manipulatives throughout (including on exit ticket if consistent with accommodations).
   • Break directions into single steps; provide a checklist the student can mark as they go.
   • For fine-motor needs: allow drawing with stamps/pre-drawn block stickers or digital drag-and-drop base-ten blocks.
   • Behavior/attention supports: short movement break after guided practice (30 seconds: ‘stand, stretch, sit’) and clear time reminders.

   Advanced Learners

   • Create a number with exactly 5 blocks total (flats/rods/cubes) and write the standard and expanded form; explain constraints.
   • Given two numbers (e.g., 406 and 460), write a comparison using >, <, or = and justify in 2 sentences using place value reasoning.
   • Write three different numbers that have 7 hundreds and are between 720 and 790; represent each in expanded form.
   • Error analysis: teacher provides an incorrect expanded form (e.g., 348 = 300 + 4 + 8). Student identifies the mistake and corrects it with an explanation.
   • Challenge: Build the greatest and least number you can using 4 hundreds, 9 tens, and 3 ones—then discuss what happens if you regroup tens into hundreds (preview concept without requiring mastery).

   形成性检查

   • Warm-up number talk responses: accuracy and use of tens/ones language noted.
   • Direct instruction mini-whiteboard check: students write expanded form for 348; teacher scans for 300 + 40 + 8.
   • Guided practice observation: teacher checks correct block selection and correct placement on place value chart.
   • Independent practice teacher checklist: model correctness, H/T/O counts, standard form, expanded form, and explanation sentence.

   退出票

   Exit Ticket: The number is 604. Write H/T/O, expanded form, and one sentence explaining the value of the digit 6.

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 This template supports the lesson's explicit vocabulary terms related to place value and base-ten blocks, reinforcing key math language for grade 2 students.
   • Worksheet 匹配活动 The matching activity aligns with the optional base-ten picture cards and number/expanded form cards mentioned for student centers or extensions.
   • Worksheet T-图 A T-Chart organizer helps students visually compare and organize the components of hundreds, tens, and ones, matching the lesson's focus on place value structure.
   • Worksheet 3-2-1 退出票 The 3-2-1 Exit Ticket provides a simple formative assessment tool suitable for grade 2 to quickly gauge student understanding at lesson closure, matching the exit ticket requirement.

   Storypie 内容

   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory
   • Storypie Content Addition Addition is a fundamental mathematical operation that represents the total amount of objects together in a collection. It is signified by the plus sign (+).
   • Storypie Content Cash Register A mechanical or electronic device for registering and calculating transactions at a point of sale, which also includes a drawer for storing cash and often a receipt printer.
   • Storypie Content Fractions Fractions represent parts of a whole or, more generally, any number of equal parts. They are a fundamental concept in mathematics used to express division, ratios, and numbers that are not whole.
   • Storypie Content Division Division is a fundamental arithmetic operation that is the inverse of multiplication. It is the process of splitting a number into equal parts or groups.

   准备清单

   • Pre-bag base-ten blocks for pairs; include extra rods/cubes in a separate ‘swap’ bin.
   • Copy/place student place value charts and independent practice recording sheets; prepare exit tickets.
   • Prepare 3 warm-up visuals (e.g., 2 tens 7 ones; 1 hundred; 9 tens) and test projection/document camera.
   • Post or prepare board plan: learning targets, vocabulary, sentence frames, and example 348.
   • Create optional matching cards (base-ten pictures, standard form, expanded form) and place in a bin for fast finishers.
   • Plan partner assignments (consider ELL and behavior supports).
   • Set up a small-group reteach station with place value mats and a reduced practice set (101, 110, 205, 300).

   常见误解

   • A ten is ‘one’ because it is one rod (confusing unit with value).
   • If a place has 0, students think it ‘doesn’t count’ and leave it out of the numeral (e.g., write 64 for 604).
   • Students read 348 as ‘three four eight’ instead of ‘three hundred forty-eight.’
   • Students believe the leftmost digit always means the number of blocks, not the value (e.g., 3 means 3, not 300).
   • Students reverse tens and ones when recording (e.g., build 215 but write 251).
2. 2 Read, Write, and Say Numbers to 1,000 (Standard, Word, Expanded Form) 完整课程 Read, Write, and Say Numbers to 1,000 (Standard, Word, Expanded Form)

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group → partners → independent (with small-group reteach at front table as needed)

   学习目标

   • I can read and say three-digit numbers (100–999) and tell how many hundreds, tens, and ones they have. Understand

     成功标准:

     • When shown a 3-digit number, I read it aloud correctly using number names (e.g., 584 = “five hundred eighty-four”).
     • I identify the value of each digit as hundreds, tens, or ones (e.g., 584 has 5 hundreds, 8 tens, 4 ones).
     • I explain using precise place-value language (hundreds/tens/ones; zero tens/zero ones when needed).

   • I can read, write, and represent numbers to 1,000 (including 1,000) in standard form and word form. Apply

     成功标准:

     • When I hear a number name, I write the correct base-ten numeral.
     • When I see a numeral, I write a matching number name using place-value words (e.g., “hundred”).
     • My numeral and word form match each other (the same value).

   • I can write numbers to 1,000 in expanded form as hundreds + tens + ones, and I can check by recombining. Apply

     成功标准:

     • I write expanded form as the sum of hundreds, tens, and ones (e.g., 584 = 500 + 80 + 4).
     • I represent zeros correctly when present (e.g., 706 = 700 + 0 + 6 or 700 + 6).
     • I verify at least one expanded form by adding parts to get the original number.

   标准

   • CCSS.MATH.CONTENT.2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
   • CCSS.MATH.CONTENT.2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
   • CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
   • CCSS.MATH.PRACTICE.MP6 Attend to precision.

   材料

   • Place value chart (poster/anchor chart) labeled Hundreds–Tens–Ones · 1 class set display (plus optional student mini charts)Include large columns; leave space for digits and base-ten drawings.
   • Base-ten blocks (hundreds flats, tens rods, ones cubes) or printable base-ten visuals · 1 set per pair (or shared tubs)Used for quick concrete checks; printable images acceptable.
   • Number form cards (standard, word, expanded) for matching · 6–12 cards for whole-class modeling + 2–3 sets per pairInclude at least one zero-in-the-middle (706/508) and one near 1,000 (999).
   • Mini-whiteboards, dry-erase markers, erasers (or paper/pencils) · 1 per studentFor warm-up and quick checks; paper can substitute.
   • Student practice page/worksheet (read/write/expanded form) · 1 per studentInclude: 5 numeral→word, 3 listen→numeral, 4 expanded (one with 0 tens or 0 ones).
   • Exit ticket slips (or half-sheets) · 1 per studentTwo items as described; collect at door.
   • Document camera or projector for modeling examples · 1Optional but recommended to model writing and to annotate.
   • Optional: sentence frames for math talk · 1 class set (poster or handout)Support academic language and precision.

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Facilitate a fast number talk that normalizes mistakes, invites multiple response modes (say/point/write), and previews place-value thinking. Display numbers one at a time: 307, 430, 999.

   学生操作: Whisper-read each number, then join choral reading. Show thinking using fingers for hundreds/tens/ones (e.g., 3-0-7), point to digits, or write the number name/expanded form on a mini-whiteboard.

   教师脚本（完整）

   “Eyes on the first number. Whisper-read it to yourself… ready… let’s say it together: 307.” “Now show me hundreds, tens, and ones. You can use fingers, point to the digits, or write it. There are many correct ways to show your thinking.” “Turn your head to your partner and answer: What does the 0 mean in 307?” (After 10 seconds) “I’m listening for precise words: hundreds, tens, ones.” (For 430) “Say it with me: 430. Is it ‘four hundred thirty’ or ‘four hundred and thirty’? In math class today we will say ‘four hundred thirty.’” (For 999) “This one is big. Whisper-read… now say it: 999, nine hundred ninety-nine.”

   Direct Instruction10 min

   教师行动: Use explicit modeling with a place value chart and connect standard, word, and expanded forms. Model a typical number (584) and a zero-in-the-middle example (706). Use choral response and quick checks for understanding.

   学生操作: Track the model on the chart, repeat key language, answer quick oral questions, and mirror the teacher by writing one example on whiteboards.

   教师脚本（完整）

   “Today our goal is to read, write, and say numbers all the way to 1,000 in three forms: standard form, word form, and expanded form.” “Watch me first. This is the place value chart: Hundreds, Tens, Ones.” (Write 584 in the chart) “I place 5 in the hundreds column, 8 in the tens column, and 4 in the ones column.” “I read it: five hundred eighty-four.” “Listen carefully: I’m being precise. The 8 is not just ‘eight.’ It is ‘eight tens,’ and eight tens is 80.” (Write) “Standard form: 584.” “Word form: five hundred eighty-four.” “Expanded form: 500 + 80 + 4.” “These are three different ways to name the same number. My job is to keep the value the same, even when the form changes.” (Now model 706) “Now I’m going to model a tricky one with a zero: 706.” “Seven is in the hundreds place: 700. Zero is in the tens place: zero tens. Six is in the ones place: 6.” “The 0 means there are zero tens. I still say ‘seven hundred six.’ I do not say ‘seven hundred zero six.’” “Choral response: Read 430.” (Pause) “Say it.” “Choral response: What is the expanded form of 430?”

   理解检查: Use “Show Me” boards: students write (1) word form for 430 and (2) expanded form for 430. Teacher scans for: correct omission of ‘and’, correct tens value (30), and 0 ones awareness (400 + 30 + 0 or 400 + 30).

   Guided Practice15 min

   教师行动: Lead ‘Match the Forms’ with one whole-class set, then release to partner sets. Prompt students to justify matches using place-value reasoning; monitor for precision and misconceptions about zeros and tens/ones values.

   学生操作: As a class, match three cards (standard/word/expanded) and justify. In pairs, complete 2–3 matching rounds, reading aloud and explaining using sentence frames.

   教师脚本（完整）

   “Now we do it together. This activity is called ‘Match the Forms.’ Your job is to prove the cards match by pointing out the hundreds, tens, and ones.” (Whole-class round: show cards for 392) “Here are three cards. Which ones belong together?” “Before we decide, let’s prove it.” “Where do you see the hundreds? Where do you see the tens? Where do you see the ones?” “Turn and tell your partner using the frame: ‘I know ___ because ___.’” (After partner talk) “Who can prove the match using place-value language?” (Partner rounds) “Now you and your partner will do two rounds. One partner reads the standard form, the other partner reads the word form, and together you check the expanded form.” “Remember: attend to precision. If the tens digit is 0, we say ‘zero tens,’ and we decide how that shows up in expanded form.” (Mid-lesson check) “Thumb check: 1 means ‘I need help,’ 2 means ‘I’m getting it,’ 3 means ‘I can teach it.’ Show me now.” “If you’re at 1, bring your cards and join me at the front table for the next example. We’ll do it slowly together.”

   支架提示: Point to the hundreds digit. How many hundreds is that? What is the value in hundreds? (Example: 5 hundreds = 500.) | Point to the tens digit. Say it as ‘___ tens.’ What is the value? (Example: 8 tens = 80.) | Point to the ones digit. How many ones? What is the value? | Read the number name slowly. Did you hear ‘hundred’? What comes after ‘hundred’—tens, ones, or both? | If there is a 0, say out loud: ‘zero tens’ or ‘zero ones.’ Where do we see that in expanded form? | Check: If you add the expanded parts, do you get the original number? | Does your word form match the digits? For example, if you said ‘five hundred eight,’ should there be a tens word like ‘twenty’ or ‘forty’?

   Independent Practice15 min

   教师行动: Launch independent task with clear expectations, circulate using a quick monitoring checklist, provide brief prompts (not solutions), and pull a small group for targeted reteach (especially zeros and tens value).

   学生操作: Complete practice page: numeral→word form, listen→numeral, expanded form. Use place value chart or base-ten visuals as needed. Fast finishers create-and-swap task.

   教师脚本（完整）

   “Now it’s your turn. Work silently first so I can see your thinking.” “If you get stuck, circle the problem and try a different form. Use the place value chart to help you.” “When I come by, I might ask you to point to the hundreds, tens, and ones to explain.” (While circulating—prompting script) “Tell me which digit is the hundreds digit.” “Now write just the hundreds value.” “Great. Repeat for tens and ones.” “Read your word form back to yourself. Does it match your numeral?” (Fast-finisher script) “If you finish early, create a new 3-digit number. Write it in standard, word, and expanded form. Then swap with a partner and check each other for precision.”

   监控清单: Student reads 3-digit numerals with correct number name (no extra ‘zero’ spoken; correct tens word). | Student identifies hundreds/tens/ones correctly when asked to point. | Expanded form uses correct values (e.g., 6 tens = 60, not 6). | Student handles zeros correctly (e.g., 508 includes 0 tens; 700s with 0 tens/ones). | Numeral written from dictation matches spoken number name. | Word form matches numeral (e.g., 641 is not written as ‘six hundred fourteen’). | Student uses place-value vocabulary (hundreds/tens/ones) during explanation.

   Closure5 min

   教师行动: Administer exit ticket, collect, and facilitate a brief share-out focused on the meaning of zero and keeping value constant across forms.

   学生操作: Complete exit ticket independently; optionally share one takeaway; respond to closing question verbally or with fingers.

   教师脚本（完整）

   “Before you go, prove to me you can keep the number’s value the same in different forms. If you can do that, you’ve got powerful place value skills.” “Exit ticket: Work quietly. Do your best; this helps me plan tomorrow’s lesson.” (After 3 minutes) “Pencils down. Quick closing question: What does a zero tell us in a number?” (Select 1–2 students) “Everyone else: show with your fingers—does zero mean zero tens or zero ones in the example we discussed?”

   退出票: 1) Write the word form and expanded form for 641. 2) I will say a number: “nine hundred two.” Write the numeral.

   place value

   A digit is worth different amounts depending on where it is in the number.

   digit

   A single number symbol like 3 or 0.

   standard form

   The regular way we write numbers with digits.

   word form (number name)

   Writing the number using words.

   expanded form

   Showing the number by adding the hundreds, tens, and ones parts.

   English Language Learners

   • I can name the hundreds, tens, and ones in a 3-digit number using the sentence frame: “The ___ digit is ___, so its value is ___.”
   • I can read and write number names to 1,000 using key words: hundred, tens, ones.
   • Pre-teach vocabulary with visuals: digit (single symbol), place value chart with labeled columns and color-coding (hundreds=blue, tens=green, ones=yellow).
   • Provide sentence frames on desk strips: “I know ___ because ___.” “___ hundreds, ___ tens, ___ ones.” “Expanded form is ___ + ___ + ___.”
   • Use choral reading and echo reading of number names; teacher models, students repeat (focus on pronunciation of -ty in forty, fifty, sixty, seventy, eighty, ninety).
   • Allow multiple response modes: point to chart, use fingers (H/T/O), draw base-ten blocks, or write.
   • Chunk spoken numbers during dictation: “six hundred… forty… one” with pauses; repeat once at normal speed.
   • Provide bilingual glossary or home-language support when available for key terms (hundred, tens, ones) and number names; allow partner translation briefly to confirm meaning.
   • Clarify language convention: in math class, avoid ‘and’ in number names; explicitly teach and practice this expectation.

   Struggling Learners

   • Use concrete manipulatives first: build the number with base-ten blocks, then record standard/word/expanded forms (CRA progression).
   • Provide a simplified practice page option with fewer items (e.g., 3 numeral→word, 2 expanded) while maintaining the same objective; offer extra time.
   • Chunk tasks: Step 1 circle hundreds digit; Step 2 write hundreds value; Step 3 tens; Step 4 ones; Step 5 combine/expand.
   • Give a personal mini place-value chart and a digit-value mat: ‘___ hundreds = ___’ ‘___ tens = ___’ ‘___ ones = ___’.
   • Use peer support strategically: pair with a patient, accurate partner; assign roles (Reader/Checker) to reduce cognitive load.
   • Offer guided small-group reteach focusing on zeros (0 tens/0 ones) and the difference between digit and value (8 vs 80).
   • Provide visual anchors for tens words: chart showing 20 twenty, 30 thirty, 40 forty, etc., to reduce word-form errors.
   • Modified expectation when needed: accept expanded form with explicit zero term first (e.g., 500 + 0 + 8) before moving to shortened form (500 + 8).

   IEP / 504 Accommodations

   • Preferential seating close to instruction and visuals; minimize distractions during dictation items.
   • Provide extended time and reduced-copy demands: offer pre-printed place value chart and allow students to fill blanks rather than write full charts repeatedly.
   • Read directions aloud and check for understanding with a brief restatement prompt: “Tell me what you will do first.”
   • Allow use of assistive tools as documented: number line, place value chart, manipulatives, pencil grip, slant board, or speech-to-text for word form (if appropriate and permitted).
   • Break multi-step tasks into clearly numbered steps with checkboxes; frequent teacher check-ins (e.g., after every 2 problems).
   • For students with fine-motor or writing challenges: allow oral responses recorded by teacher/aide for some items, while still assessing place-value understanding.
   • Provide frequent positive, specific feedback tied to precision: “You said ‘eight tens’—that is precise.”
   • If attention impacts performance, use brief movement break between guided and independent practice (30-second stretch) without reducing instructional rigor.

   Advanced Learners

   • Write two different expanded forms for the same number (e.g., 508 = 500 + 0 + 8 and 500 + 8) and explain why both are correct.
   • Create a ‘mystery number’ riddle using place-value clues (e.g., “I have 6 hundreds, 0 tens, 9 ones…”) and have peers solve.
   • Compare two close numbers (e.g., 706 and 760): explain how changing the tens and ones changes the value; write each in all three forms.
   • Explore 1,000 as a special case: represent 1,000 with ten hundreds; discuss how it would appear on an extended place value chart (Thousands | Hundreds | Tens | Ones).
   • Design a mini-quiz of 4 items for a classmate including one tricky zero and one near 1,000; include an answer key with explanations using place-value language.
   • Error analysis: teacher provides an incorrect word/expanded form (e.g., 641 = 600 + 4 + 1); students identify and correct the error using precise reasoning.

   形成性检查

   • Warm-up number talk: observe student accuracy reading numbers and explaining zero’s meaning (307).
   • Whiteboard CFU during direct instruction: word and expanded form of 430; scan for precision and correct tens value.
   • Guided practice observation checklist: correctness of matches and justifications using hundreds/tens/ones language.
   • Independent practice monitoring: targeted conferencing using prompts; note students who confuse digit vs value (e.g., writing 8 instead of 80).
   • Thumb check (1–3) during guided practice to identify who needs immediate reteach.

   退出票

   1) Write the word form and expanded form for 641. 2) Write the numeral for “nine hundred two.”

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 This template supports the lesson's explicit vocabulary terms related to place value and number forms, reinforcing key math language for grade 2 students.
   • Worksheet 匹配活动 The matching activity aligns with the use of number form cards to connect standard, word, and expanded forms, providing hands-on practice.
   • Worksheet 填空 Fill in the blank worksheets complement the student practice page by allowing students to write numbers in various forms, matching lesson objectives.
   • Worksheet 3-2-1 退出票 The 3-2-1 Exit Ticket serves as an effective closure activity to assess students' understanding at the end of the lesson, matching the exit ticket requirement.

   Storypie 内容

   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory

   准备清单

   • Print and pre-cut number form cards into matching sets; place sets in labeled bags/envelopes (Set A, Set B, Set C).
   • Prepare anchor chart: Place Value Chart (Hundreds | Tens | Ones) with space to add 584 and 706 during the lesson.
   • Queue/display warm-up numbers (307, 430, 999) and guided practice set (392 and 508).
   • Copy practice pages and exit tickets; prepare a ‘simplified’ version for struggling learners if needed.
   • Gather mini-whiteboards/markers OR confirm paper/pencils are ready.
   • Set up base-ten blocks or printable visuals in pair tubs; confirm enough hundreds flats, tens rods, ones cubes (or pictures).
   • Post sentence frames and vocabulary where students can see them; print desk strips for students who need them.
   • Plan small-group reteach spot (front table) with place value chart and a small set of manipulatives ready.
   • Decide the 3 numbers for “Listen & write” section (include one with 0 tens, e.g., 902; one with 0 ones, e.g., 470; one typical, e.g., 356) and write them on a private teacher note (not visible).

   常见误解

   • Thinking the digit 8 in 584 means 8 ones instead of 8 tens (80).
   • Believing zero means ‘nothing so we skip it’ without stating ‘zero tens/zero ones,’ leading to incorrect expanded form or numeral writing.
   • Writing 641 as ‘six hundred fourteen’ (confusing tens/ones structure).
   • Writing expanded form as 5 + 8 + 4 instead of 500 + 80 + 4.
   • Reading 430 as ‘four hundred three’ (misreading the tens digit).
3. 3 Bundling and Trading: 10 Ones = 1 Ten; 10 Tens = 1 Hundred 完整课程 Bundling and Trading: 10 Ones = 1 Ten; 10 Tens = 1 Hundred

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group (mini-lesson), then partners for guided practice, then independent work with optional partner check

   学习目标

   • I can explain and show that 10 ones can be bundled/traded for 1 ten, and 10 tens can be bundled/traded for 1 hundred using models. Understand

     成功标准:

     • I can accurately trade 10 ones for 1 ten using base-ten blocks or drawings.
     • I can accurately trade 10 tens for 1 hundred using base-ten blocks or drawings.
     • I can explain my trade using the words ones, tens, and hundreds (or write a sentence describing it).

   • I can represent a number (up to 1,000) in hundreds, tens, and ones, and regroup (trade) when needed so each place has fewer than 10. Apply

     成功标准:

     • Given a model, I can write the number as a base-ten numeral (e.g., 1 hundred 3 tens 5 ones = 135).
     • When I have 10 or more ones, I can regroup them into tens; when I have 10 or more tens, I can regroup them into hundreds.
     • My final representation uses fewer than 10 ones and fewer than 10 tens (standard regrouped form).

   • I can read and write a number (up to 1,000) from a model using a base-ten numeral, a number name, and expanded form. Apply

     成功标准:

     • From a shown model (blocks or H-T-O chart), I can write the correct base-ten numeral.
     • I can write the number name that matches the numeral (e.g., 213 is "two hundred thirteen").
     • I can write the expanded form that matches the model (e.g., 213 = 200 + 10 + 3).

   • I can use skip-counting by 5s, 10s, and 100s to count groups efficiently and check my totals. Apply

     成功标准:

     • I can skip-count by 10s to find the value of tens (10, 20, 30, …).
     • I can skip-count by 100s to find the value of hundreds (100, 200, 300, …).
     • I can skip-count by 5s (5, 10, 15, …) when prompted and stay on the correct pattern.

   • I can compare two three-digit numbers by checking hundreds first, then tens, then ones, and record the comparison using >, <, or =. Analyze

     成功标准:

     • I can identify which number has more hundreds; if hundreds are equal, I compare tens; if tens are equal, I compare ones.
     • I can correctly use >, <, or = to compare two three-digit numbers.
     • I can justify my comparison using place-value language (hundreds/tens/ones).

   标准

   • CCSS.MATH.CONTENT.2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens — called a "hundred." b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
   • CCSS.MATH.CONTENT.2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.
   • CCSS.MATH.CONTENT.2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
   • CCSS.MATH.CONTENT.2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

   材料

   • Base-ten blocks (ones/cubes, tens/rods, hundreds/flats) OR linking cubes + bands/pipe cleaners for bundling · 1 set per pair (or per student if available)If using linking cubes, pre-make a few ten-sticks for demo; allow students to build and band 10-cube trains.
   • Place-value mats/charts labeled Hundreds–Tens–Ones · 1 per studentLaminated mats allow repeated use with dry-erase markers.
   • Document camera or chart paper and markers · 1Use for live modeling and recording the trades and numerals.
   • Student recording sheet or math notebook page with H-T-O table · 1 per studentInclude space for: model/drawing, trades, final numeral, and one sentence explanation.
   • Pencils and erasers · 1 per studentOptional: crayons/colored pencils to distinguish hundreds/tens/ones in drawings.
   • Exit ticket slips (half-sheet) · 1 per studentCollect for quick scoring (0-1-2 rubric).
   • Optional: pocket chart number cards 0–9 and labels Hundreds/Tens/Ones · 1 setUseful for whole-group place-value chart and quick checks.

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Display quick-count prompts (tens and hundreds). Facilitate choral counting and a brief notice/wonder about patterns. Connect counting to place value language.

   学生操作: Choral count by 10s and by 100s; respond to quick questions; track patterns verbally or with finger counts.

   教师脚本（完整）

   (Point to the first sequence on the board.) “Class, eyes on the numbers. We will count together by tens. Ready?” (Gesture for choral response.) “30, 40, 50, …” (Pause.) “What comes next?” (After students respond.) “Yes—60. When we count by 10s, we are counting tens.” (Point to second sequence.) “Now we’ll count by hundreds. Ready?” “100, 200, …” (Pause.) “What comes next?” “Right—300. When we count by 100s, we are counting hundreds.” “Today we will use that idea to bundle and trade ones, tens, and hundreds. Trading helps us organize our blocks so each place has fewer than 10.”

   Direct Instruction10 min

   教师行动: Explicitly model trades with manipulatives under the document camera: 10 ones → 1 ten; 10 tens → 1 hundred. Connect to a place-value chart and written numerals. Model a quick regroup example (12 ones).

   学生操作: Watch, repeat key statements, answer CFU questions using thumbs/choral response, and mirror the trade with their own blocks when prompted.

   教师脚本（完整）

   “I’m going to show you a rule that makes place value work.” (Show 10 ones/cubes.) “Look closely. I have ones. Let’s count them together.” (Count 1–10.) “I have 10 ones.” (Trade for 1 ten rod or band into a ten.) “Watch closely: Ten ones are the same value as one ten. I can trade 10 ones for 1 ten without changing the total amount—only the way it is grouped.” “Say it with me: 10 ones equals 1 ten.” (Show 10 tens rods.) “Now I have tens. Let’s count tens by skip-counting.” (Point to each rod.) “10, 20, 30, 40, 50, 60, 70, 80, 90, 100.” (Trade 10 tens for 1 hundred flat.) “Now watch: 10 tens are the same as 1 hundred. I can trade 10 tens for 1 hundred.” “Say it with me: 10 tens equals 1 hundred.” (Place-value chart on board.) “Here is our rule we will always use: If I have 10 or more in a place, I can trade 10 of them for 1 in the next place to the left.” (Model 12 ones.) “If I have 12 ones, I trade 10 ones for 1 ten. Then I have 1 ten and 2 ones. My number is 12.”

   理解检查: CFU prompts (oral): 1) “If I have 10 ones, what can I trade for?” (Expected: 1 ten.) 2) “If I have 10 tens, what can I trade for?” (Expected: 1 hundred.) 3) “Does trading change the amount or just the grouping?” (Expected: grouping only.) Use thumbs up/down to check confidence; call on 2–3 students to explain in a complete sentence.

   Guided Practice15 min

   教师行动: Lead three structured rounds of building, trading, and recording. Use think-aloud and prompt students to check ones first, then tens. Circulate to correct counting, trading accuracy, and place-value language. Record each round on chart paper/board with an H-T-O table.

   学生操作: Work with a partner using blocks and place-value mats; build the quantities, trade when needed, record the result (words and numeral), and explain using sentence frames.

   教师脚本（完整）

   “Now we do it together. Partners, keep your blocks in the middle so both people can see.” “Trading steps every time:” (Point to board.) “Step 1: Check the ones. Do we have 10 or more ones? Step 2: Trade 10 ones for 1 ten. Step 3: Check the tens. Do we have 10 or more tens? Step 4: Trade 10 tens for 1 hundred. We trade until every place has fewer than 10.” “Round A: Build 14 ones.” (Pause while students build; circulate.) “Point to your ones. Count them. Do you have 10 or more ones?” “Trade 10 ones for 1 ten.” “Tell your partner: ‘I traded 10 ones for 1 ten. Now I have ___ tens and ___ ones.’” “Record: 1 ten 4 ones. Write the numeral 14.” “Round B: Build 10 tens.” “Let’s skip-count by tens to check.” (Choral count to 100.) “Do you have 10 tens? Trade 10 tens for 1 hundred.” “Record: 1 hundred 0 tens 0 ones. Write the numeral 100.” “Round C: Build 1 hundred, 9 tens, and 12 ones.” “First, check the ones: do we have 10 or more ones?” “Trade 10 ones for 1 ten. Now check the tens: what do you have?” “If you have 10 tens, trade for 1 hundred.” “Record the final: 2 hundreds 0 tens 2 ones. Write 202.”

   支架提示: Where will you look first—ones, tens, or hundreds? Why? | How many ones make a ten? Show me the group of 10 ones. | Use this sentence frame: ‘I traded ___ ones for ___ ten(s) because ___ ones equals ___ ten.’ | After you trade, what changes: the amount or the grouping? Prove it by counting. | How can we check the tens quickly? Can you skip-count by 10s to confirm? | If your tens column has 10, what trade must you make? What new number of hundreds will you have? | What should be true in standard form? (Fewer than 10 ones and fewer than 10 tens.) | If you disagree with your partner, what can you do to verify? (Recount, skip-count, compare to chart.)

   Independent Practice15 min

   教师行动: Assign task set; clarify expectations and tools (blocks or drawings). Circulate with a monitoring checklist and conduct 1–2 minute conferences, prompting students to identify where a trade is needed and to justify. Provide quick reteach at a small table for students needing it.

   学生操作: Complete tasks using blocks or quick drawings; record trades and final standard form; use skip-counting to check; optionally complete challenge representation task if finished early.

   教师脚本（完整）

   “Now it’s your turn. You may use blocks or quick drawings. For every problem, you must do three things: (1) show the model, (2) show the trade, and (3) write the final number.” “Remember our rule: If I have 10 or more in a place, I trade 10 for 1 in the next place to the left.” (Conference script while circulating.) “Show me where you see a group of ten. Which place has 10 or more? Tell me the trade you will make and why it keeps the value the same.” (If a student is stuck.) “Let’s just check one place at a time. Count your ones. Are there 10 or more ones? What do we do with 10 ones?”

   监控清单: Student correctly counts ones/tens without skipping or double-counting | Student trades exactly 10 ones for 1 ten (not 9 or 11) | Student trades exactly 10 tens for 1 hundred when needed | Student final representation has <10 ones and <10 tens | Student records correct numeral to match the final model | Student uses place-value words (ones/tens/hundreds) in explanation | Student uses skip-counting (10s/100s) to verify at least once

   Closure5 min

   教师行动: Facilitate brief reflection, emphasize core rule, administer and collect exit ticket. Preview that trading supports adding/subtracting later.

   学生操作: Complete exit ticket independently; share one takeaway if called on; hand in ticket.

   教师脚本（完整）

   “Let’s lock in our learning. Trading changes the grouping, not the amount.” “Turn and tell your partner: ‘10 ones equals ___.’ and ‘10 tens equals ___.’” (Pause for partner talk.) “Now complete the exit ticket quietly. Show your thinking. If you finish early, reread your work and check: Do I have fewer than 10 ones and fewer than 10 tens?” “Before you leave, remember: If you can explain ‘10 ones = 1 ten’ and ‘10 tens = 1 hundred,’ you are building strong place-value power that will help us add and subtract later.”

   退出票: 1) Circle the true statement: (A) 10 ones = 10 tens (B) 10 tens = 1 hundred (C) 1 ten = 1 hundred. 2) You have 1 hundred, 11 tens, 3 ones. Trade to show the value in standard form and write the number.

   ones

   Single cubes—each one is worth 1.

   tens

   A ten is a group of 10 ones bundled together.

   hundreds

   A hundred is 10 tens bundled together.

   bundle (trade/regroup)

   Swap 10 small pieces for 1 bigger piece, but the amount stays the same.

   place-value chart

   A chart with columns that helps us keep track of hundreds, tens, and ones.

   English Language Learners

   • I can use the sentence frame ‘I traded 10 ones for 1 ten’ to explain a trade.
   • I can name the place-value units (ones, tens, hundreds) while pointing to a model or place-value chart.
   • I can orally describe a number using the frame ‘___ hundreds, ___ tens, ___ ones is ___’.
   • Pre-teach vocabulary with visuals (picture cards of cube/rod/flat) and gestures (one finger for ones, two hands for tens bundle, wide arms for hundreds).
   • Provide sentence frames on a small card: ‘I have __ ones. I trade 10 ones for 1 ten. Now I have __ tens and __ ones.’ and ‘I have __ tens. I trade 10 tens for 1 hundred.’
   • Use a bilingual glossary or allow first-language rehearsal before sharing in English.
   • Pair ELL students with a supportive partner; assign roles (Builder, Checker/Explainer) and rotate.
   • Use color-coding in drawings: ones = small dots, tens = long lines, hundreds = big squares; keep consistent across tasks.
   • Frequent comprehension checks: “Show me 10 ones,” “Point to tens,” “Which column is ones?”

   Struggling Learners

   • Use concrete manipulatives first; delay drawings until accuracy with blocks is shown.
   • Chunk tasks: complete only problems 1–2 first; then check in with teacher before moving to 3.
   • Provide a simplified place-value mat with only Tens and Ones for first two tasks; add Hundreds once successful.
   • Offer a ‘trade checklist’ card: 1) Count ones; 2) If 10+, trade; 3) Count tens; 4) If 10+, trade; 5) Write numeral.
   • Use pre-bundled sets (bags of 10 ones labeled ‘TEN’) so students can physically swap without recounting each time; gradually remove as independence grows.
   • Provide worked example side-by-side with practice: e.g., “18 ones → trade 10 → 1 ten 8 ones → 18.”
   • Allow peer support: partner checks counting and confirms that exactly 10 were traded.
   • Modified expectations as needed: accuracy on trading and naming units is prioritized over neat drawings; allow oral explanation instead of written sentence.

   IEP / 504 Accommodations

   • Preferential seating near teacher/modeling area; reduce distractions during independent practice.
   • Allow additional processing time and reduce item count if specified (e.g., complete 2 of 3 independent tasks plus exit ticket).
   • Provide enlarged place-value chart and/or tactile/raised-line mat for students with visual-motor needs.
   • Offer alternative response modes: point and verbalize trades; use stamps/stickers for ones/tens/hundreds instead of drawing.
   • Use assistive tools as needed: pencil grip, slant board, or dry-erase with thicker markers for motor fatigue.
   • Provide step-by-step directions one at a time; check for understanding after each step.
   • Frequent breaks (30–60 seconds) between tasks for attention needs; use a timer or visual schedule.
   • Positive behavior supports: clear goal (“Show one correct trade”) and immediate feedback.

   Advanced Learners

   • Create two or more equivalent representations for the same number (e.g., 146 as 1H 4T 6O; 14T 6O; 1H 3T 16O) and explain why they are equal.
   • Write a ‘Trading Rule Book’ page: include the two trade rules, a drawing, and an example with explanation.
   • Challenge problem: Start with 3 hundreds, 19 tens, 28 ones. Trade to standard form and write the number; then explain each trade step.
   • Connect to expanded form: after trading, write 213 as 200 + 10 + 3; then compare to pre-trade form (100 + 110 + 3) and explain equivalence.
   • Reasoning prompt: ‘Can you ever trade 10 ones for 1 hundred? Why or why not?’ Provide a written explanation using place-value logic.
   • Compare two regrouped numbers using >, <, = and justify (ties to CCSS.MATH.CONTENT.2.NBT.A.4).

   形成性检查

   • Warm-up choral counting accuracy by 10s and 100s (teacher notes students who hesitate).
   • CFU during direct instruction: oral responses to ‘10 ones equals?’ and ‘10 tens equals?’ plus thumbs check.
   • Guided practice observation: teacher uses checklist to note who trades correctly and records numeral correctly.
   • Partner talk: listen for correct use of vocabulary and sentence frames.
   • Independent practice work sample review during circulation (spot-check 2 students per table).

   退出票

   1) Circle the true statement: (A) 10 ones = 10 tens (B) 10 tens = 1 hundred (C) 1 ten = 1 hundred. 2) You have 1 hundred, 11 tens, 3 ones. Trade to show the value in standard form and write the number.

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 The lesson includes specific vocabulary terms related to place value, so a vocabulary practice template will help reinforce these key concepts for grade 2 students.
   • Worksheet 匹配活动 A matching activity aligns well with the bundling and trading concept by allowing students to connect terms and representations, supporting hands-on learning at grade 2.
   • Worksheet T-图 A T-Chart organizer will help students visually compare and organize the concept of ones, tens, and hundreds, matching the lesson's focus on place-value grouping.
   • Worksheet 3-2-1 退出票 The lesson mentions an exit ticket for quick assessment, so a 3-2-1 Exit Ticket template is appropriate for formative assessment and closure at this grade level.

   Storypie 内容

   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory
   • Storypie Content Addition Addition is a fundamental mathematical operation that represents the total amount of objects together in a collection. It is signified by the plus sign (+).
   • Storypie Content Cash Register A mechanical or electronic device for registering and calculating transactions at a point of sale, which also includes a drawer for storing cash and often a receipt printer.
   • Storypie Content Fractions Fractions represent parts of a whole or, more generally, any number of equal parts. They are a fundamental concept in mathematics used to express division, ratios, and numbers that are not whole.
   • Storypie Content Division Division is a fundamental arithmetic operation that is the inverse of multiplication. It is the process of splitting a number into equal parts or groups.

   准备清单

   • Copy/prepare place-value mats and exit tickets (one per student + extras).
   • Prepare base-ten blocks or linking cubes; ensure each pair has at least 30 ones, 15 tens (or ability to make tens), and 3 hundreds (or picture substitutes).
   • If using linking cubes, pre-band 2–3 tens for demonstration and have extra rubber bands/pipe cleaners ready.
   • Set up document camera/board space with H-T-O chart and anchor statements (‘10 ones = 1 ten’ and ‘10 tens = 1 hundred’).
   • Prepare an independent practice recording sheet with spaces for model, trade, and final numeral.
   • Plan partner pairings (consider language and support needs).
   • Decide on a quick signal for trade checks (e.g., students hold up a ten rod when they made a trade).

   常见误解

   • ‘10 ones = 10 tens’ because both have a 10 in them (confusing count with value).
   • Thinking the digit 0 means ‘nothing in the whole number’ instead of ‘0 in that place’ (e.g., 202 has 0 tens).
   • Believing you can trade any number of ones for a ten (not specifically 10).
   • Trading in the wrong direction (trying to turn 1 ten into 10 hundreds).
   • Recording the number based on the count of blocks rather than their place value (e.g., counting 1 hundred flat as ‘1’ instead of 100).
4. 4 Compare Three-Digit Numbers Using Place Value Reasoning 完整课程 Compare Three-Digit Numbers Using Place Value Reasoning

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group for warm-up/direct instruction; pairs for guided practice; independent for practice and exit ticket; optional small group reteach at teacher table during independent practice.

   学习目标

   • I can compare two three-digit numbers by looking at the hundreds, tens, and ones and decide which is greater, less, or equal. Analyze

     成功标准:

     • I compare the hundreds digits first and only compare tens/ones if the hundreds are the same.
     • I use place value language (hundreds, tens, ones) to explain my comparison.
     • I choose the correct symbol (>, <, =) to show the comparison.

   • I can record my comparison using >, <, or = and read the comparison out loud as a complete sentence using correct number names. Apply

     成功标准:

     • I write a true comparison statement (example: 438 > 384).
     • I read it correctly using number names (example: “Four hundred thirty-eight is greater than three hundred eighty-four.”).
     • My symbol matches what I explained using place value.

   • I can write a three-digit number in expanded form and use it to support place value reasoning when comparing. Apply

     成功标准:

     • I write expanded form correctly (example: 560 = 500 + 60 + 0).
     • I connect the expanded form to hundreds/tens/ones language.
     • I can use expanded form to justify why one number is greater/less/equal.

   标准

   • CCSS.MATH.CONTENT.2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
   • CCSS.MATH.CONTENT.2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
   • CCSS.MATH.CONTENT.2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

   材料

   • Teacher place value chart (hundreds–tens–ones) for modeling (poster, document camera, or slides) · 1Large enough for all students to see; include headings H/T/O.
   • Student place value charts (laminated or paper) · 1 per studentOptional: dry-erase sleeves for reuse.
   • Base-ten blocks or place value disks (hundreds flats, tens rods, ones cubes/disks) · Class set; at least 2 sets per pairInclude extras for modeling 0 tens/0 ones with empty column.
   • Comparison symbol cards (>, <, =) · 1 set per studentCan be index cards or printed; students hold up for checks.
   • Whiteboards/markers/erasers OR math notebooks/pencils · 1 per studentUse for quick responses and written explanations.
   • Guided practice problem set (projected or chart paper) · 1 teacher setInclude the 6 pairs listed; add space for recording reasoning.
   • Independent practice worksheet or task cards (8–10 comparisons) · 1 per studentInclude mixed types and at least two with zeros.
   • Exit ticket slips (2 items) · 1 per studentCollect at door for quick sorting.
   • Optional: sentence frames handout/desk strip · As neededFor ELL/struggling learners: '___ is greater than ___ because ___.'

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Run a rapid place value flash routine: display 3-digit numbers and ask students to name hundreds/tens/ones. Then pose two quick comparison prompts for thumbs up/down and one-phrase justifications.

   学生操作: Respond chorally and/or on whiteboards: identify digits in hundreds/tens/ones places. Use thumbs up/down to indicate true/false comparisons and give a brief justification using place value language.

   教师脚本（完整）

   “Mathematicians, eyes on the number. Number one: 584. Say it with me: five hundred eighty-four. What digit is in the hundreds place?” (Pause.) “Yes—5. How many hundreds?” (Students: “5 hundreds.”) “Tens place?” “Ones place?” “Next number: 706. Say it: seven hundred six. What do you notice about the tens digit?” (Pause.) “It’s 0 tens.” “Now a quick compare. Thumbs up if you think it’s true; thumbs down if you think it’s false: 512 is greater than 521.” (Pause; scan.) “Turn and say one short reason using place value words.” “Second compare: 439 is less than 398.” (Pause.) “One phrase reason: start with ‘I compared the ___ first.’”

   Direct Instruction10 min

   教师行动: Explicitly model the comparison process using the place value chart and/or base-ten blocks. Include: (1) different hundreds, (2) same hundreds different tens, (3) same hundreds/tens different ones, (4) zeros in tens/ones. Record comparisons with symbols and read them as full sentences.

   学生操作: Track teacher modeling, answer prompted questions, repeat the comparison steps, and practice reading comparison sentences chorally.

   教师脚本（完整）

   “Today we will compare three-digit numbers by using place value. Our rule is: hundreds first, then tens, then ones.” (Write on board: Compare hundreds → Compare tens → Compare ones.) “I’m going to model one. Watch my thinking.” “Problem: 472 ___ 429. First, I compare the hundreds. 472 has 4 hundreds. 429 has 4 hundreds. The hundreds are the same, so I can’t decide yet.” “Next, I compare the tens. 472 has 7 tens. 429 has 2 tens. Seven tens is more than two tens, so 472 is greater than 429.” “I record it with the symbol for greater than: 472 > 429.” “Now we read it as a complete sentence: ‘Four hundred seventy-two is greater than four hundred twenty-nine.’ Say it with me.” (Second model with zeros.) “Now watch one with a zero: 506 ___ 560. Hundreds: both have 5 hundreds—same. Tens: 506 has 0 tens; 560 has 6 tens. Zero tens is less than six tens, so 506 is less than 560. I write 506 < 560.” (Equal model.) “If the hundreds, tens, and ones are all the same, the numbers are equal, and I use the symbol equals: =.” “Class, say the steps with me: hundreds first… then tens… then ones.”

   理解检查: Quick oral CFU: Teacher shows 391 and 319. Ask: 'Which place do we compare first?' 'Do we need to compare tens here? Why?' Students hold up >/< cards after 10 seconds; teacher cold-calls 2 students to justify using place value language.

   Guided Practice15 min

   教师行动: Lead students through 6 comparison problems using a place value chart and/or blocks. Require students to verbalize the rule before writing the symbol. Conduct quick checks after every two items using symbol cards. Address misconceptions immediately (e.g., comparing ones first, misreading 0 tens).

   学生操作: Work with a partner to represent or analyze each number, state the comparison step aloud (hundreds → tens → ones), write the correct symbol on whiteboard/notebook, and read the sentence aloud when called on.

   教师脚本（完整）

   “Now we do it together. Before we write any symbol, we will say the rule: ‘Compare hundreds first.’ Ready?” “Problem 1: 305 ___ 350. Partners, point to the hundreds digit in both numbers.” (Pause.) “What do you notice?” (After responses.) “Yes, both have 3 hundreds. So what’s our next step?” “Compare the tens. 305 has 0 tens. 350 has 5 tens. Which has more tens?” (Pause.) “So which number is greater?” “Write the symbol. Hold up your card: >, <, or =.” (Scan.) “Now read the comparison as a full sentence with your partner.” “Problem 2: 610 ___ 601. Hundreds?” (Students respond.) “Tens?” “Ones?” (After two problems.) “Quick check: If the hundreds are different, do we even look at the tens? Show me with a thumbs up for yes, thumbs down for no.” “Problem 3: 478 ___ 487.” “Problem 4: 420 ___ 402.” “After you decide, I will call on someone to use this sentence starter: ‘They have the same ____, so I compared the ____.’” “Problem 5: 599 ___ 600.” “Problem 6: 700 ___ 700.” “Remember: equals means exactly the same hundreds, tens, and ones.”

   支架提示: Where do your eyes go first in a three-digit number? Point to it. | What is the value of the hundreds digit? (___ hundreds = ___) | Are the hundreds the same or different? What does that tell us? | If hundreds are the same, what place do we compare next? Why? | How many tens is 0 tens? What does that mean on a place value chart? | Can you say it in a full sentence: ‘___ is greater/less than ___ because ___.’ | Does your symbol match your words ‘greater’ or ‘less’? (Greater → > ; Less → < ; Same → =)

   Independent Practice15 min

   教师行动: Distribute independent practice (8–10 comparisons). Remind students to use the step-by-step rule and to write explanations for 2 selected items. Circulate using a monitoring checklist; pull a quick reteach group if needed. Provide targeted prompts rather than answers.

   学生操作: Complete comparisons, select 2 problems to explain in writing using place value words, and check work by rereading each comparison statement as a sentence. Ask for help using agreed-upon signal (e.g., hand raised, help card).

   教师脚本（完整）

   “Now it’s your turn. You will solve these comparisons on your own. Remember our steps: hundreds first, then tens, then ones.” “On your paper, you will also choose TWO problems to explain with words. Use place value words like hundreds, tens, and ones. Your explanation must match your symbol.” “If you get stuck, do not guess. Point to the hundreds digit and tell yourself: ‘Compare hundreds first.’ You may use the place value chart or blocks.” (While circulating, quiet prompt script.) “Tell me the hundreds digits. Are they the same or different?” “What’s your next step?” “Read your statement out loud: does it sound true?”

   监控清单: Student compares hundreds digits first (does not start with ones). | Student correctly interprets 0 in tens/ones place (e.g., 506 has 0 tens). | Student selects correct symbol that matches comparison (> < =). | Student can verbally justify using place value language when prompted. | Student writes at least one complete explanation sentence for selected problems. | Student reads comparison correctly as a sentence (greater than/less than/equal to).

   Closure5 min

   教师行动: Reinforce the comparison routine; facilitate a brief share-out of one strong explanation. Administer and collect exit ticket; remind students that explanation must match symbol.

   学生操作: Complete exit ticket independently; optionally share reasoning if called on; turn in ticket at collection point.

   教师脚本（完整）

   “Let’s finish by saying our strategy together: Hundreds first… then tens… then ones.” “Listen to this strong math sentence: ‘506 is less than 560 because they both have 5 hundreds, but 0 tens is less than 6 tens.’ That explanation matches the symbol.” “Now complete your exit ticket quietly. Before you turn it in, check two things: (1) Did I choose the right symbol? (2) Does my explanation match my symbol?”

   退出票: 1) Compare and circle the correct symbol: 506 __ 560 (>, <, =) 2) Write one sentence explaining how you know, using hundreds/tens/ones.

   hundreds

   How many hundreds are in the number.

   tens

   How many tens are in the number.

   ones

   How many ones are in the number.

   compare

   To see which number is bigger, smaller, or the same.

   greater than / less than / equal to

   Bigger than, smaller than, or the same as.

   English Language Learners

   • I can use the sentence frame '___ is greater/less than ___ because ___ hundreds/tens/ones.' to explain a comparison.
   • I can orally name the hundreds, tens, and ones in a three-digit number using academic vocabulary (hundreds, tens, ones).
   • I can correctly read comparison statements aloud using 'is greater than/is less than/is equal to.'
   • Pre-teach and post on board: greater than, less than, equal to, compare; include symbol visuals and arrows (greater than > points to smaller number).
   • Provide sentence frames: 'They both have ___ hundreds. Next I compare ___. ___ is ___ than ___.'
   • Use gestures: point to hundreds column first, then tens, then ones; students mirror the gesture each problem.
   • Provide a bilingual glossary/translated keywords if available; allow students to explain first in home language to a partner, then restate in English.
   • Use consistent choral repetition for number names (e.g., 'five hundred sixty') and comparison sentences.
   • Partner ELL with a supportive peer; assign roles: 'digit pointer' and 'sentence reader.'

   Struggling Learners

   • Use concrete-representational-abstract progression: build with base-ten blocks first, then draw quick sketches in H/T/O chart, then write symbol.
   • Chunk tasks: start with only different-hundreds comparisons (first 3 items), check with teacher, then proceed to same-hundreds comparisons.
   • Provide a highlighted place value chart where the hundreds column is shaded to cue 'start here.'
   • Reduce choice load: initially offer two symbol options (>, <) and introduce = after mastery, or provide a symbol word bank next to the problem.
   • Provide guided checklist card on desk: 1) Compare hundreds 2) Compare tens 3) Compare ones 4) Write symbol 5) Read it.
   • Use peer support: structured partner talk with scripted prompts ('Hundreds are… so next is…').
   • Modified expectations as needed: complete 6 of 10 independent items with accuracy and explain 1 problem instead of 2.
   • Teacher-led small group during independent practice using 2–3 targeted examples with zeros and immediate feedback.

   IEP / 504 Accommodations

   • Preferential seating near instruction and visual model; ensure clear sightline to place value chart.
   • Read directions aloud; check for understanding by asking student to restate steps.
   • Provide extended time for independent practice/exit ticket as documented; allow completion in a quiet space if needed.
   • Allow use of manipulatives and/or a laminated place value chart on all tasks.
   • Reduce writing load if required: student may dictate explanation to teacher/scribe or use fill-in-the-blank sentence frame.
   • Provide frequent breaks or movement: quick stand-and-point to hundreds/tens/ones between problems.
   • Use large-print materials and high-contrast symbols for students with visual needs.
   • For attention/executive functioning: provide a mini goal ('Finish #1–#4, then check in') and use a timer/checklist.

   Advanced Learners

   • Order three or four numbers from least to greatest and justify using place value language (e.g., 402, 420, 409, 490).
   • Create two different numbers that fit a comparison statement (e.g., make ___ < ___ where both have 6 hundreds and 0 tens).
   • Write a short 'How to Compare' mini-lesson poster with examples including zeros and an equals example.
   • Challenge: Compare using expanded form reasoning (e.g., 560 = 500 + 60 + 0) and explain why that helps.
   • Error analysis: Given an incorrect comparison (e.g., '610 < 601 because 1 < 0'), identify the mistake and correct it with explanation.

   形成性检查

   • Warm-up: place value flash responses and justification phrases during thumbs up/down comparisons.
   • CFU during direct instruction: students hold up >/< cards for 391 vs 319 and explain the step used.
   • Guided practice: symbol card holds after every two problems; teacher listens for correct use of 'hundreds/tens/ones' language.
   • Independent practice: teacher monitoring checklist notes and quick conferences with students; collect 2 written explanations for spot-checking.

   退出票

   1) Compare and circle the correct symbol: 506 __ 560 (>, <, =) 2) Write one sentence explaining how you know, using hundreds/tens/ones.

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 The lesson includes specific vocabulary terms related to place value and comparison, making vocabulary practice essential for student understanding.
   • Worksheet 匹配活动 A matching activity aligns well with practicing the comparison of three-digit numbers and reinforcing place value concepts interactively.
   • Worksheet 3-2-1 退出票 The lesson includes an exit ticket to assess student understanding, so a 3-2-1 exit ticket template supports this formative assessment.
   • Worksheet T-图 A T-Chart organizer can help students visually compare numbers and record reasoning, supporting the lesson's focus on place value reasoning and comparison.

   Storypie 内容

   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory

   准备清单

   • Print/prepare comparison symbol cards (>, <, =) for each student.
   • Prepare and test the visual display (document camera/slides) for guided practice problems and place value chart.
   • Organize base-ten blocks/place value disks into pair-ready bins; ensure enough hundreds/tens/ones pieces.
   • Copy independent practice sheets and exit tickets; label class set.
   • Post or prepare an anchor chart with comparison steps (hundreds→tens→ones) and example sentence frames.
   • Plan partner assignments (especially supportive pairings for ELL/struggling learners).
   • Prepare a small-group reteach set with 3–4 targeted comparisons involving zeros (e.g., 407 vs 470; 500 vs 450; 609 vs 690).

   常见误解

   • Bigger ones digit always means bigger number (ignoring hundreds/tens).
   • Thinking 0 means the number is 'nothing' instead of '0 groups' in that place (e.g., 506 has 0 tens, not 0 value overall).
   • Believing you must always compare all three places even when hundreds differ (not understanding you can stop once a larger place differs).
   • Reversing the meaning of > and < when writing the symbol between numbers.
5. 5 Number Lines to 1,000: Benchmarks and Estimating Locations 完整课程 Number Lines to 1,000: Benchmarks and Estimating Locations

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group for warm-up and modeling; pairs for guided practice; independent for task page; brief whole-group share at closure.

   学习目标

   • I can locate a three-digit number on a 0–1,000 number line by identifying the two bounding hundreds and placing the number between them. Apply

     成功标准:

     • I correctly name the two hundreds my number is between (e.g., 623 is between 600 and 700).
     • I place the point in the correct interval between those hundreds.
     • My placement matches the magnitude of the number (numbers increase left to right).

   • I can explain my number-line placement using hundreds, tens, and ones (place-value language and/or expanded form). Analyze

     成功标准:

     • I represent the number as hundreds, tens, and ones (e.g., 623 is 6 hundreds, 2 tens, 3 ones) and/or expanded form (600 + 20 + 3).
     • I connect the hundreds to the starting benchmark (e.g., ‘6 hundreds means just after 600’).
     • I connect the tens/ones to how far into the hundred my point should be (e.g., ‘20 and 3 means a little past 600’).

   • I can check and revise my estimate by skip-counting by 10s/100s or using a midpoint within the same hundred interval. Evaluate

     成功标准:

     • I use at least one check strategy (skip-count by 10s or find the midpoint like 650 between 600 and 700).
     • If needed, I revise my placement and state what I changed and why.
     • My final placement is consistent with my check strategy (e.g., before/after midpoint correctly).

   • I can compare two three-digit numbers using >, =, or < and justify the comparison using place value and/or number-line position. Apply

     成功标准:

     • I choose the correct symbol (> , < , =) to compare two three-digit numbers.
     • I justify by referencing hundreds first, then tens/ones if needed.
     • I can also justify using number-line language (left/right, closer to).

   标准

   • CCSS.Math.Content.2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
   • CCSS.Math.Content.2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.
   • CCSS.Math.Content.2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
   • CCSS.Math.Content.2.NBT.B.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

   材料

   • Large classroom number line from 0 to 1,000 (poster or projected) with space to add benchmarks · 1Should allow teacher to mark/label hundreds and midpoints; keep visible for entire lesson.
   • Student number lines (0–1,000 versions with different benchmark labels; plus one zoomed 600–800 line) · 1 set per studentPrepare three versions for independent practice; consider pre-labeled set for supports.
   • Sticky notes or number cards for placing estimates on the class number line · 1–2 per student (plus extras)Use different colors for different pairs or for revisions.
   • Dry-erase boards, markers, and erasers (or math notebooks and pencils) · 1 per studentFor quick responses and partner justification rehearsal.
   • Base-ten blocks (hundreds flats, tens rods, ones cubes) · At least 1 demonstration set + small sets for a support tableUsed briefly during modeling; optional for students who need concrete support.
   • Document camera or projector for modeling placements and thinking · 1Project number line and model benchmark selection and spacing.
   • Exit ticket slips · 1 per student0–1,000 line labeled 0, 500, 1,000; prompt and space for short explanation.

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Display three numbers: 472, 519, 886. Lead a quick number sense routine: ‘Which is closer?’ Prompt students to use benchmark hundreds and justify. Record 1–2 student justifications using the sentence frames.

   学生操作: Students chorally read numbers, show quick choices with fingers (1=left benchmark, 2=right benchmark), then turn-and-talk using the sentence frame. A few students share aloud.

   教师脚本（完整）

   “Eyes on the board. Our first number is 472. Say it with me: four hundred seventy-two.” “Which is 472 closer to: 400 or 500? Show with your fingers—1 for 400, 2 for 500.” “Turn to your partner and use this frame: ‘472 is between __ and __. It is closer to __ because __.’” (After 20–30 seconds) “Let’s hear one partner share. Start with: ‘472 is between…’” (Repeat quickly with 519 and 886) “Today we are going to be number-line detectives. We will not always know the exact spot right away, but we can make a smart estimate using benchmarks—numbers we already know well.”

   Direct Instruction10 min

   教师行动: Introduce the day’s learning targets and connect to prior knowledge about place value. Model estimating on a 0–1,000 number line with equally spaced hundreds. Use think-aloud and explicitly name steps: choose benchmarks, use place value, consider midpoint, check reasonableness. Model with 680 then 205. Briefly connect with base-ten blocks and emphasize equal intervals.

   学生操作: Students track the number line with their eyes/fingers, answer quick CFU questions (thumbs up/down, choral responses), and repeat key vocabulary. Students explain what benchmarks were used and why.

   教师脚本（完整）

   “Let’s read our first target together: ‘I can use benchmark numbers to estimate where a 3-digit number belongs on a 0–1,000 number line.’” “Benchmarks are helper numbers. On this number line, our hundreds are great benchmarks: 0, 100, 200, all the way to 1,000.” (Place 680 as model) “Watch how I place 680. Step 1: I find two benchmarks. I’m looking for the hundreds it is between.” “I see 600 and 700. I’m going to point: 600… 700.” “Step 2: I use place value. 680 is 6 hundreds, 8 tens, 0 ones. Six hundreds means it must be after 600—so it’s in the 600 neighborhood.” “Eight tens is 80. 80 is a lot closer to 100 than to 0, so 680 is closer to 700 than 600.” “Step 3: I can use a midpoint to check. Halfway between 600 and 700 is 650. Since 680 is 30 more than 650, it goes past the middle, closer to 700.” “I’ll place it here—past 650, not all the way to 700.” (Brief base-ten connection) “I’m going to show 680 with blocks: 6 hundreds flats, 8 tens rods, 0 ones cubes. The 6 hundreds tells me: start past 600 on the number line.” (Model 205) “Now I’ll place 205. Step 1: benchmarks. It’s between 200 and 300.” “Step 2: place value. 205 is 2 hundreds, 0 tens, 5 ones. Two hundreds means just after 200. Zero tens means I’m not moving far into the 200s. Five ones means just a tiny bit past 200.” (Emphasize equal spacing) “Important: on a number line, the spaces between the hundreds must be equal. If my spacing changes, my estimate won’t be fair. Equal intervals help everyone’s estimate mean the same thing.”

   理解检查: CFU prompts: (1) “What two benchmarks would you use for 732?” (expected: 700 and 800). (2) “If a number has 9 hundreds, where must it be on the number line?” (between 900 and 1,000). (3) “True or false: 205 should be near 250.” (false; it’s just after 200).

   Guided Practice15 min

   教师行动: Distribute partner number lines (0–1,000 with hundreds labeled) and sticky notes. Assign pairs and roles (Partner A places first, Partner B justifies; then switch). Provide four numbers: 340, 598, 721, 909. Facilitate the routine: benchmarks → closer/midpoint → place → justify. Circulate with a checklist; give immediate feedback, prompt revisions, and highlight strong reasoning. Address misconceptions publicly when they appear (wrong hundred neighborhood, uneven spacing, reversing left/right).

   学生操作: In pairs, students identify benchmarks, discuss closeness using tens/midpoints, place sticky notes on their number line, and rehearse/perform justifications using sentence frames. Students revise when prompted.

   教师脚本（完整）

   “Now it’s our turn together. You and your partner will be detectives.” “Here is our routine for each number. Say it with me: 1) Benchmarks. 2) Closer or midpoint. 3) Place it. 4) Justify it.” “Partner A, you will place the first number. Partner B, you will explain using the sentence frame. Then you switch roles.” (For each number, prompt the routine) “Number 1 is 340. Point to your left benchmark. Point to your right benchmark.” “Now tell your partner: ‘My number is between __ and __.’” “Next: Is it closer to the left benchmark or the right benchmark? You may whisper-count by tens if that helps.” “Place your sticky note. Now justify: ‘I placed it near __ because __.’” (Misconception script, as needed) “I’m noticing a common mix-up. If two numbers are in the 700s, they do not belong near 600. The hundreds digit tells us the neighborhood first. Then tens help us get more exact.” (Revision prompt) “If your partner disagrees, that’s okay—prove it. Use benchmarks, tens, or the midpoint to convince each other, and then decide where to place it.”

   支架提示: What is the hundreds digit? What ‘neighborhood’ does that put you in? | Say the number as hundreds, tens, ones: __ hundreds, __ tens, __ ones. How does that help you start? | Which two hundreds is your number between? Point to them. | Is your number closer to the left hundred or the right hundred? How do you know? | What is the midpoint between those hundreds? Is your number before or after the midpoint? | Skip-count by 10s from the left benchmark: __, __, __. Where would your number land? | If your point is very close to a benchmark, what does that tell you about the tens and ones? | Check left-to-right: Is your number bigger than the left benchmark? Is it smaller than the right benchmark? | Does your spacing match the spacing of other hundreds on the line (equal intervals)? | Use the frame: ‘I placed __ between __ and __, closer to __ because __.’

   Independent Practice15 min

   教师行动: Distribute independent task page with three number lines (A: only 0 and 1,000 labeled; B: 0, 500, 1,000 labeled; C: 600–800 zoomed). Assign numbers: 147, 512, 768, 695. Require students to add benchmarks on A before plotting. Require 1–2 sentence explanations for at least two numbers (teacher may specify which two). Circulate to monitor using checklist, provide short conferences, and note students for small-group reteach.

   学生操作: Students work independently to add benchmarks, estimate and plot points, and write brief justifications using benchmarks and place-value language. Students self-check by skip-counting or midpoint comparisons and revise if needed.

   教师脚本（完整）

   “Now you will show your own detective thinking.” “Your job is to make your thinking visible. If I only see a dot, I can’t learn how you decided. Show benchmarks, then place the number, then write how you know.” “For Number Line A, you must add at least three helpful benchmarks before you place any numbers. Choose benchmarks that will help you—hundreds are a great choice.” “After you place each number, do a quick check: bigger numbers go farther right. If it doesn’t make sense, revise and write what you changed.”

   监控清单: Student adds at least three benchmarks on Line A before plotting. | Student chooses correct hundred interval for each number (e.g., 147 between 100 and 200). | Student’s point is reasonably placed relative to closeness (e.g., 512 slightly after 500). | Student explanation uses benchmark language (between/near/closer to). | Student explanation includes place value (hundreds/tens/ones) or expanded form. | Student uses a check strategy (midpoint, skip-count by 10s/100s) and revises if needed. | Student maintains equal-interval idea on their own markings (no bunching/uneven spacing).

   Closure5 min

   教师行动: Facilitate a brief share: select two students/pairs who used different strategies (midpoint vs tens-after-hundred). Synthesize key steps and connect back to objectives. Administer exit ticket and give directions for independent completion. Collect and preview for grouping decisions.

   学生操作: Students listen to peer strategies, compare them to their own, and restate the lesson’s key idea. Students complete the exit ticket independently and turn it in.

   教师脚本（完整）

   “Let’s bring our thinking back together. I’m going to call on two mathematicians to share two different strategies.” (After student 1) “Class, what benchmarks did you hear? What was the check strategy?” (After student 2) “I heard a different strategy: using tens after a hundred. That’s powerful because tens tell us how far into the hundred we are.” (Synthesis) “Today we learned that benchmarks help us make smart estimates. First we find the hundreds, then we use tens to get more exact, and we can use midpoints or skip-counting to check reasonableness.” (Exit ticket directions) “Exit ticket time. You will place 623 on this 0–1,000 number line. Remember: show your benchmarks and write one sentence to explain.” “Use this frame if you want: ‘I used the benchmarks __ and __. I placed it near __ because __.’”,

   退出票: On a 0–1,000 number line labeled 0, 500, and 1,000, place 623. Then write: “I used the benchmarks __ and __. I placed it near __ because __.” Use place-value language (hundreds/tens/ones) or expanded form in your explanation.

   number line

   A line where numbers go in order and the spaces stay the same size.

   benchmark

   A ‘helper number’ you know well that helps you decide where another number goes.

   estimate

   A smart guess that makes sense.

   interval

   The same-size space from one mark to the next.

   midpoint

   The number right in the middle between two numbers.

   English Language Learners

   • I can use comparative language (between, closer to, near, left/right) to explain a number’s location on a number line.
   • I can say a 3-digit number using place-value language: ‘__ hundreds, __ tens, __ ones.’
   • I can justify my estimate using a sentence frame: ‘I used the benchmarks __ and __. I placed it near __ because __.’
   • Pre-teach and display a mini word bank with visuals: between (two arrows), closer (two dots with one shorter arrow), benchmark (star on 100s), midpoint (halfway mark).
   • Provide sentence frames on desk strips; allow students to point to benchmarks on the line while speaking.
   • Choral repetition of key comparative phrases: “between 600 and 700,” “closer to 600,” “past 600.”
   • Use gestures consistently (left hand for smaller/left benchmark, right hand for larger/right benchmark).
   • Partner ELLs with supportive peers; assign roles: one points/places, one speaks using the frame.
   • Allow oral explanation instead of full written sentences for one item during independent practice (teacher or aide scribes if needed).
   • Provide translated number words support as appropriate (home-language glossary) while keeping the math language in English during the share.
   • Use base-ten blocks as a language bridge: students build the number then say “__ hundreds” while touching the hundreds flats.

   Struggling Learners

   • Use a pre-marked number line with every hundred labeled for guided and independent practice; reduce cognitive load of creating benchmarks.
   • Chunk the task: (1) circle the hundreds digit, (2) write the two nearest hundreds, (3) decide closer using tens, (4) place point.
   • Modified expectation option: accurately place numbers only to the correct hundred interval first; then attempt closer-to-left/right as a second step.
   • Provide a ‘midpoint card’ reminding: midpoint of 600 and 700 is 650; encourage using 650 only after correct interval is identified.
   • Offer a small-group table with teacher where students physically move a clip along a large number line from 600 to 700 while skip-counting by 10s.
   • Use fewer numbers in independent practice (e.g., choose 2 of 4) while maintaining explanation for at least 1 number.
   • Provide visual aids: hundreds chart to 1,000 and a place-value mat (H-T-O) to map the number before placing it.
   • Structured peer support: assign a ‘coach’ partner who asks scripted questions: “What’s the hundreds digit? What hundreds is it between?”
   • Simplified materials: number lines with tick marks every 50 (or every 100) to help spacing; allow students to place closer estimates without fine-grain precision initially.

   IEP / 504 Accommodations

   • Extended time for independent practice and exit ticket as needed; allow completion in a quieter space.
   • Read-aloud of directions and items; check for understanding by having student restate the steps.
   • Reduce copying demands: provide printed numbers and benchmarks; allow student to point and verbally explain.
   • Frequent breaks/behavior supports: quick movement break after guided practice (e.g., stand-stretch, then return).
   • Preferential seating near instruction and away from distractions; clear view of number line model.
   • Use assistive tools: thicker pencil/marker, slant board, or adapted paper for fine-motor needs.
   • Provide a graphic organizer for explanations: ‘Benchmarks: __ and __ / Closer to: __ / Place value: __ hundreds __ tens __ ones / Reason: __’.
   • For attention/executive function: provide a step checklist on desk and highlight only the current number being solved.
   • Allow alternative response mode: place with sticker and record explanation via brief audio (if available) or dictated to adult.

   Advanced Learners

   • Challenge: place two close numbers (e.g., 695 and 705) on the same 600–800 zoomed line; explain why one is left of 700 and one is right of 700 using tens/ones.
   • Add an ‘unknown point’ task: teacher marks a point and students estimate the number, justify using benchmarks and midpoints.
   • Introduce additional benchmarks beyond hundreds (e.g., 650, 750) and require justification for why those benchmarks are efficient.
   • Error analysis: present a flawed placement (e.g., 623 placed near 700); students identify the mistake and write a correction with reasoning.
   • Create-your-own: students design a 0–1,000 number line with only 0 and 1,000 labeled, choose five benchmarks, and defend their choices.
   • Comparison extension (connect to CCSS.Math.Content.2.NBT.B.4): given two numbers placed on a line (e.g., 598 and 621), write a comparison using >, <, = and explain using location and hundreds/tens.
   • Efficiency challenge: solve placements using the fewest benchmark marks while still being convincing; explain strategy choice.

   形成性检查

   • Warm-up finger check and partner explanations for closeness to hundreds (teacher listens for benchmark language).
   • CFU questions during modeling (benchmarks for 732; 9 hundreds location; true/false about 205 near 250).
   • Guided practice circulation checklist: correct hundred interval, reasonable spacing, use of place-value justification, revision when prompted.
   • Anecdotal notes: students who consistently confuse neighborhoods (hundreds digit) flagged for reteach.
   • Independent practice work sample review: accuracy across Lines A/B/C and quality of written explanations.

   退出票

   On a 0–1,000 number line labeled 0, 500, and 1,000, place 623. Then write: “I used the benchmarks __ and __. I placed it near __ because __.” Use place-value language (hundreds/tens/ones) or expanded form.

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 This template supports the lesson's vocabulary terms related to number lines and estimation, reinforcing key math language for grade 2 students.
   • Worksheet 匹配活动 A matching activity aligns well with the warm-up and practice of connecting numbers to benchmarks and midpoints on the number line.
   • Worksheet T-图 A T-Chart organizer helps students compare numbers to benchmarks and justify their estimates, matching the turn-and-talk and justification activities.
   • Worksheet 3-2-1 退出票 The 3-2-1 Exit Ticket provides a simple formative assessment to capture student understanding and reflections at lesson closure, matching the exit ticket requirement.

   Storypie 内容

   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Measurement Measurement is the process of associating numbers with physical quantities and phenomena. It is a fundamental concept in science, engineering, construction, and daily life.
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory
   • Storypie Content Addition Addition is a fundamental mathematical operation that represents the total amount of objects together in a collection. It is signified by the plus sign (+).
   • Storypie Content Cash Register A mechanical or electronic device for registering and calculating transactions at a point of sale, which also includes a drawer for storing cash and often a receipt printer.
   • Storypie Content Geometry Geometry is a branch of mathematics concerned with the properties of space, such as the distance, shape, size, and relative position of figures.

   准备清单

   • Print student number lines for guided practice (hundreds labeled) and independent practice (Lines A/B/C) plus a few extras.
   • Prepare and post anchor chart: steps for estimating with benchmarks; add sentence frames.
   • Set up large class number line (projected or posted) with clear, equal hundred intervals; ensure visibility from all seats.
   • Prepare sticky notes/number cards labeled: 340, 598, 721, 909 (guided) and any additional examples.
   • Organize base-ten blocks in a tray for quick access; pre-build 680 and 205 sets if helpful for speed.
   • Create exit ticket slips and a quick sorting system (three folders: Score 0/1/2).
   • Plan partner assignments (consider language and support needs) and decide roles (placer/explainer).
   • Prepare a small-group support station with pre-labeled number line, hundreds chart, place-value mat, and extra sentence frames.
   • Test document camera/projection and have markers ready for clear labeling.

   常见误解

   • On a number line, bigger numbers can go left if the student is not attending to directionality.
   • All midpoints are 500 (confusing the whole line midpoint with local midpoints).
   • If a number has a 9 in it, it must be near 900 (over-attending to a single digit rather than place value).
   • Unequal intervals are acceptable (students bunch marks near one end).
   • Students think 205 is near 250 because they focus on the ‘2’ and assume middle-of-200s without considering tens/ones.
   • Students believe exact placement is required and become stuck; they may not understand estimating as reasonable placement with justification.
6. 6 Skip-Count by 10s Within 1,000 (Starting from Any Number) 完整课程 Skip-Count by 10s Within 1,000 (Starting from Any Number)

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group for warm-up and direct instruction; partners for guided practice; independent for practice; whole group for closure.

   学习目标

   • I can skip-count by 10s starting from any 3-digit number within 100–900 and generate the next 10 numbers. Apply

     成功标准:

     • Given a starting number from 100–900, I write the next 10 numbers by adding 10 each time with no more than 1 error.
     • Across the sequence, I keep the ones digit the same and correctly change the tens/hundreds when needed (e.g., 298, 308, 318...).

   • I can explain how adding 10 changes the place value digits in a 3-digit number using the words hundreds, tens, and ones. Understand

     成功标准:

     • I explain that adding 10 increases the tens by 1 while the ones stay the same, and I describe regrouping when tens reach 10 tens.
     • I show my thinking with a place value chart, number line, or equation (e.g., 356 + 10 = 366; 396 + 10 = 406).

   • I can mentally add 10 to a given number from 100–900 and check my answer using a second representation. Analyze

     成功标准:

     • I correctly answer at least 4 out of 5 problems that require adding 10 (one step or repeated steps) within 100–900.
     • I verify at least 3 answers using a different strategy (e.g., after mental math, I confirm with a place value chart or number line) and correct mistakes.

   标准

   • CCSS.MATH.CONTENT.2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.
   • CCSS.MATH.CONTENT.2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
   • CCSS.MATH.CONTENT.2.NBT.B.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

   材料

   • Place value chart (Hundreds–Tens–Ones) displayed for whole group · 1Large chart on board/document camera; include labels and color-coding by place.
   • Teacher place value chart and digit cards or magnetic digits (0–9) · 1 setUse to change digits quickly and model regrouping.
   • Student place value chart mats (paper or laminated) · 1 per studentInclude boxes for hundreds/tens/ones; optional sentence frame at bottom.
   • Base-ten blocks (hundreds flats, tens rods, ones cubes) · Class set or small group setsOptional but recommended for struggling learners/IEP; use selectively to save time.
   • Mini whiteboards, markers, and erasers (or paper/pencils) · 1 per studentWhiteboards for fast checks during guided practice.
   • Number line display and/or open number line templates · 1 class display; 1 per student template optionalOpen number line for jumps of +10 to emphasize pattern.
   • Independent practice sheet or task cards (skip-count by 10s within 1,000) · 1 per student10–12 items; include sequences, missing numbers, and 3 word problems; keep results ≤ 1,000.
   • Exit ticket (2-question slip) · 1 per studentCollect for quick scoring (0–1–2 rubric).

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Facilitate a fast-paced number talk focused on ‘10 more.’ Use hand signal for ‘whisper’ then ‘say it.’ Record a few student responses and quickly underline the ones digit to highlight it stays the same.

   学生操作: Students mentally find 10 more, whisper to themselves, then say the answer on the teacher’s signal. Students notice and name patterns (ones digit stays the same; tens/hundreds change).

   教师脚本（完整）

   (Point to 47) “Today we will practice skip-counting by 10s from any number—not just numbers that end in 0. When I point to a number, whisper the number that is 10 more. Keep it to yourself… and on my signal, say it out loud. Ready.” (Signal) “47.” (Pause) “Say it.” (After response) “I’m underlining the 7 in 47. What is the ones digit in 57?” (Take 1–2 responses.) “Yes—7. The ones digit stayed the same.” (Repeat with 130 and 298.) “When we add 10, we’re adding one ten. That helps us predict what changes.”

   Direct Instruction10 min

   教师行动: Model on a place value chart with digits. Explicitly connect +10 to adding one ten; show what stays the same and what changes. Include one example without regrouping and one that crosses a hundred (tens regrouping). Use choral responses for targeted checks.

   学生操作: Students track the teacher’s modeling, answer targeted questions, and use quick gestures (point to tens place / ones place) when prompted. Students repeat the rule using place value language.

   教师脚本（完整）

   “Look at our place value chart: Hundreds, Tens, Ones. I’m building the number 356: 3 hundreds, 5 tens, 6 ones.” “Key idea: Ten means one group of ten. When we add 10, we add one ten.” “Watch what happens when we add 10. Ten means one group of ten. That changes the tens place. The ones digit stays the same because we are not adding any ones. So 356 plus 10 is 366. The 6 ones stay 6 ones, and the tens go from 5 tens to 6 tens.” (Write: 356 + 10 = 366) “Everyone, point to the ones digit in 356. Now point to the ones digit in 366. What do you notice?” (Wait) “The ones digit stayed the same.” “Now watch a trickier one: 396 + 10.” (Build 396.) “We add one ten. The ones stay 6.” “Here’s the important part: If the tens become 10 tens, that is the same as 1 hundred. So 396 becomes 406. The hundreds increase by 1 and the tens become 0.” (Write: 396 + 10 = 406) “Say the regrouping rule with me: ‘Ten tens make one hundred.’”

   理解检查: Quick CFU (fist to five or thumbs): “If I add 10, does the ones digit change?” (Students show.) Then ask: “What is 478 + 10?” Students write on whiteboards and hold up. Scan for errors; choose one correct and one common error to address (e.g., 478→479) and restate: “We added ten, not one.”

   Guided Practice15 min

   教师行动: Lead students through short sets where they generate the next 4 numbers by +10. Use ‘predict first’ routine. Cold call for reasoning using sentence frames. Provide immediate feedback and reteach moment for boundary crossings. Record one set on the board using two representations (place value chart and open number line).

   学生操作: Students use mini whiteboards and place value chart mats to write sequences. Partners discuss what stayed the same/changed using ones/tens/hundreds language. Students correct errors after feedback.

   教师脚本（完整）

   “Now we do it together. Before you write, predict: which digit will stay the same every time we add 10? Which digit will change? Turn and tell your partner using the words ones, tens, hundreds.” (30 seconds) “Problem 1: Start at 74. Write the next 4 numbers when counting by 10s.” (After 30–45 seconds) “Boards up.” (Scan.) “Let’s say it together: 74, 84, 94, 104, 114. Notice what happened when we crossed from 94 to 104: the tens regrouped into a hundred.” “Problem 2: Start at 209. Next 4 numbers.” (After boards up) “Turn and tell: What stayed the same? What changed?” “Use this sentence frame: ‘The ones digit stayed ___. The tens digit ___. The hundreds digit ___ when ___.’” “Problem 3: Start at 458. Next 4.” “Problem 4: Start at 590. Next 4.” “Problem 5: Start at 697. Next 4.” (If error appears) “I’m seeing a common mistake: some answers changed the ones digit. Let’s check: Are we adding ones? No. We’re adding one ten. So the ones digit must stay the same.”

   支架提示: Predict prompt: “If we add 10, which place changes? Say: tens.” | Focus on invariance: “Circle the ones digit in the start number. Will it change? Why or why not?” | Boundary prompt (crossing 99→109 or 590→600): “What happens when the tens digit would become 10? What does 10 tens equal?” | Place value language prompt: “Say it as groups: ___ hundreds, ___ tens, ___ ones. Now add one ten. What changed?” | Error-analysis prompt: “Compare these two answers: 697→707 vs 697→706. Which is 10 more? How do you know?” | Representation prompt: “Show it on an open number line: start at ___. Make one jump of +10. Where do you land?”

   Independent Practice15 min

   教师行动: Distribute independent practice. Remind students to show thinking with at least one representation and check with a second method for early finishers. Circulate with a clipboard checklist; pull a quick table-side reteach group for students making the same error (changing ones digit or adding 1 instead of 10).

   学生操作: Students complete practice items independently, showing work (place value chart, number line, or equations). Students who finish early check answers using a different representation and correct mistakes.

   教师脚本（完整）

   “Now it’s your turn. Work quietly and do your best thinking.” “For each problem, you must show your thinking in at least one way: a place value chart, a number line jump by 10s, or an equation like 478 + 10 = 488.” “If you finish early, check your answers by using a different representation. Checking means you prove it a second way and fix any mistakes you find.” “If you need help, first reread the problem, then try the place value chart, then raise your hand.”

   监控清单: Student adds 10 each step (not 1). | Ones digit remains constant across +10 sequence. | Correct regrouping when tens move from 9 to 0 and hundreds increase by 1 (e.g., 590→600; 697→707). | Student writes legible 3-digit numbers in correct order. | Student uses at least one representation on each required item (chart/number line/equation). | Student checks at least 3 answers using a second representation (for those who finish early/at pace).

   Closure5 min

   教师行动: Facilitate a brief synthesis using the class rule statement. Collect and preview exit tickets for trends. Reinforce the place value change pattern and regrouping condition.

   学生操作: Students complete exit ticket independently and then participate in a quick choral response of the rule sentence. Students turn in exit tickets.

   教师脚本（完整）

   “Let’s close with our rule.” “Tell me the rule in a complete sentence: When I add 10, the ______ place increases by 1, the ______ place stays the same, and sometimes the ______ place changes because we regroup.” (After students respond) “Now complete the exit ticket. Show neat work. When you’re done, put it face down and pass it to the corner.”

   退出票: 1) Start at 368. Write the next 5 numbers counting by 10s. 2) Explain in one sentence what changes (and what stays the same) when you add 10.

   skip-count

   Counting by jumping the same amount each time, like +10, +10, +10.

   tens place

   The middle digit in a 3-digit number that shows groups of ten.

   ones place

   The last digit that shows single ones.

   hundreds place

   The first digit in a 3-digit number that shows groups of 100.

   add 10

   Ten more means one more group of ten.

   English Language Learners

   • I can orally describe a +10 change using the sentence frame: ‘The ones stay the same. The tens go up by 1.’
   • I can use the words ones, tens, hundreds to explain my answer to a partner.
   • I can ask for clarification using: ‘Can you repeat?’ ‘Can you show me on the chart?’
   • Pre-teach vocabulary with visuals (labeled place value chart; color-code ones/tens/hundreds).
   • Provide sentence frames on desk strip: ‘Start at ___. Add 10. The ones stay ___. The tens become ___.’ and regrouping frame: ‘10 tens = 1 hundred, so ___.’
   • Use gesture supports: touch ones column when saying ‘ones stay’; touch tens column when saying ‘tens change’; sweep tens→hundreds when regrouping.
   • Pair ELLs with supportive peer for partner talk; assign roles (Speaker A uses sentence frame; Speaker B points on chart).
   • Allow responses with numbers + pointing to chart before full sentences; then recast into full academic language (teacher repeats in complete sentence).
   • Provide bilingual glossary or translated key terms when available (school-approved).

   Struggling Learners

   • Use base-ten blocks for first 2 guided practice numbers: physically add one tens rod each time; trade 10 tens for 1 hundred with teacher support.
   • Reduce cognitive load: for independent practice, assign 6–8 items instead of 10–12; prioritize sequences and 1 word problem.
   • Chunk tasks: cover the page so only 2 problems show at a time; provide a checklist: 1) circle ones digit 2) add 10 3) check ones stayed same.
   • Provide a printed place value chart with arrows: ‘+10 → tens +1’ and a reminder: ‘Ones stay.’
   • Offer number line template with pre-marked jumps of +10 (blank landing spots).
   • Peer support: strategic partner for one “check together” after completing each problem (not copying; verifying pattern).
   • Modified expectation for Objective 1: generate next 5 numbers (instead of 10) with no more than 1 error, then extend if successful.

   IEP / 504 Accommodations

   • Provide extended time as needed; allow completion of fewer items with mastery focus.
   • Preferential seating near instruction and away from distractions; clear view of board/anchor chart.
   • Provide directions both orally and in writing; check for understanding with a private prompt: ‘Tell me what you do first.’
   • Use large-print materials or increased spacing for students with visual-motor needs; allow use of marker instead of pencil for grip support.
   • Allow use of manipulatives and/or place value chart during independent and exit ticket if documented accommodation.
   • Frequent breaks/micro-break option (30 seconds stand/stretch) between guided and independent practice.
   • For attention/executive function: provide a timer and a two-step goal: ‘Finish problems 1–4, check with number line, then raise hand.’

   Advanced Learners

   • ‘Missing start’ challenge: Given a sequence (e.g., 263, 273, 283, __, 303), determine the missing number(s) and justify.
   • Create-your-own: Students design a 10-step +10 sequence that crosses a hundred exactly once, then explain why it crosses there.
   • Error analysis: Provide two incorrect student sequences; advanced learners identify the first incorrect term and write feedback using place value language.
   • Two-way thinking: Include subtracting 10 within 1,000 (e.g., 402, 392, 382…) and connect to CCSS.MATH.CONTENT.2.NBT.B.8.
   • Word problem extension: ‘If you add 10 eight times to 345, what number do you reach? Show two strategies and explain which is more efficient.’

   形成性检查

   • Warm-up number talk: listen for correct ‘10 more’ responses; note students who change ones digit or add 1.
   • Whiteboard checks during guided practice after each start number; record quick tally of class accuracy.
   • Partner explanation check: circulate and listen for use of ones/tens/hundreds language; prompt with sentence frames.
   • Independent practice monitoring checklist notes (ones digit consistency, regrouping accuracy, representation use).

   退出票

   1) Start at 368. Write the next 5 numbers counting by 10s. 2) Explain in one sentence what changes (and what stays the same) when you add 10.

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 3-2-1 退出票 The lesson includes an exit ticket activity, so a 3-2-1 Exit Ticket template provides a quick formative assessment for student understanding.
   • Worksheet 词汇练习 The lesson specifies key vocabulary terms related to place value and skip-counting, making a vocabulary practice template essential.
   • Worksheet 填空 A fill-in-the-blank practice sheet aligns well with the independent practice of skip-counting sequences and missing numbers.
   • Worksheet T-图 A T-Chart organizer supports students in comparing digits that change versus digits that stay the same when adding 10, reinforcing place value concepts.

   Storypie 内容

   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory
   • Storypie Content Fractions Fractions represent parts of a whole or, more generally, any number of equal parts. They are a fundamental concept in mathematics used to express division, ratios, and numbers that are not whole.
   • Storypie Content Division Division is a fundamental arithmetic operation that is the inverse of multiplication. It is the process of splitting a number into equal parts or groups.
   • Storypie Content Calculator Watch A device that performs arithmetic operations. Calculators have evolved from ancient counting tools and mechanical devices to modern, pocket-sized electronic instruments.

   准备清单

   • Prepare and copy: independent practice sheets/task cards (10–12 items) and exit tickets (2 items).
   • Set up board plan and write learning targets and vocabulary before students arrive.
   • Prepare place value chart (large) and ensure digit cards/magnetic digits are organized for fast swapping.
   • Place student materials at tables: whiteboards/markers/erasers and place value chart mats.
   • Optional: set out base-ten blocks in bins for quick access during reteach.
   • Prepare open number line templates for students who need them.
   • Decide partner pairs and roles for turn-and-talk (Speaker/Pointer).

   常见误解

   • “Adding 10 changes the ones digit.”
   • “Adding 10 always makes the number end in 0.”
   • “When the tens digit is 9, adding 10 makes the tens digit 10 (written as a digit).”
   • “Crossing a hundred means only the hundreds changes; students forget tens becomes 0.”
   • “Skip-counting by 10s only works when starting number ends in 0.”
7. 7 Skip-Count by 5s Within 1,000: Patterns and Real-World Connections 完整课程 Skip-Count by 5s Within 1,000: Patterns and Real-World Connections

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group mini-lesson; partners for guided practice; independent choice task; brief partner share during closure

   学习目标

   • I can skip-count by 5s within 1,000 starting at any number and record the next 10 numbers in the pattern. Apply

     成功标准:

     • I add 5 each time (my numbers increase by 5).
     • I can say and write at least 10 numbers in sequence.
     • My sequence stays within 1,000 and does not skip or repeat numbers.

   • I can analyze a skip-count-by-5s sequence and explain how the ones and tens digits change using place-value words (ones, tens, hundreds). Analyze

     成功标准:

     • I describe the ones-digit pattern accurately (0 and 5 alternate when starting from a multiple of 5).
     • I explain when/why the tens digit changes (regrouping 10 ones into 1 ten).
     • I use place-value language (ones/tens/hundreds) in my explanation.

   • I can use skip-counting by 5s to solve real-world problems: (a) tell and write time to the nearest 5 minutes using a.m. and p.m., and (b) solve a word problem involving nickels and record the total using the ¢ symbol. Apply

     成功标准:

     • For time, I write the correct time to the nearest 5 minutes and include a.m. or p.m.
     • For money, I count nickels by 5s and write the correct total with the ¢ symbol.
     • I show my counting (list, number line, clock counts, or repeated +5) and label units (minutes or cents).

   标准

   • CCSS.MATH.CONTENT.2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.
   • CCSS.MATH.CONTENT.2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
   • CCSS.MATH.CONTENT.2.MD.C.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
   • CCSS.MATH.CONTENT.2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

   材料

   • Hundreds chart (projected and/or class set) · 1 projected + optional 1 per studentUsed to highlight multiples of 5 and visualize patterns.
   • Student whiteboards, markers, erasers · 1 set per studentFor quick checks and choral practice.
   • Open number line worksheets or blank strips · 1 per student + a few extrasStudents draw and label +5 jumps.
   • Analog demo clock + student clocks (if available) · 1 demo; optional 1 per pair/studentUse to model counting by 5 minutes around the clock.
   • Play money nickels or nickel images/cutouts · At least 10 per pair or picture cardsSupport concrete counting by 5 cents.
   • Anchor chart paper and markers · 1 chart + markersCreate “Skip-Counting by 5s” chart during mini-lesson.
   • Exit tickets (printed or projected) · 1 per student2-item exit ticket for mastery check.
   • Optional: base-ten blocks (tens rods/ones cubes) · Small set for teacher tableFor targeted support connecting +5 to 5 ones and regrouping to a ten.

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Lead a fluency routine: “5s Quick Count.” Display a partial sequence and cue choral response. Then count forward to 100 and backward from 50 to 0, listening for accuracy and pace. Prompt students to use the ones-digit pattern as a self-check.

   学生操作: Chorally skip-count by 5s, track the pattern, and correct if they notice an error. Students use finger tracking or point to the displayed sequence as they count.

   教师脚本（完整）

   “Eyes on the board. We’re doing a quick count by 5s. When I point, you say the next number by adding 5. Ready… 0… (point) 5… (point) 10… (point) 15… (point) 20… Now I’m going to stop pointing and you keep the pattern going to 100. If you get stuck, use this pattern check: the ones digit goes 0, 5, 0, 5. If your number ends in anything else, pause and fix it. Now we’ll count backward from 50 to 0 by 5s. Ready… 50, 45, 40…”

   Direct Instruction10 min

   教师行动: Teach the skip-count by 5s pattern using a hundreds chart and an anchor chart. Explicitly connect skip-counting to place value changes using a 3-digit example (235). Make real-world connections to clocks (5-minute intervals) and money (nickels). Model think-aloud and record observations on the anchor chart.

   学生操作: Watch and listen, answer quick questions, and repeat key ideas. Students track highlighted numbers on the hundreds chart and describe patterns using place-value language.

   教师脚本（完整）

   “Today our goal is to skip-count by 5s within 1,000, notice patterns, and use those patterns to solve real-world problems like time and money. First, let’s build our anchor chart: ‘Skip-Counting by 5s.’ I’m going to highlight numbers on this hundreds chart. Watch what I highlight: 5, 10, 15, 20… What do you notice about the last digit?” (Allow 2–3 students to respond.) “Exactly: multiples of 5 end in 0 or 5. I’m writing that: ‘Multiples of 5 end in 0 or 5.’ Now let’s connect it to place value with a bigger number. Watch me start at 235. I add 5: 240. I add 5 again: 245. I add 5 again: 250. I notice the ones digits go 5, 0, 5, 0—so the ones digit alternates. I’m writing: ‘Ones digit alternates 0 and 5.’ Now look at the tens place: from 235 to 240, the tens digit changed because 35 + 5 makes 40. Then from 240 to 245 the tens stayed the same. From 245 to 250, the tens changed again. I’m writing: ‘The tens digit increases by 1 after two jumps of +5.’ Real-world connection: On a clock, each number you say around the clock is 5 minutes. On money, each nickel is 5 cents. So skip-counting by 5s helps us with telling time and counting nickels.”

   理解检查: Quick oral CFU: (1) “Thumbs up if 372 is a multiple of 5; thumbs sideways if you’re not sure.” (Expect thumbs down/sideways; discuss last digit.) (2) “Say the next two numbers after 495 when counting by 5s.” (Expect 500, 505.) (3) “What happens to the ones digit when we count by 5s?” (Expect alternates 0 and 5.)

   Guided Practice15 min

   教师行动: Facilitate three rounds of “We Do” practice. Use whiteboards for immediate feedback, then an open number line for representation, then a clock connection task. Cold-call students to explain patterns using a sentence starter. Circulate to correct errors (missing numbers, incorrect +5 jumps, mislabeling units).

   学生操作: Complete each round using whiteboards/number lines/clock models, explain reasoning using sentence frames, and revise work after feedback. Partners briefly compare answers and check each other’s ones-digit pattern.

   教师脚本（完整）

   “Now we practice together. Remember: start on a multiple of 5—ends in 0 or 5—and add 5 each time. Round A: Whiteboards. Start at 60. Write the next 8 numbers when we count by 5s. Don’t shout—write first. 10 seconds… show me.” (Scan boards.) “Check with me: 60, 65, 70, 75, 80, 85, 90, 95, 100. If yours doesn’t end in 0 or 5, circle the first place it went off and fix it.” “Round B: Open number line. Start at 195. Draw 6 jumps of +5. Label every landing number.” (After 1–2 minutes, cold-call.) “Use our sentence starter: ‘I started at __ and added 5 __ times, so I landed on __.’” “Round C: Clock connection. Here is 2:00. Each time we move to the next number, we add 5 minutes. Let’s find 2:25. Count with me by 5 minutes: 5, 10, 15, 20, 25. Now find 2:40 and 2:55 the same way.” “Partner check: tell your partner one pattern you noticed in the ones or tens place. Use this frame: ‘I notice __ changes because __.’”,

   支架提示: Look at the last digit. Does it end in 0 or 5? If not, you may have added the wrong amount. | Say it out loud in a whisper: ‘plus 5, plus 5…’ while you write each number. | Circle the ones digit in each number. What pattern do you see? 0, 5, 0, 5… | If you are stuck at a number ending in 5, ask: ‘What number ends in 0 and is 5 more?’ | Use place value: ‘If I add 5 ones and I have 5 ones already, that makes 10 ones, so I trade for 1 ten.’ | On the number line, each jump must be the same size and labeled +5; check that your labels increase by 5 each time. | On the clock, point to each number you pass and count: 5, 10, 15…; stop when you reach the target minutes. | Check tens change: does the tens digit change every two steps? If not, re-check your sequence.

   Independent Practice15 min

   教师行动: Offer a choice between a pattern-focused task and a real-world task. Provide clear expectations for silence/time, circulate with a monitoring checklist, and pull a quick small group for targeted reteach (e.g., students who confuse +5 with +10 or start from a non-multiple of 5). Collect student work for quick scoring against success criteria.

   学生操作: Select one task, complete the work independently, show thinking with a list/number line/clock, and write brief pattern observations (if Task 1) or label units (if Task 2). Use the self-check strategy: ones digit ends in 0 or 5.

   教师脚本（完整）

   “You’re ready for ‘You Do.’ Choose ONE task. Task 1: Pattern Task. Complete the skip-count sequences and then write two pattern observations using the words ones, tens, hundreds. Task 2: Real-World Task. Solve the money and time problems using skip-counting by 5s. You must show your counting and label cents or minutes. Work silently for the first 10 minutes. If you need help, first try the self-check: ‘Does my number end in 0 or 5?’ Then raise your hand. If you finish early, take the extension card: Start at 875 and skip-count by 5s for 10 numbers, then circle every time the tens digit changes.”

   监控清单: Student starts from a multiple of 5 (ends in 0 or 5). | Student adds 5 consistently (no +10 jumps, no missing numbers). | Student sequence stays within 1,000. | Student labels units correctly (¢ for money; minutes/time for clock). | Student uses pattern check (ones digit alternation) to correct errors. | Student explanation uses place-value language (ones/tens/hundreds) at least once. | Student representations match the numbers written (number line landings equal written sequence; clock counts match minutes).

   Closure5 min

   教师行动: Administer exit ticket, then facilitate a brief partner share using a sentence frame. Reinforce the day’s big idea: patterns in ones/tens help us skip-count accurately and connect to money/time. Preview next lesson connection (e.g., skip-count by 10s/5s mixed or counting coins/time).

   学生操作: Complete exit ticket independently and submit. Then share one pattern noticed and how it helps, using the provided frame. Listen respectfully to partner and optionally add on.

   教师脚本（完整）

   “Before we go, show what you know on the exit ticket. Do it independently—this helps me plan tomorrow. After you finish, turn to your partner and say: ‘One pattern I noticed is __. This helps me because __.’ Remember: skip-counting by 5s is not just a list—it’s a pattern in the ones and tens place, and it shows up in nickels and in telling time.”

   退出票: 1) Continue: 485, 490, __, __, __ 2) Circle the best explanation: “When skip-counting by 5s, the ones digit (A) stays the same (B) alternates 0 and 5 (C) increases by 5 each time.”

   skip-count

   counting by fives instead of by ones

   multiple of 5

   a number that ends in 0 or 5

   pattern

   a repeat that helps you predict what comes next

   ones place / tens place / hundreds place

   the digit spots that tell how many ones, tens, and hundreds you have

   English Language Learners

   • I can use the sentence frame ‘I started at __ and added 5 __ times, so I landed on __.’
   • I can describe a pattern using place-value words: ‘The ones digit ___. The tens digit ___.’
   • I can label units correctly: ‘___ cents’ and ‘___ minutes’ or ‘It is __:__.’
   • Pre-teach vocabulary with visuals: show a ‘multiple of 5’ card set (ending in 0 or 5) vs. not multiples.
   • Use gestures and visuals: point to ones/tens place on enlarged numbers; highlight/circle the ones digit in alternating colors (0 in blue, 5 in green).
   • Provide bilingual glossary cards if available; allow students to rehearse explanations with a partner before sharing whole-class.
   • Sentence frames posted and on student desk strips; allow oral responses before written responses.
   • Use real objects (nickels, clock hands) to reduce language load while maintaining cognitive demand.
   • Chunk directions: “Step 1: Start number. Step 2: Add 5. Step 3: Check last digit.”

   Struggling Learners

   • Limit the range at first: start within 0–200 for practice before moving to larger 3-digit numbers.
   • Provide a “0 or 5?” self-check card on desk; students must touch the last digit before writing the next number.
   • Use a numbered strip/marked number line with tick marks pre-drawn; student only labels landings.
   • Offer concrete manipulatives: give 5 ones cubes to add each step; regroup to a ten rod when reaching 10 ones to visualize tens changes.
   • Modified expectation during independent practice: complete 2 sequences of 6 numbers (instead of 3 sequences of 10) OR solve one real-world problem with full explanation.
   • Partner support: assign a peer coach to check each step: ‘Did you add 5? Does it end in 0 or 5?’
   • Provide a mini-anchor chart at the table: ‘ones: 0/5; tens changes every two jumps.’

   IEP / 504 Accommodations

   • Preferential seating near instruction and away from distractions; ensure clear sightline to board/anchor chart.
   • Provide printed notes/anchor chart snapshot and a filled example (e.g., 235→240→245→250) to reduce copying demands.
   • Allow extended time for exit ticket or reduce items (complete item 1 only with verbal explanation for item 2) as appropriate per plan.
   • Allow alternative response mode: verbal response, pointing on a clock model, or using manipulatives to demonstrate +5.
   • Use frequent checks for understanding and discreet cues (tap the ones digit; point to +5 on number line).
   • For fine-motor needs: allow larger marker, pencil grip, or digital number line tool; accept typed numbers if available.
   • Break tasks into smaller steps with checkboxes; provide immediate feedback after each step to prevent error accumulation.

   Advanced Learners

   • Start from non-zero hundreds: begin at 735 and skip-count by 5s past the next ten and next hundred; explain what changes at 740, 750, and 800.
   • Challenge: determine the 12th number in a +5 sequence starting at 465 without writing every number; explain strategy.
   • Create-and-swap: write a real-world problem involving 5-minute intervals or nickels that results in a 3-digit total (e.g., 27 nickels). Solve and justify.
   • Compare patterns: explain how skip-counting by 5s relates to skip-counting by 10s (every other number in the 5s sequence).
   • Error analysis: given an incorrect sequence (e.g., 195, 200, 205, 215…), identify the first error and explain the fix using place value language.

   形成性检查

   • Warm-up choral counting accuracy (teacher listens for +5 pattern and correct backward counting).
   • Whiteboard Round A: immediate visual check of next 8 numbers from 60.
   • Number line Round B: check for equal +5 jumps and correct labeled landings from 195.
   • Clock Round C: observe whether students count by 5-minute intervals and match to target times.
   • Teacher circulation notes using monitoring checklist during independent practice.

   退出票

   1) Continue: 485, 490, __, __, __ 2) Circle the best explanation: ones digit alternates 0 and 5.

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 3-2-1 退出票 Includes a 3-2-1 exit ticket to provide a quick mastery check as specified in the lesson's exit ticket activity.
   • Worksheet 词汇练习 Supports the lesson's vocabulary terms related to skip-counting and place value for grade 2 students.
   • Worksheet 匹配活动 Engages students with practice matching skip-counting patterns and real-world connections like clocks and money.
   • Worksheet KWL 图表 Provides an organizer to activate prior knowledge and track learning about skip-counting patterns and place value concepts.

   Storypie 内容

   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory

   准备清单

   • Prepare and post learning targets and vocabulary on the board.
   • Print/prepare: open number line sheets, independent practice tasks (Task 1 and Task 2), extension card, exit tickets.
   • Ready the hundreds chart (project or distribute) and plan how to highlight multiples of 5 (digital highlight or colored marker).
   • Set up anchor chart paper with title ‘Skip-Counting by 5s’ and space for 3 bullets (ends in 0/5; ones alternates; tens changes after two jumps).
   • Gather and bag materials by pair: nickels/cutouts and (optional) student clocks.
   • Test demo clock visibility and ensure hands can be moved smoothly.
   • Prepare a small-group reteach kit: base-ten blocks, a mini hundreds chart, and a short +5 practice strip.
   • Decide cold-call list for guided practice (ensure equitable participation).

   常见误解

   • Any number can be a starting point for skip-counting by 5s without affecting the pattern (students must understand the lesson’s focus is starting from multiples of 5).
   • The ones digit increases by 5 each time (instead of alternating 0 and 5 in base ten).
   • Adding 5 never changes the tens digit (students may not anticipate regrouping when ones digit is 5 and becomes 0 with tens +1).
   • On a clock, moving from one number to the next equals 1 minute (rather than 5 minutes).
   • Counting nickels: students may confuse nickel value (5¢) with dime (10¢) or count coins by ones rather than by 5s.
8. 8 Skip-Count by 2s: Efficient Counting and Early Even/Odd Noticing 完整课程 Skip-Count by 2s: Efficient Counting and Early Even/Odd Noticing

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group for warm-up/direct instruction; partners for guided practice; independent for practice; whole group for closure.

   学习目标

   • I can determine whether a group of objects (up to 20) is odd or even by making pairs and/or counting by 2s, and I can explain how I know. Analyze

     成功标准:

     • I can make pairs (groups of 2) and check for leftovers.
     • If there is no leftover, I identify the total as even; if there is 1 leftover, I identify the total as odd.
     • I can explain my decision using the words pair, leftover, even, and odd (spoken, drawn, or written).

   • I can count by 2s to keep track of paired objects and to continue a +2 pattern from a given start number (within 50 as practice). Apply

     成功标准:

     • I start at the given number and say/write the next numbers by adding 2 each time.
     • I keep the pattern consistent (no missing or repeated numbers).
     • I can use a tool (number line or pairs) to self-correct if I get stuck.

   • I can write an equation to show an even number as a sum of two equal addends, using my pairs as evidence. Apply

     成功标准:

     • Given an even total (up to 20), I can split it into two equal groups and write an equation (example: 12 = 6 + 6).
     • My addends are equal and the sum matches the total.
     • I can connect the equation to a picture/model (pairs or two equal groups).

   标准

   • CCSS.MATH.CONTENT.2.OA.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
   • CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
   • CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

   材料

   • Counters or connecting cubes · 20+ per pair (plus a small teacher set)Use two colors if possible to support pairing (e.g., red/blue).
   • Class number line 0–50 (projected/anchor chart) · 1Large enough to point; include tick marks for every number or every 1 with labeled even numbers if needed.
   • Student number line strips 0–50 · 1 per student (optional)Helpful for struggling learners/ELLs; can be laminated for dry-erase use.
   • Hundreds chart · 1 class chart; optional mini chartsUsed for pattern noticing (even numbers form a column pattern).
   • Teacher whiteboard/chart paper + markers · 1 setFor modeling sequences and writing equations (2+2+2...).
   • Student dry-erase boards/markers (or math notebooks) · 1 per studentFor quick responses during CFUs.
   • Independent practice page or task cards · 1 per student3 sections: missing numbers, start-at sequences, even/odd noticing.
   • Exit ticket slips · 1 per student1 prompt with space for sequence + even/odd statement.
   • Document camera (optional) · 1For live modeling of pairing and student work examples.

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Lead quick choral count by 1s to 20. Present 12 counters, prompt efficiency question, and facilitate a 30-second turn-and-talk. Cold-call 2–3 students to share reasoning.

   学生操作: Choral count by 1s. Observe counters. Turn-and-talk about faster counting method and explain why. Listen to peers and be ready to share.

   教师脚本（完整）

   Mathematicians, today we will count in a smarter, faster way when things come in pairs. First, warm-up: count by 1s with me from 1 to 20. Ready… go. (Teacher counts with students, tracking with finger.) Now, look at these counters. (Show 12.) If I keep them in a messy pile, I might count 1, 2, 3… one by one. But if I put them into pairs—groups of 2—do I have to count by 1s? Or can I count by 2s? Turn and tell your partner: Which way would be faster and why? You have 20 seconds. Go. (After turn-and-talk) Eyes on me in 3…2…1. Who can share? Use this sentence starter: “Counting by ___ is faster because ___.”

   Direct Instruction10 min

   教师行动: Model making pairs with counters (10–14). Skip-count by 2s while pointing to each pair. Connect to number line hops (+2). Lead noticing conversation about even numbers and repeated reasoning. Create/record an anchor statement: “Skip-counting by 2s means add 2 each time.”

   学生操作: Watch and listen. Answer noticing questions. Choral respond to key phrasing. Track hops on number line with finger/eyes. Participate in brief CFU responses on boards (next number, what is +2).

   教师脚本（完整）

   Watch me closely. I’m going to organize the counters to help my brain. (Teacher places counters into pairs.) I am making groups of 2—these are pairs. I’m lining them up so I don’t lose track. Instead of counting each counter, I’m going to count by 2s. I will point to each pair one time. Ready: 2… 4… 6… 8… 10… 12. I stop because I used every counter. That tells me there are 12 counters. Now I’m going to show what my counting is doing on a number line. My start is 0. Each hop is 2. (Hop: 0→2→4→6→8→10→12.) Let’s name the pattern: Skip-counting by 2s means I add 2 each time. Say it with me: “Add 2 each time.” What do you notice about the numbers I said—2, 4, 6, 8, 10, 12? I notice they are all even numbers. When I count by 2s starting at 2, I land on even numbers. I’m going to ask a quick check: If I’m at 16, what is 2 more? Show it on your board. (Pause.) Hold up… 3, 2, 1.

   理解检查: Thumb-check: “Thumbs up if you added 2 to get your answer, thumbs sideways if you’re unsure.” Then call on 2 students to explain: “I knew 2 more than 16 is 18 because…” Ensure students are pointing to pairs/number line, not skipping randomly.

   Guided Practice15 min

   教师行动: Lead whole-group number line hopping by 2s from 0 to 20, then from 14 to 30. Transition to partner 'Pair and Count' task with 16–20 counters. Circulate, prompt pairing accuracy, and listen for explanations (words/drawings/equations).

   学生操作: Whole group: say numbers in sequence while tracking hops. Partners: make pairs, check for leftovers, skip-count by 2s, and record total (and optional equation). Explain reasoning to partner using sentence frames.

   教师脚本（完整）

   We are going to practice together. Remember our rule: add 2 each time. Activity A: Number line hops. My finger starts at 0. Each hop is +2. Ready—say the numbers with me: 2… 4… 6… 8… 10… 12… 14… 16… 18… 20. Now we’ll start somewhere else. My finger starts at 14. Each hop is +2. Ready: 16… 18… 20… 22… 24… 26… 28… 30. Activity B: Pair and Count with a partner. When I say “Go,” each pair will take a cup of counters. Step 1: Make pairs. Step 2: Check—any leftovers? Step 3: Point to each pair and count by 2s. Step 4: Write your total. Use this partner sentence: “I know the total is ___ because I made ___ pairs and counted by 2s: ___.” Go ahead and begin.

   支架提示: Show me your pairs. Are they groups of exactly 2? Fix any group that has 1 or 3. | Point to each pair one time as you count. How will you keep track so you don’t double-count? | If you have a leftover, what does that tell you about the number—odd or even? How do you know? | What number comes after 12 when counting by 2s? How did you decide? | Start at your first number and ask: 'What is 2 more?' Repeat. | If you get stuck, use the number line: find your number and hop +2. | Say the pattern out loud: 'Add 2 each time.' Does your list match that rule? | Can you write an equation for your total using 2s? Example: 2+2+2+2=8.

   Independent Practice15 min

   教师行动: Distribute independent practice. Read directions aloud and model one item briefly (not the whole page). Monitor with a checklist; pull a small group for immediate reteach as needed (use counters/number line).

   学生操作: Complete tasks independently: (1) fill missing by-2s numbers (within 50), (2) start-at sequences for 8 steps, (3) circle numbers that appear when counting by 2s from 2. Use tools if needed; show thinking with hops, pairs, or +2 notes.

   教师脚本（完整）

   Now it’s your turn to show what you know. On this page you have three short parts. Part 1: Fill in the missing numbers when counting by 2s. Part 2: Start at the number and count by 2s for 8 numbers. Part 3: Circle the numbers you would say if you were counting by 2s starting at 2. Watch me do one example so you know what to do: If it says 10, __, 14, __, 18, I ask myself: 'What is 2 more than 10?' That’s 12. Then 'What is 2 more than 14?' That’s 16. Work quietly and show your thinking. If you get stuck, ask yourself: 'What number is 2 more?' You may use counters or a number line if that helps. I will be walking around. If I tap your paper, it means I want you to explain your thinking in one sentence.

   监控清单: Student maintains +2 pattern without skipping or repeating numbers. | Student starts at the given number (does not restart at 2 unless told). | Student uses a tracking strategy (finger, hops, circles) rather than guessing. | Student correctly identifies even numbers in the by-2s sequence in Part 3. | Student work shows at least one representation when needed (number line hops, pairing sketch, or +2 annotations).

   Closure5 min

   教师行动: Facilitate share-out of one strategy. Revoice and connect to efficiency and structure (MP7/MP8). Administer exit ticket; collect and plan grouping for next lesson based on rubric.

   学生操作: Orally complete sentence frame about skip-counting by 2s. Complete exit ticket independently. Turn in ticket.

   教师脚本（完整）

   Bring your eyes to the board. Finish this sentence in your own words: “Skip-counting by 2s means __________.” (Select 2 students.) I heard you say “add 2 each time” and “counting pairs.” That is the structure mathematicians use—when things come in pairs, we can count faster. Now complete your exit ticket quietly. Remember: start at the number given, then keep adding 2. Check your list: Did you keep the pattern the whole time?

   退出票: Start at 12. Write the next 6 numbers when counting by 2s. Then answer: Are these numbers mostly even or odd? Explain in one sentence using the word “pairs” or “even.”

   skip-count

   Counting by jumping numbers instead of saying every number.

   pair

   Two things that go together.

   even

   You can make groups of 2 and none are left alone.

   odd

   After making pairs, one is left by itself.

   pattern

   A rule that helps you predict what comes next.

   English Language Learners

   • I can use the sentence frame “I started at __ and added 2 each time: __, __, __.”
   • I can use the words pair, even, odd to explain my thinking: “__ is even because __.”
   • I can ask for clarification using a help phrase: “Can you repeat the number?” or “Can you show me on the number line?”
   • Pre-teach vocabulary with visuals: picture of two objects labeled 'pair'; T-chart even/odd with paired vs leftover.
   • Provide sentence frames and word bank (pair, leftover, add 2, hop, even, odd).
   • Use gestures consistently: two fingers for +2; hand motion for 'hop' on number line.
   • Choral counting with rhythm/clap every hop to support auditory patterning.
   • Partner ELLs strategically with supportive peers; assign roles: 'Pointer' (tracks pairs) and 'Speaker' (says numbers).
   • Allow responses via pointing to number line or circling answers before producing full oral explanation.
   • Provide bilingual glossary if available (district resource) and allow native-language rehearsal before sharing in English.

   Struggling Learners

   • Use smaller ranges first (0–20 or within 30) and fewer steps (count 6 numbers instead of 10) until accuracy is stable.
   • Provide pre-paired counters (already in groups of 2) to reduce cognitive load; then transition to student-created pairs.
   • Offer a highlighted number line showing only even numbers labeled (2,4,6...) with arrows indicating +2 hops.
   • Chunk independent practice: complete Part 1 first, check with teacher, then Part 2, etc.
   • Use a consistent tracking tool: dot under each number said; or move a small sticky note along the number line each hop.
   • Provide immediate corrective feedback with a script: “Let’s go back. What was your start number? Now add 2.”
   • Peer support: pair with a steady counter; use 'echo counting' (partner says, student repeats).
   • Simplify materials: reduce distractor numbers in Part 3 (fewer choices, larger font).

   IEP / 504 Accommodations

   • Preferential seating near instruction and visual models (number line/anchor chart).
   • Provide extended time for independent practice and exit ticket as needed; allow completion in a quieter setting.
   • Allow manipulatives at all times (counters, cubes, number line strip).
   • Reduce copying demands: offer a printed sequence line with blanks rather than requiring writing all numbers from scratch.
   • Frequent checks for understanding and discreet prompts (e.g., point to start number, tap next hop).
   • Support executive function: provide a 3-step checklist card: 1) Start number 2) Add 2 each time 3) Check pattern.
   • For fine-motor needs: allow oral response or use stamps/dots to mark hops; scribe accommodation if documented.
   • For attention needs: movement-based counting (standing hops with two steps) during guided practice.

   Advanced Learners

   • Start at an odd number and count by 2s; describe what kind of numbers you land on (odd) and compare to starting at 2 (even).
   • Write an equation for a counted set: represent 18 as 2+2+2+2+2+2+2+2+2 and also as 9+9 (two equal addends) when appropriate.
   • Predicting task: 'Will 37 ever be said when counting by 2s starting at 2? Explain why or why not.'
   • Create a mini-poster showing two representations of counting by 2s: pairs of objects and number line hops; include a written rule and one 'notice' statement.
   • Connect to structure on the hundreds chart: highlight the by-2s numbers and describe the pattern in columns/diagonals.
   • Challenge sequence: count by 2s from 86 for 12 steps and identify which ones cross a decade boundary; explain how you know what happens at 98→100.

   形成性检查

   • Warm-up turn-and-talk: listen for 'pairs' and 'faster' reasoning.
   • CFU during direct instruction: student boards for '2 more than 16' and quick oral next-number prompts.
   • Guided practice observation: checklist for pairing accuracy and one-to-one pointing to pairs.
   • Partner explanation: students use sentence frame to justify even/odd with leftovers.
   • Independent practice: spot-check 3 students per table; collect 2–3 samples for misconceptions.

   退出票

   Start at 12. Write the next 6 numbers when counting by 2s. Then answer: Are these numbers mostly even or odd? Explain in one sentence using the word “pairs” or “even.”

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 The lesson includes specific vocabulary terms related to skip-counting and even/odd concepts, making vocabulary practice essential for reinforcing these terms.
   • Worksheet 匹配活动 A matching activity supports the hands-on and conceptual nature of the lesson by pairing terms with definitions or examples, aiding second graders' understanding.
   • Worksheet 3-2-1 退出票 The lesson mentions an exit ticket with a prompt for sequences and even/odd statements, so a 3-2-1 exit ticket template fits well for formative assessment.
   • Worksheet T-图 A T-Chart organizer can help students visually compare even and odd numbers or organize their observations from skip-counting by 2s, supporting the lesson's noticing and reasoning activities.

   Storypie 内容

   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory

   准备清单

   • Prepare counter cups/bags with 20 counters per pair (include some odd totals available for quick demonstration if desired).
   • Post or project class number line 0–50; ensure visibility from carpet.
   • Prepare anchor chart space: 'Counting by 2s = add 2 each time' and an example sequence.
   • Print independent practice pages and exit tickets; set aside extras.
   • Decide partner groups ahead of time (consider language and support needs).
   • Optional: prepare a hundreds chart with even numbers lightly highlighted for noticing.
   • Have sentence frames ready on board or printed strip: 'I started at __ and added 2 each time: __.'
   • Set a timer for transitions (warm-up to modeling; partner work to independent).

   常见误解

   • Skip-counting means skipping random numbers rather than following a constant addend (+2).
   • Even means 'ends in 0,2,4,6,8' as a memorized rule without understanding pairing/no leftovers.
   • Counting pairs by 2s counts pairs (2,4,6...) but student forgets each count represents total objects, not number of pairs.
   • Starting number confusion: counting 'the numbers by 2s' always begins at 2, instead of beginning at the stated start number.
   • Misalignment between objects and counting words (touching two different pairs per spoken number or touching one pair twice).
9. 9 Mixed Skip-Counting: Missing Numbers, Error Analysis, and Strategy Choice 完整课程 Mixed Skip-Counting: Missing Numbers, Error Analysis, and Strategy Choice

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group (launch/mini-lesson), partners (guided practice stations/cards), independent (practice + exit ticket)

   学习目标

   • I can skip-count by 5s, 10s, and 100s within 1,000 to find missing numbers in a sequence. Apply

     成功标准:

     • I identify the skip-count pattern (by 5, 10, or 100) from the numbers shown.
     • I fill in missing numbers correctly in at least 4 out of 5 sequences.
     • I can explain my steps using place value words (hundreds, tens, ones).

   • I can find and explain an error in someone’s skip-counting and show the corrected sequence. Analyze

     成功标准:

     • I point to the exact place the pattern breaks and describe what should happen instead.
     • I correct the sequence and check it by continuing the pattern for at least two more numbers.
     • My explanation includes why the incorrect step does not match counting by 5s, 10s, or 100s.

   • I can choose an efficient strategy (number line, hundreds chart, place value thinking) to solve a skip-counting problem and explain why I chose it. Evaluate

     成功标准:

     • I select a strategy that matches the pattern (5s/10s/100s) and the numbers given.
     • I use my strategy to get an accurate answer on at least 3 out of 4 problems.
     • I can say or write one clear reason my strategy helped (for example: 'Counting by 100s changes only the hundreds digit').

   • I can read and write a three-digit number in expanded form and number name to show what each digit means. Apply

     成功标准:

     • Given a number from today’s sequences (e.g., 495), I write it in expanded form (e.g., 400 + 90 + 5).
     • I write the number name correctly (e.g., 'four hundred ninety-five').
     • I connect the expanded form to place value language (hundreds, tens, ones).

   • I can compare two three-digit numbers using >, =, and < and explain my comparison using place value. Analyze

     成功标准:

     • I choose the correct symbol (> , = , <) to compare two numbers.
     • I explain my decision by comparing hundreds first, then tens, then ones.
     • My explanation uses at least one place value sentence (e.g., 'They have the same hundreds, but 9 tens is greater than 0 tens.').

   标准

   • CCSS.MATH.CONTENT.2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.
   • CCSS.MATH.CONTENT.2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
   • CCSS.MATH.CONTENT.2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
   • CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
   • CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

   材料

   • Individual whiteboards, dry-erase markers, and erasers · 1 set per studentUsed for warm-up responses and quick checks during mini-lesson.
   • Projected slides or chart paper with skip-counting sequences (missing numbers + error analysis) · 1 teacher setPrepare slides with reveal/cover for step-by-step modeling.
   • Hundreds chart(s) (0–100 and/or 1–120) · 1 per student + 1 large displayOptional reference; emphasize it’s a tool, not the only method.
   • Open number line templates (paper or reusable mats) · 1 per studentEspecially helpful for counting by 5s crossing 100 or 200.
   • Base-ten blocks (hundreds flats, tens rods, ones cubes) · Class set; at least 6 small bags for table groupsSupport concrete checks (e.g., adding a hundred flat each step).
   • Guided practice task cards (3 problems) or projected practice · 1 card set per pair OR 1 projected setIf using cards: print, cut, and clip each set together.
   • Independent practice worksheet (mixed skip-counting: missing numbers, error analysis, strategy choice) · 1 per student8 items total; include space for strategy checkboxes and one-sentence reasons.
   • Exit tickets (half-sheet or digital form) · 1 per studentCollect for end-of-lesson data; sort into 0/1/2 piles.

   • Warm-up 5 min
   • Direct Instruction 12 min
   • Guided Practice 18 min
   • Independent Practice 20 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Project three short sequences (one by 5s, one by 10s, one by 100s) with one missing number each. Facilitate a quick Number Talk using silent think time, show-on-whiteboards, and 1–2 student shares focused on pattern recognition.

   学生操作: Students look for the pattern, write the missing number on their whiteboard, and hold it up on the signal. Selected students explain how they knew, using place value language when possible.

   教师脚本（完整）

   (Display routines) “Pencils down—Number Talk. I’m going to show a sequence. First, think quietly. Then write ONLY the missing number on your board.” (After think time) “Boards up in 3…2…1…up.” “Today we will practice skip-counting in different ways—by 5s, 10s, and 100s. When you see a sequence, ask yourself: What stays the same? What changes?” (After a share) “I heard you say the numbers were jumping by 10. Say it with me: ‘The jump is 10.’ Now, which digit is changing when we add 10?”

   Direct Instruction12 min

   教师行动: Teach a consistent routine: (1) Identify the jump, (2) Decide the tool/strategy, (3) Fill missing numbers or locate the break, (4) Check by extending the pattern. Model three examples: missing number by 10s; error analysis intended by 100s; strategy choice counting by 5s across 100. Connect each to place value structure (which digits change).

   学生操作: Students track with finger/eyes, answer choral-response questions, and do quick turn-and-talks to name the jump and identify which digit changes. Students copy one key idea into math notebook/worksheet header if used (e.g., “+10 changes tens”).

   教师脚本（完整）

   “Watch my routine. Every time I see a sequence, I do four steps: Jump, Tool, Solve, Check.” (Model 1: Missing numbers) “Example A: 235, 245, __, 265. First, I find the jump. From 235 to 245, it went up… (pause) 10. So we are skip-counting by 10s.” “Now I think place value: adding 10 changes the tens digit. The hundreds digit usually stays the same, and the ones digit stays the same.” “So after 245 comes 255, then 265. The missing number is 255.” “Check: 245 + 10 = 255. Yes.” (Model 2: Error analysis) “Example B: 400, 500, 550, 600. I’m going to be a math detective.” “Step 1: What is the intended jump? The first jump from 400 to 500 is +100.” “If we are counting by 100s, each step should add 100. From 500, adding 100 should be 600—not 550.” “So the pattern breaks right here at 550. The correct number should be 600, and then the next would be 700.” “Notice the structure: counting by 100s changes the hundreds digit.” (Model 3: Strategy choice) “Example C: 95, 100, 105, __. Here the jump is +5. We are crossing 100, so I choose a tool that helps me track each jump.” “I choose an open number line because I can draw equal jumps of 5 and not lose my place.” (Teacher draws number line) “95 to 100 is +5, 100 to 105 is +5, so 105 to 110 is +5. The missing number is 110.” “Turn and tell your partner: In your own words, what does ‘check’ mean in our routine?”

   理解检查: Quick CFU (thumbs/check): Teacher says a sequence aloud: “210, 220, __, 240.” Students show thumbs-up if they think the jump is +10; thumbs-sideways if unsure. Then students write the missing number on boards. Teacher scans for accuracy and asks: “Which digit changes when we add 10?”

   Guided Practice18 min

   教师行动: Assign partners. Provide three problems (projected or task cards). Circulate using a clipboard checklist: pattern named, missing numbers correct, explanation uses place value words, and error-analysis includes ‘break point’ and correction. Pull a small group (3–6 students) for a quick re-teach using base-ten blocks if needed.

   学生操作: Partners complete each problem: (a) name the pattern (by 5/10/100), (b) solve, (c) justify using place value language. Students take turns explaining to each other using sentence frames. If stuck, students choose a tool (hundreds chart/number line/base-ten blocks) and show the jumps.

   教师脚本（完整）

   “Now we do it together with a partner. Your job on EVERY problem is to do three things: 1) Name the count-by number, 2) Solve it, 3) Justify it with place value words.” “Partner A, you talk first on Problem 1. Partner B, you must either agree and add on, or politely disagree and explain why. That’s what mathematicians do.” (As teacher circulates) “I’m going to ask you one question again and again: ‘Which digit changes each time?’ Be ready.” (When a pair finishes early) “Great—now do the CHECK step: continue the pattern two more numbers and see if it still works.”

   支架提示: Pattern identification: “What is the jump from the first number to the next? Show me with subtraction or by counting on.” | Structure prompt: “Which digit is changing—ones, tens, or hundreds? Which digits stay the same?” | Tool choice prompt: “Would a hundreds chart help you see +10 or +5 quickly? Would a number line help you track equal jumps?” | Missing number prompt: “Say the sequence out loud, touching each number. What comes next if we add the same amount?” | Error analysis prompt: “Circle the first place it stops being the same jump. What number SHOULD be there if the jump stays the same?” | Check prompt: “Keep going two more steps. Does your jump still work?” | Language support: “Use this frame: ‘The pattern is counting by __ because ___.’” | Precision prompt: “When you say ‘it goes up,’ say ‘it goes up by __.’”

   Independent Practice20 min

   教师行动: Distribute and review expectations. Monitor actively: first pass for engagement, second pass for strategy alignment and place-value explanations. Confer briefly with 4–6 students (including at least one from each need group). Provide immediate corrective feedback and direct students to use the routine: Jump → Tool → Solve → Check.

   学生操作: Students complete 8 items independently: 3 missing-number sequences; 2 error-analysis items (circle error, correct, write one-sentence explanation); 3 strategy-choice items (check one tool and solve, then write a reason). Students show work using number lines or notes about digit changes.

   教师脚本（完整）

   “This is your chance to show what you can do on your own.” “Work quietly and show your thinking. If you choose a strategy, you must use it and write one short reason why it helped.” “If you feel stuck, do NOT guess. Do the routine: 1) Find the jump, 2) Pick a tool, 3) Solve, 4) Check by continuing two more numbers.” (If students ask ‘Is this right?’) “I’m going to ask you a checking question: ‘What is your jump, and does it stay the same for the next two numbers?’ Show me your check.”

   监控清单: Student identifies the jump correctly (5/10/100). | Student’s missing numbers match the pattern. | Student uses at least one representation when needed (number line/hundreds chart/place value notes). | Student’s error analysis marks the FIRST incorrect term and provides a corrected term. | Student checks by extending the pattern at least two terms on error-analysis items. | Student strategy choice matches the task (e.g., +5 crossing 100 → number line; +100 → place value). | Student explanation includes place value words (hundreds/tens/ones) at least once. | Student stays within expected time (completes at least 6/8 items).

   Closure5 min

   教师行动: Administer exit ticket and facilitate a 30–60 second share of one strong strategy explanation (anonymous or volunteer). Collect exit tickets and do a quick sort (0/1/2) to plan Lesson 10 review groups.

   学生操作: Students complete the exit ticket independently and hand it in. If time, students do a quick whisper-check: reread and confirm the jump is constant (5/10/100).

   教师脚本（完整）

   “We’re closing with an exit ticket. Do it silently so I can see what YOU know.” “Today, you practiced three powerful skills: finding missing numbers, spotting errors, and choosing a strategy. Before you hand in your exit ticket, ask yourself: Did I keep the same jump each time—5, 10, or 100?” (After collection) “If you finished, put your pencil down and look at the strategy menu on the board. In your head, answer: ‘Which strategy helps you most, and why?’”,

   退出票: 1) Fill in the missing number: 485, 490, __, 500. 2) Error analysis: 700, 800, 850, 900. What’s wrong? Fix the sequence so it counts by 100s.

   skip-count

   I say numbers in a pattern by adding the same amount each time.

   sequence

   Numbers in order that follow the same rule.

   pattern

   The rule for what number comes next.

   error analysis

   I find the mistake, tell why it’s a mistake, and correct it.

   place value

   Where a digit is tells what it means: ones, tens, or hundreds.

   English Language Learners

   • I can orally name the pattern using a sentence frame: “The pattern is counting by ___ because it goes up by ___ each time.”
   • I can use place value words in an explanation: “Only the ___ digit changes when we add ___.”
   • I can critique reasoning politely using a frame: “I agree/disagree because ___.”
   • Pre-teach vocabulary with visuals (icons for +5, +10, +100; labeled place value chart hundreds/tens/ones).
   • Provide sentence frames on a small card: “The jump is __.” “The digit that changes is __.” “The error is at __ because __.”
   • Allow students to point to digits while speaking; encourage gestures (circle changing digit).
   • Use partner roles with structured talk: Partner A explains; Partner B repeats in their own words.
   • Offer bilingual glossary if available; allow brief home-language processing, then restate in English.
   • Provide worked example strip students can reference (one for +5 crossing 100, one for +10, one for +100).

   Struggling Learners

   • Chunk tasks: cover all but the first two numbers; identify the jump before seeing the rest of the sequence.
   • Reduced workload option: complete 6 of 8 independent items (teacher selects: 2 missing-number, 2 error-analysis, 2 strategy-choice) with accuracy goal of 4/6.
   • Use concrete-to-representational support: build +100 with hundreds flats; build +10 with tens rods; then write numbers.
   • Provide a highlighted place value chart and have students color the digit that changes each step.
   • Offer a pre-drawn number line with the starting point labeled; student fills in equal jumps (especially for +5 crossing 100).
   • Peer support: strategic pairing with a patient, high-accuracy peer; assign roles (Reader/Checker).
   • Simplified sequences for practice at teacher table (stay within same hundred first, then introduce crossing).

   IEP / 504 Accommodations

   • Extended time for independent practice and exit ticket as needed (e.g., finish during math workshop).
   • Small-group or quiet setting for independent work to reduce distractions.
   • Read-aloud of directions and items (not the answers); check for understanding by having student restate the task.
   • Provide enlarged print versions of sequences and number lines; use high-contrast colors for changing digits.
   • Allow alternative response mode: verbal explanation recorded to teacher or written with sentence starters.
   • Frequent check-ins (every 3–5 minutes) using the routine prompt card: Jump → Tool → Solve → Check.
   • Use of manipulatives and graphic organizers (place value mat) as an accommodation, not a modification, unless specified in the plan.

   Advanced Learners

   • Create two original sequences within 1,000 (one missing-number, one error-analysis). Trade with a partner and solve; include an answer key and a written justification.
   • Add a ‘mystery jump’ challenge: sequences that could be +10 or +100 depending on placement; students explain how they know which is correct using structure (digits changing).
   • Strategy comparison: solve the same +5 sequence using a number line and place value reasoning; write which was more efficient and why.
   • Introduce skip-counting backward (within 1,000) on one optional problem: e.g., 520, 510, __, 490; explain the pattern as -10.
   • Generalization prompt: “What digit patterns do you notice when counting by 100s? by 10s? by 5s?” Students write a rule in kid-friendly language.

   形成性检查

   • Warm-up whiteboard scan: identify students confusing +5 and +10 or missing crossing-ten patterns.
   • CFU during mini-lesson: thumbs + board response for identifying the jump and the changing digit.
   • Guided practice teacher observation: checklist for (pattern named, correct missing numbers, correct error location, place value explanation).
   • Independent practice spot-check: conference notes on strategy choice alignment and explanation quality.

   退出票

   1) Fill in: 485, 490, __, 500. 2) Error analysis: 700, 800, 850, 900 (What’s wrong? Fix it.)

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 3-2-1 退出票 Includes an exit ticket template to align with the lesson's closure activity collecting end-of-lesson data.
   • Worksheet 词汇练习 Supports the lesson's explicit vocabulary terms like skip-count and error analysis with targeted practice.
   • Worksheet 匹配活动 Provides practice with matching skip-counting sequences and strategies, reinforcing the lesson's focus on pattern recognition and strategy choice.
   • Worksheet KWL 图表 Offers an organizer to help students activate prior knowledge and set learning goals related to skip-counting and error analysis.

   Storypie 内容

   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory

   准备清单

   • Prepare slides/chart paper with the 3 warm-up sequences and 3 mini-lesson models (include reveal steps).
   • Print/copy: guided practice cards (3 per pair) OR prepare projected problems; print independent practice (1 per student); print exit tickets (1 per student).
   • Set up tool bins: hundreds charts, open number line templates, base-ten blocks accessible for students who need them.
   • Create/print ‘routine’ and ‘sentence frame’ strips for desks or small group: Jump → Tool → Solve → Check; explanation frames.
   • Plan partner pairings in advance (including supportive peer matches) and identify 1 small-group table location.
   • Prepare a quick teacher checklist/clipboard sheet with student names for guided and independent monitoring.
   • Test projector/document camera and ensure markers/erasers are ready at each table.

   常见误解

   • Misconception: Counting by 10s always means the tens digit increases without changing the hundreds digit (students forget about carrying when crossing 290 to 300).
   • Misconception: When counting by 100s, students change the tens or ones digits instead of the hundreds digit.
   • Misconception: In sequences, the pattern can change mid-way without being an error (students accept inconsistent jumps).
   • Misconception: ‘Bigger number means add more’—students may think 95 to 100 is +10 because the digits look different; reinforce the constant difference.
   • Misconception: Error analysis means ‘find any wrong-looking number’ instead of verifying each equal jump and locating the first break.
10. 10 Unit Synthesis: Represent Numbers in Multiple Ways and Explain Your Thinking 完整课程 Unit Synthesis: Represent Numbers in Multiple Ways and Explain Your Thinking

    概述 时间与活动 词汇 差异化 评估 资源 教师笔记

    🌏 Massachusetts, USA Whole group on rug for warm-up and direct instruction; partners for guided practice; independent seating for independent practice; quick turn-and-talk during closure

    学习目标

    • I can represent a three-digit number in at least three different ways (base-ten blocks or drawings, place value chart, standard form, number name, expanded form). Apply

      成功标准:

      • I show hundreds, tens, and ones that match the number.
      • I write the number in standard form correctly.
      • I write the number in expanded form correctly (hundreds + tens + ones).
      • My representations all match each other.

    • I can explain how each digit in a three-digit number shows hundreds, tens, or ones using math words and/or pictures. Analyze

      成功标准:

      • I name what each digit means (___ hundreds, ___ tens, ___ ones).
      • I use place value vocabulary accurately (hundreds, tens, ones, digit, place value).
      • I can check my work by connecting my explanation to my model or drawing.

    • I can skip-count by 10s or 100s to help me build and verify three-digit numbers. Apply

      成功标准:

      • I can count by 100s to reach the hundreds part of the number.
      • I can count by 10s to reach the tens part of the number.
      • I use skip-counting to check that my model matches the written number.

    • I can compare two three-digit numbers using >, =, or < and explain my thinking using hundreds, tens, and ones. Analyze

      成功标准:

      • I compare hundreds first; if the hundreds are the same, I compare tens; if tens are the same, I compare ones.
      • I write the correct symbol (> , < , or =) between the numbers.
      • I explain my comparison using place value words (hundreds/tens/ones).

    标准

    • CCSS.MATH.CONTENT.2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
    • CCSS.MATH.CONTENT.2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.
    • CCSS.MATH.CONTENT.2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
    • CCSS.MATH.CONTENT.2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
    • CCSS.MATH.PRACTICE.MP.3 Construct viable arguments and critique the reasoning of others.
    • CCSS.MATH.PRACTICE.MP.6 Attend to precision.

    材料

    • Base-ten blocks (hundreds flats, tens rods, ones cubes) or virtual base-ten tool · 1 class set + a demo set for teacherEnsure enough rods/cubes; include a tray for organizing hundreds/tens/ones.
    • Place value charts (Hundreds–Tens–Ones) for each student · 1 per student + a large chart for displayOptional: laminated for dry-erase use.
    • Dry-erase boards/markers and erasers OR math notebooks and pencils · 1 per studentUse boards for fast checks; notebooks for final independent task (teacher choice).
    • Hundreds chart (0–999) or open number line strip · 1 posted + small reference per tableUse for skip-counting checks (100s/10s).
    • Prepared task cards/number cards · 1 set for teacher + 1 small set per tableInclude numbers with 0 in tens (e.g., 406) and 0 in ones (e.g., 780). Differentiate ranges: Level A (100–300), Level B (301–700), Level C (701–999).
    • Anchor chart paper titled “Ways to Show a Number” + markers · 1 chartLeave space for examples and student language.
    • Exit ticket copies · 1 per student + a few extrasPrint with clear H-T-O boxes and lines for expanded form and words.

    • Warm-up 5 min
    • Direct Instruction 10 min
    • Guided Practice 15 min
    • Independent Practice 15 min
    • Closure 5 min

    Warm-up5 min

    教师行动: Facilitate a quick Number Talk focused on multiple representations and reasoning. Record student strategies without evaluating immediately; highlight precision and matching representations.

    学生操作: Mentally generate at least two ways to represent the displayed number and share using a sentence frame; listen and respond respectfully to peers.

    教师脚本（完整）

    Mathematicians, eyes on the board. Our number is 538. Don’t write yet—think in your head. Show me a quiet thumb when you have one way to show 538. Now think of a second way. Turn to your partner and say: “I know 538 is ___ because ___.” Use math words like hundreds, tens, and ones. Let’s share. When you speak, be precise: tell us the hundreds, tens, and ones. I’m going to record your thinking exactly as you say it.

    Direct Instruction10 min

    教师行动: Model a synthesis routine: choose a 3-digit number, represent it in multiple ways, explain digit values, then self-check with skip-counting. Explicitly address the role of 0 in a place. Use Gradual Release: I Do with one full example (406).

    学生操作: Track the model, answer brief CFU questions, chorally respond to place value prompts, and use hand signals to indicate understanding.

    教师脚本（完整）

    Today we are finishing our unit by putting everything together. Here is our routine: 1) Choose a number. 2) Show it in different ways. 3) Explain what each digit means. 4) Check your work with skip-counting. Watch me do the whole routine with the number 406. Step 1: The number is 406 in standard form. Step 2: I’m going to show it with a place value chart. In the hundreds place, I write 4. In the tens place, I write 0. In the ones place, I write 6. Now I’ll build it with base-ten blocks: I take 4 hundreds flats, 0 tens rods—none—and 6 ones cubes. I can also write expanded form: 400 + 0 + 6. And number name: four hundred six. Step 3: Now I explain each digit. The 4 means 4 hundreds, which is 400. The 0 means 0 tens. That means there are no groups of ten—nothing in the tens place. The 6 means 6 ones. Step 4: I check with skip-counting. I can count by hundreds: 100, 200, 300, 400. That matches 4 hundreds. Now I count by tens starting at 400. Since I have 0 tens, I do not add any tens. Now I count ones: 401, 402, 403, 404, 405, 406. My model matches 406. Notice: the zero is important. It holds the tens place so the 4 stays in the hundreds place. If I forgot the zero, 46 would be a totally different number.

    理解检查: CFU questions (cold call/choral): 1) “In 406, how many tens are there?” 2) “What does the 0 tell us?” 3) “Say the expanded form with me.” 4) “If I had 4 hundreds and 6 ones, what number is that? Why do we still need the 0 in the tens place?”

    Guided Practice15 min

    教师行动: Lead two shared examples (one with a 0 in tens or ones place; one with all nonzero digits). Co-create an anchor chart “Ways to Show a Number.” Prompt for reasoning (MP3) and precision (MP6). Circulate to listen, select student work to share, and correct misconceptions in-the-moment.

    学生操作: Work with a partner to build/represent numbers using at least three methods; contribute ideas to anchor chart; explain and critique reasoning using sentence frames.

    教师脚本（完整）

    Now we do it together. You will work with your partner, but we will stop and share to build an anchor chart. Number 1 is 780. Step 1: Say it with me: 780. Step 2: With your partner, build 780 using either blocks or a drawing AND fill in your place value chart. Then write expanded form. You have 2 minutes. Go. (After 2 minutes) Let’s check for matching representations. Hold up your place value chart. I’m looking for 7 in hundreds, 8 in tens, 0 in ones. Who can explain the 0? Use this frame: “The 0 means ___.” Great. Now we add to our anchor chart. (Write) Ways to Show a Number: - Base-ten blocks/drawing - Place value chart (H-T-O) - Standard form - Expanded form - Number name Number 2 is 354. This time, you will represent it in at least three ways and be ready to explain each digit: “___ hundreds, ___ tens, ___ ones.” Remember: all representations must match. If one part doesn’t match, we fix it. Mathematicians revise their work.

    支架提示: Point to the digit. What place is it in: hundreds, tens, or ones? | How many hundreds do you see/need? Show me with flats or with a quick drawing. | How many tens rods? How do you know it’s tens and not ones? | What does the 0 mean in this number? What do we NOT have? | Say it in a complete sentence: “___ hundreds, ___ tens, ___ ones.” | Check: If I skip-count by 100s, where should I land? If I skip-count by 10s next, where should I land? | Do your expanded form parts add back to the standard form? | If your partner disagrees, ask: “Can you show me where you see that in the model?” | Precision check: Did you write the digits in the correct places on the chart?

    Independent Practice15 min

    教师行动: Assign or have students choose one number from differentiated sets. Provide a clear product expectation: at least three representations plus a 2–3 sentence explanation. Circulate using a monitoring checklist; conference briefly with 4–6 students (prioritize those needing support). Offer optional compare-and-justify extension when ready.

    学生操作: Independently complete the synthesis task: represent a number in multiple ways, write a short explanation of digit values, and optionally compare their number to a partner’s using <, >, or = with justification.

    教师脚本（完整）

    Now it’s your turn to show what you know. Choose one number card from your table’s stack, or I will assign you one. Your job: 1) Show the number in at least three ways. 2) Write 2–3 sentences explaining what each digit means. 3) Check your work using skip-counting by 100s and/or 10s. Here is what ‘finished’ looks like: I can point to every representation and prove they match. If you finish early, do the extension: compare your number to a partner’s using <, >, or =, and write one sentence that explains how you know.

    监控清单: Student selected/was assigned an appropriate number and wrote it correctly in standard form | Place value chart digits are in correct columns (H-T-O) | Model/drawing matches the H-T-O amounts (including correct handling of 0) | Expanded form is correct and includes 0 when needed (e.g., 400 + 0 + 6) | Number name is reasonable and matches the digits (especially with 0 tens/ones) | Written explanation includes “hundreds/tens/ones” and correctly interprets each digit | Student used skip-counting to verify (not just restating the number) | Work is neat/legible; labels are clear (MP6)

    Closure5 min

    教师行动: Facilitate a brief share-out focused on checking strategies and precision. Administer exit ticket and set calm, quick expectations. Collect and preview for patterns to plan next steps.

    学生操作: Complete exit ticket independently; then share one checking strategy using a sentence frame.

    教师脚本（完整）

    Bring your eyes to the board. Before we go, you will show one last snapshot of your learning. On the exit ticket, do two things: 1) Represent the number in expanded form and in words. 2) Choose one digit and explain what it means—hundreds, tens, or ones. Work silently for 4 minutes. If you get stuck, re-read the directions and use the place value chart to help. When you finish, whisper to your partner using this frame: “One way I checked my work was ___.”

    退出票: Exit Ticket: A) Write 672 in expanded form: ____________ B) Write 672 in words: ____________ C) Choose one digit (6, 7, or 2). Circle it and explain what it means: “The ___ means ___.”

    place value

    Where a digit is in the number tells how much it is worth.

    digit

    A digit is one number symbol, like 7 or 0.

    expanded form

    Expanded form shows the parts added together.

    standard form

    Standard form is the regular way we write a number.

    skip-count

    Skip-counting means you count by jumps, not ones.

    English Language Learners

    • I can say and write: “___ hundreds, ___ tens, ___ ones” to describe a 3-digit number.
    • I can use the sentence frame “The ___ digit means ___.” to explain place value.
    • I can read a 3-digit number aloud using a model and key vocabulary (hundreds, tens, ones).
    • Pre-teach vocabulary with visuals: label a large H-T-O chart and real base-ten blocks; keep a word bank posted.
    • Sentence frames on desk/board: “I know ___ because ___.” “The 0 means ___.” “My expanded form is ___ + ___ + ___.”
    • Partner ELLs with supportive peers; assign roles: Builder (blocks) and Reporter (sentence frame).
    • Use gestures and pointing: teacher points to digit then to place on chart while speaking.
    • Provide bilingual glossary if available (home language support) and allow oral responses before writing.
    • Reduce language load: allow explanation using a labeled drawing + one complete sentence rather than 2–3 at first.

    Struggling Learners

    • Modified task expectation: require 2 representations (place value chart + blocks/drawing) before adding expanded form; then add a third if ready.
    • Chunk the routine with a checklist card: Step 1 standard form; Step 2 H-T-O; Step 3 build/draw; Step 4 expanded form; Step 5 explain one digit; Step 6 check.
    • Use simplified number sets (100–300) and avoid two zeros until confidence improves; then introduce one-zero numbers with teacher support.
    • Provide a pre-drawn place value chart with arrows: hundreds → tens → ones, plus example filled in (not the same number) as a model.
    • Use color-coding: hundreds digit in blue, tens in green, ones in red; match colors on chart and expanded form.
    • Peer support: “Ask 3 before me” with a clear help protocol (partner shows where in the model).
    • Use concrete materials first (base-ten blocks) before drawings; allow tracing around blocks to create drawings.

    IEP / 504 Accommodations

    • Provide extended time for independent practice and exit ticket as needed (e.g., finish during a calm transition).
    • Preferential seating near instruction and away from distractions; frequent check-ins (every 3–4 minutes) during independent work.
    • Offer alternate response modes: oral explanation to teacher, recorded response, or pointing/labeling instead of full sentences when documented.
    • Provide enlarged print exit ticket and place value chart; reduce visual clutter on the page.
    • Use assistive tools as appropriate: speech-to-text for explanation, pencil grips, or dry-erase instead of pencil to reduce fine-motor demands.
    • Break directions into single steps and confirm understanding: student repeats the first step before starting.
    • Allow use of a reference card (H-T-O chart, sentence frames, skip-counting by 100s/10s chart) consistent with accommodations.

    Advanced Learners

    • Create two different representations of the same number using regrouping (e.g., 406 as 3 hundreds + 10 tens + 6 ones) and explain why both are correct.
    • Choose two numbers and compare using >, <, or =; write a justification that references hundreds first, then tens, then ones (CCSS.MATH.CONTENT.2.NBT.A.4).
    • Write a “trick” number riddle that includes a zero in one place (e.g., “I have 5 hundreds, 0 tens, and 9 ones. What am I?”) and swap with a partner.
    • Order three 3-digit numbers from least to greatest and explain the strategy using place value language and/or a number line.
    • Error analysis: teacher provides an incorrect expanded form or model; student finds the mistake and writes a correction with an explanation (MP3).

    形成性检查

    • Warm-up Number Talk: listen for accurate identification of hundreds/tens/ones and ability to express a second representation
    • Direct instruction CFU: targeted questions about the meaning of 0 in the tens place and matching expanded form
    • Guided practice: partner work observation—do representations match? Can students justify using place value language?
    • Independent practice conference notes using monitoring checklist (focus students)
    • Closure share: students articulate at least one checking strategy (skip-counting or matching representations)

    退出票

    A) Write 672 in expanded form. B) Write 672 in words. C) Explain the value of one chosen digit using hundreds/tens/ones.

    与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

    工作表与活动

    • Worksheet 词汇练习 The lesson includes specific vocabulary terms related to place value and number representation, making a vocabulary practice template essential for reinforcing these concepts.
    • Worksheet 匹配活动 A matching activity aligns well with the lesson's focus on connecting numbers to their multiple representations and explanations.
    • Worksheet 3-2-1 退出票 An exit ticket is explicitly mentioned for closure, so the 3-2-1 Exit Ticket template supports formative assessment and reflection on the lesson objectives.
    • Worksheet T-图 A T-Chart organizer supports students in comparing and explaining multiple ways to represent numbers, fitting the lesson's synthesis and explanation focus for grade 2.

    Storypie 内容

    • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
    • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
    • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
    • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory

    准备清单

    • Print and organize number cards into differentiated ranges (A: 100–300, B: 301–700, C: 701–999) and include at least 3 numbers with a 0 in tens or ones in each set
    • Set out base-ten blocks in table bins (confirm enough rods and ones cubes; add extras to high-need tables)
    • Copy/prepare place value charts (laminate if using dry-erase) and exit tickets
    • Post or prepare a large H-T-O chart and a hundreds chart/open number line reference
    • Pre-write board plan: learning targets, vocabulary box, sentence frames
    • Prepare anchor chart title “Ways to Show a Number” with space for student examples
    • Plan partner pairings (supportive peer matches; note students needing preferential seating)
    • Decide the two guided practice numbers (recommend 780 and 354) and pre-check all representations

    常见误解

    • A zero means “nothing” so it can be ignored (misunderstanding placeholder role).
    • Digits are confused with value (e.g., thinking the 7 in 780 means 7, not 700).
    • Expanded form written as 7 + 8 + 0 instead of 700 + 80 + 0.
    • Tens and ones swapped in models/drawings (e.g., 34 tens instead of 3 tens and 4 ones).
    • Number names mismatch the digits (e.g., saying “seven hundred eight” for 780).

基本问题

• How can different strategies show the same sum or difference?
• How do we decide if a word problem requires addition or subtraction?

标准

1. 1 Fluency Foundations: Within 20 (Make 10, Doubles/Near Doubles, and Think-Addition) 完整课程 Fluency Foundations: Within 20 (Make 10, Doubles/Near Doubles, and Think-Addition)

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group mini-lesson; partner work for guided practice; independent practice; optional teacher-led small group during independent practice

   学习目标

   • I can add within 20 by using mental strategies (make a ten, doubles/near doubles, and think-addition) to find sums efficiently. Apply

     成功标准:

     • I can choose a strategy (make a ten, doubles/near doubles, or think-addition) for a given addition fact within 20.
     • I can explain my strategy using words, numbers, or a drawing.
     • I can correctly solve at least 8 out of 10 addition problems within 20 within the given time limit.

   • I can subtract within 20 by thinking about the related addition fact (think-addition) to find the missing part. Apply

     成功标准:

     • I can rewrite a subtraction problem as a related addition equation with a missing number (e.g., 15 − 7 = ? becomes 7 + ? = 15).
     • I can correctly solve at least 8 out of 10 subtraction problems within 20.
     • I can check my subtraction answer using addition.

   • I can represent and solve an addition or subtraction word problem (within 100; using smaller numbers in this lesson) by writing an equation with a symbol for the unknown and answering with a labeled sentence. Apply

     成功标准:

     • I can identify what the unknown represents in a word problem.
     • I can write an equation with a symbol for the unknown (□, ?, or a letter) that matches the situation.
     • I can solve the problem and label the answer with a word from the problem.

   标准

   • CCSS.MATH.CONTENT.2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
   • CCSS.MATH.CONTENT.2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

   材料

   • Whiteboard/markers or interactive board · 1 setPre-draw two ten-frames or a rekenrek picture area.
   • Ten-frames and counters OR rekenrek · 1 per student pair (or 1 per student if available); 1 teacher demoUse to model make-a-ten and near-doubles visually.
   • Fluency sprint sheets (warm-up) · 1 per student + 3 extrasHalf-sheet preferred; include mixed add/subtract within 20.
   • Guided practice problem set (8 problems) · 1 per studentMay be projected and also on paper; include space to write the strategy name.
   • Independent practice sheet · 1 per studentPart A: 10 computation items with strategy checkboxes; Part B: 1 word problem requiring an equation with an unknown.
   • Exit tickets · 1 per student3 items total; collected at end.
   • Pencils and erasers · 1 per studentHave sharpened pencils ready for quick start.
   • Optional: Strategy anchor chart · 1Make 10 / Doubles / Near Doubles / Think-Addition with a visual example for each.
   • Timer (visual preferred) · 1Use for sprint and pacing transitions.

   • Warm-up 7 min
   • Direct Instruction 13 min
   • Guided Practice 15 min
   • Independent Practice 20 min
   • Closure 5 min

   Warm-up7 min

   教师行动: Distribute fluency sprint; set timer; reinforce expectations for speed + accuracy; circulate to notice strategies students are using and note 2–3 students to call on later.

   学生操作: Complete sprint quietly; work left to right; skip and return if stuck; put pencil down when time is called; be ready to share one strategy they used.

   教师脚本（完整）

   Mathematicians, today we are building our fluency toolbox for facts within 20. In a moment, you’ll do a quick sprint. Remember: fluency means accurate and efficient. When I say ‘Go,’ start at number 1 and do as many as you can. If you get stuck, circle it and move on—don’t let one problem stop you. Ready… Go. (After time) Stop. Put your pencil down and look at me. Take a quiet moment to star one problem where you used a smart strategy—make a ten, doubles/near doubles, or think-addition. We’ll talk about strategies next.

   Direct Instruction13 min

   教师行动: State learning targets; explicitly model each strategy using ten-frames/rekenrek and equations; connect addition to subtraction via related facts; do quick choral responses and turn-and-talk checks.

   学生操作: Track speaker; respond to quick questions; use hand signals (thumbs up/side/down) for understanding; turn-and-talk to explain a modeled strategy; mimic teacher modeling on their own ten-frame/rekenrek when prompted.

   教师脚本（完整）

   Today’s learning targets: 1) I can add within 20 using mental strategies. 2) I can subtract within 20 by using think-addition. 3) I can solve a word problem by writing an equation with an unknown. We are not trying to memorize by guessing—we are using strategies. Strategy 1: Make a Ten. Watch me solve 8 + 7. I know 8 needs 2 more to make 10. I can break 7 into 2 and 5. So 8 + 7 becomes 8 + 2 + 5. 8 + 2 = 10, and 10 + 5 = 15. I’m going to say it in one sentence: ‘I took 2 from 7 to make 10 with 8, then added the leftover 5.’ Turn and tell your partner: What did I do first, and why? Strategy 2: Doubles and Near Doubles. If I see 6 + 6, that’s a double. I know 6 + 6 = 12. Now look at 6 + 7. That is near doubles—one more than 6 + 6. So 6 + 7 = 12 + 1 = 13. Say it with me: ‘Near doubles uses a double I know, then I adjust by 1.’ Strategy 3: Think-Addition for subtraction. Let’s solve 13 − 9. Instead of taking away and counting, I can ask: 9 plus what makes 13? I write: 9 + □ = 13. I know 9 + 4 = 13, so the missing part is 4. Therefore, 13 − 9 = 4. Then I check: 9 + 4 = 13. Yes. Today, when you subtract, I want to hear you say: ‘I’m going to think-addition.’

   理解检查: CFU 1 (Make a Ten): Ask: “For 9 + 6, what number does 9 need to make 10?” Students respond chorally: “1.” Then ask: “So 9 + 6 = 10 + what?” (5). CFU 2 (Near Doubles): Show 7 + 8 and ask: “What double can help?” (7+7 or 8+8). CFU 3 (Think-Addition): Ask: “Rewrite 14 − 8 as an addition equation with an unknown.” (8 + □ = 14). Use thumbs up/side/down; reteach quickly if many show side/down.

   Guided Practice15 min

   教师行动: Facilitate partner problem-solving for 8 curated problems; pause after each 1–2 problems for brief strategy shares; record 2–3 different strategies; press for reasoning and efficient choices; correct misconceptions in the moment.

   学生操作: Work in pairs; solve, then name the strategy used; use a ten-frame/rekenrek if needed; justify strategy choice; compare solutions with another pair when prompted.

   教师脚本（完整）

   Now we do some together. You and your partner will solve 8 problems. After each problem, you must do two things: 1) Write the answer. 2) Say the strategy name: make a ten, doubles, near doubles, or think-addition. Partner A solves the first problem out loud. Partner B listens and asks, ‘Why did you choose that strategy?’ Then switch roles. Let’s start with Problem 1. Work. (After 1 minute) Eyes up. I’m going to call on one pair. Tell us your strategy, not just the answer. (After share) Class, show me with your fingers: 1 for make a ten, 2 for doubles/near doubles, 3 for think-addition. What did you use? I’m noticing we can solve the same problem in different ways, but we want to choose an efficient strategy. If you’re stuck, point to the ten-frame and ask yourself: ‘How can I make 10?’ or ‘What double do I know?’ or ‘What plus what equals the total?’ Keep going.

   支架提示: What number would help you make 10 first? | Can you break the second addend into two parts (___ and ___) to make 10? | Is this problem a double (same + same)? If not, is it one more or one less than a double? | What double do you already know that is close to this fact? | For subtraction: Can you rewrite it as ___ + □ = ___? | What is the whole? What are the parts? | Show it on your ten-frame or rekenrek—what do you see? | How can you check your answer using the opposite operation? | Which strategy is most efficient here, and why?

   Independent Practice20 min

   教师行动: Release students to independent practice; remind about strategy selection and circling; circulate with a clipboard using a monitoring checklist; confer with 3–5 students; pull a small group (3–6 students) for targeted support or extension.

   学生操作: Complete Part A (10 computation items) and circle the strategy used for each; complete Part B word problem with an equation using an unknown and an answer sentence; ask for help using a predetermined signal (hand on head or help card).

   教师脚本（完整）

   Now it’s your turn to show what you can do independently. Part A: Solve each problem and circle the strategy you used. If you used a ten-frame or drew a quick picture, that’s okay—just keep it quick. Part B: Read the word problem carefully. Underline what the problem is asking. Then write an equation with a symbol for the unknown, solve it, and write an answer sentence. If you finish early, do these in order: 1) Check your answers by using the opposite operation. 2) Pick two problems and write one sentence explaining your strategy. Begin.

   监控清单: Student selects a reasonable strategy (not counting all) for most facts. | Student can correctly make a ten by decomposing the second addend. | Student uses doubles/near doubles accurately (adjusts by 1 appropriately). | Student rewrites subtraction as a missing addend equation (think-addition). | Student checks at least one subtraction using addition. | Student circles a strategy for each computation item. | Student sets up the word problem with an equation including an unknown symbol. | Student labels the final answer with a word from the question (e.g., 'stickers', 'apples').

   Closure5 min

   教师行动: Administer exit ticket; select 2 students to share a concise strategy explanation; reinforce strategy names; collect exit tickets and preview next lesson connection.

   学生操作: Complete exit ticket silently; write related equation for subtraction item; optionally share strategy aloud; turn in exit ticket when done.

   教师脚本（完整）

   Show what you know on the exit ticket. This is quiet, independent work. Remember: - For addition, choose an efficient strategy. - For subtraction, use think-addition and write the related equation. When you finish, put your pencil down and look at me. (After 3–4 minutes) I’m going to choose two people to share one strategy in one clear sentence. Sentence frame: ‘I used ___ because ___.’ Today we built our fluency toolbox within 20. Tomorrow we will use these strategies to help us solve bigger problems quickly and accurately.

   退出票: 1) Make-a-ten: 9 + 8 = ____ 2) Near doubles: 7 + 8 = ____ 3) Think-addition: 14 − 6 = ____ . Write the related addition equation with an unknown: 6 + □ = ____

   make a ten

   I make 10 first because it’s easy, then I add the rest.

   doubles

   Same + same.

   near doubles

   It’s almost a double—just one more or one less.

   related facts

   The same numbers can make an addition and a subtraction family.

   unknown

   A number we don’t know yet.

   English Language Learners

   • I can name the strategy I used (make a ten, doubles, near doubles, think-addition) using a complete sentence: “I used ___ because ___.”
   • I can restate a subtraction problem as an addition equation using the frame: “___ + □ = ___.”
   • I can identify the question in a word problem by underlining key information and circling what is being asked.
   • Pre-teach vocabulary with visuals: ten-frame images labeled ‘10’ and ‘some more’; doubles picture cards (e.g., 6 and 6).
   • Sentence frames on desk strip: “I used ___.” “First I ___, then I ___.” “I know ___ + ___ = ___.”
   • Gestures and consistent cues: point to ‘10’ on ten-frame when saying “make a ten”; show ‘same-same’ hands for doubles.
   • Provide bilingual glossary (if available) for strategy names and math symbols (+, −, =, □).
   • Partner ELLs with supportive peers; assign roles (Solver / Strategy Speaker) so oral practice is structured.
   • Reduce language load on word problem: provide a graphic organizer with icons (Who/What? Total? Change? Unknown?).

   Struggling Learners

   • Scaffold with concrete models first: require ten-frame/rekenrek use for the first 4 independent items, then gradually fade.
   • Chunk tasks: complete Part A items 1–5, check with teacher, then complete 6–10.
   • Modified expectation option (without reducing rigor): aim for accuracy on 6/10 items with correct strategy identification; extend time by 2–3 minutes if needed.
   • Provide a simplified strategy chooser card: “If it’s close to 10 → make a ten; if it’s same numbers → doubles; if one away → near doubles; if it’s subtraction → think-addition.”
   • Use peer support: assign a consistent math partner; partners must show on ten-frame before writing the answer.
   • Provide number bond templates for make-a-ten (e.g., 7 split into 2 and 5) to reduce working memory demand.
   • Offer immediate corrective feedback prompts: “Show me the 10 first,” “Which part is missing?”

   IEP / 504 Accommodations

   • Provide extended time for sprint/exit ticket as documented; allow completion of fewer sprint items while still practicing strategies.
   • Preferential seating near instruction and away from distractions; ensure clear view of ten-frame/rekenrek modeling.
   • Allow alternative response modes: verbal responses or pointing to strategy cards instead of writing full explanations.
   • Use large-print materials and reduced visual clutter versions of worksheets as needed.
   • Provide frequent checks for understanding and directions repeated in short steps; post directions visually: ‘Solve → Circle strategy → Check.’
   • Allow use of manipulatives (counters/rekenrek) for all tasks, including exit ticket, if listed as an accommodation.
   • For fine-motor needs: allow marker on laminated sheet, pencil grip, or scribe for word problem equation while student dictates.

   Advanced Learners

   • Solve each guided practice problem in two different ways (e.g., near doubles and make-a-ten) and compare efficiency.
   • Create two new near-doubles facts and write the related doubles fact (e.g., 8+9 related to 8+8 and 9+9).
   • Write a word problem within 20 that matches an equation with an unknown in a non-end position (e.g., □ + 7 = 16) and trade with a partner to solve.
   • Mental-math challenge: explain how make-a-ten supports adding within 100 (preview connection), e.g., 38 + 7 relates to 8 + 7.
   • Error analysis: given an incorrect student strategy (teacher-provided), identify the mistake and correct it using a model.

   形成性检查

   • Warm-up sprint observation notes: which students rely on counting vs. strategy use
   • Thumbs up/side/down CFUs after each modeled strategy
   • Guided practice partner talk: teacher listens for correct naming and justification of strategies
   • Independent practice monitoring checklist during circulation
   • Student explanation during share-out using sentence frame

   退出票

   1) 9 + 8 2) 7 + 8 3) 14 − 6 and write: 6 + □ = 14

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 The lesson includes specific vocabulary terms related to addition strategies, so a vocabulary practice template supports learning these key terms.
   • Worksheet 填空 The independent practice involves computation items and strategy checkboxes, which align well with a fill-in-the-blank practice format for fluency building.
   • Worksheet 3-2-1 退出票 The lesson explicitly mentions exit tickets with 3 items, making the 3-2-1 exit ticket template appropriate for formative assessment.
   • Worksheet T-图 A T-Chart organizer can help students visually compare and contrast strategies like make a ten and doubles, supporting conceptual understanding.

   Storypie 内容

   • Storypie Content Addition Addition is a fundamental mathematical operation that represents the total amount of objects together in a collection. It is signified by the plus sign (+).
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory
   • Storypie Content Division Division is a fundamental arithmetic operation that is the inverse of multiplication. It is the process of splitting a number into equal parts or groups.
   • Storypie Content Fractions Fractions represent parts of a whole or, more generally, any number of equal parts. They are a fundamental concept in mathematics used to express division, ratios, and numbers that are not whole.
   • Storypie Content Calculator Watch A device that performs arithmetic operations. Calculators have evolved from ancient counting tools and mechanical devices to modern, pocket-sized electronic instruments.

   准备清单

   • Print and cut fluency sprint half-sheets; prepare 3–5 extras.
   • Print guided practice set (8 problems) and independent practice sheets (Part A/B).
   • Print exit tickets; stack for quick distribution.
   • Prepare manipulatives: ten-frames/rekenreks and counters in bins for each table/pair.
   • Create or post the strategy anchor chart (Make a Ten / Doubles / Near Doubles / Think-Addition) with one example each.
   • Pre-select 8 guided practice problems that highlight the three strategies (suggested mix below).
   • Set up a timer and decide sprint time (e.g., 2 minutes) and independent work time.
   • Plan small-group roster: identify students likely needing make-a-ten support and students ready for extension.

   常见误解

   • Make-a-ten misunderstanding: students break the wrong addend or do not keep track of the leftover part.
   • Students think doubles only means ‘two numbers’ rather than ‘same + same.’
   • Students believe subtraction must be solved by counting backwards rather than using related addition facts.
   • Students treat the unknown symbol as a cue to do an operation without considering meaning (e.g., writing any equation that has the right answer).
2. 2 Adding Within 100 Without Regrouping (Tens and Ones, Open Number Line) 完整课程 Adding Within 100 Without Regrouping (Tens and Ones, Open Number Line)

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group for warm-up and modeling; partners for guided practice; independent work for practice; quick whole-group closure.

   学习目标

   • I can add two two-digit numbers within 100 without regrouping by adding tens and ones. Apply

     成功标准:

     • I split each number into tens and ones (example: 34 = 30 + 4).
     • I add tens to tens and ones to ones.
     • I write a correct equation and final sum.
     • I check that my ones sum is less than 10 (no regrouping).

   • I can show addition within 100 without regrouping on an open number line using tens jumps and ones jumps. Apply

     成功标准:

     • I start at the first addend on the number line.
     • I make tens jumps first, then ones jumps.
     • I label my jumps clearly and end at the correct sum.
     • My number line matches my equation.

   • I can explain why my addition strategy works using place value language (tens, ones) and/or a drawing (equation and open number line). Analyze

     成功标准:

     • I use the words tens and ones to describe what I did.
     • I explain why no regrouping is needed (ones total is less than 10).
     • I connect my equation to my open number line jumps to show they represent the same addition.

   标准

   • CCSS.MATH.CONTENT.2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
   • CCSS.MATH.CONTENT.2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
   • CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
   • CCSS.MATH.PRACTICE.MP4 Model with mathematics.
   • CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

   材料

   • Base-ten blocks (tens rods and ones cubes) or printed base-ten visuals · 1 class set + small teacher demo setUse for quick modeling and for students who need concrete support; not required for all students.
   • Chart paper/whiteboard and markers · 1 setCreate an anchor chart with the steps and show worked examples.
   • Document camera or projector · 1Display teacher modeling and one student sample during guided practice.
   • Student whiteboards, markers, and erasers · 1 per studentUsed in warm-up and quick checks during modeling.
   • Open number line templates/strips (blank lines) · 2–3 per studentProvide pre-drawn versions for supports; blank for most students.
   • Independent practice page (no-regrouping two-digit addition) · 1 per studentInclude a mix of equation method and open number line method prompts.
   • Exit tickets · 1 per student2-item exit ticket with computation + explanation frame.
   • Math journals or scratch paper · 1 per studentFor showing work and writing explanation.

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Facilitate a Number Talk with a single problem (23 + 14). Establish norms: mental math first, multiple strategies, respectful listening. Record strategies using tens/ones language and/or a quick number line sketch.

   学生操作: Solve mentally; signal readiness; share answers and explain strategies using tens and ones; listen and build on classmates’ ideas.

   教师脚本（完整）

   “Today we’re going to add two-digit numbers using place value and a number line. Let’s warm up with a quick Number Talk. Look at this: 23 + 14. Solve it in your head. Put your thumb up when you have an answer—and keep thinking of a second way. (Wait, scan.) Remember our math community rule: Different strategies are welcome here; we learn from each other. What answer did you get? … Now tell us how you got it using tens and ones. I’m going to record your thinking. If you hear a strategy that’s different from yours, that’s great—see if you can understand it.”

   Direct Instruction10 min

   教师行动: Explicitly model adding within 100 without regrouping using (1) tens-and-ones decomposition and (2) an open number line. Emphasize the no-regrouping check (ones sum < 10). Use 46 + 23. Conduct quick checks for understanding with targeted questions.

   学生操作: Track teacher modeling; respond to CFU questions; use whiteboards to answer quick prompts (e.g., identify tens/ones; what is added first on number line).

   教师脚本（完整）

   “Now I’m going to show two strong strategies for adding within 100 when we do NOT need to regroup. Problem: 46 + 23. Strategy 1: Tens and ones. Watch how I break apart each number. 46 is 40 and 6. (I underline tens, circle ones.) 23 is 20 and 3. I add the tens: 40 + 20 = 60. I add the ones: 6 + 3 = 9. Now I put them together: 60 + 9 = 69. So 46 + 23 = 69. Important check: I always check the ones. Is 6 + 3 less than 10? Yes—so I don’t need to make a new ten. That means no regrouping today. Strategy 2: Open number line. Now I’ll model the SAME problem on an open number line. I start at 46 because that’s my first addend. First, I jump the tens from 23: +20. 46 plus 20 lands on 66. Then I jump the ones: +3. 66 plus 3 lands on 69. The number I land on is my sum: 69. Notice: The +20 jump matches the ‘add tens’ part, and the +3 jump matches the ‘add ones’ part.”

   理解检查: CFU 1 (choral): “What are the tens and ones in 46?” Expected: “4 tens and 6 ones.” CFU 2 (turn and talk): “Why didn’t I regroup?” Expected: “Because 6 + 3 = 9, and 9 is less than 10.” CFU 3 (quick whiteboard): “Start at 58, jump +20. Where do you land?” Expected: 78.

   Guided Practice15 min

   教师行动: Lead three problems with gradual release (I/We → We → You with support). Prompt partner talk with roles. Circulate to observe, correct misconceptions, and select one student sample to display under document camera. Reinforce ethos: multiple strategies, precise language, kind feedback.

   学生操作: Problem 1: Participate chorally in naming tens/ones and computing. Problem 2: Work with partner to choose a strategy and justify no regrouping. Problem 3: Choose strategy independently, then share reasoning. Use tens/ones language and/or open number line labels.

   教师脚本（完整）

   “Now we’ll practice together. Remember: our goal is accuracy and clear thinking. We can use tens-and-ones or an open number line. Problem 1: 35 + 42. Let’s do this together. Class, say the tens and ones in 35.” (Pause.) “Yes: 3 tens and 5 ones. “And the tens and ones in 42?” (Pause.) “Yes: 4 tens and 2 ones. “Let’s add tens: 30 + 40 = __.” “Let’s add ones: 5 + 2 = __.” “Combine: 70 + 7 = __.” “Check: Is 5 + 2 less than 10?” Problem 2: 58 + 21. “Now you will work with your partner. Partner A: Say the tens and ones. Partner B: Ask, ‘Do we need regrouping?’ and explain why. Then switch roles. Choose one strategy: tens/ones OR open number line.” (After 1–2 minutes) “I’m going to cold-call one pair to explain using tens and ones, and another pair to explain using the number line. Remember to speak clearly and respectfully.” Problem 3: 64 + 15. “Now try this one with more independence. Choose your strategy and show your work. I will walk around to see your thinking. If you get stuck, start by writing: 64 = __ + __ and 15 = __ + __.” Error-friendly correction (as needed): “Let’s slow down and check the ones. If the ones add to 9 or less, we can stay in tens-and-ones without regrouping. Point to your ones—what do they add to?”

   支架提示: Decompose prompt: “Show me the tens part and the ones part. What is ___ as tens and ones?” | No-regrouping check prompt: “What do the ones add to? Is it less than 10? How do you know?” | Structure prompt (MP7): “What stays the same if we use the number line instead of the equation?” | Open number line prompt: “Where will you start? Which jump is the tens jump? Which jump is the ones jump?” | Labeling prompt: “Can you label each jump with +___ and circle the number you land on at the end?” | Reasonableness prompt (MP2): “About how many tens is your answer? Does that match where you landed?” | Partner language prompt: “I agree/disagree because… The tens are… The ones are… We did/did not regroup because…”

   Independent Practice15 min

   教师行动: Distribute practice page and number line templates as needed. Restate expectations and success criteria. Circulate with a monitoring checklist; pull a quick small group (2–5 students) if multiple students show the same need (e.g., decomposing). Provide immediate feedback focused on process (tens/ones, labeling, no-regrouping check).

   学生操作: Complete 8–10 no-regrouping addition problems within 100. Solve at least 4 using tens-and-ones equations and at least 4 using an open number line. Star one problem and write 1–2 sentences explaining the strategy using ‘tens’ and ‘ones’. Check work by comparing representations and verifying ones sum < 10.

   教师脚本（完整）

   “Now it’s your turn. On this page you will solve addition problems within 100 that do NOT need regrouping. You must: 1) Solve at least 4 using tens-and-ones equations. 2) Solve at least 4 using an open number line. 3) Star ONE problem and write 1–2 sentences explaining your strategy using the words ‘tens’ and ‘ones.’ Work quietly and try your best. If you finish early, check two ways: • Do my tens and ones add up to my total? • Does my number line end at the same sum as my equation? If you need help, first try this: circle the ones, underline the tens.”

   监控清单: Student correctly decomposes each addend into tens and ones. | Student adds tens to tens and ones to ones (no mixing tens with ones). | Student checks that ones sum is < 10 and states ‘no regrouping’ when asked. | Open number line starts at an addend, not at 0 (unless intentionally explained). | Tens jumps are multiples of 10; ones jumps are 1–9. | Jumps are labeled (+10, +20, +3, etc.) and endpoint is identified as the sum. | Student’s equation and number line match the same sum. | Written explanation includes the words ‘tens’ and ‘ones’ and is logically accurate.

   Closure5 min

   教师行动: Administer exit ticket (2 items). Prompt brief reflection and quick strategy survey (hands). Collect exit tickets at the door or in a bin labeled “Math Exit Ticket.” State how data will guide next lesson. Reinforce ethos of multiple strategies.

   学生操作: Complete exit ticket independently. Use preferred representation and write explanation sentence frame. Participate in quick reflection on strategies used. Turn in exit ticket before lining up/transitioning.

   教师脚本（完整）

   “We’re going to close with a quick exit ticket. This is independent so I can see what you can do on your own. 1) Compute 27 + 32. You choose: tens-and-ones or an open number line. 2) Finish the sentence: ‘I did not regroup because ______.’ Take your time, show clear work, and use the words tens and ones. (After 3 minutes) Raise your hand if you used an open number line. (Pause.) Raise your hand if you used tens and ones. (Pause.) Both are strong strategies. Before you line up, hand me your exit ticket—this helps me choose tomorrow’s problems.”

   退出票: 1) Solve: 27 + 32. Show your work using tens-and-ones OR an open number line. 2) Complete: “I did not regroup because ______.”

   tens

   Tens are bundles of 10.

   ones

   Ones are single pieces.

   place value

   Where a digit is tells what it is worth.

   open number line

   A blank line where we draw jumps to show adding.

   sum

   The total when you add.

   English Language Learners

   • I can say a two-digit number as tens and ones using a sentence frame (e.g., “46 is 4 tens and 6 ones.”).
   • I can explain my strategy using the words tens, ones, and sum (e.g., “I added the tens first, then the ones, to get the sum.”).
   • I can justify no regrouping using a frame (e.g., “I did not regroup because ___ ones + ___ ones = ___, and ___ is less than 10.”).
   • Pre-teach vocabulary with visuals: tens rod/ones cube pictures; post a mini word bank with icons.
   • Provide sentence frames on desk strips: “__ is __ tens and __ ones.” “I started at __ and jumped +__ and +__.” “I did not regroup because __ + __ = __ (<10).”
   • Use gestures while speaking (bundle hands for tens; tap fingers for ones) and point to digits when naming tens/ones.
   • Allow partner rehearsal before sharing out; use structured partner roles (Speaker/Checker).
   • Offer bilingual glossary or translation tools where permitted; accept oral explanations in home language followed by key math words in English (tens/ones/sum).
   • Use consistent number line language: start, jump, land; provide picture cue cards for these words.

   Struggling Learners

   • Concrete-first option: build each addend with base-ten blocks, then combine tens and ones physically before writing equations.
   • Provide a tens/ones organizer (two-column mat labeled TENS and ONES) and require students to place numbers before adding.
   • Pre-drawn open number lines with the start point already written; students only add jumps (+10, +1) and the landing number.
   • Chunk the independent practice: assign 4 problems first; teacher checks; then assign the next 4.
   • Reduced problem set expectation if needed (e.g., 6 total instead of 8–10) while still requiring both representations at least once each.
   • Use peer support: pair with a patient, trained peer tutor; provide a “checklist buddy” routine: Decompose → Add tens → Add ones → Check ones < 10 → Combine.
   • Simplify numbers initially (e.g., ones add to 5 or less) then move to harder within no-regrouping (ones add to 9).
   • Error-proofing cue: highlight/circle ones digits in each addend before solving to prompt the regrouping check.

   IEP / 504 Accommodations

   • Preferential seating near instruction and away from distractions; clear view of board/modeling.
   • Provide copies of anchor steps and a personal checklist card for the desk (Break apart → Add tens → Add ones → Check ones < 10 → Combine).
   • Allow extended time on independent practice/exit ticket as needed; reduce written output while maintaining the same learning goal (e.g., oral explanation to teacher instead of written sentence).
   • Use large-print number line templates; provide a straightedge or finger spacer for tracking.
   • Permit alternative response modes: explain orally, point to jumps, or use manipulatives to demonstrate thinking.
   • Frequent check-ins (every 3–4 minutes) and immediate corrective feedback; confirm understanding of directions by asking student to restate the first step.
   • For fine-motor needs: provide thicker markers, pencil grips, or allow drawing fewer but larger jumps on number line.

   Advanced Learners

   • Create-your-own problem: Students generate two two-digit addends that will NOT require regrouping, solve it two ways, and explain why no regrouping is needed.
   • Strategy comparison writing: “How are the tens-and-ones method and open number line the same? How are they different?” Include an example.
   • Introduce compensation (still no regrouping): solve 46 + 23 by doing 46 + 20 + 3; then generalize the pattern.
   • Word problem extension (no regrouping): Provide 2 story problems within 100; students choose representation and write an equation with a label for the answer.
   • Challenge set with three addends (no regrouping in ones): e.g., 21 + 34 + 12; require a plan (add tens, add ones) and verify ones < 10 at each step.
   • Error analysis: Provide an incorrect student work sample (e.g., added 6 + 3 = 63) and ask students to identify and correct the mistake using place value language.

   形成性检查

   • Warm-up Number Talk: listen for correct decomposition (20+3, 10+4) and accurate sum; note strategy variety.
   • CFU during modeling: choral response on tens/ones; quick whiteboard land-on number after a tens jump.
   • Guided practice observation: teacher checklist of decomposition, ones-check, and correct number line labeling; cold-call explanations.
   • Collect/display one student number line sample to assess clarity of jumps and match to equation.
   • Independent practice monitoring: spot-check 3 problems per student for representation requirements and reasoning sentence.

   退出票

   1) Solve: 27 + 32. Show your work using tens-and-ones OR an open number line. 2) Complete: “I did not regroup because ______.”

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 The lesson includes specific vocabulary terms related to place value and addition strategies, so vocabulary practice supports student understanding of key concepts.
   • Worksheet 匹配活动 A matching activity can reinforce the connection between vocabulary terms and their definitions or representations, aiding comprehension for grade 2 students.
   • Worksheet 填空 Fill in the blank practice allows students to apply their knowledge of adding within 100 without regrouping in a straightforward, grade-appropriate format.
   • Worksheet 3-2-1 退出票 The lesson specifies an exit ticket with computation and explanation, so a 3-2-1 exit ticket template fits well for formative assessment and closure.

   Storypie 内容

   • Storypie Content Addition Addition is a fundamental mathematical operation that represents the total amount of objects together in a collection. It is signified by the plus sign (+).
   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory
   • Storypie Content Division Division is a fundamental arithmetic operation that is the inverse of multiplication. It is the process of splitting a number into equal parts or groups.
   • Storypie Content Fractions Fractions represent parts of a whole or, more generally, any number of equal parts. They are a fundamental concept in mathematics used to express division, ratios, and numbers that are not whole.
   • Storypie Content Calculator Watch A device that performs arithmetic operations. Calculators have evolved from ancient counting tools and mechanical devices to modern, pocket-sized electronic instruments.

   准备清单

   • Print independent practice pages and exit tickets; prepare 3 extra copies for absent/late students.
   • Prepare open number line templates (blank for most; pre-drawn start point and tick marks for support group).
   • Gather base-ten blocks or printed visuals; place a small demo set near teacher station.
   • Write board plan before class: learning targets, vocabulary, anchor steps, and blank space for number line model.
   • Set up document camera/projection and test visibility of number line and equations.
   • Prepare partner role cards (Partner A: tens/ones; Partner B: regrouping check) or display roles on board.
   • Plan small-group roster: identify 4–6 students who may need concrete support with decomposition based on prior data.
   • Create an exit-ticket sorting system (folders or trays labeled 0, 1, 2) for quick analysis.

   常见误解

   • Belief that you always must regroup when adding two-digit numbers (overgeneralization from later lessons).
   • Starting an open number line at 0 automatically, even when using a ‘count on’ strategy.
   • Treating digits as separate numbers without place value (e.g., 46 as 4 and 6, not 40 and 6).
   • Adding tens and ones together incorrectly (e.g., 60 + 9 written as 609).
   • Making ones jumps first on the number line and losing track of total (not wrong, but can cause errors without careful tracking).
3. 3 Subtracting Within 100 Without Regrouping (Tens and Ones, Counting Up/Back) 完整课程 Subtracting Within 100 Without Regrouping (Tens and Ones, Counting Up/Back)

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group (Number Talk + modeling), partners (guided practice), independent work (practice + exit ticket)

   学习目标

   • I can represent a subtraction problem within 100 (no regrouping) using tens and ones and explain what each part means. Understand

     成功标准:

     • I can show both numbers using tens and ones (e.g., base-ten blocks or a place value drawing).
     • I can subtract tens from tens and ones from ones without trading.
     • I can use the words tens, ones, and difference correctly to explain my work.
     • I can explain why my strategy works using place value (tens and ones).

   • I can subtract within 100 without regrouping by counting back or counting up and check that my answer makes sense. Apply

     成功标准:

     • I can choose counting back or counting up and use it accurately to find the difference.
     • I can record my strategy clearly (jumps on a number line or counting steps).
     • I can check my answer using the inverse (addition) or a quick estimate (about how many tens).
     • I can explain why my counting strategy works (my jumps add up to the difference).

   • I can solve one- and two-step subtraction word problems within 100 (no regrouping) and write an equation that matches the story. Apply

     成功标准:

     • I can underline what the problem is asking and identify the important numbers.
     • I can write an equation with a symbol for the unknown (e.g., 56 − 23 = □ or □ + 23 = 56).
     • For a two-step problem, I can write two connected equations (Step 1 and Step 2).
     • My answer matches my model/strategy and includes a unit/label when needed.

   标准

   • CCSS.MATH.CONTENT.2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
   • CCSS.MATH.CONTENT.2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
   • CCSS.MATH.CONTENT.2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects.

   材料

   • Base-ten blocks (tens rods and ones cubes) or place value disks · 1 set per pair (or per student if available)Prepare bins/baggies with at least 10 tens and 20 ones per pair.
   • Place value chart (tens/ones) · 1 large for board + optional student matsBoard chart should be visible; student mats support representation.
   • Open number line templates · 1 half-sheet per student (plus a few extras)Students can also draw number lines in notebooks.
   • Hundreds chart (optional) · Class set or a few reference copiesUse for students who need counting support; do not require for all.
   • Dry-erase boards/markers/erasers · 1 per studentFor Number Talk responses and quick checks.
   • Independent practice worksheet · 1 per student8–10 items, including 2 short word problems; specify representation requirements.
   • Exit ticket · 1 per studentProblem: 64−23 + sentence stem; collect at door.
   • Document camera or projector · 1To model and to display 2 student strategies during share-outs.
   • Pencils and crayons · 1 per studentCrayons optional for tens/ones drawings (tens as sticks, ones as dots).

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 25 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Facilitate a Number Talk focused on mental subtraction without regrouping; elicit and record two strategies (place value and counting). Establish norms: quiet think time, multiple strategies, respectful listening.

   学生操作: Mentally solve each problem; show a quiet thumb when ready; share strategies using math vocabulary; listen and compare approaches.

   教师脚本（完整）

   Mathematicians, eyes on the board. Today we will subtract within 100 without regrouping. I’m going to show a problem. Think quietly in your head. Put a quiet thumb up when you have an answer, and be ready to explain your thinking. First problem: 54 − 20. (Wait 5–10 seconds.) Show me your thumb when you’re ready. Turn and tell your partner: How did you get your answer? Who can share a strategy using tens? (Select 1 student.) (Record: 54 is 5 tens 4 ones; subtract 2 tens → 3 tens 4 ones = 34.) Second problem: 54 − 24. (Wait.) How did you use tens and ones? Did anyone count up instead of count back? Tell us where you started and what jumps you made. Third problem: 68 − 30. (Wait.) What stayed the same? What changed? Remember our norms: mistakes are data. We learn from them. We can disagree with ideas, but we speak kindly to people.

   Direct Instruction10 min

   教师行动: Explicitly model 76−42 using (1) tens/ones with place value chart and blocks/drawing, (2) counting back on open number line, (3) counting up on open number line. Highlight why no regrouping is needed and how to check using addition. Ask brief CFU questions.

   学生操作: Attend to modeling; respond chorally or with signals; answer CFU questions; use quick turn-and-talk to explain why no regrouping is needed; track the three representations.

   教师脚本（完整）

   Learning target: I can subtract within 100 without regrouping using tens and ones or counting, and I can explain my thinking. Let’s model: 76 − 42. First, tens and ones. I’m reading 76 as 7 tens and 6 ones. (Point to place value chart.) I’m subtracting 42, which is 4 tens and 2 ones. Watch: I can take away 4 tens from 7 tens. (Remove 4 tens rods.) That leaves 3 tens. Now I can take away 2 ones from 6 ones. (Remove 2 ones.) That leaves 4 ones. So I have 3 tens and 4 ones, which is 34. No trading is needed because I had enough ones: 6 ones is more than 2 ones. Check for understanding: Thumbs up if you agree we did NOT need to trade. Thumbs to the side if you’re unsure. Turn and tell a partner: Why didn’t we need to trade? Now, let’s use counting back on an open number line. I start at 76 because that’s the whole. I count back 40 to land on 36. (Draw a jump labeled −40.) Then I count back 2 more to land on 34. (Draw a jump labeled −2.) The difference is 34. Now, counting up. I start at 42 because that’s the part being taken away. I count up to 76. From 42 to 72 is +30. From 72 to 76 is +4. I add my jumps: 30 + 4 = 34. The difference is 34. Both strategies give the same difference. We value multiple strategies. If you make a mistake, that is useful information—we can fix it by checking. One check is the inverse: if 76 − 42 = 34, then 42 + 34 should equal 76.

   理解检查: Ask: (1) ‘In 76, how many tens? how many ones?’ (2) ‘What tells you regrouping is not needed?’ (3) ‘If you counted up, where do you start?’ (4) ‘What addition equation can check 76 − 42 = 34?’ Listen for: start at smaller for count up; enough ones; correct inverse equation.

   Guided Practice15 min

   教师行动: Assign partner work for three problems; require students to choose and justify a strategy. Circulate using quick checks; provide prompts and corrective feedback. Conduct a midpoint share-out; record one example of each strategy on the board.

   学生操作: Work with partner to solve 85−50, 93−21, 67−35 using a chosen method; create a representation (tens/ones or number line); explain strategy choice using sentence frame; participate in share-out and revise if needed.

   教师脚本（完整）

   Now it’s your turn with support—We Do. With your partner, you will solve three problems: 85 − 50, 93 − 21, and 67 − 35. You get to choose your strategy: 1) Tens-and-ones model 2) Counting back on a number line 3) Counting up on a number line But you must be able to say: ‘I chose this strategy because ____.’ Partner A, start by reading the first problem aloud. Partner B, decide which strategy you want to use first. Then switch roles for the next problem. (After 5–6 minutes) Stop and look up. I’m going to cold-call two pairs. Tell us your strategy and why it works. As you share, use our vocabulary: tens, ones, difference, count back, count up. (After shares) Notice: different strategies can still be correct. What matters is that your representation matches the numbers and your jumps or blocks make sense. Go back and finish the third problem. If you’re stuck, choose one prompt on the board and try it.

   支架提示: Tens/ones prompt: ‘Say the first number as __ tens and __ ones.’ | No regrouping check: ‘Do you have enough ones to subtract the ones?’ | Tens step: ‘Subtract the tens first: __ tens − __ tens = __ tens.’ | Ones step: ‘Subtract the ones: __ ones − __ ones = __ ones.’ | Counting back prompt: ‘Start at the larger number. Jump back the tens first. Then jump back the ones.’ | Counting up prompt: ‘Start at the smaller number. Jump to the next friendly ten. Then jump by tens. Then finish with ones.’ | Representation check: ‘Point to your model and tell what each part means.’ | Reasonableness check: ‘About how many tens is the answer? Does your answer fit that estimate?’ | Inverse check: ‘Write an addition sentence to check: smaller + difference = larger.’ | Error-correction prompt: ‘Where did your number line start? Should it start at the larger or smaller number for your strategy?’

   Independent Practice25 min

   教师行动: Distribute practice sheet; review representation requirements; monitor with a checklist; conference with 4–6 students for targeted feedback; pull a quick small group if several students show the same error (e.g., reversing start point on number line). Provide challenge option for early finishers.

   学生操作: Solve 8–10 problems independently; show required representations (at least 2 tens/ones and at least 2 number line counting); complete 2 word problems with equations; check answers with addition or estimation; attempt challenge if finished.

   教师脚本（完整）

   Now it’s You Do—independent practice. On this page you have subtraction problems within 100. None of these require regrouping. Here are the expectations: - Show at least 2 problems using tens and ones (blocks, place value drawing, or place value chart). - Show at least 2 problems using a number line (counting back OR counting up). - For the word problems, underline what it is asking, and write an equation with a box or symbol for the unknown. Work quietly and show your strategy so I can see your thinking. If you finish early, do the Challenge at the bottom: write your own subtraction story problem that matches 72 − 31, and solve it with a strategy. (Conference script used at desks) Tell me what 67 means in tens and ones. Show me where you subtracted the tens. Show me where you subtracted the ones. How do you know you didn’t need to trade? How can you check your answer with addition?

   监控清单: Student correctly represents two-digit numbers as tens and ones. | Student subtracts tens from tens and ones from ones without regrouping. | If using counting back, student starts at larger number and makes correct jumps (tens then ones). | If using counting up, student starts at smaller number and makes jumps that land exactly on the larger number. | Jumps are labeled and total difference is computed correctly. | Student uses vocabulary in written explanations when prompted (tens, ones, difference). | Student checks at least one answer using inverse addition (e.g., subtrahend + difference = minuend) or an estimate. | Word problem: student underlines question, identifies numbers, writes matching equation with unknown symbol, includes label/unit in answer.

   Closure5 min

   教师行动: Administer and collect exit ticket; prompt strategy reflection; reinforce key idea ‘no regrouping = enough ones’; preview next lesson. Use exit ticket data plan to group students for next day.

   学生操作: Complete exit ticket (64−23) with strategy and sentence stem; turn in at door; briefly reflect on strategy choice.

   教师脚本（完整）

   Before you line up, complete the exit ticket. Exit Ticket: 1) Solve 64 − 23. Show your strategy. 2) Write one sentence: ‘I used ___ because ___.’ Your goal is to prove your answer with your strategy, not just write the answer. (After collection) Today we learned that subtracting without regrouping means we have enough ones, so we can subtract tens and ones directly, or we can count back or count up to find the difference. Tomorrow we’ll build on this with problems where we might need to trade a ten for ones.

   退出票: Solve 64 − 23. Show your strategy (tens/ones model OR counting up/back on a number line). Then complete: “I used ___ because ___.”

   subtract

   Subtract means you take some away.

   difference

   The difference is how many more or how many left.

   tens

   Tens are bundles of 10.

   ones

   Ones are single units.

   counting up / counting back

   You can jump back from the big number or jump up from the small number to find the difference.

   English Language Learners

   • I can say a subtraction strategy using sentence frames: ‘I started at __ and counted (up/back) by __ to get __.’
   • I can use math vocabulary in a complete sentence: ‘__ has __ tens and __ ones. The difference is __.’
   • I can ask for clarification using a frame: ‘Can you show me where you subtracted the tens/ones?’
   • Pre-teach and gesture vocabulary (tens = bundled sticks; ones = single cubes; difference = space between numbers with hands apart).
   • Provide sentence frames on desk strip: ‘__ is __ tens and __ ones.’ ‘I subtracted __ tens and __ ones.’ ‘I counted up/back by __.’
   • Use visual word bank with pictures (tens rod, ones cube, number line arrow).
   • Allow partner rehearsal (think-pair-share) before whole-group share; assign supportive bilingual/peer partner when possible.
   • Use consistent language for number line: ‘Start at __. Jump by tens. Then jump by ones.’ and point while speaking.
   • Reduce linguistic load on word problems: highlight/underline key phrases; provide a ‘Read-Draw-Write’ organizer with icons.

   Struggling Learners

   • Concrete-first: require base-ten blocks or place value disks for first 3–4 independent problems before allowing drawings/number lines.
   • Simplify number line: provide pre-printed number lines with decade marks (0,10,20,…,100) and space to fill in endpoints.
   • Chunk tasks: complete only first 6 problems initially; teacher checks; then assign remaining problems if accurate (mastery-based release).
   • Modified expectation option: ‘Show strategy for 1 problem of each type (tens/ones + number line)’ instead of 2 each, if student needs reduced writing demand.
   • Error-proofing checklist taped to desk: 1) Circle bigger number 2) Check ones: enough? 3) Subtract tens 4) Subtract ones 5) Check with addition.
   • Peer support: structured partner check during independent work—students compare one finished problem using the question ‘Do our models match the numbers?’
   • Use color-coding: tens in blue, ones in red on drawings and on place value chart to reduce place-value confusion.

   IEP / 504 Accommodations

   • Provide extended time and reduced-distraction seating for independent practice and exit ticket.
   • Allow oral explanation in place of or in addition to written explanation (teacher scribes if documented).
   • Use large-print worksheets and number line templates; provide pencil grips or slant board as needed.
   • Frequent check-ins: after every 2 problems, student signals for a quick accuracy check to prevent practicing errors.
   • Break directions into single steps; provide a visual ‘First/Next/Then’ card for strategies.
   • Permit manipulatives and reference charts (place value chart, hundreds chart) as accommodations.
   • For attention/EF needs: highlight required problems to represent (e.g., star #2 and #5 for tens/ones; circle #3 and #6 for number line) to reduce planning load.

   Advanced Learners

   • Efficiency comparison: Solve one problem two ways (tens/ones and counting up) and write which is more efficient and why.
   • Create-and-swap: Write two original ‘no regrouping’ subtraction problems within 100 and trade with a partner; verify using inverse addition.
   • Number line sophistication: Use ‘friendly tens’ jumps when counting up (e.g., 47→50→70→76) and justify jump choices.
   • Early bridge to regrouping conceptually: Given a pair like 64−29, explain (without solving) why regrouping would be needed, using tens/ones language.
   • Word problem challenge: Write a two-step story problem with subtraction within 100 (no regrouping) and an unknown in a different position (e.g., □ − 23 = 41), then model and solve.

   形成性检查

   • Number Talk: observe mental strategies and accuracy on 54−20, 54−24, 68−30; note who uses place value vs counting.
   • CFU during modeling: thumbs signals for ‘no regrouping needed’ and quick oral questions about tens/ones and starting points.
   • Guided practice observation: listen for accurate explanations and correct number line setup; collect one partner work sample to display.
   • Independent practice monitoring: teacher checklist + quick conferences; spot-check 2 problems per student for representation accuracy and correct checks.

   退出票

   Solve 64 − 23. Show your strategy and complete: ‘I used ___ because ___.’

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 Includes key vocabulary terms like subtract, difference, tens, and ones to support understanding of math concepts in grade 2.
   • Worksheet 填空 Provides targeted practice on subtracting within 100 without regrouping, matching the lesson's independent practice needs.
   • Worksheet T-图 Supports organizing and comparing the two subtraction strategies (place value and counting) explicitly taught in the lesson.
   • Worksheet 3-2-1 退出票 Offers a simple exit ticket format aligned with the lesson's exit ticket to assess understanding before dismissal.

   Storypie 内容

   • Storypie Content Subtraction Subtraction is one of the four basic arithmetic operations; it is the process of removing a quantity from another to find the difference.
   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory
   • Storypie Content Division Division is a fundamental arithmetic operation that is the inverse of multiplication. It is the process of splitting a number into equal parts or groups.
   • Storypie Content Fractions Fractions represent parts of a whole or, more generally, any number of equal parts. They are a fundamental concept in mathematics used to express division, ratios, and numbers that are not whole.
   • Storypie Content Calculator Watch A device that performs arithmetic operations. Calculators have evolved from ancient counting tools and mechanical devices to modern, pocket-sized electronic instruments.

   准备清单

   • Print: independent practice sheets (class set + 5 extra) and exit tickets (class set + 5 extra).
   • Prepare base-ten materials: baggies/bins labeled by table/pair; verify enough tens and ones.
   • Prepare board materials: draw place value chart and three-column strategy anchor space (tens/ones, count back, count up).
   • Copy open number line half-sheets or ensure notebooks are available.
   • Select 2–3 students in advance who can share different strategies (if known) while still allowing authentic student thinking.
   • Ensure document camera/projector is working; test visibility of base-ten blocks and number line drawings.
   • Create or post sentence frames for strategy justification and ELL supports.
   • Prepare a small-group reteach spot with manipulatives and a pre-marked number line for quick intervention during independent practice.

   常见误解

   • ‘No regrouping’ means you never cross a ten on a number line (false); you can cross tens when counting, but you do not need to trade ones.
   • Counting up gives the sum instead of the difference (students may forget to add jumps); reinforce: ‘Add the jumps to get the difference.’
   • On a number line, students may label jumps incorrectly (e.g., +40 but move 4); reinforce labeling and endpoint checking.
   • Students may subtract the smaller digit from the larger digit regardless of place (e.g., in 64−23, do 4−2 and 6−3 without understanding tens/ones); anchor to tens/ones meaning and show with blocks.
4. 4 Word Problems Within 100 (Add To, Take From, Put Together/Take Apart, Compare) 完整课程 Word Problems Within 100 (Add To, Take From, Put Together/Take Apart, Compare)

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group for warm-up and mini-lesson; pairs for guided practice; independent for practice; whole group for closure.

   学习目标

   • I can identify the word-problem situation (add to, take from, put together/take apart, or compare) and decide whether to add or subtract within 100. Analyze

     成功标准:

     • I can name the problem type using the situation words in the problem.
     • I can tell whether the problem is asking for a total, a part, or a difference.
     • I can choose addition or subtraction and explain my choice using evidence from the story.

   • I can represent and solve a word problem within 100 using a drawing and an equation with a symbol for the unknown. Apply

     成功标准:

     • My drawing matches the story and shows the quantities clearly.
     • My equation matches my drawing and includes a symbol (e.g., □) for the unknown.
     • My answer is correct and includes a unit/label from the problem.

   • I can explain my solution strategy and check that my answer makes sense. Evaluate

     成功标准:

     • I can explain my steps using math words (total, difference, compare).
     • I can check by using the inverse operation or estimating to see if the answer is reasonable.
     • I can correct my work if my check shows an error.

   标准

   • CCSS.MATH.CONTENT.2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
   • CCSS.MATH.CONTENT.2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

   材料

   • Whiteboard or document camera · 1Used for modeling drawings/bar models and equations; keep anchor chart visible.
   • Prepared anchor chart: Word problem types (Add To, Take From, Put Together/Take Apart, Compare) with sentence starters and clue words · 1Include: “in all/total,” “left,” “more/fewer,” “altogether,” “how many more.”
   • Problem cards or slides (at least 7 total: 3 warm-up snippets, 2 guided practice, 4 independent practice, 1 exit ticket) · 1 setHave problems pre-written with clear font; include unknown in different positions.
   • Student math journals or recording sheets with space for: situation type, drawing/model, equation with □, solution, check · 1 per studentAdd a checklist box next to each requirement for self-monitoring.
   • Pencils, crayons/colored pencils · Class setColor helps label parts in bar models (part A/part B/total).
   • Base-ten blocks or tens/ones sticks (optional) · 1 tub per table or a shared stationSupport concrete modeling for subtraction/unknown addend.
   • Small dry-erase boards and markers (optional) · 1 per pairFor quick partner reasoning during guided practice.
   • Timer · 1Keep pacing tight, especially during independent practice.

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Facilitate a quick sort of story situations (no numbers) and a brief number talk to activate operation-choice reasoning and place-value strategies.

   学生操作: Students signal operation choice (add/subtract) and justify with a brief reason; then solve two mental math prompts and share strategies.

   教师脚本（完整）

   Today we are math detectives. Our job is to read a story and decide: Is it an add to, take from, put together/take apart, or compare situation? Warm-up, part 1: I’m going to show a short story snippet with no numbers. Your job is to tell me which operation it sounds like and why. Snippet A: “Lena has some crayons. She gets more crayons for her birthday.” Show me with your fingers: 1 for add, 2 for subtract. Now whisper to your partner: Why? Snippet B: “There were some cookies. After snack, there were fewer cookies left.” Fingers: 1 add, 2 subtract. Tell your partner: Why? Snippet C: “Sam has some marbles. Tia has some marbles. Who has more, and how many more?” Fingers: 1 add, 2 subtract. Tell your partner: Why? Warm-up, part 2: Number talk. No pencils. 1) 38 + 20. Think… thumbs up when you have it. Who can explain their strategy using tens? 2) 65 − 30. Think… thumbs up. Who can explain using tens? Remember: tens change tens; ones stay the same when we add or subtract a multiple of 10.

   Direct Instruction10 min

   教师行动: Explicitly model the 7-step routine: Read, Name situation, Find unknown, Draw model, Write equation with □, Solve, Check. Use one problem with unknown in a non-final position (unknown addend) and demonstrate inverse-checking.

   学生操作: Students track the model, answer CFU questions, and chorally repeat the routine steps; students help identify situation type and unknown placement.

   教师脚本（完整）

   Watch me solve a word problem like a math detective. Our steps are on the board. Step 1: Read the whole problem. Problem: “Nina has some stickers. Her friend gives her 27 more stickers. Now Nina has 54 stickers. How many stickers did Nina have at the start?” Step 2: Name the situation type. I hear: “gives her 27 more” and “now she has 54.” That is an ADD TO situation. Step 3: Find what is unknown. The unknown is the start amount. We don’t know how many she had at the start. Step 4: Draw a model. I’m going to draw a bar model. One whole bar is 54 (that’s the total at the end). One part is 27 (the stickers she got). The other part is the start—unknown. I label: total = 54 stickers; part = 27 stickers; unknown part = □ stickers. Step 5: Write an equation with □. Because it’s add to, I can write: □ + 27 = 54. Step 6: Solve. To find an unknown part, I can subtract: 54 − 27. I’ll use place value: 54 − 20 = 34; 34 − 7 = 27. So □ = 27. Step 7: Check. I check with addition: 27 + 27 = 54. That matches the story total. So Nina started with 27 stickers. Important: I always label my answer with the unit from the story. Stickers. Say the routine with me: Read, Name, Unknown, Draw, Equation, Solve, Check.

   理解检查: CFU prompts: (1) “Is this add to, take from, put together/take apart, or compare? How do you know?” (2) “What is the unknown—start, change, or result?” (3) “Point to where the 54 belongs in the model: part or whole?” (4) “What operation can help us solve □ + 27 = 54?” Teacher listens for: unknown addend implies subtraction; correct identification of whole/parts.

   Guided Practice15 min

   教师行动: Facilitate two problems with gradual release: first as a whole-class We Do, second as partner We Do/You Do. Prompt students to justify situation type, place the unknown, and connect drawing to equation. Circulate to coach with targeted prompts.

   学生操作: Students co-construct models and equations, then solve with partners; students share strategies and checks.

   教师脚本（完整）

   We are going to solve two problems together. I will ask questions, and you will help me build the model and equation. Guided Practice Problem 1 (We Do: Put Together/Take Apart): “Mr. Chen has 18 red markers and 25 blue markers. How many markers does he have in all?” 1) What situation type is this? 2) Are we looking for a total or a part? 3) Let’s draw: two parts (18 and 25) make one whole (□). 4) What equation matches? 18 + 25 = □. Now let’s solve using tens and ones. I’ll write: (10+8) + (20+5) = (10+20) + (8+5) = 30 + 13 = 43. So Mr. Chen has 43 markers in all. How can we check quickly? Does 43 sound bigger than both parts? Yes. Guided Practice Problem 2 (We Do/You Do: Compare): “In the library, there are 46 animal books and 29 science books. How many more animal books are there than science books?” First, tell your partner: What type is it and what are we finding? Now, as a class: compare means we are finding the difference. Let’s draw a compare bar model: one bar for 46, one bar for 29. The extra part on the 46 bar is □. Write an equation: 29 + □ = 46 or 46 − 29 = □. Partners: Choose one equation, solve, and show a check. When I say ‘share,’ one pair will explain their model and check.

   支架提示: Problem-type prompts: “What words tell you what’s happening (in all, left, more, fewer)?” “Is the amount getting bigger, getting smaller, or being compared?” | Unknown prompts: “Are we missing the start, the change, the total, or the difference?” “Which number is the whole? Which are parts?” | Model prompts: “Show me where each number goes in your bar model.” “What does your □ stand for in the story?” | Equation prompts: “Read your equation out loud like a sentence.” “Does your equation match your picture exactly?” | Strategy prompts (NBT): “Can you break into tens and ones?” “Can you add/subtract tens first, then ones?” “Can you make a ten?” | Check prompts: “How can you check using the inverse?” “Does your answer make sense compared to the numbers in the story?” | Language supports during talk: “I know it is ___ because the problem says ___.” “The unknown is ___ because we don’t know ___.”

   Independent Practice15 min

   教师行动: Assign a 4-problem set with a required representation routine. Circulate with a monitoring checklist, pull a quick reteach group if 4+ students show the same error (e.g., wrong situation type or unlabeled unknown).

   学生操作: Students complete each problem using the checklist: circle key info, name situation type, draw, write equation with □, solve, label answer, show check. Students use base-ten blocks if needed.

   教师脚本（完整）

   Now you will be the math detective on your own. You must do EVERY step for EACH problem: 1) Circle the important information. 2) Write the situation type: add to, take from, put together/take apart, or compare. 3) Draw a model. 4) Write an equation with □. 5) Solve and label your answer with the unit. 6) Show a check (inverse operation or a quick reasonableness check). If you get stuck, do this first: reread the question sentence and ask, ‘Am I finding a total, a part, or a difference?’ Work quietly. If you finish early, choose one problem and write 2–3 sentences explaining your strategy using math words like total, part, difference, compare.

   监控清单: Student labels the situation type correctly. | Student identifies the unknown correctly (start/change/result or difference). | Model (bar/quick picture/base-ten) matches the story quantities. | Equation includes □ and matches the model (correct structure). | Computation within 100 is reasonable and accurate (place-value strategy evident). | Answer includes correct unit/label from the problem. | Student shows a check using inverse operation or reasonableness statement. | Student can verbally explain why they chose addition or subtraction when asked.

   Closure5 min

   教师行动: Administer exit ticket, prompt a brief reflection, and select 1–2 students to share how they checked their work. Collect exit tickets for data analysis and grouping for the next lesson.

   学生操作: Students complete the exit ticket independently and write a short justification for operation choice; volunteers share check strategies.

   教师脚本（完整）

   Let’s show what we can do as math detectives. Exit Ticket: Read carefully and show your thinking. “Jayden has 58 trading cards. Maya has 35 trading cards. Jayden has □ more trading cards than Maya. How many more cards does Jayden have?” On your paper, you must write: 1) The operation and why. 2) An equation with □. 3) The answer with a label. 4) A check. When you finish, put your pencil down and hold your paper at your chest. Quick share: Who can explain how they checked their answer? Use this sentence starter: ‘I checked by ___ because ___.’

   退出票: Jayden has 58 trading cards. Maya has 35 trading cards. Jayden has □ more trading cards than Maya. How many more cards does Jayden have? Write: (1) operation and why, (2) equation with □, (3) solution with label, (4) a check.

   add to

   You have some, then you get more.

   take from

   You have some, then some go away.

   put together/take apart

   Parts make a total, or a total is split into parts.

   compare

   Two amounts—find how many more or how many fewer.

   unknown

   The missing number we need to solve for.

   English Language Learners

   • I can use sentence frames to name the word-problem type (add to, take from, put together/take apart, compare).
   • I can explain my operation choice using because (e.g., “It is compare because it asks how many more.”).
   • I can use math vocabulary (total, part, difference, more, fewer, unknown) when describing my model and equation.
   • Pre-teach vocabulary with pictures/icons: arrow up (add to), arrow down (take from), two parts to one whole (put together), two bars with gap (compare).
   • Provide sentence frames on desk strip: “This is a ___ problem because ___.” “The unknown is ___.” “My equation is ___.” “I checked by ___.”
   • Color-coding: highlight question in yellow (unknown), numbers in blue, comparison words (more/fewer) in green.
   • Allow oral rehearsal with partner before writing; accept oral explanation recorded by teacher/aide as needed.
   • Use visuals for bar models with labeled ‘whole’ and ‘parts’; provide partially completed bar model templates.
   • Clarify language that can mislead: ‘more’ can appear in add to and compare—teach students to look for ‘how many more than.’
   • Provide bilingual glossary (when available) and allow use of translated directions while maintaining math work in English.
   • Check for understanding with yes/no and either/or questions before open-ended questions (e.g., “Are we finding total or difference?”).

   Struggling Learners

   • Use a reduced problem set (2–3 problems) but require full routine (type, model, equation with □, solve, check).
   • Provide a “fill-in-the-blank” equation scaffold: “___ + ___ = ___” or “___ − ___ = ___” with □ box to place the unknown.
   • Offer bar model templates with one part already labeled; students place remaining labels.
   • Chunk tasks with a checklist and teacher stop-points: “Complete steps 1–3, then show me.”
   • Allow and encourage base-ten blocks/counters to represent tens and ones, especially for unknown addend and subtraction across tens.
   • Partner with a supportive peer; use structured roles: Reader (reads problem), Mapper (places numbers in model), Solver (computes), Checker (does inverse). Rotate roles.
   • Use simpler numbers (within 50) for parallel problems if within-100 computation is a barrier; then bridge back to the class numbers.
   • Provide visual keyword cards, but emphasize meaning over memorizing: “in all/altogether,” “left,” “more/fewer than.”
   • Teacher-led small group during independent practice to model one additional example with immediate feedback.
   • Modified expectation for explanation: one sentence using frame + correct equation/model is acceptable.

   IEP / 504 Accommodations

   • Preferential seating with reduced distractions and clear view of anchor chart.
   • Extended time on independent practice and/or reduced number of required problems without reducing rigor of representation steps.
   • Read-aloud of word problems (teacher or text-to-speech) and permission to have problems repeated; clarify without leading to operation choice.
   • Provide graphic organizer/structured recording sheet with large writing spaces; allow use of lined or graph paper as needed.
   • Allow alternative response modes: oral explanation, pointing to model, or using manipulatives to demonstrate reasoning.
   • Frequent checks for understanding and immediate corrective feedback; use “show me where the unknown is” before computation.
   • Use of calculation supports only if documented (e.g., number line, hundred chart, base-ten blocks); avoid replacing thinking with answer-getting.
   • Breaks as needed; timer cues for transitions.
   • For fine-motor needs: allow marker/whiteboard, scribing for equation labels, or use of stamps for □ and operation symbols.

   Advanced Learners

   • Create: Write your own word problem for each situation type with an unknown in a different position; swap with a partner to solve and critique for clarity.
   • Solve a two-step problem (within 100) that combines put together then compare (e.g., total two categories, then compare to a third).
   • Represent one problem in two different ways (bar model and number line) and write two related equations (e.g., 35 + □ = 58 and 58 − 35 = □).
   • Add a data/graph connection (CCSS.MATH.CONTENT.2.MD.D.10): Provide a small bar graph with up to four categories (e.g., favorite fruits) and ask students to write and solve one compare and one put-together question using the graph.
   • Explain: Write a short ‘Math Detective Report’ that justifies operation choice and critiques a common mistake (e.g., choosing addition because of the word ‘more’).
   • Fluency challenge: Solve using two different place-value strategies (compensation vs. tens/ones decomposition) and compare efficiency.

   形成性检查

   • Warm-up operation signals + partner justifications (listen for correct situation-type reasoning).
   • CFU during mini-lesson (whole vs. parts; identifying unknown position).
   • Guided practice partner work: teacher observation of model-to-equation alignment and use of check.
   • Independent practice monitoring checklist; quick conferences with 2 targeted questions: “What type is it?” “What does □ mean here?”

   退出票

   Jayden has 58 trading cards. Maya has 35 trading cards. Jayden has □ more trading cards than Maya. How many more cards does Jayden have? (operation & why; equation with □; answer with label; check).

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 This lesson includes key vocabulary terms related to word problem types, so a vocabulary practice template supports student understanding of these terms.
   • Worksheet 匹配活动 A matching activity aligns well with the warm-up sorting of story situations and operation choices, reinforcing conceptual understanding.
   • Worksheet T-图 A T-Chart organizer helps students categorize and compare the different types of word problems (Add To, Take From, etc.) as modeled in the lesson.
   • Worksheet 3-2-1 退出票 The lesson includes an exit ticket activity, so a 3-2-1 Exit Ticket template provides a structured formative assessment for closure.

   Storypie 内容

   • Storypie Content Addition Addition is a fundamental mathematical operation that represents the total amount of objects together in a collection. It is signified by the plus sign (+).
   • Storypie Content Subtraction Subtraction is one of the four basic arithmetic operations; it is the process of removing a quantity from another to find the difference.
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory
   • Storypie Content Division Division is a fundamental arithmetic operation that is the inverse of multiplication. It is the process of splitting a number into equal parts or groups.
   • Storypie Content Fractions Fractions represent parts of a whole or, more generally, any number of equal parts. They are a fundamental concept in mathematics used to express division, ratios, and numbers that are not whole.
   • Storypie Content Calculator Watch A device that performs arithmetic operations. Calculators have evolved from ancient counting tools and mechanical devices to modern, pocket-sized electronic instruments.

   准备清单

   • Print/copy student recording sheets with routine checklist (type, model, equation with □, solve, check).
   • Prepare anchor chart with the four situation types, clue phrases, and a small example equation for each.
   • Create/queue slides or cards: 3 warm-up snippets; 1 mini-lesson problem; 2 guided practice problems; 4 independent problems; 1 exit ticket.
   • Prepare bar model template sheets (optional) for scaffolding and small group support.
   • Set out base-ten blocks/tens-ones sticks in an accessible bin; confirm enough for students who need them.
   • Decide partner pairs ahead of time (supportive pairings; consider language proficiency and behavior).
   • Plan where to stand/circulate during independent practice; set timer intervals (e.g., 7 minutes checkpoint).
   • Prepare a small-group reteach space with mini-whiteboard and manipulatives.
   • Verify consistent unknown symbol use (□) across all materials.

   常见误解

   • The word “more” always means addition (ignoring compare contexts).
   • The unknown is always at the end of the equation.
   • In compare problems, students subtract in the wrong order (smaller − larger) without noticing it yields a negative/unreasonable result.
   • Students treat ‘in all’ as subtract because they see two numbers and assume one is taken away.
   • Students compute correctly but don’t connect the answer back to the question (missing label/unit or answering the wrong quantity).
5. 5 Adding Within 100 With Regrouping (Compose a Ten) Using Models and Written Methods 完整课程 Adding Within 100 With Regrouping (Compose a Ten) Using Models and Written Methods

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group for warm-up and direct instruction; partners (pairs) for guided practice; independent for practice and exit ticket.

   学习目标

   • I can add two two-digit numbers within 100 by composing a ten (regrouping) using base-ten models or drawings. Apply

     成功标准:

     • I represent each addend with tens and ones (or a clear drawing).
     • I show when 10 ones are composed into 1 ten.
     • My final sum matches my model/drawing and is within 100.

   • I can explain, using place-value words, why we regroup when the ones place totals 10 or more. Understand

     成功标准:

     • I use the words ones, tens, compose, and regroup correctly.
     • I can state: “10 ones = 1 ten,” and connect it to my work.
     • I can point to where the new ten appears in my model and in my written work.

   • I can solve an addition word problem within 100 that requires regrouping and write an equation that matches my strategy. Apply

     成功标准:

     • I identify the two quantities being added and what the question asks.
     • I write an equation with the correct addends and sum (or a symbol for the unknown).
     • I use a model/drawing or written method that shows composing a ten, and my answer makes sense.

   标准

   • CCSS.MATH.CONTENT.2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
   • CCSS.MATH.CONTENT.2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

   材料

   • Base-ten blocks (tens rods and ones cubes) OR linking cubes bundled in tens · 1 set per pair + 1 teacher setEnsure at least 10–20 ones per pair and 10 tens rods available for regrouping.
   • Place value mats labeled Tens and Ones · 1 per studentOptional laminated mats with dry-erase markers for reuse.
   • Student recording sheet or math journal page with Tens/Ones drawing boxes · 1 per studentInclude space for: model/drawing, equation, and 1–2 sentence explanation.
   • Document camera/interactive whiteboard · 1For live modeling of blocks and written method side-by-side.
   • Pencils and crayons/markers · 1 per studentDifferent colors helpful: tens in one color, ones in another.
   • Hundreds chart (optional) · 1 class set or displayUse to check if answers are reasonable (estimate by tens).
   • Exit ticket slips · 1 per studentInclude: 48+36 and an explanation prompt about the regrouped 1.

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Facilitate a quick Number Talk focused on making a ten; record student strategies; explicitly connect “make a ten” (within 20) to “compose a ten” (within 100).

   学生操作: Mentally solve each expression; share strategies using sentence frames; listen and compare methods.

   教师脚本（完整）

   “Today we’re going to use what you already know about making a ten to help us add bigger numbers. Let’s warm up our brains. Look at 8 + 7. Don’t call out—think. Put your thumb up when you have an answer. Who can share an answer and a strategy? When you share, start with: ‘I broke apart ___ because ___.’ (After a student shares making 10) “I heard you say you made a ten. That is the same idea we will use today, but with tens and ones.” Now 9 + 6… (pause) …and 15 + 8… (pause) “Turn and tell your partner: What does it mean to make a ten?” (pause) “Let’s say it together: 10 ones equals 1 ten.”

   Direct Instruction10 min

   教师行动: State the learning target and success criteria; model 38+27 using base-ten blocks or a drawn model; explicitly demonstrate composing a ten; connect the model to the written method (ones first, regroup/carry 1 ten).

   学生操作: Track the model with eyes and finger; answer quick CFU questions; repeat key language; help label tens and ones; copy a quick sketch into journals if directed.

   教师脚本（完整）

   “Learning target: I can add two two-digit numbers within 100 by composing a ten using models and written methods. Watch my hands and listen for tens and ones language. I’m building 38. I need 3 tens and 8 ones. (Place 3 tens rods and 8 ones.) I’m building 27. I need 2 tens and 7 ones. (Place 2 tens rods and 7 ones.) Now I combine the ones first because ones are the smallest place. Let’s count: 8 ones and 7 ones makes 15 ones. Do I have enough ones to make a new ten? Yes—because 15 is 10 and 5 more. Watch: I trade 10 ones for 1 ten, because 10 ones = 1 ten. This is called regrouping or composing a ten. (Physically trade 10 ones for a tens rod.) Now I have 5 ones left, and I have a new ten. Now I add the tens: 3 tens + 2 tens + 1 new ten = 6 tens. So I have 6 tens and 5 ones. That number is 65. Now I connect it to written work.” (Write vertically) 38 + 27 ---- “I add the ones: 8 + 7 = 15. I write 5 in the ones place, and I regroup 1 ten to the tens place. This ‘1’ is not 1 one—it means 1 ten. Then I add tens: 3 tens + 2 tens + 1 ten = 6 tens. The sum is 65. Say it with me: ‘The regrouped 1 means 1 ten.’”

   理解检查: Quick CFU prompts (choral response + cold call): 1) “In 15 ones, how many tens can we compose?” (Students: “1 ten.”) 2) “How many ones are left?” (Students: “5 ones.”) 3) “What does the small 1 above the tens place mean?” (Students: “1 ten.”)

   Guided Practice15 min

   教师行动: Lead a consistent routine for each problem (model/draw → compose a ten if needed → connect to written method). Circulate to prompt with questions; select 1–2 students to share and compare strategies; correct misconceptions in the moment.

   学生操作: Work with a partner to build/draw each addend; combine ones, trade 10 ones for 1 ten when applicable; record equation and written method; explain thinking using place-value words.

   教师脚本（完整）

   “Now it’s your turn, but we’ll do it together. Problem 1: 46 + 38. Step 1: Build or draw 46 and 38 in tens and ones. Step 2: Combine the ones. Step 3: If you have 10 or more ones, compose a ten. Step 4: Combine tens. Step 5: Write the sum as a number and check it matches your model. Partner A, point to the ones for 46. Partner B, point to the ones for 38. Now combine them. (After 1–2 minutes) “Hold up your mat/journal so I can see your tens and ones.” “Who can tell us: How many ones did you get first? Do you need to compose a ten? How do you know?” “Now connect to the written method: Where does your new ten show up when you write the problem?” (Repeat routine with 59 + 24 and 27 + 36) “As you work, keep saying the place-value sentence: ‘I had ___ ones. I composed ___ ten(s). I have ___ tens and ___ ones.’”

   支架提示: “Show me only the ones. How many ones do you have altogether?” | “Circle or box a group of 10 ones in your drawing. What can you trade it for?” | “Say the trade out loud: ‘10 ones equals 1 ten.’ Now do the trade.” | “Where will your new ten go—ones place or tens place? Why?” | “Point to the regrouped 1 in your written method. What does it stand for?” | “Read your answer as tens and ones: ‘___ tens and ___ ones.’ What number is that?” | “Does your answer make sense? Estimate by tens: 46 is about 50 and 38 is about 40, so the sum should be about 90. Is yours close?”

   Independent Practice15 min

   教师行动: Assign practice set with clear expectations for showing work; circulate using a monitoring checklist; pull a quick small group (2–4 students) if multiple students struggle with composing a ten; provide immediate feedback using prompts instead of telling answers.

   学生操作: Solve problems independently; show a model/drawing and/or written method; write at least one sentence explaining regrouping for one chosen problem; complete the word problem with an equation and answer statement.

   教师脚本（完整）

   “Now you will practice on your own so I can see what you can do. You must show your thinking in one of these ways: Option A: tens/ones drawing + equation. Option B: written method + one sentence that explains the regrouping. Complete these: 28+47, 35+29, 64+18, 57+36, 49+27. Word problem: ‘Mia has 38 stickers. Her friend gives her 27 more. How many stickers does Mia have now?’ If you get stuck, do not erase everything. Put a star by the spot you got confused and try a model. I may ask you, ‘Where are the ones? Where are the tens?’ Work quietly. If you finish early, choose one problem and write a clear explanation using the words ones, tens, compose, regroup.”

   监控清单: Student correctly represents each addend as tens and ones (model or drawing). | Student combines ones first and determines whether total ones is 10 or more. | Student correctly composes a ten (trades 10 ones for 1 ten) when needed. | Student places the regrouped ten in the tens place (written method aligns with model). | Student final sum is accurate and reasonable (estimate by tens). | Student can verbally explain what the regrouped 1 means using place-value vocabulary.

   Closure5 min

   教师行动: Administer exit ticket; prompt for place-value explanation; collect and sort quickly into 0/1/2 piles for next-day grouping; reinforce key takeaway.

   学生操作: Complete exit ticket problem and explanation; turn in work silently; share one reflection statement if called on.

   教师脚本（完整）

   “Before you go, show me your best work and your best words. Exit Ticket: 1) Solve 48 + 36. Show a model or a clear written method. 2) Answer: ‘What does the regrouped 1 mean?’ Use the words tens and ones. Remember: I’m looking for how you know, not just the answer. When you are done, put your pencil down, reread your explanation, and turn it in.”

   退出票: 1) Solve 48 + 36. Show your work with a tens/ones model or a written method that shows regrouping. 2) Explain: What does the regrouped “1” mean? Use the words tens and ones.

   ones

   Ones are single cubes—just one at a time.

   tens

   A ten is a bundle of 10 ones.

   compose a ten

   When you have 10 ones, you can make them into 1 ten.

   regroup

   Regroup means trade to keep the digits in the right places.

   sum

   The answer to an addition problem.

   English Language Learners

   • I can say and write a sentence explaining regrouping using the words ones, tens, compose, regroup, sum.
   • I can use a sentence frame to explain: ‘I had ___ ones. I composed ___ ten(s). Now I have ___ tens and ___ ones.’
   • Pre-teach vocabulary with visuals: show a single cube (one) and a ten rod (ten) and label them on a mini-anchor chart.
   • Provide sentence frames on the desk/recording sheet: ‘___ ones + ___ ones = ___ ones. I regroup ___ ones into ___ ten.’
   • Use gestures consistently: point to ones column, then tens column; make a “bundle” motion when composing a ten.
   • Allow home-language partner talk for 30 seconds before sharing in English; then share using the sentence frame.
   • Use color-coding: ones in one color, tens in another; regrouped ten circled in the model and highlighted in the written method.
   • Check for understanding with yes/no and either/or questions before open-ended questions (e.g., ‘Do we have enough ones to make a ten: yes or no?’).

   Struggling Learners

   • Use concrete-only first: require base-ten blocks (not just drawings) for the first 2 independent problems; transition to drawings after accuracy is shown.
   • Provide a simplified, chunked checklist card: (1) Build tens/ones (2) Add ones (3) Trade 10 ones for 1 ten (4) Add tens (5) Write number.
   • Reduce problem set: complete 3 problems + the word problem (teacher-selected) with high accuracy rather than all items.
   • Use a place-value mat with built-in “trade box”: a square labeled ‘Trade 10 ones here’ to physically move 10 ones before exchanging.
   • Offer guided partner roles: Partner A builds first addend; Partner B builds second; both count ones together; switch roles next problem.
   • Use number choices to support accuracy: provide a small bank of possible sums for 2 problems (multiple choice) to reduce cognitive load and focus on regrouping concept.
   • Frequent teacher check-ins every 2–3 minutes using one prompt: ‘Show me your group of 10 ones.’

   IEP / 504 Accommodations

   • Preferential seating near instruction/modeling area; minimize visual distractions.
   • Provide extended time for independent practice and exit ticket as needed (finish exit ticket at start of next block if required).
   • Allow alternative response modes: student may explain regrouping orally to teacher instead of writing full sentences; teacher scribes key words if accommodation allows.
   • Provide enlarged print recording sheets with clearly separated tens/ones columns and extra spacing for writing numbers.
   • Use tactile/kinesthetic supports (base-ten blocks, Velcro tens/ones mat, or magnetic blocks) to reduce fine-motor load.
   • Chunk directions one at a time; teacher checks off steps with the student.
   • If attention support is needed: use a visual timer and a “finish 2 problems, then check-in” goal.

   Advanced Learners

   • Add up to three or four two-digit numbers (aligns with CCSS.MATH.CONTENT.2.NBT.B.6), requiring multiple regroupings, e.g., 24+38+17 or 16+27+35+19; require a written explanation of each regroup.
   • Create-your-own word problem that results in regrouping; trade with a partner to solve and verify with a model.
   • Error analysis: provide an incorrect worked example (e.g., carried 1 as a one) and ask students to find and fix the error, then write what the ‘1’ should represent.
   • Introduce compensation/mental strategy: (38+27) as (40+25)=65; students must connect the strategy back to place value and explain why it works.
   • Challenge: Find two different addends that make a sum of 84 and require regrouping; show at least two solutions with models.

   形成性检查

   • Number Talk strategy sharing: listen for place-value language and making-a-ten reasoning.
   • During direct instruction CFU: choral response to ‘What does the regrouped 1 mean?’
   • Guided practice observation: teacher uses prompts to verify students can compose a ten and connect model to written method.
   • Independent practice check: spot-check 2 problems per student for correct regrouping and alignment of model/written work.
   • Turn-and-talk explanations using sentence frames: teacher notes who can articulate ‘10 ones = 1 ten.’

   退出票

   1) Solve 48 + 36. Show regrouping. 2) Explain what the regrouped ‘1’ means using tens and ones.

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 The lesson includes specific vocabulary terms related to place value and regrouping, so vocabulary practice will reinforce these key concepts for second graders.
   • Worksheet 填空 Fill in the blank practice supports students in applying the addition concepts and written methods explicitly taught in the lesson.
   • Worksheet 故事地图 A story map organizer can help students visually sequence the steps involved in composing a ten and regrouping during addition, aligning with the modeling and journal drawing activities.
   • Worksheet 3-2-1 退出票 The lesson includes an exit ticket activity with a problem and explanation prompt, so a 3-2-1 exit ticket template is appropriate for formative assessment and closure.

   Storypie 内容

   • Storypie Content Addition Addition is a fundamental mathematical operation that represents the total amount of objects together in a collection. It is signified by the plus sign (+).
   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory
   • Storypie Content Division Division is a fundamental arithmetic operation that is the inverse of multiplication. It is the process of splitting a number into equal parts or groups.
   • Storypie Content Fractions Fractions represent parts of a whole or, more generally, any number of equal parts. They are a fundamental concept in mathematics used to express division, ratios, and numbers that are not whole.
   • Storypie Content Calculator Watch A device that performs arithmetic operations. Calculators have evolved from ancient counting tools and mechanical devices to modern, pocket-sized electronic instruments.

   准备清单

   • Prepare base-ten toolkits for each pair (count out enough ones to trade at least once).
   • Print/place value mats and recording sheets; ensure pencils/markers available.
   • Prepare exit ticket slips and a sorting system (three bins labeled 0, 1, 2).
   • Set up document camera/board with the model problem (38+27) and space to display blocks and written method side-by-side.
   • Post or have ready a mini-anchor chart: ‘10 ones = 1 ten’ and ‘Regrouped 1 means 1 ten.’
   • Pre-assign partner groups (consider language support and math readiness).

   常见误解

   • “The 1 I carry is 1 one.” (It represents 1 ten.)
   • Regrouping means ‘add an extra 1’ rather than trading 10 ones for 1 ten.
   • Students may add tens and ones all at once without place-value organization, leading to errors.
   • Students may write 15 in the ones place instead of writing 5 ones and regrouping 1 ten.
   • Students may forget to add the regrouped ten to the tens column.
6. 6 Subtracting Within 100 With Regrouping (Decompose a Ten) Using Models and Written Methods 完整课程 Subtracting Within 100 With Regrouping (Decompose a Ten) Using Models and Written Methods

   概述 时间与活动 词汇 差异化 评估 资源 教师笔记

   🌏 Massachusetts, USA Whole group mini-lesson; partners for turn-and-talk; independent work with teacher conferring; optional small group reteach table

   学习目标

   • I can subtract within 100 when I need to decompose one ten into ten ones (regroup) using a place-value model. Apply

     成功标准:

     • I represent both numbers with tens and ones using a drawing (quick tens/ones sketch) or base-ten blocks.
     • I show decomposing 1 ten into 10 ones when there are not enough ones to subtract.
     • I correctly find the difference and explain each step using tens and ones language.

   • I can solve a one- or two-step subtraction word problem within 100 that may require regrouping, and I can write an equation with a symbol for the unknown to match the story. Apply

     成功标准:

     • I identify the quantities and what the problem is asking.
     • I write an equation with a symbol for the unknown (e.g., 52 − 28 = □).
     • I solve accurately using a model and/or a written method and check my answer using addition.

   • I can explain why decomposing a ten works and connect my model to a written subtraction method. Analyze

     成功标准:

     • I use place-value language (tens, ones, decompose) to explain regrouping.
     • I match parts of my model (tens/ones) to the written method steps.
     • I justify my answer by checking with addition or by estimating whether it makes sense.

   标准

   • CCSS.MATH.CONTENT.2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
   • CCSS.MATH.CONTENT.2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

   材料

   • Base-ten blocks (tens rods and ones cubes) or place-value disks · 1 set per pair + 1 teacher setPre-bag sets for quick distribution; include extra ones cubes for regrouping.
   • Tens-and-ones mat (printed or drawn on whiteboards) · 1 per studentTwo columns labeled Tens / Ones; optional trade arrow box.
   • Student whiteboards, markers, and erasers (or math notebooks/pencils) · 1 per studentWhiteboards preferred for quick checks and corrections.
   • Document camera or chart paper/markers · 1Use to model tens/ones drawings and connect to the written method.
   • Prepared practice sheet with mixed regrouping/non-regrouping subtraction within 100 · 1 per studentInclude starred items requiring BOTH model + written method; include 1 regrouping word problem.
   • Exit ticket slip · 1 per studentSingle problem: 62 − 47 with space for sketch and equation.
   • Optional: hundreds chart or open number line strips · Class set or small-group setFor students who benefit from additional visual support/checking.

   • Warm-up 5 min
   • Direct Instruction 10 min
   • Guided Practice 15 min
   • Independent Practice 15 min
   • Closure 5 min

   Warm-up5 min

   教师行动: Lead quick oral counting, display quick subtraction facts, and facilitate a notice/wonder to prime regrouping. Listen for students anticipating the need to trade a ten.

   学生操作: Count aloud, solve quick facts on boards, and talk with a partner about what could be tricky in 52 − 28.

   教师脚本（完整）

   Count with me by tens: 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Now by ones from 90: 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100. On your board, solve these quickly: 64 minus 20… show me. Now 64 minus 4… show me. Now 78 minus 8… show me. Now 55 minus 5… show me. Look at this: 52 minus 28. Don’t solve yet. Notice and wonder. What do you notice? What do you wonder? Turn and tell your partner: What might be tricky about this one? Today we’ll subtract numbers like 52 minus 28. Sometimes we don’t have enough ones to subtract, so we will decompose a ten into ten ones and show it with a model and a written method.

   Direct Instruction10 min

   教师行动: Model regrouping with a tens/ones drawing or blocks. Use explicit place-value language. Connect the model to a written vertical method. Then run a second example with choral responses and quick checks.

   学生操作: Watch, respond to questions, chorally repeat key language, and track how the model matches the written method.

   教师脚本（完整）

   Watch my hands and my math words. I’m going to solve 52 minus 28. First, I build 52. I have 5 tens and 2 ones. (I draw 5 tens and 2 ones / or place blocks on the tens/ones mat.) Now I need to subtract 28. That means take away 2 tens and 8 ones. Key question: Do I have enough ones to take away 8 ones? I only have 2 ones. I do NOT have enough ones. Here is what I do: I decompose one ten into ten ones. I am trading 1 ten for 10 ones. My total is still 52, just regrouped. Now I have 4 tens and 12 ones. Now I can subtract: 12 ones minus 8 ones leaves 4 ones. And 4 tens minus 2 tens leaves 2 tens. So the difference is 24. Now I connect it to a written method. Watch how my drawing matches my numbers. I write 52 on top and 28 underneath. I look at the ones: 2 ones can’t take away 8 ones, so I decompose a ten. In my written work, the tens digit goes down by 1: 5 tens becomes 4 tens. And the ones become 12 ones. Now 12 minus 8 equals 4, and 4 tens minus 2 tens equals 2 tens. Answer: 24. The model and the written method are telling the same place-value story. Let’s try one together out loud: 63 minus 27. Do we have enough ones to subtract? (Students respond.) If we don’t have enough ones, what do we do? Say it with me: Decompose one ten into ten ones.

   理解检查: Ask: “In 52 − 28, why did 52 become 4 tens and 12 ones?” and “Where do you see the trade in the written method?” Use thumb-check: thumbs up = I can explain the trade; sideways = I need another example.

   Guided Practice15 min

   教师行动: Lead students through 3 problems with decreasing support. Require a model first, then connect to written method. Circulate to correct regrouping errors in the moment. Use cold call for reasoning and place-value explanations.

   学生操作: Build/draw tens and ones, decide whether to decompose, subtract ones then tens, and write the matching written subtraction. Explain thinking to partner and whole group when called.

   教师脚本（完整）

   We are solving together. You will show tens and ones first, then write the matching subtraction. Problem 1: 41 minus 26. Step 1: Show me 41 as tens and ones. (Pause. Scan.) Step 2: Are there enough ones to take away 6 ones? If not, what will you do? Say it with me: Decompose one ten into ten ones. Now solve the ones. Now solve the tens. Write the answer. Turn and tell your partner: What changed when you decomposed? Problem 2: 70 minus 38. Show 70. What do you notice about the ones? (Pause.) Are there enough ones to take away 8 ones? What must we do? Do the trade, then subtract ones, then tens. Problem 3: 86 minus 59. Build 86. Check the ones. Decide if you need to decompose. Now solve and write the matching written method. Listen carefully: When we regroup, we are not changing the total. We are trading 1 ten for 10 ones so we can subtract in the ones place.

   支架提示: Tell me how many tens and how many ones you start with. | Point to the ones. Do you have enough ones to subtract? How do you know? | If not, what can you trade? Say the full sentence: “I will decompose 1 ten into 10 ones.” | After the trade, say what you have now: “Now I have ___ tens and ___ ones.” | Show me where the tens decreased by 1 in your written method. | Show me where the ones became 10 more in your written method. | Does your answer make sense? About how much is the difference (estimate)? | Check: difference + subtrahend should equal the minuend. What addition equation matches?

   Independent Practice15 min

   教师行动: Assign mixed practice; monitor for correct regrouping and alignment between model and written method. Confer with a focus group (students who struggled in guided practice). Prompt students to check at least one answer with addition.

   学生操作: Solve problems independently using place-value strategies; show required models/written methods for starred items; complete one addition check and correct any errors.

   教师脚本（完整）

   Now it’s your turn. You will solve the problems on your practice sheet. Use a strategy that shows place value. For the starred problems, you must show BOTH: a tens/ones model and the written subtraction method. When you finish, choose one problem and check it using addition: difference plus the number you subtracted should equal the number you started with. If you get stuck, do this: build the number in tens and ones, then ask, ‘Do I have enough ones?’ If not, decompose one ten into ten ones. I will be walking around. Be ready to explain your trade using tens and ones language.

   监控清单: Student represents the minuend accurately in tens and ones (correct count). | Student checks the ones place before subtracting. | If ones are insufficient, student decomposes exactly 1 ten into 10 ones (tens decrease by 1; ones increase by 10). | Student subtracts ones first, then tens (or correctly uses written method steps). | Student’s model, written method, and final answer match. | Student avoids “larger minus smaller digit” error in ones place (regrouping when needed). | Student completes at least one addition check accurately (difference + subtrahend = minuend).

   Closure5 min

   教师行动: Administer exit ticket, select 1–2 students to share the regrouping step, and restate the key idea that decomposing keeps the value the same. Collect exit tickets and sort quickly for next-day grouping.

   学生操作: Complete the exit ticket independently, then listen and/or share explanation using place-value language.

   教师脚本（完整）

   Time for an exit ticket. Work silently and do your best. Solve: 62 minus 47. Show regrouping with a quick tens/ones sketch OR clear words, then write the subtraction and the answer. When you finish, put your pencil down and look at me. Let’s hear one explanation: What did you do when you saw the ones place? Use these words: tens, ones, decompose. Today you learned that if you don’t have enough ones to subtract, you can decompose one ten into ten ones. This keeps the value the same, but it makes the subtraction possible. Tomorrow we’ll keep practicing and become faster and more fluent.

   退出票: 62 − 47: Show regrouping with a quick tens/ones sketch OR words, then write the subtraction and the answer. (Optional: check with addition.)

   subtract

   Subtract means we take some away and see how many are left.

   difference

   The difference is what you get after you subtract.

   regroup

   Regroup means we trade to get more ones to subtract.

   decompose

   Decompose means break apart. One ten can be broken into ten ones.

   place value

   Place value tells what a digit is worth because of where it is.

   English Language Learners

   • I can use sentence frames to explain regrouping: “I decomposed 1 ten into 10 ones, so ___ tens became ___ tens and ___ ones became ___ ones.”
   • I can ask and answer the key question: “Do I have enough ones to subtract ___ ones?”
   • I can label my drawing with the words tens and ones.
   • Pre-teach vocabulary with visuals: tens rod = “ten,” ones cube = “one,” and a trade arrow icon for “decompose/regroup.”
   • Sentence frames posted and practiced chorally: “I start with __ tens and __ ones.” “I need to subtract __ ones.” “I decompose one ten into ten ones.” “Now I have __ tens and __ ones.”
   • Partner talk with assigned roles (Speaker/Listener) and a checklist to ensure both students say the regrouping sentence.
   • Use gestures: show ten fingers for “ten ones,” physically crossing out one tens rod and replacing with ten ones cubes.
   • Provide a bilingual glossary or picture glossary (if available) for subtract/difference/tens/ones.

   Struggling Learners

   • Concrete-first expectation: require base-ten blocks before any written method for the first 3–4 problems.
   • Chunked task card taped to desk: (1) Build number (2) Circle ones (3) If needed, trade (4) Subtract ones (5) Subtract tens (6) Check with addition.
   • Simplified practice set: fewer problems (e.g., 4 instead of 8) with more space for drawings; teacher selects problems with smaller subtrahends first (e.g., 52 − 28 before 86 − 59).
   • Color-coding: tens in one color, ones in another; in written method, highlight the tens digit that decreases and the ones that become 12/13/etc.
   • Peer support: strategic pairing with a patient, accurate partner; partner reads the steps aloud while student performs them with blocks.
   • Frequent micro-checks: after the trade step, student must say aloud: “Now I have __ tens and __ ones,” before proceeding.

   IEP / 504 Accommodations

   • Preferential seating near modeling area; reduce visual distractions during the direct instruction and exit ticket.
   • Extended time on independent practice and exit ticket as needed; allow completion of fewer items to demonstrate mastery.
   • Provide printed tens/ones mats and enlarged exit ticket with ample workspace.
   • Allow alternative response mode: manipulate blocks and verbally explain to teacher instead of extensive writing (document with teacher anecdotal notes).
   • Provide step-by-step checklist and allow student to physically check off each step.
   • For fine-motor needs: allow marker/whiteboard, stamp blocks, or pre-drawn ten sticks/ones dots to circle rather than drawing from scratch.

   Advanced Learners

   • Strategy comparison: solve one problem two ways (model + written method OR open number line) and write one sentence: “Both ways work because…”
   • Create-and-solve: write a regrouping subtraction story problem within 100, then trade papers with a partner to solve and check.
   • Efficiency challenge: find two different regrouping problems that have the same difference; explain how you know without fully solving both (reasoning about place value).
   • Bridge to within 1,000: optional extension with three-digit subtraction that decomposes a ten (e.g., 162 − 47 using hundreds/tens/ones model) for students ready for CCSS.MATH.CONTENT.2.NBT.B.7 connections.

   形成性检查

   • Warm-up whiteboard responses to no-regrouping subtraction facts (accuracy and speed check).
   • Notice/Wonder partner talk: teacher listens for recognition of “not enough ones” and trade language.
   • Direct instruction CFU questions: “Why do we decompose?” and “Where do you see it in the written method?”
   • Guided practice hold-up of tens/ones sketches to spot regrouping misconceptions in real time.
   • Independent practice teacher conference notes using the monitoring checklist.

   退出票

   62 − 47: Show regrouping with a quick tens/ones sketch OR words, then write the subtraction and the answer.

   与本课相关的资源。免费注册以下载工作表，或在新标签页中打开 Storypie 内容。

   工作表与活动

   • Worksheet 词汇练习 The lesson includes specific vocabulary terms related to subtraction and regrouping, so vocabulary practice will help reinforce these key concepts for second graders.
   • Worksheet 填空 A fill-in-the-blank practice sheet aligns well with the lesson's prepared practice sheet for mixed regrouping and non-regrouping subtraction problems within 100.
   • Worksheet T-图 A T-Chart organizer can help students visually compare subtraction problems with and without regrouping, supporting their understanding of the concept.
   • Worksheet 3-2-1 退出票 The lesson includes an exit ticket activity, so a 3-2-1 Exit Ticket template will provide a structured formative assessment to check student understanding at the end.

   Storypie 内容

   • Storypie Content Subtraction Subtraction is one of the four basic arithmetic operations; it is the process of removing a quantity from another to find the difference.
   • Storypie Content Place value Place value is the fundamental mathematical concept that the value of a digit is determined by its position within a number. This principle is the basis of modern numeral systems, such as the decimal
   • Storypie Content Leonardo da Vinci Leonardo da Vinci was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect.
   • Storypie Content Isaac Newton Sir Isaac Newton was an English mathematician, physicist, astronomer, and author who is widely recognized as one of the most influential scientists of all time. He formulated the laws of motion and un
   • Storypie Content Galileo Galilei Galileo Galilei was an Italian astronomer, physicist, and engineer whose pioneering use of the telescope led to revolutionary discoveries about the cosmos and provided crucial evidence for the theory
   • Storypie Content Division Division is a fundamental arithmetic operation that is the inverse of multiplication. It is the process of splitting a number into equal parts or groups.
   • Storypie Content Fractions Fractions represent parts of a whole or, more generally, any number of equal parts. They are a fundamental concept in mathematics used to express division, ratios, and numbers that are not whole.
   • Storypie Content Calculator Watch A device that performs arithmetic operations. Calculators have evolved from ancient counting tools and mechanical devices to modern, pocket-sized electronic instruments.

   准备清单

   • Copy practice sheets and exit tickets; label starred items requiring model + written method.
   • Prepare base-ten block bags (include extra ones for trades).
   • Set up document camera/chart paper with a pre-drawn tens/ones mat for modeling.
   • Write board plan: learning targets, vocabulary, steps for regrouping, guided practice problems.
   • Prepare sentence frames poster for regrouping explanation.
   • Plan small-group roster based on prior lesson data (who needs concrete support).

   常见误解

   • Thinking decomposing changes the value of the number (believing 52 becomes a different amount).
   • Forgetting to reduce the tens by 1 after decomposing (keeping 5 tens and also adding 10 ones).
   • Regrouping even when it isn’t needed (unnecessary trades that lead to confusion).
   • Subtracting tens first in a way that ignores the need to regroup ones (leading to incorrect written work).
7. + 还有 4 课在这个单元中 免费注册以查看完整的课程计划、活动和材料。

基本问题

• Why does choosing the right unit and tool matter when measuring?
• How can number lines help us represent and compare lengths?

标准

1. 10 课在这个单元中 免费注册以查看完整的课程计划、活动和材料。

基本问题

• How do we use time and money to solve real-life problems?
• How do graphs help us answer questions about data?

标准

1. 10 课在这个单元中 免费注册以查看完整的课程计划、活动和材料。

基本问题

• How can we describe and classify shapes based on their attributes?
• What does it mean to partition a shape into equal shares?

标准

1. 10 课在这个单元中 免费注册以查看完整的课程计划、活动和材料。

基本问题

• How do equal groups and arrays help us organize and count objects efficiently?
• How can we tell if a number is even or odd and why does it matter?

标准

1. 10 课在这个单元中 免费注册以查看完整的课程计划、活动和材料。

基本问题

• How can we represent and solve multi-step problems in more than one way?
• How do models and equations help us communicate our thinking?

标准

1. 10 课在这个单元中 免费注册以查看完整的课程计划、活动和材料。

基本问题

• How can mental strategies make computation more efficient?
• How do we explain why an answer makes sense?

标准

1. 10 课在这个单元中 免费注册以查看完整的课程计划、活动和材料。

基本问题

• Which skills do we need to revisit to become more accurate and confident?
• How can we use math to design, test, and explain a solution to a real problem?

标准

1. 10 课在这个单元中 免费注册以查看完整的课程计划、活动和材料。