Regrouping Addition

Overview

In this lesson, students use partitioning and place value to add two- and three-digit numbers without a calculator. They also practise addition facts and number bonds, noticing how regrouping supports efficient thinking.

Learning intentions

• WALT add two- and three-digit numbers using place value partitioning and regrouping.
• WALT use addition and related subtraction connections to check answers.
• WALT use known addition facts and number bonds (to support efficient mental strategies).

Success criteria

• I can split numbers into hundreds, tens and ones (or tens and ones) to help me add.
• I can regroup ones or tens when the total reaches 10 or 100 and explain why.
• I can use number bonds to 10 (and 100 where appropriate) to solve.
• I can check my solution using the inverse relationship between addition and subtraction.

Curriculum links

• Number — VC2M3N04: adding and subtracting two- and three-digit numbers using place value to partition, rearrange and regroup to assist calculations without a calculator.
• Algebra — VC2M3A01: connection between addition and subtraction as inverse operations; apply to partition numbers and find unknown values in number sentences.
• Algebra — VC2M3A02: extend addition and subtraction facts to 20 to develop efficient mental strategies with larger numbers.

Lesson structure (60 minutes)

1. 0–5 min · Start with facts. Teacher writes: “Find the missing number: 9 + __ = 15” and “14 + __ = 20”, then asks students to share their number bonds to 10. Students answer using mental strategies and explain (briefly) which bonds they used.

2. 5–15 min · Model regrouping with partitioning. Teacher models on a place-value chart: 47 + 36 by partitioning (40 + 7) + (30 + 6), then combining ones (7 + 6 = 13) to regroup (13 = 10 + 3), and updating tens (4 tens + 3 tens + 1 regrouped ten). Students watch and then complete a second example together: 58 + 25 using the same steps; teacher prompts “What do we do when ones make 10 or more?”

3. 15–25 min · Guided practice (pair work, part-part-whole). Teacher distributes 4 problem cards. Example set:

• 62 + 19
• 73 + 28
• 150 + 60 (introduce regroup when tens/ones are not the only issue)
• 234 + 145 (optional scaffolds via partitioning template) Students solve in pairs using a partitioning diagram (part-part-whole or place-value blocks/drawings) and record one strategy explanation sentence.

4. 25–35 min · Inverse check (addition ↔ subtraction). Teacher displays: “If 47 + 36 = 83, then 83 − 36 = __ and 83 − 47 = __. What do you notice?” Students calculate the two related subtractions and state how this checks the addition answer.

5. 35–50 min · Independent task (fluency + reasoning). Teacher gives a worksheet “Addition Strategies” with a mix of problems:

• 2-digit regrouping (e.g., 39 + 24, 68 + 17, 57 + 35)
• 3-digit partitioning (e.g., 305 + 248, 412 + 356) Students complete, showing partitioning and at least one regrouping moment. Teacher circulates to prompt correct place value and regrouping decisions.

6. 50–58 min · Whole-class share. Teacher selects 3 students’ methods (one with regrouping ones, one with regrouping tens/hundreds, one using number bonds) and asks: “Which part was hardest and how did you manage it?” Students compare strategies and identify what stayed the same (place value reasoning) and what changed (numbers regrouped).

7. 58–60 min · Exit ticket. Teacher writes one question on the board: “Solve and check: 59 + 27 = __. Then use subtraction to check: __ − 27 = __.” Students complete independently for quick evidence of regrouping and inverse checking.

Resources

• Place-value chart (hundreds/tens/ones) for the board
• Base-ten blocks or physical place-value cards (hundreds/tens/ones) for demonstrations
• Student place-value partitioning templates (blank hundreds/tens/ones grids)
• Problem cards for guided practice
• Worksheet: “Addition Strategies” (2- and 3-digit, regrouping focus)
• Math journals for recording a strategy explanation
• Exit ticket slips (or one board-based final question)

Assessment

• Formative during modelling: listen for correct regrouping when ones total 10+ and how students explain “why”.
• Guided practice check: teacher reviews pair recordings for accurate partitioning and regrouping steps.
• Exit ticket: confirm both the final sum and the subtraction-based inverse check.

Differentiation

• Support for students needing scaffolding:
• Provide sentence starters: “First I partition… Next I add the ones… If I make 10, I regroup…”
• Use a partially completed place-value diagram on the first two worksheet questions.
• Offer base-ten blocks or drawn tens/ones to visualise regrouping.
• Support for students who struggle with mental number bonds:
• Give a “Number bonds to 10” reference strip and allow students to underline the bond used.
• Encourage writing “7 + 6 = 10 + 3” before proceeding with tens.
• Extension for advanced learners:
• Challenge: solve 3-digit additions with a focus on efficiency, e.g., “Which regrouping happens first: ones or tens? Explain your order of operations.”
• Provide an extra inverse-check prompt: “Write two different subtraction checks for your sum.”
• Ask students to create their own two similar problems for a partner, including one that requires regrouping in both ones and tens.
• Language and comprehension considerations:
• Keep the vocabulary consistent: ones, tens, hundreds, regroup, partition, total, inverse.
• Rephrase instructions using “split the number” and “combine the parts” when needed.