Regrouping With Place Value

Overview

Students use concrete materials and place-value language to solve three-digit subtraction problems involving regrouping. They connect hands-on models to written methods, then explain why regrouping is needed and check whether answers are reasonable.

Learning intentions

Students will:

• represent three-digit numbers with hundreds, tens and ones.
• regroup one hundred as 10 tens and one ten as 10 ones.
• solve subtraction problems using materials, drawings and written notation.
• explain their strategy and check their answer using estimation or addition.

Success criteria

• I can build the starting number with hundreds, tens and ones.
• I can regroup when I do not have enough ones or tens.
• I can solve and record a subtraction problem accurately.
• I can explain how I know my answer is reasonable.

Curriculum links

• Number — add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup.
• Algebra — apply addition and subtraction facts to 20 to develop efficient mental strategies with larger numbers.
• Number — estimate to determine whether calculations and answers are reasonable.

Lesson structure (60 minutes)

1. 0–7 min · Hook and mental warm-up. Display 878 − 425 and ask, “Which place value will we subtract first, and how can we check the answer?” Open with the subtraction hook and warm-up slides. Students estimate the answer, solve mentally if possible, and share what they notice about the digits. Record an estimate such as 900 − 400 = 500.

2. 7–20 min · Explicitly teach regrouping. Use a place-value mat, bundled straws or base-ten blocks to build 878: 8 hundreds, 7 tens and 8 ones. Model subtracting 5 ones, 2 tens and 4 hundreds, recording each step vertically. Explain: “We do not need to regroup because there are enough ones and tens.” Then model a contrasting example, 732 − 295. Build 732 and show that 2 ones cannot subtract 5 ones. Exchange 1 ten for 10 ones, leaving 6 tens and making 12 ones. Explain each action aloud and record:

• 12 − 5 = 7 ones
• 6 tens cannot subtract 9 tens, so exchange 1 hundred for 10 tens
• 16 − 9 = 7 tens
• 6 − 2 = 4 hundreds
• answer: 437 Students copy the place-value drawing and use partner talk to explain what changed and what stayed the same. Refer to the place-value partitioning vocabulary cards when introducing “regroup”, “place” and “value”.

3. 20–32 min · Guided hands-on practice. Place students in groups of five, with a place-value mat and base-ten materials for each group. Students build 732, physically exchange a ten for 10 ones and a hundred for 10 tens, then solve 732 − 295 together. Circulate and ask: “Why did you exchange?” “How many tens do you have now?” “How does your model match your written recording?” Pause for a whole-class check before students record the answer on their worksheet.

4. 32–45 min · Partner investigation. Distribute the regrouping practice worksheet. Partners solve 878 − 425, 732 − 295 and 399 − 254 using materials first, then a drawing and written method. Require students to circle the place where regrouping occurred and write one sentence explaining it. For 399 − 254, discuss that there are enough ones and tens, so no regrouping is required; students should notice that the answer is 145. Students compare methods with another pair and correct errors using the materials.

5. 45–53 min · Reasonableness and error analysis. Show a worked example claiming that 732 − 295 = 563. Students use an estimate, such as 700 − 300 ≈ 400, to decide whether it is reasonable. They then use place-value materials or addition to identify the error: the regrouped tens and hundreds were not recorded correctly. Invite students to explain why 437 is more sensible.

6. 53–60 min · Plenary and exit check. Revisit the regrouping discussion and plenary slides. Students complete the final worksheet prompt: “Explain how you regroup in 732 − 295.” Select two students to demonstrate with materials while classmates listen for accurate place-value language. Collect responses and ask students to show thumbs up, sideways or down for confidence.

Resources

• the subtraction hook and warm-up slides
• the regrouping practice worksheet
• Place-value mats, one per group
• Base-ten blocks, bundled straws or linking cubes
• Tens and ones counters
• Mini-whiteboards and markers
• Pencils and erasers
• the place-value partitioning vocabulary cards

Assessment

• Observe whether students exchange one ten for 10 ones and one hundred for 10 tens accurately during guided practice.
• Question students about why regrouping is needed and listen for correct use of “hundreds”, “tens”, “ones” and “regroup”.
• Use the worksheet and exit explanation to assess written accuracy, representation, reasoning and use of estimation.

Differentiation

• Support students with a colour-coded place-value mat, pre-bundled materials and sentence starters: “I regrouped because…” and “I exchanged…”.
• Work with a small group using 2-digit examples before returning to 732 − 295; allow students to keep the concrete model beside their written work.
• Provide EAL/D learners with the vocabulary cards, gestures and partner rehearsal before written explanations.
• Extend confident students by asking them to solve one problem using an alternative strategy, such as adding from 295 to 732, and compare the efficiency of both methods.