Subtract by Regrouping

Overview

In this 30-minute lesson, students learn to regroup tens and hundreds when subtracting three-digit numbers. The lesson builds from place-value understanding and concrete trades to solving problems independently, using 432 − 158 as the model.

Learning intentions

• Students will be able to regroup to subtract.
• Students will be able to trade 1 ten for 10 ones.
• Students will be able to trade 1 hundred for 10 tens.
• Students will be able to explain that the answer to subtraction is the difference.

Success criteria

• I can trade 1 ten for 10 ones or 1 hundred for 10 tens.
• I can subtract one place at a time, starting with the ones.
• I can use color and place-value columns to show my trades.
• I can solve at least 4 of 5 regrouping examples correctly.

Curriculum links

• Measurement and Data — addition and subtraction word problems involving lengths in the same units.
• Grade 2 place-value reasoning and accurate addition and subtraction within 100, extended here to three-digit regrouping.
• Mathematical reasoning — represent a problem with drawings, equations, and place-value tools, and explain the unknown difference.

Lesson structure (30 minutes)

1. 0–4 min · Hook and connect. Teacher opens the opening regrouping question and displays 32 − 18 with drawings of tens and ones, asking, “What can we do when there are not enough ones?” Students solve or explain using fingers, sketches, or response cards, then share the words trade and regroup.

2. 4–10 min · Direct teach and model. Teacher uses the place-value model and worked example to model 432 − 158 in a place-value chart: first trade 1 ten for 10 ones, then trade 1 hundred for 10 tens, and subtract from right to left. Teacher color-codes the traded digits and explicitly says, “One ten becomes 10 ones; one hundred becomes 10 tens.” Students chorally rehearse the steps and track each move with their finger or place-value pieces.

3. 10–17 min · Guided concrete practice. Teacher displays the interactive trade-box directions and uses the Smartboard or place-value blocks to show 352 − 176 and 241 − 125. Students take turns moving a hundred or ten into a trade box and replacing it with equivalent pieces, then solve one place at a time. Teacher checks that students name the trade before recording the new digit.

4. 17–25 min · Independent supported practice. Teacher distributes the regrouping practice and quick-check sheet and completes the first problem beside students as a reference. Students solve three scaffolded problems, using concrete pieces, large trade arrows, or color-coded columns as needed. Teacher conferences with each student, prompting, “Which place needs more units? What can you trade?” Suggested problems: 263 − 147, 421 − 186, and 532 − 278.

5. 25–30 min · Assessment and close. Teacher uses the review and exit questions to present five brief questions. Students answer with A/B/C response cards, orally, or by circling answers on the worksheet, then explain one answer:

6. One ten can become: A 10 ones, B 1 one, C 100 ones.

7. If 2 ones cannot take away 8 ones, we: A regroup, B guess only, C measure.

8. 432 − 158 = A 274, B 284, C 374.

9. One hundred can become: A 10 tens, B 1 ten, C 100 ones only.

10. The answer to subtraction is the: A difference, B sum, C graph. Students complete the sentence, “I can regroup by ___,” before leaving.

Resources

• the regrouping teaching and review deck
• the regrouping practice and quick-check sheet
• Smartboard or interactive display
• Base-ten blocks or place-value disks
• Place-value chart with ones, tens, and hundreds
• A/B/C response cards
• Colored pencils or highlighters
• Large trade arrows
• Optional dry-erase boards and markers

Assessment

• During modeling and guided practice, ask students to show or explain what one ten and one hundred can be traded for.
• Check the worksheet for accurate trades, aligned place-value columns, and correct subtraction. Use prompts rather than correcting immediately.
• Record responses to the five-question check. A student meeting 4 of 5 criteria demonstrates the lesson goal; reteach with concrete blocks if fewer than 4 are correct.

Differentiation

• Support: Use base-ten blocks, a completed example beside each problem, one place at a time, and color-coded ones, tens, and hundreds. Limit the first attempt to one regrouping before combining trades.
• Language and diverse learners: Provide the oral frame, “I traded ___ for ___,” and rehearse regroup, trade, borrow, difference, ten, and hundred with gestures and place-value pieces.
• Dyslexia-friendly options: Use a large, uncluttered font, consistent column spacing, large trade arrows, short directions, and generous writing space. Read every question aloud and allow students to point, build, circle, or answer with response cards instead of writing.
• Extension within the lesson: Ask a student who finishes early to create a three-digit subtraction problem requiring two trades, solve it, and explain why each trade is valid.