Subtraction with regrouping

You will learn

Regroup a ten, hundred or thousand when the top digit is smaller.
Subtract across zeros.
Check by adding.
Explain each regrouping.

Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.

Student lesson

The lesson in 60 seconds

If the top digit is smaller, regroup.
Take one from the next place and make ten.
Zeros need extra care.
Check by adding.

Words to know

regroup
Exchange one of a bigger place for ten of the next.

borrow
Take one from the next place.

zero
The digit 0 holding a place.

check
Add to test the answer.

1. Discover: not enough ones

A store has 5,432 bags and ships 2,764. You cannot take 4 ones from 2 ones! What can you do?

2. Understand: subtraction with regrouping

When the top digit is smaller, regroup: take 1 from the next place to the left and add 10 to this place.

5,432 − 2,764: ones 2 − 4: regroup, 12 − 4 = 8. Tens (now 2) 2 − 6: regroup, 12 − 6 = 6. Hundreds (now 3) 3 − 7: regroup, 13 − 7 = 6. Thousands (now 4) 4 − 2 = 2. The answer is 2,668.

Check: 2,668 + 2,764 = 5,432.

For 6,000 − 1,234 think 6,000 − 1,000 = 5,000; 5,000 − 234 = 4,766.

Idea 1: Regroup

6,543 − 2,876. Ones: 3 is less than 6, so regroup. Tens become 3, ones 13. Work across and the difference is 3,667.

Idea 2: Across zeros

5,000 − 2,345: take 1 thousand, make 10 hundreds, then 9 hundreds and 10 tens, then 9 tens and 10 ones. The answer is 2,655.

Idea 3: Check

2,655 + 2,345 = 5,000. It matches.

Why regroup? You cannot take a bigger digit from a smaller one in the same place.

Remember: If the top digit is smaller, regroup from the next place. Check by adding.

3. Worked examples

Example 1 (I show you): Regroup

6,543 − 2,876 = ?

Regroup ones, tens and hundreds as needed.

Answer: 3,667

Example 2 (We do it together): Zeros

5,000 − 2,345 = ?

5,000 − 2,000 = 3,000 then 3,000 − 345 = 2,655.

Answer: 2,655

Example 3 (You try): Check

Check 3,667 by adding.

Show the steps and answer

3,667 + 2,876.

Answer: 6,543, so it is correct

Did you know?

Borrow is another word for regroup. We exchange one of a bigger place for ten of the next place.

Why this matters

Regrouping lets us subtract any numbers.

4. Explore: regroup it

You need squared paper.

Write 5,432 and 2,764 in columns.
Regroup for the ones, tens and hundreds.
Subtract each column.
Check by adding 2,668 + 2,764.

Think about it: what did you notice?

5,432 − 2,764 = 2,668.

5. Practise

Say it in a sentence

Use these starters when you talk about the lesson. Say them out loud.

___ is less than ___ so I regroup.
The tens digit becomes ___.
The difference is ___.
I check by adding ___ + ___.

Guided practice

Question 1. 5,432 − 2,764?

2,668.

Question 2. 6,000 − 1,234?

4,766.

Question 3. 8,000 − 1?

7,999.

Independent practice

Level 1: Start

6,543 − 2,876
5,000 − 2,345
7,206 − 3,418
9,100 − 4,550
8,432 − 6,789

Level 2: Grow

6,300 − 2,145
4,070 − 1,385
8,000 − 7,999

Level 3: Stretch

9,000 − 1
10,000 − 5,432
Kofi says 5,000 − 2,345 = 3,655. Check it.

Answers are in the answer key below. Try first, then check.

6. Apply: everyday mathematics

A depot has 5,432 bags and ships 2,764. How many are left?

Show a sample answer

2,668 bags.

Another one. A trader had 7,000 oranges and sold 3,568. How many are left? Check by adding.

Show a sample answer

3,432; 3,432 + 3,568 = 7,000

7. Common mistakes

Mistake: Taking the smaller digit from the bigger.
Fix: Regroup when the top digit is smaller.

Another mistake: Taking the smaller digit from the bigger one.
Fix: Regroup instead.

Another mistake: Forgetting to lower the next place by 1.
Fix: After borrowing, reduce that place by 1.

8. Lesson summary and revision card

I can…

I can regroup in subtraction.
I can subtract across zeros.
I can check by adding.
I can explain each regrouping.

9. Check and master

Answer all 14 questions. You will see feedback after each one.

1. 5,432 − 2,764 =

2,668 3,332 2,768

2. 6,000 − 1,234 =

5,766 4,766 4,866

3. 7,305 − 2,468 =

5,837 4,937 4,837

4. 8,000 − 1 =

7,999 7,000 8,001

5. 4,520 − 1,865 =

3,665 2,655 2,755

6. 7,000 − 3,456 =

3,544 3,654 4,544

7. 6,234 − 2,567 =

3,777 3,667 4,333

8. 9,000 − 5,555 =

4,445 3,555 3,445

9. 8,205 − 4,376 =

3,829 4,171 3,839

10. 10,000 − 4,321 =

5,789 5,679 6,679

11. 4,003 − 1,008 =

3,005 2,005 2,995

12. To check 5,000 − 2,345 = 2,655 we add…

2,655 + 2,345 5,000 + 2,345 2,655 + 5,000

Challenge 1. 10,000 − 2,345 =

8,655 7,755 7,655

Challenge 2. 9,005 − 3,987 − 1,018 =

3,000 5,018 4,000

Your result appears here after you answer every question.

10. Key takeaways

Regroup when the top digit is smaller.
Zeros need regrouping across.
Check by adding.

11. Next lesson

Next lesson: Estimating answers. Keep going with the next idea in this course.

Exam practice

These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.

6,543 − 2,876 = ? [2 marks]
5,000 − 2,345 = ? [2 marks]
Check 2,655 by adding. [2 marks]
7,206 − 3,418 = ? [2 marks]
Ama says 6,000 − 1,234 = 5,234. Show she is wrong. [3 marks]

Total: 11 marks.

Marking guide and model answers

3,667 [2]
2,655 [2]
2,655 + 2,345 [1] = 5,000 [1]
3,788 [2]
5,234 + 1,234 = 6,468 [1], not 6,000 [1]. The answer is 4,766 [1].

Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.

Printable worksheet

6,543 − 2,876
5,000 − 2,345
7,206 − 3,418
9,100 − 4,550
8,432 − 6,789
5,432 − 2,764 =
6,000 − 1,234 =
7,305 − 2,468 =
8,000 − 1 =
10,000 − 2,345 =

Homework

Pick three four-digit numbers and subtract 1,865 from each. Show your regrouping.

Answer key and marking scheme

Question	Expected response	Marks
6,543 − 2,876	3,667	2
5,000 − 2,345	2,655	2
7,206 − 3,418	3,788	2
9,100 − 4,550	4,550	2
8,432 − 6,789	1,643	2
Total		10

Practice answers: Worksheet: 1 3,667; 2 2,655; 3 3,788; 4 4,550; 5 1,643.

Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.

Extra worksheet answers (items 6 onward): 6 2,668; 7 4,766; 8 4,837; 9 7,999; 10 7,655.

Independent practice answers. Level 1: 1 3,667; 2 2,655; 3 3,788; 4 4,550; 5 1,643. Level 2: 1 4,155; 2 2,685; 3 1. Level 3: 1 8,999; 2 4,568; 3 3,655 + 2,345 = 6,000, not 5,000. The answer is 2,655..

Mastery and remediation

Objective	Bronze (Developing)	Silver (Proficient)	Gold (Advanced)
O1 Regroup a ten, hundred or thousand when the top digit is smaller	Shows this with help from an adult or a picture	Does this independently and explains how they know	Explains it clearly and uses it in a new situation
O2 Subtract across zeros	Shows this with help from an adult or a picture	Does this independently and explains how they know	Explains it clearly and uses it in a new situation
O3 Check by adding	Shows this with help from an adult or a picture	Does this independently and explains how they know	Explains it clearly and uses it in a new situation
O4 Explain each regrouping	Shows this with help from an adult or a picture	Does this independently and explains how they know	Explains it clearly and uses it in a new situation

Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.

If a learner struggles

Find the misconception: Taking the smaller digit from the bigger. Regroup when the top digit is smaller.
Explain another way: use real objects first, then pictures.
Show a simpler example: Use place value squares to exchange a hundred for ten tens.
Guided practice: work through one example together and let the learner try the next one.
Reassess: use the quiz again or the worksheet.
Move on when the learner shows Silver-level evidence independently.

For parents and guardians

In this lesson your child subtracts four-digit numbers that need regrouping, including across zeros. You do not need to be good at mathematics to help.

Practise with prices and change.
Ask: do you need to regroup?
Always check by adding.
Ask “how do you know?” after each answer, and listen.
Praise effort, not only right answers. Mistakes are how we learn.
Ten to fifteen minutes a day is better than one long session.

Teacher package

1–5. Objectives, prerequisites, materials, preparation, duration

Lesson objectives. Learners will: regroup a ten, hundred or thousand when the top digit is smaller; subtract across zeros; check by adding; explain each regrouping.

Prerequisite knowledge. Lesson 3.

Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.

Preparation. Gather the counters and draw the example pictures on the board before the lesson.

Suggested duration. 45–60 minutes. It can be split into two shorter sessions.

6–9. Teaching procedure, explanation notes, guided and independent activities

Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.

Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.

Guided activity (10 min). You need squared paper. Learners follow the Explore steps in pairs.

Independent activity (10 min). Learners complete the independent practice and the worksheet.

Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.

Key questions. Is the top digit smaller? Did I regroup? Does adding back work?

Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.

10–12. Differentiation, formative assessment, common misconceptions

Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.

Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.

Misconceptions. Taking the smaller digit from the bigger. Regroup when the top digit is smaller.

13–15. Assessment questions, answer keys, marking scheme

Use the quiz and worksheet on this page. The 11-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.

16–19. Remediation, enrichment, homework, teacher reflection

Remediation. Use place value squares to exchange a hundred for ten tens. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.

Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.

Sources and standards

This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.

Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 3 » Operations & Algebraic Thinking; Grade 3 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.

Research used to shape this lesson. Common Core 3.NBT.A.2 and 4.NBT.B.4 (subtract with regrouping); Cambridge Primary Mathematics Stage 3 (subtraction). These sources informed the lesson.