You will learn
- Regroup a ten into ten ones.
- Regroup a hundred into ten tens.
- Subtract with regrouping in columns.
- Subtract from numbers with zeros.
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
- If a digit is too small, regroup.
- Regroup a ten into ten ones.
- Regroup a hundred into ten tens.
- Check by adding.
Words to know
Exchange one of a bigger place for ten of the next.
Swap one for ten smaller ones.
Digits lined up by place.
Add to test the answer.
1. Discover: not enough ones
You have 52 stones and give away 27. You cannot take 7 ones from 2 ones! What can you do with one of the tens?
2. Understand: regrouping in subtraction
When the top digit is smaller, regroup: take 1 from the next place to the left and add 10 to the place you need.
52 − 27: 2 ones is less than 7, so take 1 ten (leaving 4 tens) and make 12 ones. 12 − 7 = 5. 4 tens − 2 tens = 2 tens. Answer: 25.
432 − 175: ones 2 − 5 cannot be done, so regroup: 12 − 5 = 7. Tens are now 2 − 7, so regroup from the hundreds: 12 − 7 = 5. Hundreds are now 3 − 1 = 2. Answer: 257.
For 300 − 146, think 300 − 100 = 200, then 200 − 46 = 154.
Idea 1: Regroup a ten
52 − 27: you cannot take 7 from 2. Regroup 1 ten into 10 ones. Now 12 − 7 = 5 and 4 − 2 = 2. The answer is 25.
Idea 2: Regroup a hundred
432 − 175: regroup a ten for the ones, then a hundred for the tens. Result 257.
Idea 3: Zeros
For 300 − 146, regroup 1 hundred into 10 tens, then 1 ten into 10 ones. Result 154.
Why regroup? A bigger place can be swapped for ten of the next smaller place.
3. Worked examples
Example 1 (I show you): Regroup a ten
71 − 36 = ?
- 1 − 6: cannot.
- Regroup: 11 − 6 = 5.
- 6 − 3 = 3.
Answer: 35
Example 2 (We do it together): Regroup twice
524 − 268 = ?
- 14 − 8 = 6.
- 11 − 6 = 5.
- 4 − 2 = 2.
Answer: 256
Example 3 (You try): From a zero
400 − 175 = ?
Show the steps and answer
- 400 = 39 tens and 10 ones.
- 10 − 5 = 5.
- Tens 9 − 7 = 2.
- Hundreds 3 − 1 = 2.
Answer: 225
Did you know?
Subtracting with zeros is tricky. Many adults find 300 − 146 harder than 354 − 146.
Why this matters
Regrouping lets us subtract when the top digit is smaller than the bottom digit.
4. Explore: exchange game
You need bundles of ten and single sticks.
- Make 52 with 5 bundles and 2 sticks.
- Untie one bundle to make 12 single sticks.
- Take away 27 (2 bundles and 7 sticks).
- Count what is left and check: 25 + 27.
Think about it: what did you notice?
52 − 27 = 25.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I cannot take ___ from ___ so I regroup.
- 1 ten is 10 ___.
- The ones give ___.
- The answer is ___.
Guided practice
Question 1. 52 − 27?
25.
Question 2. 83 − 39?
44.
Question 3. 300 − 146?
154.
Independent practice
Level 1: Start
- 71 − 36
- 524 − 267
- 400 − 175
- 90 − 47
- 612 − 348
Level 2: Grow
- 82 − 45 = ___.
- 605 − 238 = ___.
- 300 − 128 = ___.
Level 3: Stretch
- A shop has 400 mangoes and sells 168. How many are left?
- Check 83 − 39 = 44 by adding.
- Ama says 42 − 18 = 36 because 8 − 2 = 6 and 4 − 1 = 3. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A school has 432 pupils; 175 are on a trip. How many are at school?
Show a sample answer
257 pupils.
Another one. A farm has 305 eggs and uses 147 for baking. How many are left?
Show a sample answer
158
7. Common mistakes
Fix: Regroup when the top digit is smaller.
Fix: Regroup when the top digit is too small.
Fix: After lending, reduce the next digit by 1.
8. Lesson summary and revision card
- I can regroup a ten into ten ones.
- I can regroup a hundred into ten tens.
- I can subtract with regrouping in columns.
- I can subtract from numbers with zeros.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Regroup when the top digit is smaller.
- Take 1 from the next place, add 10.
- Check by adding.
11. Next lesson
Next lesson: Checking 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.
- Work out 62 − 38. [2 marks]
- Work out 351 − 276. [2 marks]
- Work out 400 − 123. [2 marks]
- A box has 205 sweets. 118 are eaten. How many are left? [2 marks]
- Ali says 53 − 28 = 35. Check his answer by adding. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 62 − 38: 12 − 8 = 4 [1]; 24 [1]
- 75 [2]. Give 1 mark for the method.
- 277 [2]. Give 1 mark for one regroup correct.
- 205 − 118 [1] = 87 [1]
- 35 + 28 [1] = 63 [1]; he is wrong, the answer is 25 [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
- 71 − 36
- 524 − 267
- 400 − 175
- 90 − 47
- 612 − 348
- 52 − 27 = ___.
- 432 − 175 = ___.
- 83 − 39 = ___.
- 300 − 146 = ___.
- 705 − 248 = ___.
Homework
Pick three numbers and subtract 28 from each, showing your regrouping.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 71 − 36 | 35 | 2 |
| 524 − 267 | 257 | 2 |
| 400 − 175 | 225 | 2 |
| 90 − 47 | 43 | 2 |
| 612 − 348 | 264 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 35; 2 257; 3 225; 4 43; 5 264.
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 25; 7 257; 8 44; 9 154; 10 457.
Independent practice answers. Level 1: 1 35; 2 257; 3 225; 4 43; 5 264. Level 2: 1 37; 2 367; 3 172. Level 3: 1 232; 2 44 + 39 = 83; 3 She cannot take 8 from 2. Regroup. 42 − 18 = 24..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Regroup a ten into ten ones | 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 Regroup a hundred into ten tens | 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 Subtract with regrouping in columns | 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 Subtract from numbers with 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 |
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 digit. Regroup when the top digit is smaller.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use sticks to exchange a bundle for ten ones.
- 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 numbers where regrouping is needed. You do not need to be good at mathematics to help.
- Use coins to show a regroup: swap a 10 for ten 1s.
- Practise 100 minus a number.
- Ask: why do we regroup?
- 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 into ten ones; regroup a hundred into ten tens; subtract with regrouping in columns; subtract from numbers with zeros.
Prerequisite knowledge. Lessons 5 and 6.
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 bundles of ten and single sticks. 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. Can you take the bottom digit from the top? What do you regroup? Does adding check it?
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 digit. 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 sticks to exchange a bundle for ten ones. 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 2 » Operations & Algebraic Thinking; Grade 2 » 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 2.NBT.B.7 (subtract within 1000 with regrouping); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.