You will learn
- Line up digits for subtraction.
- Regroup (borrow) when a digit is too small.
- Subtract across zeros.
- Check subtraction by addition.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Line up digits.
- Subtract column by column from the right.
- Regroup when the top digit is smaller.
- Check by adding.
Words to know
The number we start with.
The number taken away.
The answer to subtraction.
Take ten from the next place.
1. Discover: a water tank
A tank holds 82,305 litres. 47,168 litres are used. How many are left?
2. Understand: column subtraction
Subtract from the right. If the top digit is smaller, regroup from the next place.
- 82,305 − 47,168: ones 5 < 8, so regroup. Work across the zero.
- Result: 35,137.
- Check: 35,137 + 47,168 = 82,305.
Always check by adding the difference to the number taken away.
Idea 1: Regroup
82,305 − 47,168: ones 5 − 8, regroup; the answer is 35,137.
Idea 2: Zeros
60,000 − 12,345 = 47,655. 100,000 − 9,999 = 90,001.
Idea 3: Check
47,655 + 12,345 = 60,000. It works.
Why check? Addition undoes subtraction.
3. Worked examples
Example 1 (I show you): Regroup
82,305 − 47,168
- Borrow from the tens, hundreds and so on.
Answer: 35,137
Example 2 (We do it together): Zeros
60,000 − 12,345
- Borrow across the zeros.
Answer: 47,655
Example 3 (You try): Check
Check 60,000 − 12,345 = 47,655.
Show the steps and answer
- 47,655 + 12,345.
Answer: 60,000, so it is correct
Did you know?
Borrow is another word for regroup.
Why this matters
Subtraction tells us how much is left or how far apart numbers are.
4. Explore: subtract and check
You need paper and a pencil.
- Write 82,305 above 47,168.
- Subtract from the right.
- Regroup across zeros.
- Check by adding.
Think about it: what did you notice?
35,137.
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 difference is ___.
- I check by adding ___ + ___.
- I get ___.
Guided practice
Question 1. 82,305 − 47,168?
35,137.
Question 2. How do we check?
Add the difference to the number taken away.
Question 3. 50,000 − 1?
49,999.
Independent practice
Level 1: Start
- 60,000 − 12,345
- 90,000 − 1,234
- 45,678 − 23,456
- 100,000 − 9,999
- 70,500 − 8,250
Level 2: Grow
- 67,890 − 12,345
- 50,000 − 4,321
- 9,000 − 2,468
Level 3: Stretch
- 100,000 − 45,678
- 83,400 − 19,750
- Kofi says 60,000 − 12,345 = 52,345. Check it.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A tank has 82,305 litres. 47,168 are used. How many remain?
Show a sample answer
35,137 litres.
Another one. A farmer has 90,000 kg of grain and sells 1,234 kg. How much is left?
Show a sample answer
88,766 kg
7. Common mistakes
Fix: Regroup when the top is smaller.
Fix: Regroup instead.
Fix: Add the answer to the number taken away.
8. Lesson summary and revision card
- I can line up digits for subtraction.
- I can regroup when a digit is too small.
- I can subtract across zeros.
- I can check by adding.
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 needed.
- Work across zeros carefully.
- Check with addition.
11. Next lesson
Next lesson: Estimation. 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.
- Find 82,305 − 47,168. [2 marks]
- Find 60,000 − 12,345. [2 marks]
- Check 60,000 − 12,345 = 47,655. [2 marks]
- Find 100,000 − 9,999. [2 marks]
- Ana says 45,678 − 23,456 = 22,332. Check it. [3 marks]
Total: 11 marks.
Marking guide and model answers
- Regroup [1]; 35,137 [1]
- Borrow across zeros [1]; 47,655 [1]
- 47,655 + 12,345 [1] = 60,000 [1]
- 100,000 − 10,000 = 90,000 [1]; +1 = 90,001 [1]
- 22,332 + 23,456 = 45,788 [1], not 45,678 [1]. The answer is 22,222 [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
- 60,000 − 12,345
- 90,000 − 1,234
- 45,678 − 23,456
- 100,000 − 9,999
- 70,500 − 8,250
- 82,305 − 47,168 =
- 60,000 − 12,345 =
- 90,000 − 1,234 =
- 45,678 − 23,456 =
- 100,000 − 9,999 =
Homework
Subtract two large numbers and check by adding.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 60,000 − 12,345 | 47,655 | 2 |
| 90,000 − 1,234 | 88,766 | 2 |
| 45,678 − 23,456 | 22,222 | 2 |
| 100,000 − 9,999 | 90,001 | 2 |
| 70,500 − 8,250 | 62,250 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 47,655; 2 88,766; 3 22,222; 4 90,001; 5 62,250.
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 35,137; 7 47,655; 8 88,766; 9 22,222; 10 90,001.
Independent practice answers. Level 1: 1 47,655; 2 88,766; 3 22,222; 4 90,001; 5 62,250. Level 2: 1 55,545; 2 45,679; 3 6,532. Level 3: 1 54,322; 2 63,650; 3 52,345 + 12,345 = 64,690, not 60,000. The answer is 47,655..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Line up digits for subtraction | 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 (borrow) when a digit is too small | 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 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 |
| O4 Check subtraction by addition | 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Subtracting the smaller digit from the larger. Regroup when the top is smaller.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise 4-digit subtraction with regrouping.
- 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 up to hundreds of thousands. You do not need to be good at mathematics to help.
- Subtract prices on paper.
- Ask: did you regroup? did you check?
- Always add back.
- 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: line up digits for subtraction; regroup (borrow) when a digit is too small; subtract across zeros; check subtraction by addition.
Prerequisite knowledge. Lesson 1.
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 paper and a pencil. 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. Are the places lined up? Do 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. Subtracting the smaller digit from the larger. Regroup when the top 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. Practise 4-digit subtraction with regrouping. 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
Alignment is pending verification and no external 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. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 4.NBT.B.4 (subtract multi-digit numbers); Cambridge Primary Mathematics Stage 4 (subtraction). These sources informed the lesson; no official alignment is claimed.