You will learn
- Subtract tens and ones.
- Count back on a number line.
- Find the difference by counting up.
- Check with addition.
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
- Subtract the tens, then the ones.
- Count back or count up to find the difference.
- Use addition to check.
- Think: how many are left?
Words to know
Take away.
How much more or less.
Say the numbers going down.
The opposite operation.
1. Discover: selling cassava
A farmer has 78 cassava roots and sells 45. How many roots are left?
2. Understand: subtracting within 100
Partition: 78 − 45: subtract the tens, 70 − 40 = 30, and the ones, 8 − 5 = 3. So 33.
Count back on a number line: 90 − 34: back 30 to 60, then back 4 to 56.
Count up to find the difference: 50 − 18: from 18 jump +2 to 20, +30 to 50. 2 + 30 = 32.
Check by adding: 33 + 45 = 78.
Idea 1: Tens and ones
78 − 45: subtract the tens, 70 − 40 = 30. Subtract the ones, 8 − 5 = 3. Then 30 + 3 = 33.
Idea 2: Count back and count up
On a number line, 85 − 20 is 65 (two jumps of 10 back). To find the difference between 63 and 18, count up from 18 to 63.
Idea 3: Check with addition
The inverse of subtraction is addition. If 59 − 24 = 35 then 35 + 24 = 59.
Why check? Addition undoes subtraction.
3. Worked examples
Example 1 (I show you): Subtract
59 − 24 = ?
- Tens: 50 − 20 = 30.
- Ones: 9 − 4 = 5.
Answer: 35
Example 2 (We do it together): Count back by tens
72 − 30 = ?
- Three jumps of 10 back.
Answer: 42
Example 3 (You try): Check
Check 59 − 24 = 35.
Show the steps and answer
- Add 35 + 24.
Answer: 59. It matches.
Did you know?
Shopkeepers subtract to find change. They often count up from the price to the money paid.
Why this matters
Subtraction tells us what is left, how many more and how much change.
4. Explore: number line back-jumps
Draw a number line from 50 to 100.
- Start at 90.
- Jump back 30 to 60.
- Jump back 4 to 56.
- Check: 56 + 34 = 90.
Think about it: what did you notice?
90 − 34 = 56.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The tens give ___.
- The ones give ___.
- The difference is ___.
- To check I add ___ and ___.
Guided practice
Question 1. 78 − 45?
33.
Question 2. 90 − 34?
56.
Question 3. 50 − 18?
32.
Independent practice
Level 1: Start
- 59 − 24
- 80 − 35
- 72 − 30
- 63 − 18
- 100 − 25
Level 2: Grow
- 86 − 41 = ___.
- 70 − 26 = ___.
- 95 − 60 = ___.
Level 3: Stretch
- 64 − 29 = ___.
- A market has 92 mangoes and sells 47. How many are left?
- Ali says 52 − 27 = 35 because 7 − 2 = 5 and 5 − 2 = 3. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A farmer has 78 roots and sells 45. How many are left?
Show a sample answer
33 roots.
Another one. A class has 100 pencils and uses 64. How many are left?
Show a sample answer
36
7. Common mistakes
Fix: Always take the second number away from the first.
Fix: Always take the bottom number from the top number.
Fix: Add the answer and the number you took away.
8. Lesson summary and revision card
- I can subtract tens and ones.
- I can count back on a number line.
- I can find the difference by counting up.
- I can check with addition.
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
- Subtract tens, then ones.
- Count back or count up.
- Check by adding.
11. Next lesson
Next lesson: Subtraction within 1,000. 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 87 − 32. [1 mark]
- Work out 73 − 28. [2 marks]
- Work out 100 − 41. [1 mark]
- A shop has 90 eggs and sells 36. How many are left? [2 marks]
- Kofi says 64 − 29 = 45. Check it with addition. Is he right? [3 marks]
Total: 9 marks.
Marking guide and model answers
- 55 [1]
- 73 − 30 = 43 [1]; 45 [1]
- 59 [1]
- 90 − 36 [1] = 54 [1]
- 45 + 29 [1] = 74 [1]; not 64 so he is wrong [1]. The answer is 35.
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 59 − 24
- 80 − 35
- 72 − 30
- 63 − 18
- 100 − 25
- 78 − 45 = ___.
- 85 − 20 = ___.
- 90 − 34 = ___.
- 67 − 23 = ___.
- 50 − 18 = ___.
Homework
Take a number between 50 and 99 and subtract 3 different numbers from it. Show your jumps.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 59 − 24 | 35 | 2 |
| 80 − 35 | 45 | 2 |
| 72 − 30 | 42 | 2 |
| 63 − 18 | 45 | 2 |
| 100 − 25 | 75 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 35; 2 45; 3 42; 4 45; 5 75.
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 33; 7 65; 8 56; 9 44; 10 32.
Independent practice answers. Level 1: 1 35; 2 45; 3 42; 4 45; 5 75. Level 2: 1 45; 2 44; 3 35. Level 3: 1 35; 2 45; 3 You cannot take 7 from 2, so regroup. 52 − 27 = 25..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Subtract tens and 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 Count back on a number line | 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 Find the difference by counting up | 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 with 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 |
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: Subtracting the smaller digit from the bigger digit in each column. Always take the second number away from the first.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use sticks: take away tens then ones from a bundle.
- 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 two-digit numbers within 100 and checks by addition. You do not need to be good at mathematics to help.
- Work out change from 100 in a shop.
- Count back on a number line together.
- Ask: how can you check this 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: subtract tens and ones; count back on a number line; find the difference by counting up; check with addition.
Prerequisite knowledge. Lessons 1 to 4.
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). Draw a number line from 50 to 100. 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. Do you count back or count up? How can you check?
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 bigger digit in each column. Always take the second number away from the first.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-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: take away tens then ones from a bundle. 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.5 (subtract within 100); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.