You will learn
- Take away objects from a group.
- Count what is left.
- Write the subtraction sentence.
- Check by recounting.
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
- Start with a group. Take some away.
- Count what is left.
- Write the sentence: 8 − 3 = 5.
- Check: the left and the taken away make the start.
Words to know
Remove some from a group.
What is left over.
Draw a line through to show taken away.
Make sure an answer is right.
1. Discover: the cookie jar
There are 9 biscuits in a tin. You eat 4. How can you find out how many are left?
2. Understand: taking away objects
- Make the whole group: 9 counters.
- Take away 4. Put them aside.
- Count what is left: 5.
- Write: 9 − 4 = 5.
Count the ones taken away too. 5 left and 4 taken away make 9 again. That is how we check.
Idea 1: Take away real objects
Put 8 stones on the table. Move 3 away. Count the stones still on the table: 5. So 8 − 3 = 5.
Idea 2: Take away all or none
If you take away all of them, none are left: 7 − 7 = 0.
If you take away none, they all stay: 7 − 0 = 7.
Idea 3: Check with addition
8 − 3 = 5. Check: 5 left and 3 taken away make 8. 5 + 3 = 8, so the answer is right.
Why does it work? What is left plus what was taken must give the start.
3. Worked examples
Example 1 (I show you): 8 − 3
Start with 8 stones: 🔴🔴🔴🔴🔴🔴🔴🔴 Take away 3.
- Count 8 stones.
- Move 3 away.
- Count what is left: 5.
Answer: 8 − 3 = 5
Example 2 (We do it together): 7 − 7
You have 7 sweets. You eat all 7.
- Start with 7.
- Take away all 7.
- None are left.
Answer: 7 − 7 = 0
Example 3 (You try): Check 9 − 4 = 5
Check 9 − 4 = 5 by adding.
Show the steps and answer
- 5 are left and 4 were taken away.
- Add: 5 + 4 = 9.
- 9 is the start number.
Answer: The answer is correct.
Did you know?
The answer to a take-away sum is often called the difference. In everyday talk we say how many are left.
Why this matters
We take away when we share, spend, eat or lose things. Checking stops mistakes.
4. Explore: act it out
You need 12 counters.
- Make a group of 8 counters.
- Take away 3 and put them in a cup.
- Count what is left.
- Check: do the left ones and the cup ones make 8?
Think about it: what did you notice?
8 − 3 = 5, and 5 + 3 = 8.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I started with ___.
- I took away ___.
- There are ___ left.
- I checked by ___.
Guided practice
Question 1. 7 − 2 = ?
5.
Question 2. 10 counters, take away 5. Left?
5.
Question 3. 6 − 6 = ?
0. Nothing is left.
Independent practice
Level 1: Start
- 8 − 3 = __
- 9 − 5 = __
- 7 − 7 = __
- 10 − 1 = __
- Make a story for 6 − 2.
Level 2: Grow
- 9 − 6 = __
- 10 − 4 = __
- You have 8 beads and lose 5. How many are left?
Level 3: Stretch
- A tray has 12 eggs. 5 break. How many are not broken?
- Write a subtraction sentence with the answer 0.
- Check 10 − 3 = 6 by adding. Is it right?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
There are 10 children on the bus. 4 get off. How many children are on the bus now?
Show a sample answer
10 − 4 = 6 children.
Another one. A basket has 11 oranges. You take out 4. How many are left?
Show a sample answer
11 − 4 = 7 oranges.
7. Common mistakes
Fix: Count only what remains.
Fix: After taking away, count only the objects that are still there.
Fix: Add the left and the taken away. You should get the start number.
8. Lesson summary and revision card
- I can take away objects from a group.
- I can count what is left.
- I can write the subtraction sentence.
- I can check by recounting.
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
- Make the whole group, take some away, count what is left.
- Taking away all leaves zero.
- Check by adding the parts back.
11. Next lesson
Next lesson: Finding how many remain. 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 9 − 4. [1 mark]
- Write a subtraction sentence for 8 stones when you take away 3. [2 marks]
- A bag has 12 sweets. 5 are eaten. How many are left? [2 marks]
- Use addition to check that 10 − 6 = 4. [2 marks]
- What is 7 − 7? Explain. [2 marks]
Total: 9 marks.
Marking guide and model answers
- 5 [1]
- 8 − 3 [1] = 5 [1]
- 12 − 5 [1] = 7 [1]
- 4 + 6 [1] = 10, so it is correct [1]
- 0 [1]. You take away all of them, so none are left [1].
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
- 7 − 4 = __
- 9 − 9 = __
- 6 − 1 = __
- 10 − 6 = __
- Write the sentence for 8 stones, take away 2.
- 8 − 5 = __
- 10 − 10 = __
- 6 − 4 = __
- You have 9 sweets and eat 3. How many are left?
- Check 7 − 2 = 5 by adding.
Homework
Make a group of 9 small things. Take some away and count what is left. Do it three times with different amounts and write each sentence.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 7 − 4 = __ | 3 | 2 |
| 9 − 9 = __ | 0 | 2 |
| 6 − 1 = __ | 5 | 2 |
| 10 − 6 = __ | 4 | 2 |
| Write the sentence for 8 stones, take away 2. | 8 − 2 = 6 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 3; 2 0; 3 5; 4 4; 5 8 − 2 = 6.
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 3; 7 0; 8 2; 9 6; 10 5 + 2 = 7, so it is correct.
Independent practice answers. Level 1: 1 5; 2 4; 3 0; 4 9; 5 a story such as: 6 mangoes, 2 are eaten, 4 are left. Level 2: 1 3; 2 6; 3 3. Level 3: 1 7; 2 For example 6 − 6 = 0; 3 6 + 3 = 9, not 10. So it is wrong. 10 − 3 = 7..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Take away objects from a group | 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 what is left | 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 Write the subtraction sentence | 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 by recounting | 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: Counting the ones taken away instead of the ones left. Count only what remains.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Take 1 or 2 away from a group of 5 and count what is left.
- 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 takes objects away and writes the subtraction sentence. You do not need to be good at mathematics to help.
- Take away real objects: 8 beans, move 3 away, count what is left.
- Ask: how can we check?
- Use daily life: 10 cups, 4 used.
- 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: take away objects from a group; count what is left; write the subtraction sentence; check by recounting.
Prerequisite knowledge. Lesson 1: the meaning of subtraction.
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 12 counters. 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. What did you start with? What did you take away? 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. Counting the ones taken away instead of the ones left. Count only what remains.
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. Take 1 or 2 away from a group of 5 and count what is left. 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 K.OA.A.2 and 1.OA.A.1; Cambridge Primary Mathematics Stage 1. These sources informed the lesson; no official alignment is claimed.