You will learn
- Subtract within 20.
- Count back to subtract.
- Use number bonds to subtract.
- Explain a way to subtract.
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
- Count back to subtract small numbers.
- Use number bonds: if 8 + 7 = 15, then 15 − 7 = 8.
- Go down to 10 first: 15 − 7 is 15 − 5, then 2 more.
- Say how you worked it out.
Words to know
Say numbers going down from a start number.
A pair of parts that make a total.
A plan to solve.
The answer to a subtraction.
1. Discover: bigger take-aways
What is 14 − 6? Counting back 6 steps is slow. Is there a quicker way?
2. Understand: subtracting within 20
Count back for small take-aways: 14 − 2 is 13, 12.
Use a ten: 14 − 6. Take 4 away to reach 10, then 2 more: 10 − 2 = 8.
Use number bonds: 6 + 8 = 14, so 14 − 6 = 8. The numbers in a bond work for subtraction too.
Idea 1: Count back
For 13 − 3, start at 13 and count back 3: 12, 11, 10. This works well when you take away 1, 2 or 3.
Idea 2: Use a number bond
For 14 − 6, ask: what goes with 6 to make 14? 6 + 8 = 14, so 14 − 6 = 8.
Why? Subtraction and addition are linked. You already know many adding facts.
Idea 3: Go down through ten
For 15 − 7: take away 5 to reach 10 (15 − 5 = 10). You still have 2 more to take away: 10 − 2 = 8.
3. Worked examples
Example 1 (I show you): 14 − 4
Work out 14 − 4.
- 14 is 10 and 4.
- Take away the 4.
- 10 is left.
Answer: 14 − 4 = 10
Example 2 (We do it together): 13 − 6 with a bond
Work out 13 − 6 using a number bond.
- Ask: 6 + __ = 13.
- 6 + 7 = 13.
Answer: 13 − 6 = 7
Example 3 (You try): 15 − 7 through ten
Work out 15 − 7 by going through ten.
Show the steps and answer
- 15 − 5 = 10.
- 7 is 5 and 2. Take away 2 more.
- 10 − 2 = 8.
Answer: 15 − 7 = 8
Did you know?
Subtraction and addition are linked. If you know your adding facts, you know your taking-away facts too.
Why this matters
Subtraction within 20 is used in money, time and measuring. A good method is faster than counting back every time.
4. Explore: go through ten
Use 20 counters and a ten frame.
- Make 13 (a full ten frame and 3 more).
- Take away 3 to leave 10. Then take away 2 more.
- Count what is left.
- Try 15 − 7 and 12 − 5.
Think about it: what did you notice?
13 − 5 = 8. 15 − 7 = 8. 12 − 5 = 7.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I count back ___.
- ___ + ___ = ___, so ___ − ___ = ___.
- I go down to ten by taking away ___ first.
- My method was ___.
Guided practice
Question 1. 13 − 3 = ?
10.
Question 2. 16 − 6 = ?
10.
Question 3. 12 − 5 = ? (5 + 7 = 12)
7.
Independent practice
Level 1: Start
- 15 − 5 = __
- 14 − 4 = __
- 13 − 6 = __
- 17 − 8 = __
- Explain how you solve 15 − 7.
Level 2: Grow
- 16 − 6 = __
- 12 − 3 = __
- 17 − 9 = __
Level 3: Stretch
- Use 7 + 6 = 13 to work out 13 − 6.
- Show 14 − 8 by going down to ten.
- Tom says 15 − 9 = 7. Check by adding.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
There are 18 apples. 9 are eaten. How many apples are left?
Show a sample answer
18 − 9 = 9 apples.
Another one. A shelf has 18 books. 9 are taken. How many remain?
Show a sample answer
9 + 9 = 18, so 18 − 9 = 9 books remain.
7. Common mistakes
Fix: Go through 10 or use a number bond to be accurate.
Fix: Do not count the start. Check by adding: the answer plus the take-away number should give the start.
Fix: After you reach ten, take away the rest: 10 − 2.
8. Lesson summary and revision card
- I can subtract within 20.
- I can count back to subtract.
- I can use number bonds to subtract.
- I can explain a way to subtract.
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
- Count back for small take-aways.
- Go through 10 for bigger ones.
- Number bonds work for subtraction too.
11. Next lesson
Next lesson: Relationship between addition and subtraction. 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 13 − 4. [1 mark]
- If 8 + 6 = 14, what is 14 − 6? [1 mark]
- Work out 15 − 8 by going down through ten. Show the steps. [3 marks]
- A box has 17 pencils. 8 are used. How many are left? [2 marks]
- Zoe says 12 − 5 = 8. Check with addition and say if she is right. [2 marks]
Total: 9 marks.
Marking guide and model answers
- 9 [1]
- 8 [1]
- 15 − 5 = 10 [1]; 10 − 3 = 7 [1]; answer 7 [1]
- 17 − 8 [1] = 9 [1]
- 8 + 5 = 13, not 12 [1]; she is wrong and the answer is 7 [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
- 15 − 5 = __
- 13 − 6 = __
- 17 − 8 = __
- 12 − 9 = __
- 20 − 10 = __
- 14 − 5 = __
- 11 − 2 = __
- 16 − 8 = __
- If 7 + 5 = 12, then 12 − 5 = __
- 20 − 10 = __
Homework
Pick three numbers from 12 to 20 and take away a number from 2 to 9. Use a strategy. Tell a family member how you solved one.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 15 − 5 = __ | 10 | 2 |
| 13 − 6 = __ | 7 | 2 |
| 17 − 8 = __ | 9 | 2 |
| 12 − 9 = __ | 3 | 2 |
| 20 − 10 = __ | 10 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 10; 2 7; 3 9; 4 3; 5 10.
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 9; 7 9; 8 8; 9 7; 10 10.
Independent practice answers. Level 1: 1 10; 2 10; 3 7; 4 9; 5 15 − 5 = 10, then 10 − 2 = 8, so 15 − 7 = 8. Level 2: 1 10; 2 9; 3 8. Level 3: 1 7; 2 14 − 4 = 10, then 10 − 4 = 6; 3 7 + 9 = 16, not 15. So 15 − 9 = 6..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Subtract within 20 | 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 to subtract | 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 Use number bonds to subtract | 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 a way to subtract | 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: Counting back and losing count. Go through 10 or use a number bond to be accurate.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Subtract within 10 using a ten frame before going to 20.
- 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 within 20 by counting back, using number bonds and going through ten. You do not need to be good at mathematics to help.
- Practise adding facts. They help with taking away.
- Ask: what goes with 6 to make 14?
- Use a number line from 0 to 20 and hop 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: subtract within 20; count back to subtract; use number bonds to subtract; explain a way to subtract.
Prerequisite knowledge. Lessons 1 to 4 and number bonds to 10.
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). Use 20 counters and a ten frame. 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 number goes with 6 to make 14? How do you go through ten? 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 back and losing count. Go through 10 or use a number bond to be accurate.
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. Subtract within 10 using a ten frame before going to 20. 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 1 » Operations & Algebraic Thinking; Grade 1 » 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 1.OA.C.6 and 1.OA.B.4 (subtraction as an unknown addend; going through ten); Cambridge Primary Mathematics Stage 1. These sources informed the lesson.