You will learn
- See that addition and subtraction are opposites.
- Write a fact family with three numbers.
- Use addition to check subtraction.
- Find a missing number using the family.
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
- Addition and subtraction are opposites.
- Three numbers make a fact family of four sentences.
- Check subtraction by adding.
- Find a missing number using the family.
Words to know
Does the reverse.
Addition and subtraction sentences that use the same three numbers.
Make sure an answer is right.
A number we need to find.
1. Discover: three numbers, many stories
3, 4 and 7. You can say: 3 + 4 = 7. You can also say: 7 − 3 = 4. The same three numbers tell different stories!
2. Understand: addition and subtraction are linked
Subtraction undoes addition. If 3 + 4 = 7, then 7 − 4 = 3 and 7 − 3 = 4.
A fact family for 3, 4, 7: 3 + 4 = 7, 4 + 3 = 7, 7 − 3 = 4, 7 − 4 = 3.
To check 9 − 5 = 4, add: 4 + 5 = 9. It works!
Idea 1: Opposites
Add 3, then take away 3. You are back where you started. Addition and subtraction are opposites. One undoes the other.
Idea 2: Fact family
The numbers 3, 4 and 7 make a fact family:
- 3 + 4 = 7
- 4 + 3 = 7
- 7 − 3 = 4
- 7 − 4 = 3
The biggest number (the whole) comes first in the subtractions.
Idea 3: Check and find the missing number
Check 7 − 4 = 3 by adding: 3 + 4 = 7. It matches.
To find 8 + __ = 12, use subtraction: 12 − 8 = 4.
3. Worked examples
Example 1 (I show you): Fact family for 3, 4, 7
Write the fact family for 3, 4 and 7.
- Add the two parts: 3 + 4 = 7 and 4 + 3 = 7.
- Take away from the whole: 7 − 3 = 4 and 7 − 4 = 3.
Answer: 3 + 4 = 7, 4 + 3 = 7, 7 − 3 = 4, 7 − 4 = 3
Example 2 (We do it together): Check 9 − 4 = 5
Check 9 − 4 = 5 by adding.
- Add what is left and what was taken away.
- 5 + 4 = 9.
- 9 is the start number.
Answer: The answer is correct.
Example 3 (You try): 6 + __ = 10
Find the missing number: 6 + __ = 10
Show the steps and answer
- Use the family: 10 − 6.
- 10 − 6 = 4.
Answer: The missing number is 4.
Did you know?
Mathematicians say subtraction is the inverse of addition. Inverse means it undoes.
Why this matters
Knowing the family helps you check answers and solve missing-number problems.
4. Explore: build a fact family
You need 10 counters.
- Make 6 counters. Add 2 more. Write 6 + 2 = 8.
- Take 2 away from the 8. Write 8 − 2 = 6.
- Take 6 away from the 8. Write 8 − 6 = 2.
- Write the 4 sentences for 2, 6 and 8.
Think about it: what did you notice?
6 + 2 = 8, 2 + 6 = 8, 8 − 2 = 6, 8 − 6 = 2.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ + ___ = ___, so ___ − ___ = ___.
- The three numbers are ___, ___ and ___.
- I check ___ − ___ by adding ___ + ___.
- The missing number is ___.
Guided practice
Question 1. 4 + 5 = 9. What is 9 − 5?
4.
Question 2. Fact family for 2, 3, 5?
2 + 3 = 5, 3 + 2 = 5, 5 − 2 = 3, 5 − 3 = 2.
Question 3. Check 8 − 3 = 5 with addition.
5 + 3 = 8. It works.
Independent practice
Level 1: Start
- 6 + 4 = 10, so 10 − 4 = __
- 9 − 2 = 7, so 7 + 2 = __
- Write the fact family for 5, 5, 10.
- Write the fact family for 1, 8, 9.
- 7 + __ = 12. What is 12 − 7?
Level 2: Grow
- 7 + 3 = 10, so 10 − 3 = __
- 15 − 6 = 9, so 9 + 6 = __
- Write the four sentences for 2, 6 and 8.
Level 3: Stretch
- 9 + __ = 17. Use subtraction to find the missing number.
- Write a fact family for 4, 9 and 13.
- Ana says 14 − 5 = 8. Use addition to check.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
You have 5 marbles. Your friend gives you some. Now you have 9. How many did you get?
Show a sample answer
9 − 5 = 4 marbles.
Another one. You have some marbles. You get 6 more and now have 15. How many did you have at first?
Show a sample answer
15 − 6 = 9 marbles at first.
7. Common mistakes
Fix: Use the same three numbers to make all the sentences.
Fix: There are four sentences when the three numbers are different.
Fix: The biggest number (the whole) always comes first in a subtraction.
8. Lesson summary and revision card
- I can say that addition and subtraction are opposites.
- I can write a fact family with three numbers.
- I can use addition to check subtraction.
- I can find a missing number using the family.
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
- Addition and subtraction undo each other.
- Three numbers can make a fact family of four sentences.
- Use addition to check subtraction.
11. Next lesson
Next lesson: Subtraction word problems. 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.
- Write the four sentences in the fact family for 4, 5 and 9. [4 marks]
- If 8 + 7 = 15, what is 15 − 7? [1 mark]
- Check 13 − 6 = 7 by using addition. [2 marks]
- Find the missing number: 9 + __ = 16. Show how. [2 marks]
- Aisha says 11 − 4 = 8. Use addition to show she is wrong. [2 marks]
Total: 11 marks.
Marking guide and model answers
- 4 + 5 = 9, 5 + 4 = 9, 9 − 4 = 5, 9 − 5 = 4 [1 each]
- 8 [1]
- 7 + 6 [1] = 13, so it is correct [1]
- 16 − 9 [1] = 7 [1]
- 8 + 4 = 12, not 11 [1]; the answer is 7 [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
- 5 + 3 = 8, so 8 − 3 = __
- 10 − 4 = 6, so 6 + 4 = __
- Write one subtraction for 4, 6, 10.
- 7 + __ = 9
- Check 12 − 5 = 7 by adding.
- If 6 + 5 = 11, then 11 − 5 = __
- 10 − 3 = 7, so 7 + 3 = __
- __ + 4 = 9
- Write one subtraction fact from 2 + 7 = 9.
- Are add and take away opposites?
Homework
Pick three numbers that make a fact family (for example 3, 5, 8). Write the four sentences and show a family member.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 5 + 3 = 8, so 8 − 3 = __ | 5 | 2 |
| 10 − 4 = 6, so 6 + 4 = __ | 10 | 2 |
| Write one subtraction for 4, 6, 10. | 10 − 4 = 6 | 2 |
| 7 + __ = 9 | 2 | 2 |
| Check 12 − 5 = 7 by adding. | 7 + 5 = 12 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 5; 2 10; 3 10 − 4 = 6; 4 2; 5 7 + 5 = 12.
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 6; 7 10; 8 5; 9 9 − 2 = 7 or 9 − 7 = 2; 10 Yes.
Independent practice answers. Level 1: 1 6; 2 9; 3 5 + 5 = 10 and 10 − 5 = 5 (only two sentences, since both parts are the same); 4 1 + 8 = 9, 8 + 1 = 9, 9 − 1 = 8, 9 − 8 = 1; 5 5. Level 2: 1 7; 2 15; 3 2 + 6 = 8, 6 + 2 = 8, 8 − 2 = 6, 8 − 6 = 2. Level 3: 1 8; 2 4 + 9 = 13, 9 + 4 = 13, 13 − 4 = 9, 13 − 9 = 4; 3 8 + 5 = 13, not 14. So the answer is 9..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 See that addition and subtraction are opposites | 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 Write a fact family with three numbers | 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 addition to check 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 |
| O4 Find a missing number using the family | 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: Thinking addition and subtraction are not connected. Use the same three numbers to make all the sentences.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use counters to show a fact family for 2, 3, 5, then repeat with other numbers.
- 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 sees that addition and subtraction are linked. You do not need to be good at mathematics to help.
- Say a fact and its family out loud: 3, 4, 7.
- Ask: if 5 + 3 = 8, what is 8 − 3?
- Check subtraction answers 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: see that addition and subtraction are opposites; write a fact family with three numbers; use addition to check subtraction; find a missing number using the family.
Prerequisite knowledge. Addition and subtraction within 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). You need 10 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. Which number comes first in a subtraction? How do you check a take-away? What is the family of 3, 4 and 7?
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. Thinking addition and subtraction are not connected. Use the same three numbers to make all the sentences.
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 counters to show a fact family for 2, 3, 5, then repeat with other numbers. 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.B.4 and 1.OA.D.8 (subtraction as unknown addend; missing numbers); Cambridge Primary Mathematics Stage 1. These sources informed the lesson.