Step-by-step Maths Level 1: Fact families of three numbers
Part of the Step-by-step Maths Level 1 adding and taking away within 10 chapter. Chapter overview · whole chapter on one page
Fact families of three numbers
Three numbers can make a fact family. For example, 3, 6 and 9 make these facts:
3 + 6 = 9, 6 + 3 = 9, 9 − 6 = 3 and 9 − 3 = 6.
Key ideas
- Swapping the two parts does not change the total.
- Subtraction undoes addition.
- One family gives four facts.
Method. Take away the second number from the first. Count back to check.
- Start with the first number. It is the number of things we begin with.6
- Take away 2. Cross out or count back this many.6 - 2
- Write the answer. This is how many are left.4
Check. Add back: 4 + 2 = 6. The answer is right.
Watch out. Count back from the first number, not up from the second.
Method. Put the two groups together. Start at the bigger number and count on.
- Start at the bigger number. It is quicker to count on from the bigger one.5
- Count on 3 more. We add 3 to 5.5 + 3
- Write the answer. 8
Check. Count on from the other number too. You get 8 both ways.
Watch out. Count on, do not start again from one.
Method. The fact family gives a subtraction fact.
- Read the addition. 2 + 7 = 9.2 + 7 = 9
- Take one part away from the total. Take away 2 from 9.9 - 2 = 7
- Write the answer. 7
Check. Add back: 7 + 2 = 9. It works.
Watch out. The subtraction takes away the part that was added.
Watch out
Watch out. You cannot swap the numbers in a subtraction: 9 − 2 is not the same as 2 − 9.
Exam tip
Grown-up tip. Write one family on a card. Ask your child to say the four facts out loud, then cover one number and ask which number is hidden.
Exercise 8B Fact families
Non-calculatorMethod. Put the two groups together. Start at the bigger number and count on.
- Start at the bigger number. It is quicker to count on from the bigger one.4
- Count on 1 more. We add 1 to 4.4 + 1
- Write the answer. 5
Check. Count on from the other number too. You get 5 both ways.
Watch out. Count on, do not start again from one.
Method. Take away the second number from the first. Count back to check.
- Start with the first number. It is the number of things we begin with.8
- Take away 3. Cross out or count back this many.8 - 3
- Write the answer. This is how many are left.5
Check. Add back: 5 + 3 = 8. The answer is right.
Watch out. Count back from the first number, not up from the second.
Method. Take away the second number from the first. Count back to check.
- Start with the first number. It is the number of things we begin with.10
- Take away 4. Cross out or count back this many.10 - 4
- Write the answer. This is how many are left.6
Check. Add back: 6 + 4 = 10. The answer is right.
Watch out. Count back from the first number, not up from the second.
Method. Use the same three numbers in both facts.
- Read the addition. 9 + 1 = 10.9 + 1 = 10
- Take the second part away from the total. This gives the first part.10 - 1 = 9
- Write the answer. 9
Check. Add back: 9 + 1 = 10. ✓
Watch out. The same three numbers make a family of facts.
Method. Put the two groups together. Start at the bigger number and count on.
- Start at the bigger number. It is quicker to count on from the bigger one.5
- Count on 4 more. We add 4 to 5.5 + 4
- Write the answer. 9
Check. Count on from the other number too. You get 9 both ways.
Watch out. Count on, do not start again from one.
Method. Take away the second number from the first. Count back to check.
- Start with the first number. It is the number of things we begin with.8
- Take away 7. Cross out or count back this many.8 - 7
- Write the answer. This is how many are left.1
Check. Add back: 1 + 7 = 8. The answer is right.
Watch out. Count back from the first number, not up from the second.
Method. Take away the second number from the first. Count back to check.
- Start with the first number. It is the number of things we begin with.10
- Take away 7. Cross out or count back this many.10 - 7
- Write the answer. This is how many are left.3
Check. Add back: 3 + 7 = 10. The answer is right.
Watch out. Count back from the first number, not up from the second.
Method. Use the same three numbers in both facts.
- Read the addition. 4 + 5 = 9.4 + 5 = 9
- Take the second part away from the total. This gives the first part.9 - 5 = 4
- Write the answer. 4
Check. Add back: 4 + 5 = 9. ✓
Watch out. The same three numbers make a family of facts.
Method. Put the two groups together. Start at the bigger number and count on.
- Start at the bigger number. It is quicker to count on from the bigger one.5
- Count on 5 more. We add 5 to 5.5 + 5
- Write the answer. 10
Check. Count on from the other number too. You get 10 both ways.
Watch out. Count on, do not start again from one.
Method. Take away the second number from the first. Count back to check.
- Start with the first number. It is the number of things we begin with.8
- Take away 1. Cross out or count back this many.8 - 1
- Write the answer. This is how many are left.7
Check. Add back: 7 + 1 = 8. The answer is right.
Watch out. Count back from the first number, not up from the second.
Method. Take away the second number from the first. Count back to check.
- Start with the first number. It is the number of things we begin with.7
- Take away 3. Cross out or count back this many.7 - 3
- Write the answer. This is how many are left.4
Check. Add back: 4 + 3 = 7. The answer is right.
Watch out. Count back from the first number, not up from the second.
Method. Use the same three numbers in both facts.
- Read the addition. 3 + 3 = 6.3 + 3 = 6
- Take the second part away from the total. This gives the first part.6 - 3 = 3
- Write the answer. 3
Check. Add back: 3 + 3 = 6. ✓
Watch out. The same three numbers make a family of facts.
Method. Put the two groups together. Start at the bigger number and count on.
- Start at the bigger number. It is quicker to count on from the bigger one.4
- Count on 4 more. We add 4 to 4.4 + 4
- Write the answer. 8
Check. Count on from the other number too. You get 8 both ways.
Watch out. Count on, do not start again from one.
Method. Take away the second number from the first. Count back to check.
- Start with the first number. It is the number of things we begin with.10
- Take away 1. Cross out or count back this many.10 - 1
- Write the answer. This is how many are left.9
Check. Add back: 9 + 1 = 10. The answer is right.
Watch out. Count back from the first number, not up from the second.
Method. Take away the second number from the first. Count back to check.
- Start with the first number. It is the number of things we begin with.9
- Take away 6. Cross out or count back this many.9 - 6
- Write the answer. This is how many are left.3
Check. Add back: 3 + 6 = 9. The answer is right.
Watch out. Count back from the first number, not up from the second.
Method. Use the same three numbers in both facts.
- Read the addition. 2 + 4 = 6.2 + 4 = 6
- Take the second part away from the total. This gives the first part.6 - 4 = 2
- Write the answer. 2
Check. Add back: 2 + 4 = 6. ✓
Watch out. The same three numbers make a family of facts.