Taking away within 20
By the end of this chapter you will be able to
- Count back to subtract
- Count up to find the difference
- Use bonds to 10 to take away
- Take away 10 from a number up to 20
- Check with addition and find missing numbers
You should already know
- Adding within 20 (Chapter 5)
- Number bonds to 20 (Chapter 4)
Where this leads
- Adding and subtracting within 100 (Chapter 7)
- Money (Chapter 8)
Step-by-step practice: maths (Level 2). Small steps, repeated until fluent. Content: Subtract a 1-digit number from a number up to 20 by counting back, Find the difference between two numbers up to 20 by counting up, Use a bond to 10 to subtract, going through 10, Subtract a multiple of 10 from a 2-digit number up to 20, Use addition to check a subtraction, and find a missing number in a subtraction.
Exercise P Do you remember?
Non-calculatorMethod. Start at the first number and count back the second number.
- Start at 13. It is the number we begin with.13
- Count back 2. Say each number as you go back.13 - 2 = 11
- Write the answer. This is how many are left.11
Check. Count on 2 from 11 to check: you reach 13.
Watch out. Count back from the first number. Do not count the starting number again.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 4. We count up to the bigger number.4
- Count up to 11. Count each step as you go.11 - 4 = 7
- Write the difference. The number of steps is the difference.7
Check. 4 + 7 = 11. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.17
- Take away one ten. Take away 10 from the tens.17 - 10 = 7
- Write the answer. The ones stay the same.7
Check. Add 10 back: 7 + 10 = 17.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Find the number to take away. Check by adding it back.
- Start with 14. It is the number we begin with.14
- Find how many are taken away to reach 9. Count back, or take the answer away from the start.14 - 9 = 5
- Write the missing number. 5
Check. Add back: 9 + 5 = 14. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Work out the subtraction. Then add the number you took away to the answer.
- Work out 18 - 6. Count back from the first number.18 - 6 = 12
- Check by adding. If the answer is right, adding back gives the first number.12 + 6 = 18
- Write the answer. 12
Check. 12 + 6 = 18, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.
Counting back to take away
Taking away means making a number smaller. Start at the first number and count back.
For 15 - 4, start at 15 and count back 4: 14, 13, 12, 11. The answer is 11.
Key ideas
- Start at the first number.
- Count back the number you take away.
- The last number you say is the answer.
Method. Start at the first number and count back the second number.
- Start at 15. It is the number we begin with.15
- Count back 4. Say each number as you go back.15 - 4 = 11
- Write the answer. This is how many are left.11
Check. Count on 4 from 11 to check: you reach 15.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 19. It is the number we begin with.19
- Count back 7. Say each number as you go back.19 - 7 = 12
- Write the answer. This is how many are left.12
Check. Count on 7 from 12 to check: you reach 19.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 18. It is the number we begin with.18
- Count back 5. Say each number as you go back.18 - 5 = 13
- Write the answer. This is how many are left.13
Check. Count on 5 from 13 to check: you reach 18.
Watch out. Count back from the first number. Do not count the starting number again.
Watch out
Watch out. Do not count the starting number. Say 14 first, not 15.
Exam tip
Grown-up tip. Use a number line or stairs. Start at the top and walk down one step at a time.
Exercise 6A Practice: counting back
Non-calculatorMethod. Start at the first number and count back the second number.
- Start at 12. It is the number we begin with.12
- Count back 6. Say each number as you go back.12 - 6 = 6
- Write the answer. This is how many are left.6
Check. Count on 6 from 6 to check: you reach 12.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 9. It is the number we begin with.9
- Count back 6. Say each number as you go back.9 - 6 = 3
- Write the answer. This is how many are left.3
Check. Count on 6 from 3 to check: you reach 9.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 15. It is the number we begin with.15
- Count back 9. Say each number as you go back.15 - 9 = 6
- Write the answer. This is how many are left.6
Check. Count on 9 from 6 to check: you reach 15.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 9. It is the number we begin with.9
- Count back 9. Say each number as you go back.9 - 9 = 0
- Write the answer. This is how many are left.0
Check. Count on 9 from 0 to check: you reach 9.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 8. It is the number we begin with.8
- Count back 1. Say each number as you go back.8 - 1 = 7
- Write the answer. This is how many are left.7
Check. Count on 1 from 7 to check: you reach 8.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 5. It is the number we begin with.5
- Count back 5. Say each number as you go back.5 - 5 = 0
- Write the answer. This is how many are left.0
Check. Count on 5 from 0 to check: you reach 5.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 11. It is the number we begin with.11
- Count back 8. Say each number as you go back.11 - 8 = 3
- Write the answer. This is how many are left.3
Check. Count on 8 from 3 to check: you reach 11.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 11. It is the number we begin with.11
- Count back 4. Say each number as you go back.11 - 4 = 7
- Write the answer. This is how many are left.7
Check. Count on 4 from 7 to check: you reach 11.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 13. It is the number we begin with.13
- Count back 8. Say each number as you go back.13 - 8 = 5
- Write the answer. This is how many are left.5
Check. Count on 8 from 5 to check: you reach 13.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 6. It is the number we begin with.6
- Count back 5. Say each number as you go back.6 - 5 = 1
- Write the answer. This is how many are left.1
Check. Count on 5 from 1 to check: you reach 6.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 17. It is the number we begin with.17
- Count back 2. Say each number as you go back.17 - 2 = 15
- Write the answer. This is how many are left.15
Check. Count on 2 from 15 to check: you reach 17.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 17. It is the number we begin with.17
- Count back 5. Say each number as you go back.17 - 5 = 12
- Write the answer. This is how many are left.12
Check. Count on 5 from 12 to check: you reach 17.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 13. It is the number we begin with.13
- Count back 1. Say each number as you go back.13 - 1 = 12
- Write the answer. This is how many are left.12
Check. Count on 1 from 12 to check: you reach 13.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 9. It is the number we begin with.9
- Count back 4. Say each number as you go back.9 - 4 = 5
- Write the answer. This is how many are left.5
Check. Count on 4 from 5 to check: you reach 9.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 9. It is the number we begin with.9
- Count back 3. Say each number as you go back.9 - 3 = 6
- Write the answer. This is how many are left.6
Check. Count on 3 from 6 to check: you reach 9.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 20. It is the number we begin with.20
- Count back 3. Say each number as you go back.20 - 3 = 17
- Write the answer. This is how many are left.17
Check. Count on 3 from 17 to check: you reach 20.
Watch out. Count back from the first number. Do not count the starting number again.
Finding the difference by counting up
The difference is how far apart two numbers are.
Count up from the smaller number to the bigger one. The number of steps is the difference.
Key ideas
- Difference means how far apart.
- Count up from the smaller number.
- The number of steps is the answer.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 12. We count up to the bigger number.12
- Count up to 17. Count each step as you go.17 - 12 = 5
- Write the difference. The number of steps is the difference.5
Check. 12 + 5 = 17. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 6. We count up to the bigger number.6
- Count up to 14. Count each step as you go.14 - 6 = 8
- Write the difference. The number of steps is the difference.8
Check. 6 + 8 = 14. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 9. We count up to the bigger number.9
- Count up to 15. Count each step as you go.15 - 9 = 6
- Write the difference. The number of steps is the difference.6
Check. 9 + 6 = 15. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Watch out
Watch out. Count the steps, not the numbers. From 12 to 17 there are 5 steps, not 6.
Exam tip
Grown-up tip. Ask: “How many more is 17 than 12?” Count up on fingers.
Exercise 6B Practice: finding the difference
Non-calculatorMethod. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 1. We count up to the bigger number.1
- Count up to 13. Count each step as you go.13 - 1 = 12
- Write the difference. The number of steps is the difference.12
Check. 1 + 12 = 13. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 3. We count up to the bigger number.3
- Count up to 16. Count each step as you go.16 - 3 = 13
- Write the difference. The number of steps is the difference.13
Check. 3 + 13 = 16. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 1. We count up to the bigger number.1
- Count up to 3. Count each step as you go.3 - 1 = 2
- Write the difference. The number of steps is the difference.2
Check. 1 + 2 = 3. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 6. We count up to the bigger number.6
- Count up to 10. Count each step as you go.10 - 6 = 4
- Write the difference. The number of steps is the difference.4
Check. 6 + 4 = 10. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 11. We count up to the bigger number.11
- Count up to 16. Count each step as you go.16 - 11 = 5
- Write the difference. The number of steps is the difference.5
Check. 11 + 5 = 16. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 2. We count up to the bigger number.2
- Count up to 16. Count each step as you go.16 - 2 = 14
- Write the difference. The number of steps is the difference.14
Check. 2 + 14 = 16. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 4. We count up to the bigger number.4
- Count up to 16. Count each step as you go.16 - 4 = 12
- Write the difference. The number of steps is the difference.12
Check. 4 + 12 = 16. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 2. We count up to the bigger number.2
- Count up to 14. Count each step as you go.14 - 2 = 12
- Write the difference. The number of steps is the difference.12
Check. 2 + 12 = 14. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 15. We count up to the bigger number.15
- Count up to 20. Count each step as you go.20 - 15 = 5
- Write the difference. The number of steps is the difference.5
Check. 15 + 5 = 20. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 1. We count up to the bigger number.1
- Count up to 8. Count each step as you go.8 - 1 = 7
- Write the difference. The number of steps is the difference.7
Check. 1 + 7 = 8. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 12. We count up to the bigger number.12
- Count up to 14. Count each step as you go.14 - 12 = 2
- Write the difference. The number of steps is the difference.2
Check. 12 + 2 = 14. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 2. We count up to the bigger number.2
- Count up to 17. Count each step as you go.17 - 2 = 15
- Write the difference. The number of steps is the difference.15
Check. 2 + 15 = 17. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 7. We count up to the bigger number.7
- Count up to 16. Count each step as you go.16 - 7 = 9
- Write the difference. The number of steps is the difference.9
Check. 7 + 9 = 16. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 1. We count up to the bigger number.1
- Count up to 9. Count each step as you go.9 - 1 = 8
- Write the difference. The number of steps is the difference.8
Check. 1 + 8 = 9. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 1. We count up to the bigger number.1
- Count up to 5. Count each step as you go.5 - 1 = 4
- Write the difference. The number of steps is the difference.4
Check. 1 + 4 = 5. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 2. We count up to the bigger number.2
- Count up to 12. Count each step as you go.12 - 2 = 10
- Write the difference. The number of steps is the difference.10
Check. 2 + 10 = 12. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Taking away with bonds to 10
Sometimes you have to take away more than the ones. For 15 - 8, first take away 5 to reach 10.
Then take the rest away from 10: 10 - 3 = 7.
Key ideas
- Take away the part that gets to 10 first.
- Then take the rest away from 10.
- Check by adding back.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 5 away from 15. That leaves exactly 10.15 - 5 = 10
- Take the rest, 3, away from 10. 8 is 5 and 3, so take away 3 now.10 - 3 = 7
- Write the answer. 7
Check. Add back: 7 + 8 = 15. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 3 away from 13. That leaves exactly 10.13 - 3 = 10
- Take the rest, 3, away from 10. 6 is 3 and 3, so take away 3 now.10 - 3 = 7
- Write the answer. 7
Check. Add back: 7 + 6 = 13. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 7 away from 17. That leaves exactly 10.17 - 7 = 10
- Take the rest, 2, away from 10. 9 is 7 and 2, so take away 2 now.10 - 2 = 8
- Write the answer. 8
Check. Add back: 8 + 9 = 17. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Watch out
Watch out. Do not take all of the number from 10. Go to 10 first, then take the rest.
Exam tip
Grown-up tip. Use two colours of counters. Take away the first colour to reach 10, then the second colour.
Exercise 6C Practice: taking away through 10
Non-calculatorMethod. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 1 away from 11. That leaves exactly 10.11 - 1 = 10
- Take the rest, 6, away from 10. 7 is 1 and 6, so take away 6 now.10 - 6 = 4
- Write the answer. 4
Check. Add back: 4 + 7 = 11. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 1 away from 11. That leaves exactly 10.11 - 1 = 10
- Take the rest, 3, away from 10. 4 is 1 and 3, so take away 3 now.10 - 3 = 7
- Write the answer. 7
Check. Add back: 7 + 4 = 11. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 2 away from 12. That leaves exactly 10.12 - 2 = 10
- Take the rest, 5, away from 10. 7 is 2 and 5, so take away 5 now.10 - 5 = 5
- Write the answer. 5
Check. Add back: 5 + 7 = 12. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 2 away from 12. That leaves exactly 10.12 - 2 = 10
- Take the rest, 6, away from 10. 8 is 2 and 6, so take away 6 now.10 - 6 = 4
- Write the answer. 4
Check. Add back: 4 + 8 = 12. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 4 away from 14. That leaves exactly 10.14 - 4 = 10
- Take the rest, 2, away from 10. 6 is 4 and 2, so take away 2 now.10 - 2 = 8
- Write the answer. 8
Check. Add back: 8 + 6 = 14. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 4 away from 14. That leaves exactly 10.14 - 4 = 10
- Take the rest, 5, away from 10. 9 is 4 and 5, so take away 5 now.10 - 5 = 5
- Write the answer. 5
Check. Add back: 5 + 9 = 14. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 7 away from 17. That leaves exactly 10.17 - 7 = 10
- Take the rest, 1, away from 10. 8 is 7 and 1, so take away 1 now.10 - 1 = 9
- Write the answer. 9
Check. Add back: 9 + 8 = 17. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 1 away from 11. That leaves exactly 10.11 - 1 = 10
- Take the rest, 1, away from 10. 2 is 1 and 1, so take away 1 now.10 - 1 = 9
- Write the answer. 9
Check. Add back: 9 + 2 = 11. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 1 away from 11. That leaves exactly 10.11 - 1 = 10
- Take the rest, 7, away from 10. 8 is 1 and 7, so take away 7 now.10 - 7 = 3
- Write the answer. 3
Check. Add back: 3 + 8 = 11. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 3 away from 13. That leaves exactly 10.13 - 3 = 10
- Take the rest, 5, away from 10. 8 is 3 and 5, so take away 5 now.10 - 5 = 5
- Write the answer. 5
Check. Add back: 5 + 8 = 13. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 4 away from 14. That leaves exactly 10.14 - 4 = 10
- Take the rest, 3, away from 10. 7 is 4 and 3, so take away 3 now.10 - 3 = 7
- Write the answer. 7
Check. Add back: 7 + 7 = 14. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 5 away from 15. That leaves exactly 10.15 - 5 = 10
- Take the rest, 3, away from 10. 8 is 5 and 3, so take away 3 now.10 - 3 = 7
- Write the answer. 7
Check. Add back: 7 + 8 = 15. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 4 away from 14. That leaves exactly 10.14 - 4 = 10
- Take the rest, 1, away from 10. 5 is 4 and 1, so take away 1 now.10 - 1 = 9
- Write the answer. 9
Check. Add back: 9 + 5 = 14. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 4 away from 14. That leaves exactly 10.14 - 4 = 10
- Take the rest, 4, away from 10. 8 is 4 and 4, so take away 4 now.10 - 4 = 6
- Write the answer. 6
Check. Add back: 6 + 8 = 14. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 3 away from 13. That leaves exactly 10.13 - 3 = 10
- Take the rest, 4, away from 10. 7 is 3 and 4, so take away 4 now.10 - 4 = 6
- Write the answer. 6
Check. Add back: 6 + 7 = 13. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 6 away from 16. That leaves exactly 10.16 - 6 = 10
- Take the rest, 2, away from 10. 8 is 6 and 2, so take away 2 now.10 - 2 = 8
- Write the answer. 8
Check. Add back: 8 + 8 = 16. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Taking away 10 from a number up to 20
When you take away 10, you take away one ten.
Only the tens change. The ones stay the same.
Key ideas
- Taking away 10 changes the tens digit.
- The ones digit stays the same.
- For 18 - 10, the answer is 8.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.18
- Take away one ten. Take away 10 from the tens.18 - 10 = 8
- Write the answer. The ones stay the same.8
Check. Add 10 back: 8 + 10 = 18.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.14
- Take away one ten. Take away 10 from the tens.14 - 10 = 4
- Write the answer. The ones stay the same.4
Check. Add 10 back: 4 + 10 = 14.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.20
- Take away one ten. Take away 10 from the tens.20 - 10 = 10
- Write the answer. The ones stay the same.10
Check. Add 10 back: 10 + 10 = 20.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Watch out
Watch out. 20 - 10 is 10, not 0. Only one ten is taken away.
Exam tip
Grown-up tip. Use two ten frames. Empty one frame and count what is left in the other.
Exercise 6D Practice: taking away 10
Non-calculatorMethod. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.13
- Take away one ten. Take away 10 from the tens.13 - 10 = 3
- Write the answer. The ones stay the same.3
Check. Add 10 back: 3 + 10 = 13.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.15
- Take away one ten. Take away 10 from the tens.15 - 10 = 5
- Write the answer. The ones stay the same.5
Check. Add 10 back: 5 + 10 = 15.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.16
- Take away one ten. Take away 10 from the tens.16 - 10 = 6
- Write the answer. The ones stay the same.6
Check. Add 10 back: 6 + 10 = 16.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.19
- Take away one ten. Take away 10 from the tens.19 - 10 = 9
- Write the answer. The ones stay the same.9
Check. Add 10 back: 9 + 10 = 19.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.17
- Take away one ten. Take away 10 from the tens.17 - 10 = 7
- Write the answer. The ones stay the same.7
Check. Add 10 back: 7 + 10 = 17.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.20
- Take away one ten. Take away 10 from the tens.20 - 10 = 10
- Write the answer. The ones stay the same.10
Check. Add 10 back: 10 + 10 = 20.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.12
- Take away one ten. Take away 10 from the tens.12 - 10 = 2
- Write the answer. The ones stay the same.2
Check. Add 10 back: 2 + 10 = 12.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.16
- Take away one ten. Take away 10 from the tens.16 - 10 = 6
- Write the answer. The ones stay the same.6
Check. Add 10 back: 6 + 10 = 16.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.18
- Take away one ten. Take away 10 from the tens.18 - 10 = 8
- Write the answer. The ones stay the same.8
Check. Add 10 back: 8 + 10 = 18.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.14
- Take away one ten. Take away 10 from the tens.14 - 10 = 4
- Write the answer. The ones stay the same.4
Check. Add 10 back: 4 + 10 = 14.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.11
- Take away one ten. Take away 10 from the tens.11 - 10 = 1
- Write the answer. The ones stay the same.1
Check. Add 10 back: 1 + 10 = 11.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.18
- Take away one ten. Take away 10 from the tens.18 - 10 = 8
- Write the answer. The ones stay the same.8
Check. Add 10 back: 8 + 10 = 18.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.12
- Take away one ten. Take away 10 from the tens.12 - 10 = 2
- Write the answer. The ones stay the same.2
Check. Add 10 back: 2 + 10 = 12.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.17
- Take away one ten. Take away 10 from the tens.17 - 10 = 7
- Write the answer. The ones stay the same.7
Check. Add 10 back: 7 + 10 = 17.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.14
- Take away one ten. Take away 10 from the tens.14 - 10 = 4
- Write the answer. The ones stay the same.4
Check. Add 10 back: 4 + 10 = 14.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.11
- Take away one ten. Take away 10 from the tens.11 - 10 = 1
- Write the answer. The ones stay the same.1
Check. Add 10 back: 1 + 10 = 11.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Missing numbers and checking
A subtraction can have a missing number. Ask: “What do I take away to get from the start to the answer?”
To check any answer, add the number you took away back on to the answer.
Key ideas
- Subtraction and addition undo each other.
- Check by adding back.
- A missing number is found by working backwards.
Method. Find the number to take away. Check by adding it back.
- Start with 15. It is the number we begin with.15
- Find how many are taken away to reach 9. Count back, or take the answer away from the start.15 - 9 = 6
- Write the missing number. 6
Check. Add back: 9 + 6 = 15. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Work out the subtraction. Then add the number you took away to the answer.
- Work out 16 - 9. Count back from the first number.16 - 9 = 7
- Check by adding. If the answer is right, adding back gives the first number.7 + 9 = 16
- Write the answer. 7
Check. 7 + 9 = 16, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.
Method. Find the number to take away. Check by adding it back.
- Start with 13. It is the number we begin with.13
- Find how many are taken away to reach 9. Count back, or take the answer away from the start.13 - 9 = 4
- Write the missing number. 4
Check. Add back: 9 + 4 = 13. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Watch out
Watch out. In 15 - ? = 9, the missing number is 6, not 9. The answer is the number after the equals sign.
Exam tip
Grown-up tip. Use addition to check every subtraction. Ask: “Does the answer add back to the start?”
Exercise 6E Practice: missing numbers and checking
Non-calculatorMethod. Work out the subtraction. Then add the number you took away to the answer.
- Work out 17 - 10. Count back from the first number.17 - 10 = 7
- Check by adding. If the answer is right, adding back gives the first number.7 + 10 = 17
- Write the answer. 7
Check. 7 + 10 = 17, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.
Method. Work out the subtraction. Then add the number you took away to the answer.
- Work out 12 - 4. Count back from the first number.12 - 4 = 8
- Check by adding. If the answer is right, adding back gives the first number.8 + 4 = 12
- Write the answer. 8
Check. 8 + 4 = 12, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.
Method. Find the number to take away. Check by adding it back.
- Start with 7. It is the number we begin with.7
- Find how many are taken away to reach 3. Count back, or take the answer away from the start.7 - 3 = 4
- Write the missing number. 4
Check. Add back: 3 + 4 = 7. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Find the number to take away. Check by adding it back.
- Start with 10. It is the number we begin with.10
- Find how many are taken away to reach 7. Count back, or take the answer away from the start.10 - 7 = 3
- Write the missing number. 3
Check. Add back: 7 + 3 = 10. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Work out the subtraction. Then add the number you took away to the answer.
- Work out 12 - 5. Count back from the first number.12 - 5 = 7
- Check by adding. If the answer is right, adding back gives the first number.7 + 5 = 12
- Write the answer. 7
Check. 7 + 5 = 12, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.
Method. Find the number to take away. Check by adding it back.
- Start with 19. It is the number we begin with.19
- Find how many are taken away to reach 15. Count back, or take the answer away from the start.19 - 15 = 4
- Write the missing number. 4
Check. Add back: 15 + 4 = 19. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Work out the subtraction. Then add the number you took away to the answer.
- Work out 17 - 8. Count back from the first number.17 - 8 = 9
- Check by adding. If the answer is right, adding back gives the first number.9 + 8 = 17
- Write the answer. 9
Check. 9 + 8 = 17, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.
Method. Work out the subtraction. Then add the number you took away to the answer.
- Work out 11 - 1. Count back from the first number.11 - 1 = 10
- Check by adding. If the answer is right, adding back gives the first number.10 + 1 = 11
- Write the answer. 10
Check. 10 + 1 = 11, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.
Method. Work out the subtraction. Then add the number you took away to the answer.
- Work out 15 - 10. Count back from the first number.15 - 10 = 5
- Check by adding. If the answer is right, adding back gives the first number.5 + 10 = 15
- Write the answer. 5
Check. 5 + 10 = 15, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.
Method. Find the number to take away. Check by adding it back.
- Start with 16. It is the number we begin with.16
- Find how many are taken away to reach 15. Count back, or take the answer away from the start.16 - 15 = 1
- Write the missing number. 1
Check. Add back: 15 + 1 = 16. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Find the number to take away. Check by adding it back.
- Start with 13. It is the number we begin with.13
- Find how many are taken away to reach 2. Count back, or take the answer away from the start.13 - 2 = 11
- Write the missing number. 11
Check. Add back: 2 + 11 = 13. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Find the number to take away. Check by adding it back.
- Start with 18. It is the number we begin with.18
- Find how many are taken away to reach 8. Count back, or take the answer away from the start.18 - 8 = 10
- Write the missing number. 10
Check. Add back: 8 + 10 = 18. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Find the number to take away. Check by adding it back.
- Start with 7. It is the number we begin with.7
- Find how many are taken away to reach 6. Count back, or take the answer away from the start.7 - 6 = 1
- Write the missing number. 1
Check. Add back: 6 + 1 = 7. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Find the number to take away. Check by adding it back.
- Start with 9. It is the number we begin with.9
- Find how many are taken away to reach 4. Count back, or take the answer away from the start.9 - 4 = 5
- Write the missing number. 5
Check. Add back: 4 + 5 = 9. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Work out the subtraction. Then add the number you took away to the answer.
- Work out 18 - 3. Count back from the first number.18 - 3 = 15
- Check by adding. If the answer is right, adding back gives the first number.15 + 3 = 18
- Write the answer. 15
Check. 15 + 3 = 18, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.
Method. Find the number to take away. Check by adding it back.
- Start with 10. It is the number we begin with.10
- Find how many are taken away to reach 1. Count back, or take the answer away from the start.10 - 1 = 9
- Write the missing number. 9
Check. Add back: 1 + 9 = 10. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Chapter summary
| Skill | Method |
|---|---|
| Counting back | Start at the first number and count back |
| Difference | Count up from the smaller number; count the steps |
| Through 10 | Take away the part that reaches 10, then the rest |
| Taking away 10 | Only the tens digit changes |
| Missing and checking | Find the missing part; check by adding back |
Can you…?
- I can count back to take away a number up to 20
- I can count up to find the difference between two numbers
- I can use a bond to 10 to take away when I need to go through 10
- I can take away 10 from a number up to 20
- I can find a missing number and check by adding
Key terms
- take away
- subtract; make a number smaller
- difference
- how far apart two numbers are
- subtraction
- taking one number away from another
- check
- use addition to see if the subtraction is right
Exercise 6Z Check-up
Non-calculatorMethod. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 3. We count up to the bigger number.3
- Count up to 17. Count each step as you go.17 - 3 = 14
- Write the difference. The number of steps is the difference.14
Check. 3 + 14 = 17. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 8. We count up to the bigger number.8
- Count up to 18. Count each step as you go.18 - 8 = 10
- Write the difference. The number of steps is the difference.10
Check. 8 + 10 = 18. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 1 away from 11. That leaves exactly 10.11 - 1 = 10
- Take the rest, 3, away from 10. 4 is 1 and 3, so take away 3 now.10 - 3 = 7
- Write the answer. 7
Check. Add back: 7 + 4 = 11. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Work out the subtraction. Then add the number you took away to the answer.
- Work out 16 - 9. Count back from the first number.16 - 9 = 7
- Check by adding. If the answer is right, adding back gives the first number.7 + 9 = 16
- Write the answer. 7
Check. 7 + 9 = 16, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.
Method. Start at the first number and count back the second number.
- Start at 20. It is the number we begin with.20
- Count back 5. Say each number as you go back.20 - 5 = 15
- Write the answer. This is how many are left.15
Check. Count on 5 from 15 to check: you reach 20.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.13
- Take away one ten. Take away 10 from the tens.13 - 10 = 3
- Write the answer. The ones stay the same.3
Check. Add 10 back: 3 + 10 = 13.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Taking away 10 takes away one ten. Only the tens digit changes.
- Look at the number. It has one ten and some ones.16
- Take away one ten. Take away 10 from the tens.16 - 10 = 6
- Write the answer. The ones stay the same.6
Check. Add 10 back: 6 + 10 = 16.
Watch out. Taking away 10 changes the tens, not the ones: 17 - 10 = 7.
Method. Start at the first number and count back the second number.
- Start at 15. It is the number we begin with.15
- Count back 9. Say each number as you go back.15 - 9 = 6
- Write the answer. This is how many are left.6
Check. Count on 9 from 6 to check: you reach 15.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Start at the first number and count back the second number.
- Start at 12. It is the number we begin with.12
- Count back 8. Say each number as you go back.12 - 8 = 4
- Write the answer. This is how many are left.4
Check. Count on 8 from 4 to check: you reach 12.
Watch out. Count back from the first number. Do not count the starting number again.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 2 away from 12. That leaves exactly 10.12 - 2 = 10
- Take the rest, 4, away from 10. 6 is 2 and 4, so take away 4 now.10 - 4 = 6
- Write the answer. 6
Check. Add back: 6 + 6 = 12. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Total 19 marks. Allow about 19 minutes.
Exercise 6X Practice test questions
Non-calculatorMethod. Find the number to take away. Check by adding it back.
- Start with 11. It is the number we begin with.11
- Find how many are taken away to reach 3. Count back, or take the answer away from the start.11 - 3 = 8
- Write the missing number. 8
Check. Add back: 3 + 8 = 11. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Find the number to take away. Check by adding it back.
- Start with 8. It is the number we begin with.8
- Find how many are taken away to reach 7. Count back, or take the answer away from the start.8 - 7 = 1
- Write the missing number. 1
Check. Add back: 7 + 1 = 8. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 3. We count up to the bigger number.3
- Count up to 19. Count each step as you go.19 - 3 = 16
- Write the difference. The number of steps is the difference.16
Check. 3 + 16 = 19. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. Start at the first number and count back the second number.
- Start at 20. It is the number we begin with.20
- Count back 7. Say each number as you go back.20 - 7 = 13
- Write the answer. This is how many are left.13
Check. Count on 7 from 13 to check: you reach 20.
Watch out. Count back from the first number. Do not count the starting number again.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 5. We count up to the bigger number.5
- Count up to 8. Count each step as you go.8 - 5 = 3
- Write the difference. The number of steps is the difference.3
Check. 5 + 3 = 8. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. Find the number to take away. Check by adding it back.
- Start with 20. It is the number we begin with.20
- Find how many are taken away to reach 3. Count back, or take the answer away from the start.20 - 3 = 17
- Write the missing number. 17
Check. Add back: 3 + 17 = 20. It works.
Watch out. The missing number is the one that gets you from the start to the answer.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 5 away from 15. That leaves exactly 10.15 - 5 = 10
- Take the rest, 2, away from 10. 7 is 5 and 2, so take away 2 now.10 - 2 = 8
- Write the answer. 8
Check. Add back: 8 + 7 = 15. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. Use a bond to 10 to help. Take away the part that gets to 10 first.
- Take 5 away from 15. That leaves exactly 10.15 - 5 = 10
- Take the rest, 4, away from 10. 9 is 5 and 4, so take away 4 now.10 - 4 = 6
- Write the answer. 6
Check. Add back: 6 + 9 = 15. It is right.
Watch out. Going through 10 can be done in two steps. Do not take the whole number from 10 by mistake.
Method. The difference is how far apart the numbers are. Count up from the smaller number.
- Start at the smaller number, 6. We count up to the bigger number.6
- Count up to 14. Count each step as you go.14 - 6 = 8
- Write the difference. The number of steps is the difference.8
Check. 6 + 8 = 14. The difference is right.
Watch out. The difference is not the bigger number. It is the number of steps between them.
Method. Work out the subtraction. Then add the number you took away to the answer.
- Work out 6 - 5. Count back from the first number.6 - 5 = 1
- Check by adding. If the answer is right, adding back gives the first number.1 + 5 = 6
- Write the answer. 1
Check. 1 + 5 = 6, so the answer is right.
Watch out. Subtraction and addition undo each other. Use addition to check.