Year 1 Adding and Subtracting within 20: worked examples and questions with answers
By the end of this chapter you will be able to
- Find pairs of numbers that make a total up to 20
- Make 10 first, then add the rest
- Work out doubles and near doubles
- Add and take away within 20, counting on and back
- Find how many more one group has than another
- Find a missing number and solve one-step problems
You should already know
- Adding and taking away within 10 (Chapter 2)
- Counting on and back on a number line
- Numbers to 20 (Chapter 4)
Where this leads
- Numbers to 100 (Chapter 6)
- Grouping and sharing (Chapter 9)
National Curriculum for England, Key Stage 1 mathematics, Year 1. Content: Number bonds and related subtraction facts within 20, Add and subtract one-digit and two-digit numbers to 20, including zero, Doubles and near doubles, Make 10 to add, Find the difference, Missing number problems and one-step problems.
- 5.1 Number bonds to 20: Worksheet (PDF) · Answers (PDF) · lesson page
- 5.2 Make 10 to add: Worksheet (PDF) · Answers (PDF) · lesson page
- 5.3 Doubles and near doubles: Worksheet (PDF) · Answers (PDF) · lesson page
- 5.4 Adding and taking away to 20, including zero: Worksheet (PDF) · Answers (PDF) · lesson page
- 5.5 Finding the difference: Worksheet (PDF) · Answers (PDF) · lesson page
- 5.6 Missing numbers and one-step problems: Worksheet (PDF) · Answers (PDF) · lesson page
- Check-up and end-of-chapter quiz: Worksheet (PDF) · Answers (PDF) · lesson page
Exercise P Do you remember?
Non-calculatorMethod. Count on one at a time from 7.
- Start at 7. We count on from the number we have.7
- Say the next three numbers. Each number is one more than the one before.8, 9, 10
- Write the answer. 8, 9, 10
Check. Count back from 10 to 7 to check: 10, 9, 8, 7. ✓
Watch out. Start with the number after 7, not 7 itself.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 10. Part I know: 4.
- Take the part you know away from the whole. Subtracting finds the missing part.10 − 4 = 6
- Write the missing part. 6
Check. Check: 4 + 6 = 10. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Method. The bigger number is the one that comes later when we count.
- Look at 15 and 9. Think about which number comes later in the count.15 and 9
- Count on from 9. The number we reach later is the bigger one.9 → 15
- Write the answer. 15 is bigger.
Check. Count back from 15 to 9. You pass through the smaller number. ✓
Watch out. Do not choose a number because it has more digits. Count to see which is bigger.
Key words. A number word is the name of a number, like seven.
Method. Say the number out loud, then write its name in words.
- Say the number. Listen to how it sounds.8
- Find its name on the number list. Every number has one name.8 = eight
- Write the word. The word has 5 letters.eight
Check. Count out 8 things and say “eight” at the end. ✓
Watch out. Look at the whole word and check every letter.
Key words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 3. Then count on 2.
- Start at 3. Start with the bigger number. You do not need to start at 1.Start: 3
- Count on 2 more. Say each number as you move one step on.4, 5
- Write the answer. The last number you say is the answer.5
Check. Count back 2 from 5. You reach 3 again. ✓
Watch out. Count on from 3. Do not say 3 again as the first step.
Number bonds to 20
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A number bond is two numbers that make a total. The total is the whole. The two numbers are the parts.
Look at this picture. The whole is 14. One part is 9 and the other part is 5. Nine and five make fourteen.
One picture gives you four facts: 9 + 5 = 14, 5 + 9 = 14, 14 − 5 = 9 and 14 − 9 = 5.
Key ideas
- Two parts make one whole.
- Swap the parts and the total stays the same: 9 + 5 = 5 + 9.
- One fact gives you related facts: 9 + 5 = 14 means 14 − 5 = 9.
- To find a missing part, take the part you know away from the whole.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 14. Part I know: 9.
- Take the part you know away from the whole. Subtracting finds the missing part.14 − 9 = 5
- Write the missing part. 5
Check. Check: 9 + 5 = 14. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 20. Part I know: 12.
- Take the part you know away from the whole. Subtracting finds the missing part.20 − 12 = 8
- Write the missing part. 8
Check. Check: 12 + 8 = 20. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A fact family is four facts that use the same three numbers.
Method. Two parts make one whole. Each part can be found by taking the other part away from the whole.
- Put the two parts together, both ways. Adding the parts in either order gives the same whole.6 + 9 = 15 and 9 + 6 = 15
- Take each part away from the whole. Each take-away fact finds the part that is left.15 − 6 = 9 and 15 − 9 = 6
- Write all four facts. 6 + 9 = 15, 9 + 6 = 15, 15 − 6 = 9, 15 − 9 = 6
Check. Check one fact: 6 + 9 = 15, so 15 − 9 = 6. ✓
Watch out. Keep the whole at the start of a take-away. Write 15 − 6, not 6 − 15.
Watch out
Watch out: to find a missing part, take the part you know away from the whole. Do not add the two numbers together.
Exam tip
Grown-up tip. Put 14 buttons or pasta shapes in a pile. Hide 9 of them in one hand and show the rest. Ask: “How many are in my hand?” Then swap hands and say the facts out loud.
Exercise 5A Number bonds to 20
Non-calculatorKey words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 10. Part I know: 4.
- Take the part you know away from the whole. Subtracting finds the missing part.10 − 4 = 6
- Write the missing part. 6
Check. Check: 4 + 6 = 10. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 13. Part I know: 8.
- Take the part you know away from the whole. Subtracting finds the missing part.13 − 8 = 5
- Write the missing part. 5
Check. Check: 8 + 5 = 13. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 17. Part I know: 9.
- Take the part you know away from the whole. Subtracting finds the missing part.17 − 9 = 8
- Write the missing part. 8
Check. Check: 9 + 8 = 17. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 20. Part I know: 11.
- Take the part you know away from the whole. Subtracting finds the missing part.20 − 11 = 9
- Write the missing part. 9
Check. Check: 11 + 9 = 20. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 16. Part I know: 7.
- Take the part you know away from the whole. Subtracting finds the missing part.16 − 7 = 9
- Write the missing part. 9
Check. Check: 7 + 9 = 16. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 14. Part I know: 8.
- Take the part you know away from the whole. Subtracting finds the missing part.14 − 8 = 6
- Write the missing part. 6
Check. Check: 8 + 6 = 14. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 12. Part I know: 5.
- Take the part you know away from the whole. Subtracting finds the missing part.12 − 5 = 7
- Write the missing part. 7
Check. Check: 5 + 7 = 12. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 20. Part I know: 15.
- Take the part you know away from the whole. Subtracting finds the missing part.20 − 15 = 5
- Write the missing part. 5
Check. Check: 15 + 5 = 20. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 15. Part I know: 6.
- Take the part you know away from the whole. Subtracting finds the missing part.15 − 6 = 9
- Write the missing part. 9
Check. Check: 6 + 9 = 15. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. A fact family is four facts that use the same three numbers.
Method. Two parts make one whole. Each part can be found by taking the other part away from the whole.
- Put the two parts together, both ways. Adding the parts in either order gives the same whole.7 + 8 = 15 and 8 + 7 = 15
- Take each part away from the whole. Each take-away fact finds the part that is left.15 − 7 = 8 and 15 − 8 = 7
- Write all four facts. 7 + 8 = 15, 8 + 7 = 15, 15 − 7 = 8, 15 − 8 = 7
Check. Check one fact: 7 + 8 = 15, so 15 − 8 = 7. ✓
Watch out. Keep the whole at the start of a take-away. Write 15 − 7, not 7 − 15.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 20. Part I know: 12.
- Take the part you know away from the whole. Subtracting finds the missing part.20 − 12 = 8
- Write the missing part. 8
Check. Check: 12 + 8 = 20. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Method. Swapping the two numbers does not change the total.
- Work out 14 + 6. Add the first number and the second number.14 + 6 = 20
- Now work out 6 + 14. Swap the numbers round and add again.6 + 14 = 20
- Compare the two totals. Are they the same?20 = 20
- Write the answer. No. Both give 20.
Check. Count on 6 from 14, or count on 14 from 6. You reach 20 both ways. ✓
Watch out. The order of the numbers does not change the total. Try another pair to check.
Method. Ruby knows that 9 + 5 = 14. Use that fact to check her answer.
- Look at what Ruby says. Ruby says 14 − 5 = 4.14 − 5 = 4 (Ruby)
- Use the fact she knows. The whole is 14 and one part is 5. The missing part is the other part.14 − 5 = 9
- Compare the answers. Ruby’s answer is not the same as the missing part.4 is not 9
- Write the answer. No. 14 − 5 = 9.
Check. Check: 9 + 5 = 14. ✓
Watch out. Ruby took away the wrong number. Take the part you know away from the whole.
Make 10 to add
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A ten frame has ten boxes, in two rows of five. We put one counter in each box.
To add 8 and 5, first make 10. Put 8 counters on one ten frame. Two more counters fill it up to 10. There are 3 counters left on the other frame. So 10 and 3 make 13.
Key ideas
- Fill up the first number to 10 first.
- Then add what is left of the second number.
- Ten and some more is easy: 10 + 3 = 13.
- Some number bonds to 10 help: 8 needs 2 to make 10.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 8 counters on the first ten frame. We need 10 counters to make a full frame.8 counters
- Add 2 more to make 10. 8 needs 2 more to make 10.8 + 2 = 10
- Use the rest of the 5. 5 − 2 = 3, so 3 counters are left over.10 + 3 = 13
- Write the answer. 13
Check. Check: start at 5 and count on 8. You also reach 13. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 9 counters on the first ten frame. We need 10 counters to make a full frame.9 counters
- Add 1 more to make 10. 9 needs 1 more to make 10.9 + 1 = 10
- Use the rest of the 6. 6 − 1 = 5, so 5 counters are left over.10 + 5 = 15
- Write the answer. 15
Check. Check: start at 6 and count on 9. You also reach 15. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 7 counters on the first ten frame. We need 10 counters to make a full frame.7 counters
- Add 3 more to make 10. 7 needs 3 more to make 10.7 + 3 = 10
- Use the rest of the 9. 9 − 3 = 6, so 6 counters are left over.10 + 6 = 16
- Write the answer. 16
Check. Check: start at 9 and count on 7. You also reach 16. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Watch out
Watch out: remember to take the counters you used from the second number. For 8 + 5, 8 needs 2 to make 10, so 5 − 2 = 3 is left over. Then 10 + 3 = 13.
Exam tip
Grown-up tip. Draw two ten frames on paper, or use an egg box with 10 spaces. Ask: “How many more to fill the first one?” Then ask: “How many are left over?”
Exercise 5B Making 10 to add
Non-calculatorKey words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 9 counters on the first ten frame. We need 10 counters to make a full frame.9 counters
- Add 1 more to make 10. 9 needs 1 more to make 10.9 + 1 = 10
- Use the rest of the 3. 3 − 1 = 2, so 2 counters are left over.10 + 2 = 12
- Write the answer. 12
Check. Check: start at 3 and count on 9. You also reach 12. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 8 counters on the first ten frame. We need 10 counters to make a full frame.8 counters
- Add 2 more to make 10. 8 needs 2 more to make 10.8 + 2 = 10
- Use the rest of the 4. 4 − 2 = 2, so 2 counters are left over.10 + 2 = 12
- Write the answer. 12
Check. Check: start at 4 and count on 8. You also reach 12. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 7 counters on the first ten frame. We need 10 counters to make a full frame.7 counters
- Add 3 more to make 10. 7 needs 3 more to make 10.7 + 3 = 10
- Use the rest of the 5. 5 − 3 = 2, so 2 counters are left over.10 + 2 = 12
- Write the answer. 12
Check. Check: start at 5 and count on 7. You also reach 12. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 9 counters on the first ten frame. We need 10 counters to make a full frame.9 counters
- Add 1 more to make 10. 9 needs 1 more to make 10.9 + 1 = 10
- Use the rest of the 5. 5 − 1 = 4, so 4 counters are left over.10 + 4 = 14
- Write the answer. 14
Check. Check: start at 5 and count on 9. You also reach 14. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 6 counters on the first ten frame. We need 10 counters to make a full frame.6 counters
- Add 4 more to make 10. 6 needs 4 more to make 10.6 + 4 = 10
- Use the rest of the 7. 7 − 4 = 3, so 3 counters are left over.10 + 3 = 13
- Write the answer. 13
Check. Check: start at 7 and count on 6. You also reach 13. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 8 counters on the first ten frame. We need 10 counters to make a full frame.8 counters
- Add 2 more to make 10. 8 needs 2 more to make 10.8 + 2 = 10
- Use the rest of the 6. 6 − 2 = 4, so 4 counters are left over.10 + 4 = 14
- Write the answer. 14
Check. Check: start at 6 and count on 8. You also reach 14. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 9 counters on the first ten frame. We need 10 counters to make a full frame.9 counters
- Add 1 more to make 10. 9 needs 1 more to make 10.9 + 1 = 10
- Use the rest of the 8. 8 − 1 = 7, so 7 counters are left over.10 + 7 = 17
- Write the answer. 17
Check. Check: start at 8 and count on 9. You also reach 17. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 7 counters on the first ten frame. We need 10 counters to make a full frame.7 counters
- Add 3 more to make 10. 7 needs 3 more to make 10.7 + 3 = 10
- Use the rest of the 9. 9 − 3 = 6, so 6 counters are left over.10 + 6 = 16
- Write the answer. 16
Check. Check: start at 9 and count on 7. You also reach 16. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 5 counters on the first ten frame. We need 10 counters to make a full frame.5 counters
- Add 5 more to make 10. 5 needs 5 more to make 10.5 + 5 = 10
- Use the rest of the 8. 8 − 5 = 3, so 3 counters are left over.10 + 3 = 13
- Write the answer. 13
Check. Check: start at 8 and count on 5. You also reach 13. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 8 counters on the first ten frame. We need 10 counters to make a full frame.8 counters
- Add 2 more to make 10. 8 needs 2 more to make 10.8 + 2 = 10
- Use the rest of the 9. 9 − 2 = 7, so 7 counters are left over.10 + 7 = 17
- Write the answer. 17
Check. Check: start at 9 and count on 8. You also reach 17. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 7 counters on the first ten frame. We need 10 counters to make a full frame.7 counters
- Add 3 more to make 10. 7 needs 3 more to make 10.7 + 3 = 10
- Use the rest of the 6. 6 − 3 = 3, so 3 counters are left over.10 + 3 = 13
- Write the answer. 13
Check. Check: start at 6 and count on 7. You also reach 13. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 6 counters on the first ten frame. We need 10 counters to make a full frame.6 counters
- Add 4 more to make 10. 6 needs 4 more to make 10.6 + 4 = 10
- Use the rest of the 8. 8 − 4 = 4, so 4 counters are left over.10 + 4 = 14
- Write the answer. 14
Check. Check: start at 8 and count on 6. You also reach 14. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 4 counters on the first ten frame. We need 10 counters to make a full frame.4 counters
- Add 6 more to make 10. 4 needs 6 more to make 10.4 + 6 = 10
- Use the rest of the 9. 9 − 6 = 3, so 3 counters are left over.10 + 3 = 13
- Write the answer. 13
Check. Check: start at 9 and count on 4. You also reach 13. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 3 counters on the first ten frame. We need 10 counters to make a full frame.3 counters
- Add 7 more to make 10. 3 needs 7 more to make 10.3 + 7 = 10
- Use the rest of the 9. 9 − 7 = 2, so 2 counters are left over.10 + 2 = 12
- Write the answer. 12
Check. Check: start at 9 and count on 3. You also reach 12. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 2 counters on the first ten frame. We need 10 counters to make a full frame.2 counters
- Add 8 more to make 10. 2 needs 8 more to make 10.2 + 8 = 10
- Use the rest of the 9. 9 − 8 = 1, so 1 counters are left over.10 + 1 = 11
- Write the answer. 11
Check. Check: start at 9 and count on 2. You also reach 11. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Method. Swapping the two numbers does not change the total.
- Work out 6 + 7. Add the first number and the second number.6 + 7 = 13
- Now work out 7 + 6. Swap the numbers round and add again.7 + 6 = 13
- Compare the two totals. Are they the same?13 = 13
- Write the answer. Yes. Both give 13.
Check. Count on 7 from 6, or count on 6 from 7. You reach 13 both ways. ✓
Watch out. The order of the numbers does not change the total. Try another pair to check.
Method. Use a ten frame. Nine needs 1 more to make 10. Then take that 1 from the 4.
- Fill the first frame with 9. Nine needs 1 more to make 10.9 + 1 = 10
- Take that 1 from the 4. Four counters become 3 counters.4 − 1 = 3
- Add the rest to 10. Ten and 3 is 13.10 + 3 = 13
- Write the answer. So 9 + 4 is the same as 10 + 3. Both are 13.
Check. Count on 4 from 9: 10, 11, 12, 13. ✓
Watch out. Moving one counter does not change the total.
Doubles and near doubles
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A double is a number added to itself. Double 4 is 4 + 4. The picture has two rows that are the same.
A near double is one more or one less than a double. The picture below has rows of 4 and 5. The 4 + 4 double is 8, and one more makes 4 + 5 = 9.
Key ideas
- A double has two equal rows: 4 + 4 = 8.
- Use a double you know to find a near double.
- Near double: double the smaller number, then add one more.
- Learn the doubles up to 10 + 10 to help with other sums.
Key words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 4 is 4 + 4.
- Make two rows of 4. Both rows are the same, so the two numbers are equal.4 and 4
- Count all the things. Count one row, then count the other row.4 + 4 = 8
- Write the answer. 8
Check. Take one row away: 8 − 4 = 4. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 6 first, then add one more.
- Find the double of 6. Double 6 is 6 + 6, two equal groups.6 + 6 = 12
- Add the extra one to 12. 7 is one more than 6, so we add one more.12 + 1 = 13
- Write the answer. 13
Check. Check: start at 7 and count on 6. You also reach 13. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 8 first, then add one more.
- Find the double of 8. Double 8 is 8 + 8, two equal groups.8 + 8 = 16
- Add the extra one to 16. 9 is one more than 8, so we add one more.16 + 1 = 17
- Write the answer. 17
Check. Check: start at 9 and count on 8. You also reach 17. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Watch out
Watch out: a near double is not the double itself. 8 + 9 is one more than 8 + 8. Do not write 16 for 8 + 9. The answer is 17.
Exam tip
Grown-up tip. Put two equal piles of coins or buttons side by side. Ask your child to make a pile one bigger. Then ask: “What is the double? What is one more?”
Exercise 5C Doubles and near doubles
Non-calculatorKey words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 3 is 3 + 3.
- Make two rows of 3. Both rows are the same, so the two numbers are equal.3 and 3
- Count all the things. Count one row, then count the other row.3 + 3 = 6
- Write the answer. 6
Check. Take one row away: 6 − 3 = 3. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Key words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 5 is 5 + 5.
- Make two rows of 5. Both rows are the same, so the two numbers are equal.5 and 5
- Count all the things. Count one row, then count the other row.5 + 5 = 10
- Write the answer. 10
Check. Take one row away: 10 − 5 = 5. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Key words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 6 is 6 + 6.
- Make two rows of 6. Both rows are the same, so the two numbers are equal.6 and 6
- Count all the things. Count one row, then count the other row.6 + 6 = 12
- Write the answer. 12
Check. Take one row away: 12 − 6 = 6. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Key words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 2 is 2 + 2.
- Make two rows of 2. Both rows are the same, so the two numbers are equal.2 and 2
- Count all the things. Count one row, then count the other row.2 + 2 = 4
- Write the answer. 4
Check. Take one row away: 4 − 2 = 2. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Key words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 7 is 7 + 7.
- Make two rows of 7. Both rows are the same, so the two numbers are equal.7 and 7
- Count all the things. Count one row, then count the other row.7 + 7 = 14
- Write the answer. 14
Check. Take one row away: 14 − 7 = 7. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Key words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 9 is 9 + 9.
- Make two rows of 9. Both rows are the same, so the two numbers are equal.9 and 9
- Count all the things. Count one row, then count the other row.9 + 9 = 18
- Write the answer. 18
Check. Take one row away: 18 − 9 = 9. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Key words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 10 is 10 + 10.
- Make two rows of 10. Both rows are the same, so the two numbers are equal.10 and 10
- Count all the things. Count one row, then count the other row.10 + 10 = 20
- Write the answer. 20
Check. Take one row away: 20 − 10 = 10. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 4 first, then add one more.
- Find the double of 4. Double 4 is 4 + 4, two equal groups.4 + 4 = 8
- Add the extra one to 8. 5 is one more than 4, so we add one more.8 + 1 = 9
- Write the answer. 9
Check. Check: start at 5 and count on 4. You also reach 9. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 5 first, then add one more.
- Find the double of 5. Double 5 is 5 + 5, two equal groups.5 + 5 = 10
- Add the extra one to 10. 6 is one more than 5, so we add one more.10 + 1 = 11
- Write the answer. 11
Check. Check: start at 6 and count on 5. You also reach 11. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 6 first, then add one more.
- Find the double of 6. Double 6 is 6 + 6, two equal groups.6 + 6 = 12
- Add the extra one to 12. 7 is one more than 6, so we add one more.12 + 1 = 13
- Write the answer. 13
Check. Check: start at 7 and count on 6. You also reach 13. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 7 first, then add one more.
- Find the double of 7. Double 7 is 7 + 7, two equal groups.7 + 7 = 14
- Add the extra one to 14. 8 is one more than 7, so we add one more.14 + 1 = 15
- Write the answer. 15
Check. Check: start at 8 and count on 7. You also reach 15. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 8 first, then add one more.
- Find the double of 8. Double 8 is 8 + 8, two equal groups.8 + 8 = 16
- Add the extra one to 16. 9 is one more than 8, so we add one more.16 + 1 = 17
- Write the answer. 17
Check. Check: start at 9 and count on 8. You also reach 17. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 9 first, then add one more.
- Find the double of 9. Double 9 is 9 + 9, two equal groups.9 + 9 = 18
- Add the extra one to 18. 10 is one more than 9, so we add one more.18 + 1 = 19
- Write the answer. 19
Check. Check: start at 10 and count on 9. You also reach 19. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 7 first, then add one more.
- Find the double of 7. Double 7 is 7 + 7, two equal groups.7 + 7 = 14
- Add the extra one to 14. 8 is one more than 7, so we add one more.14 + 1 = 15
- Write the answer. 15
Check. Check: start at 8 and count on 7. You also reach 15. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Key words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 9 is 9 + 9.
- Make two rows of 9. Both rows are the same, so the two numbers are equal.9 and 9
- Count all the things. Count one row, then count the other row.9 + 9 = 18
- Write the answer. 18
Check. Take one row away: 18 − 9 = 9. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Method. Find the double first. Then check the extra one.
- Work out 8 + 8. This is the double, and it is correct for the double.8 + 8 = 16
- Work out 8 + 9. 9 is one more than 8, so the total is one more.8 + 9 = 17
- Compare the answers. The answer with the extra one is bigger.16 < 17
- Write the answer. No. 8 + 9 = 17, not 16.
Check. Count on from 16 by one more to reach 17. ✓
Watch out. In a near double, look for the extra one. Do not stop at the double.
Adding and taking away to 20, including zero
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
To add a small number to a bigger one, start at the bigger number and count on. The picture shows 14 + 3. Start at 14. Count on 3: 15, 16, 17.
To take away, start at the whole and count back. Adding zero or taking away zero does not change the number. Zero means none.
Key ideas
- Count on from the bigger number to add.
- Count back from the whole to take away.
- Adding zero does not change the number: 12 + 0 = 12.
- Taking away zero does not change the number: 12 − 0 = 12.
Key words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 14. Then count on 3.
- Start at 14. Start with the bigger number. You do not need to start at 1.Start: 14
- Count on 3 more. Say each number as you move one step on.15, 16, 17
- Write the answer. The last number you say is the answer.17
Check. Count back 3 from 17. You reach 14 again. ✓
Watch out. Count on from 14. Do not say 14 again as the first step.
Key words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 13. Then count on 6.
- Start at 13. Start with the bigger number. You do not need to start at 1.Start: 13
- Count on 6 more. Say each number as you move one step on.14, 15, 16, 17, 18, 19
- Write the answer. The last number you say is the answer.19
Check. Count back 6 from 19. You reach 13 again. ✓
Watch out. Count on from 13. Do not say 13 again as the first step.
Key words. Zero means none at all. We write it as 0.
Method. Zero means none. Adding zero, or taking away zero, changes nothing.
- Look at the sum: 12 + 0. Find the zero in the sum.12 + 0
- Nothing is added or taken away. The number stays the same as it was.12 stays 12
- Write the answer. 12
Check. Count 12 things and take away none. You still have 12. ✓
Watch out. Zero does not change a number. Do not write 0 as the answer.
Watch out
Watch out: when you count on, do not say the starting number again. For 14 + 3, say 15, 16, 17. The answer is 17, not 18.
Exam tip
Grown-up tip. Use a number line, a 20-square or your fingers. Ask: “Start at 14. Count on 3. Where do you end?” Then count back again to check.
Exercise 5D Adding and taking away to 20
Non-calculatorKey words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 11. Then count on 4.
- Start at 11. Start with the bigger number. You do not need to start at 1.Start: 11
- Count on 4 more. Say each number as you move one step on.12, 13, 14, 15
- Write the answer. The last number you say is the answer.15
Check. Count back 4 from 15. You reach 11 again. ✓
Watch out. Count on from 11. Do not say 11 again as the first step.
Key words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 15. Then count on 2.
- Start at 15. Start with the bigger number. You do not need to start at 1.Start: 15
- Count on 2 more. Say each number as you move one step on.16, 17
- Write the answer. The last number you say is the answer.17
Check. Count back 2 from 17. You reach 15 again. ✓
Watch out. Count on from 15. Do not say 15 again as the first step.
Key words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 10. Then count on 4.
- Start at 10. Start with the bigger number. You do not need to start at 1.Start: 10
- Count on 4 more. Say each number as you move one step on.11, 12, 13, 14
- Write the answer. The last number you say is the answer.14
Check. Count back 4 from 14. You reach 10 again. ✓
Watch out. Count on from 10. Do not say 10 again as the first step.
Key words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 10. Then count on 9.
- Start at 10. Start with the bigger number. You do not need to start at 1.Start: 10
- Count on 9 more. Say each number as you move one step on.11, 12, 13, 14, 15, 16, 17, 18, 19
- Write the answer. The last number you say is the answer.19
Check. Count back 9 from 19. You reach 10 again. ✓
Watch out. Count on from 10. Do not say 10 again as the first step.
Key words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 10. Then count on 7.
- Start at 10. Start with the bigger number. You do not need to start at 1.Start: 10
- Count on 7 more. Say each number as you move one step on.11, 12, 13, 14, 15, 16, 17
- Write the answer. The last number you say is the answer.17
Check. Count back 7 from 17. You reach 10 again. ✓
Watch out. Count on from 10. Do not say 10 again as the first step.
Key words. Zero means none at all. We write it as 0.
Method. Zero means none. Adding zero, or taking away zero, changes nothing.
- Look at the sum: 12 + 0. Find the zero in the sum.12 + 0
- Nothing is added or taken away. The number stays the same as it was.12 stays 12
- Write the answer. 12
Check. Count 12 things and take away none. You still have 12. ✓
Watch out. Zero does not change a number. Do not write 0 as the answer.
Key words. Zero means none at all. We write it as 0.
Method. Zero means none. Adding zero, or taking away zero, changes nothing.
- Look at the sum: 0 + 14. Find the zero in the sum.0 + 14
- Nothing is added or taken away. The number stays the same as it was.14 stays 14
- Write the answer. 14
Check. Count 14 things and take away none. You still have 14. ✓
Watch out. Zero does not change a number. Do not write 0 as the answer.
Key words. Zero means none at all. We write it as 0.
Method. Zero means none. Adding zero, or taking away zero, changes nothing.
- Look at the sum: 16 + 0. Find the zero in the sum.16 + 0
- Nothing is added or taken away. The number stays the same as it was.16 stays 16
- Write the answer. 16
Check. Count 16 things and take away none. You still have 16. ✓
Watch out. Zero does not change a number. Do not write 0 as the answer.
Key words. Zero means none at all. We write it as 0.
Method. Zero means none. Adding zero, or taking away zero, changes nothing.
- Look at the sum: 0 + 9. Find the zero in the sum.0 + 9
- Nothing is added or taken away. The number stays the same as it was.9 stays 9
- Write the answer. 9
Check. Count 9 things and take away none. You still have 9. ✓
Watch out. Zero does not change a number. Do not write 0 as the answer.
Key words. To take away is to remove some. To count back is to go down one at a time.
Method. Take away 3 from 16 by counting back 3 steps.
- Start at 16. Start with the whole amount.Start: 16
- Count back 3. Each step back is one less.15, 14, 13
- Write the answer. The last number you say is what is left.13
Check. Check: 13 + 3 = 16. ✓
Watch out. Count back, not on. Do not say the starting number as one of the steps.
Key words. To take away is to remove some. To count back is to go down one at a time.
Method. Take away 5 from 19 by counting back 5 steps.
- Start at 19. Start with the whole amount.Start: 19
- Count back 5. Each step back is one less.18, 17, 16, 15, 14
- Write the answer. The last number you say is what is left.14
Check. Check: 14 + 5 = 19. ✓
Watch out. Count back, not on. Do not say the starting number as one of the steps.
Key words. To take away is to remove some. To count back is to go down one at a time.
Method. Take away 4 from 18 by counting back 4 steps.
- Start at 18. Start with the whole amount.Start: 18
- Count back 4. Each step back is one less.17, 16, 15, 14
- Write the answer. The last number you say is what is left.14
Check. Check: 14 + 4 = 18. ✓
Watch out. Count back, not on. Do not say the starting number as one of the steps.
Key words. To take away is to remove some. To count back is to go down one at a time.
Method. Take away 2 from 13 by counting back 2 steps.
- Start at 13. Start with the whole amount.Start: 13
- Count back 2. Each step back is one less.12, 11
- Write the answer. The last number you say is what is left.11
Check. Check: 11 + 2 = 13. ✓
Watch out. Count back, not on. Do not say the starting number as one of the steps.
Key words. Zero means none at all. We write it as 0.
Method. Zero means none. Adding zero, or taking away zero, changes nothing.
- Look at the sum: 20 − 0. Find the zero in the sum.20 − 0
- Nothing is added or taken away. The number stays the same as it was.20 stays 20
- Write the answer. 20
Check. Count 20 things and take away none. You still have 20. ✓
Watch out. Zero does not change a number. Do not write 0 as the answer.
Key words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 12. Then count on 7.
- Start at 12. Start with the bigger number. You do not need to start at 1.Start: 12
- Count on 7 more. Say each number as you move one step on.13, 14, 15, 16, 17, 18, 19
- Write the answer. The last number you say is the answer.19
Check. Count back 7 from 19. You reach 12 again. ✓
Watch out. Count on from 12. Do not say 12 again as the first step.
Key words. To take away is to remove some. To count back is to go down one at a time.
Method. Take away 5 from 17 by counting back 5 steps.
- Start at 17. Start with the whole amount.Start: 17
- Count back 5. Each step back is one less.16, 15, 14, 13, 12
- Write the answer. The last number you say is what is left.12
Check. Check: 12 + 5 = 17. ✓
Watch out. Count back, not on. Do not say the starting number as one of the steps.
Method. Taking away zero takes nothing away. The number stays the same.
- Look at the take-away. Sam takes away zero.15 − 0
- Think about what is taken away. Zero means none, so nothing leaves the group.Nothing is taken away
- Write the answer. No. 15 − 0 = 15.
Check. Count 15 things and take none away. You still have 15. ✓
Watch out. Zero does not change a number. Do not write 0 as the answer.
Finding the difference
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
The difference is how many more one group has than the other. Look at the picture. Nine apples and five stars. The four orange rings show the extra apples.
To find the difference, you can match the things up one to one and count the ones left over. Or you can take the smaller number from the bigger number: 9 − 5 = 4.
Key ideas
- The difference is how many more one number is than the other.
- Match one to one to find the extra things.
- Take the smaller number from the bigger number.
- If the two numbers are the same, the difference is 0.
Key words. The difference is how many more one number is than the other.
Method. The difference is how many more. Take the smaller number from the bigger number.
- Count the first group: 9 apples. Touch each one once.9 apples
- Count the second group: 5 stars. Touch each one once.5 stars
- Take the smaller number from the bigger number. Subtraction finds how many more.9 − 5 = 4
- Write the answer. 4 more apples
Check. Match one to one: the 4 extra apples have no partner. ✓
Watch out. Subtract the smaller number from the bigger number. Do not add the two numbers together.
Key words. The difference is how many more one number is than the other.
Method. The difference is how many more. Take the smaller number from the bigger number.
- Count the first group: 15 cubes. Touch each one once.15 cubes
- Count the second group: 8 balls. Touch each one once.8 balls
- Take the smaller number from the bigger number. Subtraction finds how many more.15 − 8 = 7
- Write the answer. 7 more cubes
Check. Match one to one: the 7 extra cubes have no partner. ✓
Watch out. Subtract the smaller number from the bigger number. Do not add the two numbers together.
Key words. The difference is how many more one number is than the other.
Method. When two groups are the same, there is no difference.
- Count the first group: 11 sweets. Touch each one once.11 sweets
- Count the second group: 11 sweets. Touch each one once.11 sweets
- Match them up one to one. Every thing has a partner, so nothing is left over.11 and 11 match exactly
- Write the answer. 0. The difference is 0.
Check. Take 11 from 11: 11 − 11 = 0. ✓
Watch out. Zero means there is no difference. The two groups are the same.
Watch out
Watch out: the difference is a take-away, not an add. Take the smaller number from the bigger number. 9 + 5 is not the difference.
Exam tip
Grown-up tip. Lay out two rows of buttons. Ask: “Which row has more? How many more?” Your child can match the buttons to check.
Exercise 5E Finding the difference
Non-calculatorKey words. The difference is how many more one number is than the other.
Method. The difference is how many more. Take the smaller number from the bigger number.
- Count the first group: 7 apples. Touch each one once.7 apples
- Count the second group: 3 stars. Touch each one once.3 stars
- Take the smaller number from the bigger number. Subtraction finds how many more.7 − 3 = 4
- Write the answer. 4 more apples
Check. Match one to one: the 4 extra apples have no partner. ✓
Watch out. Subtract the smaller number from the bigger number. Do not add the two numbers together.
Key words. The difference is how many more one number is than the other.
Method. The difference is how many more. Take the smaller number from the bigger number.
- Count the first group: 8 cubes. Touch each one once.8 cubes
- Count the second group: 5 balls. Touch each one once.5 balls
- Take the smaller number from the bigger number. Subtraction finds how many more.8 − 5 = 3
- Write the answer. 3 more cubes
Check. Match one to one: the 3 extra cubes have no partner. ✓
Watch out. Subtract the smaller number from the bigger number. Do not add the two numbers together.
Key words. The difference is how many more one number is than the other.
Method. The difference is how many more. Take the smaller number from the bigger number.
- Count the first group: 10 apples. Touch each one once.10 apples
- Count the second group: 4 stars. Touch each one once.4 stars
- Take the smaller number from the bigger number. Subtraction finds how many more.10 − 4 = 6
- Write the answer. 6 more apples
Check. Match one to one: the 6 extra apples have no partner. ✓
Watch out. Subtract the smaller number from the bigger number. Do not add the two numbers together.
Key words. The difference is how far apart two numbers are.
Method. The difference is found by taking the smaller number away from the bigger number.
- Find the bigger number, 13. The bigger number goes first in the take-away.Bigger: 13
- Take away the smaller number, 6. Subtracting finds the difference.13 − 6 = 7
- Write the answer. 7
Check. Check: 6 + 7 = 13. ✓
Watch out. Take the smaller number away from the bigger one, not the other way round.
Key words. The difference is how far apart two numbers are.
Method. The difference is found by taking the smaller number away from the bigger number.
- Find the bigger number, 18. The bigger number goes first in the take-away.Bigger: 18
- Take away the smaller number, 14. Subtracting finds the difference.18 − 14 = 4
- Write the answer. 4
Check. Check: 14 + 4 = 18. ✓
Watch out. Take the smaller number away from the bigger one, not the other way round.
Key words. The difference is how far apart two numbers are.
Method. The difference is found by taking the smaller number away from the bigger number.
- Find the bigger number, 12. The bigger number goes first in the take-away.Bigger: 12
- Take away the smaller number, 7. Subtracting finds the difference.12 − 7 = 5
- Write the answer. 5
Check. Check: 7 + 5 = 12. ✓
Watch out. Take the smaller number away from the bigger one, not the other way round.
Key words. The difference is how far apart two numbers are.
Method. The difference is found by taking the smaller number away from the bigger number.
- Find the bigger number, 16. The bigger number goes first in the take-away.Bigger: 16
- Take away the smaller number, 9. Subtracting finds the difference.16 − 9 = 7
- Write the answer. 7
Check. Check: 9 + 7 = 16. ✓
Watch out. Take the smaller number away from the bigger one, not the other way round.
Key words. The difference is how far apart two numbers are.
Method. The difference is found by taking the smaller number away from the bigger number.
- Find the bigger number, 19. The bigger number goes first in the take-away.Bigger: 19
- Take away the smaller number, 11. Subtracting finds the difference.19 − 11 = 8
- Write the answer. 8
Check. Check: 11 + 8 = 19. ✓
Watch out. Take the smaller number away from the bigger one, not the other way round.
Key words. The difference is how many more one number is than the other.
Method. The difference is how many more. Take the smaller number from the bigger number.
- Count the first group: 14 marbles. Touch each one once.14 marbles
- Count the second group: 9 marbles. Touch each one once.9 marbles
- Take the smaller number from the bigger number. Subtraction finds how many more.14 − 9 = 5
- Write the answer. 5 more marbles
Check. Match one to one: the 5 extra marbles have no partner. ✓
Watch out. Subtract the smaller number from the bigger number. Do not add the two numbers together.
Key words. The difference is how far apart two numbers are.
Method. The difference is found by taking the smaller number away from the bigger number.
- Find the bigger number, 15. The bigger number goes first in the take-away.Bigger: 15
- Take away the smaller number, 8. Subtracting finds the difference.15 − 8 = 7
- Write the answer. 7
Check. Check: 8 + 7 = 15. ✓
Watch out. Take the smaller number away from the bigger one, not the other way round.
Key words. The difference is how far apart two numbers are.
Method. The difference is found by taking the smaller number away from the bigger number.
- Find the bigger number, 17. The bigger number goes first in the take-away.Bigger: 17
- Take away the smaller number, 11. Subtracting finds the difference.17 − 11 = 6
- Write the answer. 6
Check. Check: 11 + 6 = 17. ✓
Watch out. Take the smaller number away from the bigger one, not the other way round.
Method. The difference between two equal numbers is 0.
- Look at the two numbers. Both numbers are 10.10 and 10
- Take one from the other. When two numbers are the same, nothing is left over.10 − 10 = 0
- Write the answer. No. The difference is 0, not 10.
Check. Match 10 counters with 10 counters. None are left over. ✓
Watch out. Zero means no difference. The two numbers are the same.
Missing numbers and one-step problems
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A missing number is a number we do not know yet. We show it with a box, like this: 6 + ? = 15. To find it, we do the opposite. Adding undoes taking away, and taking away undoes adding.
A one-step problem is a story with just one add or one take-away. Read the story, then decide: do we add or do we take away?
Key ideas
- A box or a question mark shows the missing number.
- To find a missing number, do the opposite.
- In a story, “more” or “altogether” means add.
- In a story, “gone” or “left” means take away.
Key words. The box (?) shows the missing number.
Method. To find the missing number, take the number you know away from the total.
- Look at the total. The total is the answer to the sum.Total: 15
- Take the number you know away from the total. Taking away undoes adding.15 − 6 = 9
- Write the missing number. 9
Check. Check: 6 + 9 = 15. ✓
Watch out. Do not add the two numbers together. Take the number you know away from the total.
Method. Think about how many were taken away. Take what is left away from the start.
- Start with 14. This is the number we begin with.Start: 14
- Find what is left: 9. The answer to the take-away is what is left.Left: 9
- Take what is left away from the start. The difference is how many were taken away.14 − 9 = 5
- Write the missing number. 5
Check. Check: 14 − 5 = 9. ✓
Watch out. The missing number is the amount taken away. It is not the amount left.
Method. Put back the number that was taken away. Adding undoes taking away.
- Look at the take-away. Something was taken away and the answer is what is left.? − 4 = 11
- Add back the number that was taken away. Adding is the opposite of taking away.11 + 4 = 15
- Write the missing number. 15
Check. Check: 15 − 4 = 11. ✓
Watch out. Adding is the opposite of taking away. Use it to find the number you started with.
Watch out
Watch out: for a missing number in a sum, do not add the two numbers you can see. Take the known number away from the total.
Exam tip
Grown-up tip. Use a sum with a box, like 5 + ? = 13. Ask: “What number makes 13 with 5?” Then check: add the number back on to make sure it is right.
Exercise 5F Missing numbers and one-step problems
Non-calculatorKey words. The box (?) shows the missing number.
Method. To find the missing number, take the number you know away from the total.
- Look at the total. The total is the answer to the sum.Total: 13
- Take the number you know away from the total. Taking away undoes adding.13 − 5 = 8
- Write the missing number. 8
Check. Check: 5 + 8 = 13. ✓
Watch out. Do not add the two numbers together. Take the number you know away from the total.
Key words. The box (?) shows the missing number.
Method. To find the missing number, take the number you know away from the total.
- Look at the total. The total is the answer to the sum.Total: 16
- Take the number you know away from the total. Taking away undoes adding.16 − 9 = 7
- Write the missing number. 7
Check. Check: 9 + 7 = 16. ✓
Watch out. Do not add the two numbers together. Take the number you know away from the total.
Method. Think about how many were taken away. Take what is left away from the start.
- Start with 17. This is the number we begin with.Start: 17
- Find what is left: 12. The answer to the take-away is what is left.Left: 12
- Take what is left away from the start. The difference is how many were taken away.17 − 12 = 5
- Write the missing number. 5
Check. Check: 17 − 5 = 12. ✓
Watch out. The missing number is the amount taken away. It is not the amount left.
Method. Think about how many were taken away. Take what is left away from the start.
- Start with 15. This is the number we begin with.Start: 15
- Find what is left: 6. The answer to the take-away is what is left.Left: 6
- Take what is left away from the start. The difference is how many were taken away.15 − 6 = 9
- Write the missing number. 9
Check. Check: 15 − 9 = 6. ✓
Watch out. The missing number is the amount taken away. It is not the amount left.
Method. Put back the number that was taken away. Adding undoes taking away.
- Look at the take-away. Something was taken away and the answer is what is left.? − 6 = 7
- Add back the number that was taken away. Adding is the opposite of taking away.7 + 6 = 13
- Write the missing number. 13
Check. Check: 13 − 6 = 7. ✓
Watch out. Adding is the opposite of taking away. Use it to find the number you started with.
Key words. The box (?) shows the missing number.
Method. To find the missing number, take the number you know away from the total.
- Look at the total. The total is the answer to the sum.Total: 11
- Take the number you know away from the total. Taking away undoes adding.11 − 4 = 7
- Write the missing number. 7
Check. Check: 4 + 7 = 11. ✓
Watch out. Do not add the two numbers together. Take the number you know away from the total.
Method. Think about how many were taken away. Take what is left away from the start.
- Start with 12. This is the number we begin with.Start: 12
- Find what is left: 3. The answer to the take-away is what is left.Left: 3
- Take what is left away from the start. The difference is how many were taken away.12 − 3 = 9
- Write the missing number. 9
Check. Check: 12 − 9 = 3. ✓
Watch out. The missing number is the amount taken away. It is not the amount left.
Method. Put back the number that was taken away. Adding undoes taking away.
- Look at the take-away. Something was taken away and the answer is what is left.? − 5 = 8
- Add back the number that was taken away. Adding is the opposite of taking away.8 + 5 = 13
- Write the missing number. 13
Check. Check: 13 − 5 = 8. ✓
Watch out. Adding is the opposite of taking away. Use it to find the number you started with.
Key words. The box (?) shows the missing number.
Method. To find the missing number, take the number you know away from the total.
- Look at the total. The total is the answer to the sum.Total: 20
- Take the number you know away from the total. Taking away undoes adding.20 − 8 = 12
- Write the missing number. 12
Check. Check: 8 + 12 = 20. ✓
Watch out. Do not add the two numbers together. Take the number you know away from the total.
Method. Think about how many were taken away. Take what is left away from the start.
- Start with 15. This is the number we begin with.Start: 15
- Find what is left: 9. The answer to the take-away is what is left.Left: 9
- Take what is left away from the start. The difference is how many were taken away.15 − 9 = 6
- Write the missing number. 6
Check. Check: 15 − 6 = 9. ✓
Watch out. The missing number is the amount taken away. It is not the amount left.
Key words. The box (?) shows the missing number.
Method. To find the missing number, take the number you know away from the total.
- Look at the total. The total is the answer to the sum.Total: 15
- Take the number you know away from the total. Taking away undoes adding.15 − 8 = 7
- Write the missing number. 7
Check. Check: 8 + 7 = 15. ✓
Watch out. Do not add the two numbers together. Take the number you know away from the total.
Key words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 12. Then count on 5.
- Start at 12. Start with the bigger number. You do not need to start at 1.Start: 12
- Count on 5 more. Say each number as you move one step on.13, 14, 15, 16, 17
- Write the answer. The last number you say is the answer.17
Check. Count back 5 from 17. You reach 12 again. ✓
Watch out. Count on from 12. Do not say 12 again as the first step.
Method. A fact family uses the same three numbers, 8, 7 and 15.
- Look at the first fact. Priya adds 8 and 7 to make 15.8 + 7 = 15
- Look at the second fact. Priya takes 7 away from 15 to get 8. The same three numbers are used.15 − 7 = 8
- Write the answer. Yes. Both facts use 8, 7 and 15.
Check. Take 8 away from 15 to check: 15 − 8 = 7. ✓
Watch out. Facts in the same family use the same three numbers.
Chapter summary
| Skill | Method |
|---|---|
| Number bonds to 20 | Take the part you know away from the whole to find the missing part. |
| Make 10 to add | Fill the first ten frame up to 10, then add what is left of the second number. |
| Doubles and near doubles | A double is two equal groups. A near double is one more or one less than a double. |
| Adding and taking away to 20 | Count on to add. Count back to take away. Zero changes nothing. |
| Finding the difference | Take the smaller number from the bigger number. |
| Missing numbers | Do the opposite. Take away to undo adding. Add to undo taking away. |
Can you…?
- I can find the missing part when I know the whole
- I can make 10 first to add
- I can work out doubles and near doubles
- I can count on to add and count back to take away, including with zero
- I can find how many more one number is than another
- I can find a missing number and solve a one-step problem
Key terms
- number bond
- two numbers that make a total
- whole
- the total, the big number in a part-whole picture
- part
- one of the numbers that makes the whole
- ten frame
- a picture with 10 boxes in two rows of five
- double
- a number added to itself, like 4 + 4
- near double
- one more or one less than a double, like 4 + 5
- difference
- how many more one number is than another
- count on
- keep going up from a number, one step at a time
- count back
- go down from a number, one step at a time
- missing number
- a number we do not know yet, shown by a box
- fact family
- four facts that use the same three numbers
Exercise 5Z Check-up
Non-calculatorKey words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 14. Part I know: 6.
- Take the part you know away from the whole. Subtracting finds the missing part.14 − 6 = 8
- Write the missing part. 8
Check. Check: 6 + 8 = 14. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 8 counters on the first ten frame. We need 10 counters to make a full frame.8 counters
- Add 2 more to make 10. 8 needs 2 more to make 10.8 + 2 = 10
- Use the rest of the 6. 6 − 2 = 4, so 4 counters are left over.10 + 4 = 14
- Write the answer. 14
Check. Check: start at 6 and count on 8. You also reach 14. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 7 is 7 + 7.
- Make two rows of 7. Both rows are the same, so the two numbers are equal.7 and 7
- Count all the things. Count one row, then count the other row.7 + 7 = 14
- Write the answer. 14
Check. Take one row away: 14 − 7 = 7. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 8 first, then add one more.
- Find the double of 8. Double 8 is 8 + 8, two equal groups.8 + 8 = 16
- Add the extra one to 16. 9 is one more than 8, so we add one more.16 + 1 = 17
- Write the answer. 17
Check. Check: start at 9 and count on 8. You also reach 17. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Key words. To count on is to keep going up from a number, one at a time.
Method. Start with the bigger number, 15. Then count on 3.
- Start at 15. Start with the bigger number. You do not need to start at 1.Start: 15
- Count on 3 more. Say each number as you move one step on.16, 17, 18
- Write the answer. The last number you say is the answer.18
Check. Count back 3 from 18. You reach 15 again. ✓
Watch out. Count on from 15. Do not say 15 again as the first step.
Key words. Zero means none at all. We write it as 0.
Method. Zero means none. Adding zero, or taking away zero, changes nothing.
- Look at the sum: 12 + 0. Find the zero in the sum.12 + 0
- Nothing is added or taken away. The number stays the same as it was.12 stays 12
- Write the answer. 12
Check. Count 12 things and take away none. You still have 12. ✓
Watch out. Zero does not change a number. Do not write 0 as the answer.
Key words. To take away is to remove some. To count back is to go down one at a time.
Method. Take away 5 from 17 by counting back 5 steps.
- Start at 17. Start with the whole amount.Start: 17
- Count back 5. Each step back is one less.16, 15, 14, 13, 12
- Write the answer. The last number you say is what is left.12
Check. Check: 12 + 5 = 17. ✓
Watch out. Count back, not on. Do not say the starting number as one of the steps.
Key words. The difference is how many more one number is than the other.
Method. The difference is how many more. Take the smaller number from the bigger number.
- Count the first group: 16 apples. Touch each one once.16 apples
- Count the second group: 11 stars. Touch each one once.11 stars
- Take the smaller number from the bigger number. Subtraction finds how many more.16 − 11 = 5
- Write the answer. 5 more apples
Check. Match one to one: the 5 extra apples have no partner. ✓
Watch out. Subtract the smaller number from the bigger number. Do not add the two numbers together.
Key words. The box (?) shows the missing number.
Method. To find the missing number, take the number you know away from the total.
- Look at the total. The total is the answer to the sum.Total: 17
- Take the number you know away from the total. Taking away undoes adding.17 − 9 = 8
- Write the missing number. 8
Check. Check: 9 + 8 = 17. ✓
Watch out. Do not add the two numbers together. Take the number you know away from the total.
Key words. To take away is to remove some. To count back is to go down one at a time.
Method. Take away 4 from 13 by counting back 4 steps.
- Start at 13. Start with the whole amount.Start: 13
- Count back 4. Each step back is one less.12, 11, 10, 9
- Write the answer. The last number you say is what is left.9
Check. Check: 9 + 4 = 13. ✓
Watch out. Count back, not on. Do not say the starting number as one of the steps.
Total 15 marks. Allow about 15 minutes.
Exercise 5X End-of-chapter quiz
Non-calculatorKey words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 6 counters on the first ten frame. We need 10 counters to make a full frame.6 counters
- Add 4 more to make 10. 6 needs 4 more to make 10.6 + 4 = 10
- Use the rest of the 9. 9 − 4 = 5, so 5 counters are left over.10 + 5 = 15
- Write the answer. 15
Check. Check: start at 9 and count on 6. You also reach 15. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. A double is two equal amounts, or a number added to itself.
Method. A double is a number added to itself. Double 8 is 8 + 8.
- Make two rows of 8. Both rows are the same, so the two numbers are equal.8 and 8
- Count all the things. Count one row, then count the other row.8 + 8 = 16
- Write the answer. 16
Check. Take one row away: 16 − 8 = 8. One row is left. ✓
Watch out. A double has two equal rows. Do not forget to count the second row.
Key words. A number bond is two numbers that make a total. The whole is the total. The parts make the whole.
Method. Start from the whole. Take away the part you know to find the missing part.
- Find the whole and the part you know. The whole is the big number at the top of the picture.Whole: 20. Part I know: 13.
- Take the part you know away from the whole. Subtracting finds the missing part.20 − 13 = 7
- Write the missing part. 7
Check. Check: 13 + 7 = 20. ✓
Watch out. Start from the whole, not from the small number. Do not add the two parts together.
Key words. To take away is to remove some. To count back is to go down one at a time.
Method. Take away 4 from 13 by counting back 4 steps.
- Start at 13. Start with the whole amount.Start: 13
- Count back 4. Each step back is one less.12, 11, 10, 9
- Write the answer. The last number you say is what is left.9
Check. Check: 9 + 4 = 13. ✓
Watch out. Count back, not on. Do not say the starting number as one of the steps.
Key words. Zero means none at all. We write it as 0.
Method. Zero means none. Adding zero, or taking away zero, changes nothing.
- Look at the sum: 11 + 0. Find the zero in the sum.11 + 0
- Nothing is added or taken away. The number stays the same as it was.11 stays 11
- Write the answer. 11
Check. Count 11 things and take away none. You still have 11. ✓
Watch out. Zero does not change a number. Do not write 0 as the answer.
Key words. A fact family is four facts that use the same three numbers.
Method. Two parts make one whole. Each part can be found by taking the other part away from the whole.
- Put the two parts together, both ways. Adding the parts in either order gives the same whole.8 + 6 = 14 and 6 + 8 = 14
- Take each part away from the whole. Each take-away fact finds the part that is left.14 − 8 = 6 and 14 − 6 = 8
- Write all four facts. 8 + 6 = 14, 6 + 8 = 14, 14 − 8 = 6, 14 − 6 = 8
Check. Check one fact: 8 + 6 = 14, so 14 − 6 = 8. ✓
Watch out. Keep the whole at the start of a take-away. Write 14 − 8, not 8 − 14.
Key words. A near double is one more or one less than a double.
Method. A near double is one more or one less than a double. Double 6 first, then add one more.
- Find the double of 6. Double 6 is 6 + 6, two equal groups.6 + 6 = 12
- Add the extra one to 12. 7 is one more than 6, so we add one more.12 + 1 = 13
- Write the answer. 13
Check. Check: start at 7 and count on 6. You also reach 13. ✓
Watch out. Do not forget the extra one. The answer is one more than the double.
Key words. To make 10 is to fill up to 10 first, then add the rest.
Method. Fill the first ten frame to make 10. Then add what is left over.
- Put 9 counters on the first ten frame. We need 10 counters to make a full frame.9 counters
- Add 1 more to make 10. 9 needs 1 more to make 10.9 + 1 = 10
- Use the rest of the 7. 7 − 1 = 6, so 6 counters are left over.10 + 6 = 16
- Write the answer. 16
Check. Check: start at 7 and count on 9. You also reach 16. ✓
Watch out. Fill the frame up to 10 first. Do not forget to take the counters you used from the second number.
Key words. The difference is how many more one number is than the other.
Method. The difference is how many more. Take the smaller number from the bigger number.
- Count the first group: 18 stickers. Touch each one once.18 stickers
- Count the second group: 12 stickers. Touch each one once.12 stickers
- Take the smaller number from the bigger number. Subtraction finds how many more.18 − 12 = 6
- Write the answer. 6 more stickers
Check. Match one to one: the 6 extra stickers have no partner. ✓
Watch out. Subtract the smaller number from the bigger number. Do not add the two numbers together.
Key words. The box (?) shows the missing number.
Method. To find the missing number, take the number you know away from the total.
- Look at the total. The total is the answer to the sum.Total: 15
- Take the number you know away from the total. Taking away undoes adding.15 − 8 = 7
- Write the missing number. 7
Check. Check: 8 + 7 = 15. ✓
Watch out. Do not add the two numbers together. Take the number you know away from the total.