Year 1 Adding and Subtracting within 10: worked examples and questions with answers
By the end of this chapter you will be able to
- Put groups together and count on to add
- Take away and count back to subtract
- Use the part-whole model and number bonds to 10
- Read and write + , − and = number sentences
- Write a fact family from three numbers
- Find a missing number in a sentence
- Use zero when adding and taking away
- Solve one-step problems with pictures
You should already know
- Counting and the numbers 0 to 10 (Chapter 1)
- One more and one less (Chapter 1)
- Comparing groups (Chapter 1)
Where this leads
- Adding and subtracting within 20 (Year 1 Chapter 5)
- Numbers to 20 (Year 1 Chapter 4)
National Curriculum for England, Key Stage 1 mathematics, Year 1. Content: Part-whole model and number bonds within 10, Read, write and interpret statements with + , − and =, Add by counting on, Subtract by taking away and counting back, Related facts (fact families), Missing numbers such as 7 = [ ] − 2, Zero in addition and subtraction, One-step problems with objects and pictures.
- 2.1 Putting groups together: add: Worksheet (PDF) · Answers (PDF) · lesson page
- 2.2 Taking away and counting back: subtract: Worksheet (PDF) · Answers (PDF) · lesson page
- 2.3 Part-whole and number bonds: Worksheet (PDF) · Answers (PDF) · lesson page
- 2.4 Fact families: related facts: Worksheet (PDF) · Answers (PDF) · lesson page
- 2.5 Missing numbers: Worksheet (PDF) · Answers (PDF) · lesson page
- 2.6 Zero 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-calculatorKey words. Count on means keep going up, one number at a time.
Method. Count on one at a time from 4.
- Start at 4. We count on from the number we have.4
- Say the next 2 numbers. Each number is one more than the one before.5, 6
- Write the answer. 5, 6
Check. Count back from 6 to 4 to check. ✓
Watch out. Start with the number after 4, not 4 itself.
Method. Read the number word, then find it on the number list.
- Read the word. Read the whole word, not just the first letters.“eight”
- Find the word on the number list. Each word matches exactly one number.eight = 8
- Write the numeral. A numeral is the number written with digits.8
Check. Count 8 things. The last number you say is 8. ✓
Watch out. Check the spelling of the word before you write the numeral.
Key words. One less is the number just before.
Method. One less than 7 is the number just before 7.
- Start at 7. Put your finger on it.Start: 7
- Move one step back. One less is the number before.7 − 1
- Write the answer. 6
Check. One more than 6 is 7. ✓
Watch out. One less goes down. One more goes up.
Key words. More means a bigger number. Fewer means a smaller number.
Method. Count each group, then see which number is smaller.
- Count group A. Touch each one once.Group A: 6 apples
- Count group B. Touch each one once.Group B: 4 stars
- Compare the two numbers. The bigger number has more. The smaller number has fewer.6 > 4
- Write the answer. Group B has fewer stars.
Check. Match one to one: the group with a thing left over has more. ✓
Watch out. Groups can look bigger when the things are spread out. Always count them.
Key words. Smallest is the least. Biggest is the most.
Method. Smallest first. Put the numbers in order on the number line.
- Find each number on the number line. Numbers further to the left are smaller.9, 3, 6
- Start with the smallest number. Then go to the next one.3, 6, 9
- Write the numbers in order. 3, 6, 9
Check. There are 3 numbers in the question and 3 in the answer. ✓
Watch out. Check you have not left a number out.
Putting groups together: add
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
When we put groups together, we add. The + sign means add. The = sign shows the total.
Look at these apples and stars. There are 3 apples and 4 stars. Altogether there are 7 things.
Key ideas
- + means add, or put together.
- = means the total is the answer.
- Count on: start at the bigger number, then count on the smaller number.
- You can add in any order: 3 + 4 and 4 + 3 both make 7.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 5. It is quicker to start with the bigger number.Start: 5
- Count on 2 more. Say one number for each step on.5, then 6, 7
- Write the total. The last number you say is the total.7
Check. Count all 7 things one at a time. You get 7 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 6. It is quicker to start with the bigger number.Start: 6
- Count on 2 more. Say one number for each step on.6, then 7, 8
- Write the total. The last number you say is the total.8
Check. Count all 8 things one at a time. You get 8 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. The + sign means add. The = sign means the answer is.
Method. Count each group. Then join them with a + sign and write the total after an = sign.
- Count the first group. Say how many there are.2
- Count the second group. Say how many there are in the other group.5
- Join the groups with the + sign. The + sign shows that we put them together.2 + 5
- Write the whole sentence. The = sign comes before the total.2 + 5 = 7
Check. Count all the things in both groups: 7. ✓
Watch out. Put the + sign between the two groups, and the = sign before the total.
Watch out
Watch out: start at the bigger number. For 2 + 7, start at 7 and count on 2: 8, 9. It is quicker than starting at 2.
Exam tip
Grown-up tip. Use two groups of buttons or pasta shapes. Put them together and count all of them. Then ask your child to start at the bigger group and count on the smaller one. Say the sum out loud: “Three add four makes seven.”
Exercise 2A Putting groups together
Non-calculatorKey words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 3. It is quicker to start with the bigger number.Start: 3
- Count on 2 more. Say one number for each step on.3, then 4, 5
- Write the total. The last number you say is the total.5
Check. Count all 5 things one at a time. You get 5 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 6. It is quicker to start with the bigger number.Start: 6
- Count on 1 more. Say one number for each step on.6, then 7
- Write the total. The last number you say is the total.7
Check. Count all 7 things one at a time. You get 7 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 5. It is quicker to start with the bigger number.Start: 5
- Count on 2 more. Say one number for each step on.5, then 6, 7
- Write the total. The last number you say is the total.7
Check. Count all 7 things one at a time. You get 7 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 6. It is quicker to start with the bigger number.Start: 6
- Count on 3 more. Say one number for each step on.6, then 7, 8, 9
- Write the total. The last number you say is the total.9
Check. Count all 9 things one at a time. You get 9 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 4. It is quicker to start with the bigger number.Start: 4
- Count on 1 more. Say one number for each step on.4, then 5
- Write the total. The last number you say is the total.5
Check. Count all 5 things one at a time. You get 5 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 4. It is quicker to start with the bigger number.Start: 4
- Count on 3 more. Say one number for each step on.4, then 5, 6, 7
- Write the total. The last number you say is the total.7
Check. Count all 7 things one at a time. You get 7 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 5. It is quicker to start with the bigger number.Start: 5
- Count on 2 more. Say one number for each step on.5, then 6, 7
- Write the total. The last number you say is the total.7
Check. Count all 7 things one at a time. You get 7 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. The + sign means add. The = sign means the answer is.
Method. Count each group. Then join them with a + sign and write the total after an = sign.
- Count the first group. Say how many there are.2
- Count the second group. Say how many there are in the other group.6
- Join the groups with the + sign. The + sign shows that we put them together.2 + 6
- Write the whole sentence. The = sign comes before the total.2 + 6 = 8
Check. Count all the things in both groups: 8. ✓
Watch out. Put the + sign between the two groups, and the = sign before the total.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 5. It is quicker to start with the bigger number.Start: 5
- Count on 4 more. Say one number for each step on.5, then 6, 7, 8, 9
- Write the total. The last number you say is the total.9
Check. Count all 9 things one at a time. You get 9 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 6. It is quicker to start with the bigger number.Start: 6
- Count on 2 more. Say one number for each step on.6, then 7, 8
- Write the total. The last number you say is the total.8
Check. Count all 8 things one at a time. You get 8 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. The + sign says add. The − sign says take away. The = sign says makes.
Method. Read the first number, then the sign, then the number after the = sign.
- Read the first number. Say the number word.five
- Read the sign. The sign tells us what to do with the numbers.The sign says add
- Read the answer after the = sign. The number after the = sign is the answer.seven
- Say the whole sentence in words. Put the words together in order.Five add two makes seven
Check. Also correct: five add two makes seven. Accept "makes" or "is" after the sign words. ✓
Watch out. Read the sign as words, not as a symbol. The = sign means makes or is.
Key words. Quicker means fewer steps to count.
Method. Count the steps for each sum. The sum with fewer steps is quicker.
- Look at 2 + 8. Starting at 2 means counting on 8 steps.2 + 8: 8 steps
- Look at 8 + 2. Starting at 8 means counting on 2 steps.8 + 2: 2 steps
- Choose the quicker one. Fewer steps is quicker.8 + 2
Check. Both sums make 10, so the answer is the same. Only the number of steps changes. ✓
Watch out. Start with the bigger number, so you have fewer steps to count.
Key words. Adding can be done in any order.
Method. Work out both sums. If the totals are the same, the sums are the same.
- Work out 3 + 4. Count on from the bigger number.3 + 4 = 7
- Work out 4 + 3. Swap the numbers and count again.4 + 3 = 7
- Compare the two totals. The same total means the sums are the same.7 and 7
- Write the answer. Yes. Both make 7.
Check. Count on from 4 to check: the total is 7. ✓
Watch out. Swapping the numbers does not change the total when we add.
Taking away and counting back: subtract
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Subtract means take away. The − sign means take away.
Here are 7 balls. Cross out 2 balls, because they are taken away. Now count the balls that are left. There are 5.
Key ideas
- − means take away.
- Start with the whole number, then take away the part that goes.
- Counting back: start at the bigger number and count back one step at a time.
- The answer is the number of things that are left.
Key words. Take away means remove some. The − sign means take away.
Method. Start with all the things. Cross out the ones taken away, then count what is left.
- Start with all the things. Count the whole group first.Start: 6
- Take away (cross out) the ones that go. Taking away means removing some.6 − 2
- Count what is left. Count only the things that are not crossed out.4 left
- Write the answer. 4
Check. Add back what you took away: 4 + 2 = 6. ✓
Watch out. Count only the things that are left. Do not count the crossed-out ones.
Key words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 8 on the number line. Put your finger on the start number.Start: 8
- Count back 3. Each step back is one less than the number before.7, 6, 5
- Write the number you land on. The last number you say is the answer.5
Check. Count on from 5 to 8: that is 3 steps. ✓
Watch out. Do not count the starting number as your first step back.
Key words. The − sign means take away. The answer is after the = sign.
Method. Start with the whole. Take away the part that goes. Write the sentence.
- Start with the whole. Count everything at the start.Start: 10
- Take away the part that goes. The − sign means take away.10 − 6
- Count what is left and write the sentence. The answer goes after the = sign.10 − 6 = 4
- Write the answer. 10 − 6 = 4
Check. Add back to check: 4 + 6 = 10. ✓
Watch out. The sign is a minus, not a plus. Taking away makes the number smaller.
Watch out
Watch out: count back from the first number. For 8 − 3, start at 8 and count back 3: 7, 6, 5. Do not start at 3.
Exam tip
Grown-up tip. Use buttons or toy cars. Ask: “You had 6. You gave 2 away. How many are left?” Let your child say the sentence: “Six take away two leaves four.”
Exercise 2B Taking away and counting back
Non-calculatorKey words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 5 on the number line. Put your finger on the start number.Start: 5
- Count back 2. Each step back is one less than the number before.4, 3
- Write the number you land on. The last number you say is the answer.3
Check. Count on from 3 to 5: that is 2 steps. ✓
Watch out. Do not count the starting number as your first step back.
Key words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 7 on the number line. Put your finger on the start number.Start: 7
- Count back 4. Each step back is one less than the number before.6, 5, 4, 3
- Write the number you land on. The last number you say is the answer.3
Check. Count on from 3 to 7: that is 4 steps. ✓
Watch out. Do not count the starting number as your first step back.
Key words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 10 on the number line. Put your finger on the start number.Start: 10
- Count back 6. Each step back is one less than the number before.9, 8, 7, 6, 5, 4
- Write the number you land on. The last number you say is the answer.4
Check. Count on from 4 to 10: that is 6 steps. ✓
Watch out. Do not count the starting number as your first step back.
Key words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 9 on the number line. Put your finger on the start number.Start: 9
- Count back 3. Each step back is one less than the number before.8, 7, 6
- Write the number you land on. The last number you say is the answer.6
Check. Count on from 6 to 9: that is 3 steps. ✓
Watch out. Do not count the starting number as your first step back.
Key words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 8 on the number line. Put your finger on the start number.Start: 8
- Count back 5. Each step back is one less than the number before.7, 6, 5, 4, 3
- Write the number you land on. The last number you say is the answer.3
Check. Count on from 3 to 8: that is 5 steps. ✓
Watch out. Do not count the starting number as your first step back.
Key words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 6 on the number line. Put your finger on the start number.Start: 6
- Count back 1. Each step back is one less than the number before.5
- Write the number you land on. The last number you say is the answer.5
Check. Count on from 5 to 6: that is 1 step. ✓
Watch out. Do not count the starting number as your first step back.
Key words. Take away means remove some. The − sign means take away.
Method. Start with all the things. Cross out the ones taken away, then count what is left.
- Start with all the things. Count the whole group first.Start: 7
- Take away (cross out) the ones that go. Taking away means removing some.7 − 3
- Count what is left. Count only the things that are not crossed out.4 left
- Write the answer. 4
Check. Add back what you took away: 4 + 3 = 7. ✓
Watch out. Count only the things that are left. Do not count the crossed-out ones.
Key words. Take away means remove some. The − sign means take away.
Method. Start with all the things. Cross out the ones taken away, then count what is left.
- Start with all the things. Count the whole group first.Start: 9
- Take away (cross out) the ones that go. Taking away means removing some.9 − 4
- Count what is left. Count only the things that are not crossed out.5 left
- Write the answer. 5
Check. Add back what you took away: 5 + 4 = 9. ✓
Watch out. Count only the things that are left. Do not count the crossed-out ones.
Key words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 9 on the number line. Put your finger on the start number.Start: 9
- Count back 2. Each step back is one less than the number before.8, 7
- Write the number you land on. The last number you say is the answer.7
Check. Count on from 7 to 9: that is 2 steps. ✓
Watch out. Do not count the starting number as your first step back.
Key words. Take away means remove some. The − sign means take away.
Method. Start with all the things. Cross out the ones taken away, then count what is left.
- Start with all the things. Count the whole group first.Start: 8
- Take away (cross out) the ones that go. Taking away means removing some.8 − 5
- Count what is left. Count only the things that are not crossed out.3 left
- Write the answer. 3
Check. Add back what you took away: 3 + 5 = 8. ✓
Watch out. Count only the things that are left. Do not count the crossed-out ones.
Key words. The − sign means take away. The answer is after the = sign.
Method. Start with the whole. Take away the part that goes. Write the sentence.
- Start with the whole. Count everything at the start.Start: 6
- Take away the part that goes. The − sign means take away.6 − 2
- Count what is left and write the sentence. The answer goes after the = sign.6 − 2 = 4
- Write the answer. 6 − 2 = 4
Check. Add back to check: 4 + 2 = 6. ✓
Watch out. The sign is a minus, not a plus. Taking away makes the number smaller.
Key words. The + sign says add. The − sign says take away. The = sign says makes.
Method. Read the first number, then the sign, then the number after the = sign.
- Read the first number. Say the number word.six
- Read the sign. The sign tells us what to do with the numbers.The sign says take away
- Read the answer after the = sign. The number after the = sign is the answer.five
- Say the whole sentence in words. Put the words together in order.Six take away one leaves five
Check. Also correct: six take away one leaves five. Accept "makes" or "is" after the sign words. ✓
Watch out. Read the sign as words, not as a symbol. The = sign means makes or is.
Key words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 6 on the number line. Put your finger on the start number.Start: 6
- Count back 4. Each step back is one less than the number before.5, 4, 3, 2
- Write the number you land on. The last number you say is the answer.2
Check. Count on from 2 to 6: that is 4 steps. ✓
Watch out. Do not count the starting number as your first step back.
Part-whole and number bonds
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A part-whole model shows how a whole is made of parts. The big circle at the top is the whole. The two small circles are the parts.
The two parts put together make the whole. If you take one part away from the whole, the other part is left.
Two numbers that make a total are called a number bond. Here, 3 and 4 are a number bond to 7.
Key ideas
- The whole is the big number at the top.
- The parts are the two smaller numbers below.
- Parts put together make the whole: 3 + 4 = 7.
- The whole take away one part leaves the other part: 7 − 3 = 4.
- A number bond to 10 is two numbers that make 10, such as 6 and 4.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 5. Count on until you reach 8. The number of counts is the missing number.
- Start at 5, the number we know. Put your finger on it.Start: 5
- Count on to 8. Say each number as you count on.6, 7, 8
- Count how many numbers you said. That many is the missing number.3 numbers
- Write the missing number. 3
Check. 5 + 3 = 8. ✓
Watch out. Count the numbers after 5, not 5 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 6. Count on until you reach 10. The number of counts is the missing number.
- Start at 6, the number we know. Put your finger on it.Start: 6
- Count on to 10. Say each number as you count on.7, 8, 9, 10
- Count how many numbers you said. That many is the missing number.4 numbers
- Write the missing number. 4
Check. 6 + 4 = 10. ✓
Watch out. Count the numbers after 6, not 6 itself.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 5. It is quicker to start with the bigger number.Start: 5
- Count on 4 more. Say one number for each step on.5, then 6, 7, 8, 9
- Write the total. The last number you say is the total.9
Check. Count all 9 things one at a time. You get 9 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Watch out
Watch out: a part is always smaller than the whole. If the whole is 8 and one part is 5, the other part is 3, not 13. Count on from the part you know until you reach the whole.
Exam tip
Grown-up tip. Draw a circle on paper for the whole and two circles for the parts. Hide some small toys in one hand and ask: “I have 10 toys. I can see 6. How many are hidden?” Then check by counting.
Exercise 2C Part-whole and number bonds
Non-calculatorKey words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 2. Count on until you reach 5. The number of counts is the missing number.
- Start at 2, the number we know. Put your finger on it.Start: 2
- Count on to 5. Say each number as you count on.3, 4, 5
- Count how many numbers you said. That many is the missing number.3 numbers
- Write the missing number. 3
Check. 2 + 3 = 5. ✓
Watch out. Count the numbers after 2, not 2 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 4. Count on until you reach 9. The number of counts is the missing number.
- Start at 4, the number we know. Put your finger on it.Start: 4
- Count on to 9. Say each number as you count on.5, 6, 7, 8, 9
- Count how many numbers you said. That many is the missing number.5 numbers
- Write the missing number. 5
Check. 4 + 5 = 9. ✓
Watch out. Count the numbers after 4, not 4 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 7. Count on until you reach 10. The number of counts is the missing number.
- Start at 7, the number we know. Put your finger on it.Start: 7
- Count on to 10. Say each number as you count on.8, 9, 10
- Count how many numbers you said. That many is the missing number.3 numbers
- Write the missing number. 3
Check. 7 + 3 = 10. ✓
Watch out. Count the numbers after 7, not 7 itself.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 6. It is quicker to start with the bigger number.Start: 6
- Count on 3 more. Say one number for each step on.6, then 7, 8, 9
- Write the total. The last number you say is the total.9
Check. Count all 9 things one at a time. You get 9 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 3. Count on until you reach 10. The number of counts is the missing number.
- Start at 3, the number we know. Put your finger on it.Start: 3
- Count on to 10. Say each number as you count on.4, 5, 6, 7, 8, 9, 10
- Count how many numbers you said. That many is the missing number.7 numbers
- Write the missing number. 7
Check. 3 + 7 = 10. ✓
Watch out. Count the numbers after 3, not 3 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 6. Count on until you reach 10. The number of counts is the missing number.
- Start at 6, the number we know. Put your finger on it.Start: 6
- Count on to 10. Say each number as you count on.7, 8, 9, 10
- Count how many numbers you said. That many is the missing number.4 numbers
- Write the missing number. 4
Check. 6 + 4 = 10. ✓
Watch out. Count the numbers after 6, not 6 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 8. Count on until you reach 10. The number of counts is the missing number.
- Start at 8, the number we know. Put your finger on it.Start: 8
- Count on to 10. Say each number as you count on.9, 10
- Count how many numbers you said. That many is the missing number.2 numbers
- Write the missing number. 2
Check. 8 + 2 = 10. ✓
Watch out. Count the numbers after 8, not 8 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 3. Count on until you reach 8. The number of counts is the missing number.
- Start at 3, the number we know. Put your finger on it.Start: 3
- Count on to 8. Say each number as you count on.4, 5, 6, 7, 8
- Count how many numbers you said. That many is the missing number.5 numbers
- Write the missing number. 5
Check. 3 + 5 = 8. ✓
Watch out. Count the numbers after 3, not 3 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 2. Count on until you reach 6. The number of counts is the missing number.
- Start at 2, the number we know. Put your finger on it.Start: 2
- Count on to 6. Say each number as you count on.3, 4, 5, 6
- Count how many numbers you said. That many is the missing number.4 numbers
- Write the missing number. 4
Check. 2 + 4 = 6. ✓
Watch out. Count the numbers after 2, not 2 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 4. Count on until you reach 10. The number of counts is the missing number.
- Start at 4, the number we know. Put your finger on it.Start: 4
- Count on to 10. Say each number as you count on.5, 6, 7, 8, 9, 10
- Count how many numbers you said. That many is the missing number.6 numbers
- Write the missing number. 6
Check. 4 + 6 = 10. ✓
Watch out. Count the numbers after 4, not 4 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 5. Count on until you reach 9. The number of counts is the missing number.
- Start at 5, the number we know. Put your finger on it.Start: 5
- Count on to 9. Say each number as you count on.6, 7, 8, 9
- Count how many numbers you said. That many is the missing number.4 numbers
- Write the missing number. 4
Check. 5 + 4 = 9. ✓
Watch out. Count the numbers after 5, not 5 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 2. Count on until you reach 7. The number of counts is the missing number.
- Start at 2, the number we know. Put your finger on it.Start: 2
- Count on to 7. Say each number as you count on.3, 4, 5, 6, 7
- Count how many numbers you said. That many is the missing number.5 numbers
- Write the missing number. 5
Check. 2 + 5 = 7. ✓
Watch out. Count the numbers after 2, not 2 itself.
Key words. The = sign means the two sides are the same amount.
Method. Work out 3 + 5, then check it against the number that was said.
- Work out 3 + 5. Start at the bigger number and count on.Start at 5, count on 3: 8
- Compare with what was said. Is the total the same as the number in the sentence?8 and 9
- Write the answer. No. 3 + 5 = 8.
Check. Count all the things: 3 + 5 = 8. ✓
Watch out. Work out the total first. Do not guess from the numbers you can see.
Fact families: related facts
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A fact family is a set of number sentences that use the same three numbers.
Look at the numbers 3, 4 and 7. We can make four sentences: 3 + 4 = 7 and 4 + 3 = 7. Then 7 − 3 = 4 and 7 − 4 = 3.
The biggest number, 7, is the whole. It is the total in the addition sentences, and it starts the subtraction sentences.
Key ideas
- A fact family uses the same three numbers.
- Swap the two parts round for the second addition sentence.
- Take each part away from the whole for the two subtraction sentences.
- The whole is always the biggest number.
Key words. A fact family is a set of sentences that use the same three numbers.
Method. Use the same three numbers. Swap the parts for the second addition. Take each part away from the whole for the subtractions.
- Find the whole and the two parts. The whole is the biggest number.Whole 7, parts 2 and 5
- Write the two addition sentences. Swap the parts round for the second one.2 + 5 = 7 and 5 + 2 = 7
- Write the two subtraction sentences. Take each part away from the whole.7 − 2 = 5 and 7 − 5 = 2
- Write the whole family. 2 + 5 = 7, 5 + 2 = 7, 7 − 2 = 5, 7 − 5 = 2
Check. Check: 2 + 5 = 7 and 7 − 5 = 2. ✓
Watch out. In a subtraction sentence the whole always comes first.
Key words. The whole is the total. The parts are the two numbers that make it.
Method. Take each part away from the whole. Each part gives one subtraction sentence.
- Find the whole. The whole is the biggest number.Whole: 9
- Take away 4. Taking away the first part leaves the second part.9 − 4 = 5
- Take away 5. Taking away the second part leaves the first part.9 − 5 = 4
- Write both sentences. 9 − 4 = 5 and 9 − 5 = 4
Check. Check: 5 + 4 = 9. ✓
Watch out. Keep the whole at the front of each subtraction sentence.
Key words. Swapping means changing the order of the numbers.
Method. Swap the two parts round. The total stays the same.
- Write the first sentence. Start with the sentence we know.3 + 6 = 9
- Swap the two parts. Adding can be done in either order.6 + 3
- Check the total. Swapping the parts does not change the total.6 + 3 = 9
- Write the answer. 6 + 3 = 9
Check. Count on from 6 by 3 to check: 9. ✓
Watch out. Swap the numbers, but keep the total the same.
Watch out
Watch out: in a subtraction sentence, the whole comes first. Write 7 − 3 = 4, not 3 − 7 = 4.
Exam tip
Grown-up tip. Use three number cards: 3, 4 and 7. Lay them out like the fact family house. Ask: “What sentences can you make with these numbers?” Let your child read each sentence out loud.
Exercise 2D Fact families
Non-calculatorKey words. Swapping means changing the order of the numbers.
Method. Swap the two parts round. The total stays the same.
- Write the first sentence. Start with the sentence we know.4 + 2 = 6
- Swap the two parts. Adding can be done in either order.2 + 4
- Check the total. Swapping the parts does not change the total.2 + 4 = 6
- Write the answer. 2 + 4 = 6
Check. Count on from 4 by 2 to check: 6. ✓
Watch out. Swap the numbers, but keep the total the same.
Key words. A fact family is a set of sentences that use the same three numbers.
Method. Use the same three numbers. Swap the parts for the second addition. Take each part away from the whole for the subtractions.
- Find the whole and the two parts. The whole is the biggest number.Whole 8, parts 3 and 5
- Write the two addition sentences. Swap the parts round for the second one.3 + 5 = 8 and 5 + 3 = 8
- Write the two subtraction sentences. Take each part away from the whole.8 − 3 = 5 and 8 − 5 = 3
- Write the whole family. 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5, 8 − 5 = 3
Check. Check: 3 + 5 = 8 and 8 − 5 = 3. ✓
Watch out. In a subtraction sentence the whole always comes first.
Key words. The + sign means add. The = sign means the answer is.
Method. Count each group. Then join them with a + sign and write the total after an = sign.
- Count the first group. Say how many there are.4
- Count the second group. Say how many there are in the other group.5
- Join the groups with the + sign. The + sign shows that we put them together.4 + 5
- Write the whole sentence. The = sign comes before the total.4 + 5 = 9
Check. Count all the things in both groups: 9. ✓
Watch out. Put the + sign between the two groups, and the = sign before the total.
Key words. The − sign means take away. The answer is after the = sign.
Method. Start with the whole. Take away the part that goes. Write the sentence.
- Start with the whole. Count everything at the start.Start: 10
- Take away the part that goes. The − sign means take away.10 − 4
- Count what is left and write the sentence. The answer goes after the = sign.10 − 4 = 6
- Write the answer. 10 − 4 = 6
Check. Add back to check: 6 + 4 = 10. ✓
Watch out. The sign is a minus, not a plus. Taking away makes the number smaller.
Key words. The whole is the total. The parts are the two numbers that make it.
Method. Take each part away from the whole. Each part gives one subtraction sentence.
- Find the whole. The whole is the biggest number.Whole: 5
- Take away 2. Taking away the first part leaves the second part.5 − 2 = 3
- Take away 3. Taking away the second part leaves the first part.5 − 3 = 2
- Write both sentences. 5 − 2 = 3 and 5 − 3 = 2
Check. Check: 3 + 2 = 5. ✓
Watch out. Keep the whole at the front of each subtraction sentence.
Key words. A fact family is a set of sentences that use the same three numbers.
Method. Use the same three numbers. Swap the parts for the second addition. Take each part away from the whole for the subtractions.
- Find the whole and the two parts. The whole is the biggest number.Whole 6, parts 2 and 4
- Write the two addition sentences. Swap the parts round for the second one.2 + 4 = 6 and 4 + 2 = 6
- Write the two subtraction sentences. Take each part away from the whole.6 − 2 = 4 and 6 − 4 = 2
- Write the whole family. 2 + 4 = 6, 4 + 2 = 6, 6 − 2 = 4, 6 − 4 = 2
Check. Check: 2 + 4 = 6 and 6 − 4 = 2. ✓
Watch out. In a subtraction sentence the whole always comes first.
Key words. The = sign means the two sides are the same amount.
Method. Work out 3 + 4, then check it against the number that was said.
- Work out 3 + 4. Start at the bigger number and count on.Start at 4, count on 3: 7
- Compare with what was said. Is the total the same as the number in the sentence?7 and 8
- Write the answer. No. 3 + 4 = 7.
Check. Count all the things: 3 + 4 = 7. ✓
Watch out. Work out the total first. Do not guess from the numbers you can see.
Key words. A fact family is a set of sentences that use the same three numbers.
Method. Use the same three numbers. Swap the parts for the second addition. Take each part away from the whole for the subtractions.
- Find the whole and the two parts. The whole is the biggest number.Whole 7, parts 1 and 6
- Write the two addition sentences. Swap the parts round for the second one.1 + 6 = 7 and 6 + 1 = 7
- Write the two subtraction sentences. Take each part away from the whole.7 − 1 = 6 and 7 − 6 = 1
- Write the whole family. 1 + 6 = 7, 6 + 1 = 7, 7 − 1 = 6, 7 − 6 = 1
Check. Check: 1 + 6 = 7 and 7 − 6 = 1. ✓
Watch out. In a subtraction sentence the whole always comes first.
3 + 4 = 7 4 + 3 = 7 7 − 3 = 4 7 + 4 = 11
Method. Check which sentences use only the numbers 3, 4 and 7.
- Look at 3 + 4 = 7 and 4 + 3 = 7. Both use only 3, 4 and 7.3, 4 and 7
- Look at 7 − 3 = 4. It uses 7, 3 and 4.7, 3 and 4
- Look at 7 + 4 = 11. It has 11 in it, not 3, 4 or 7.7 + 4 = 11
- Write the odd one out. 7 + 4 = 11
Check. The family only uses 3, 4 and 7. ✓
Watch out. Look for the sentence with a number that is not in the family.
Key words. A fact family is a set of sentences that use the same three numbers.
Method. Use the same three numbers. Swap the parts for the second addition. Take each part away from the whole for the subtractions.
- Find the whole and the two parts. The whole is the biggest number.Whole 7, parts 2 and 5
- Write the two addition sentences. Swap the parts round for the second one.2 + 5 = 7 and 5 + 2 = 7
- Write the two subtraction sentences. Take each part away from the whole.7 − 2 = 5 and 7 − 5 = 2
- Write the whole family. 2 + 5 = 7, 5 + 2 = 7, 7 − 2 = 5, 7 − 5 = 2
Check. Check: 2 + 5 = 7 and 7 − 5 = 2. ✓
Watch out. In a subtraction sentence the whole always comes first.
Missing numbers
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Sometimes a number is missing. We show the missing number with a box: ?.
The sentence 4 + ? = 9 asks: what number do we add to 4 to make 9? Start at 4 and count on until you reach 9. You count 5 steps, so the missing number is 5.
The box can be on the left, in the middle or on the right of the = sign. The sentence must still be true.
Key ideas
- A box means a missing number. Find the number that makes the sentence true.
- Count on to find a missing number in an addition sentence.
- Count back to find a missing number in a subtraction sentence.
- Check your answer by putting it back in the sentence.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 6. Count on until you reach 10. The number of counts is the missing number.
- Start at 6, the number we know. Put your finger on it.Start: 6
- Count on to 10. Say each number as you count on.7, 8, 9, 10
- Count how many numbers you said. That many is the missing number.4 numbers
- Write the missing number. 4
Check. 6 + 4 = 10. ✓
Watch out. Count the numbers after 6, not 6 itself.
Key words. Adding undoes taking away.
Method. Undo the take away. Put back the number that was taken away.
- Look at the answer, 5. The answer is what is left after taking away.Answer: 5
- Add 2 back on. Adding undoes taking away.5 + 2 = 7
- Write the missing number. 7
Check. 7 − 2 = 5. ✓
Watch out. Do not take the number away again. Put it back on instead.
Key words. The box is the number we take away.
Method. Start at 8. Count back until you reach 3. The number of steps is the missing number.
- Start at 8. That is the number we begin with.Start: 8
- Count back to 3. Each step back takes one away.7, 6, 5, 4, 3
- Count how many steps you took. The steps are the number taken away.5 steps
- Write the missing number. 5
Check. 8 − 5 = 3. ✓
Watch out. Count the steps back. Do not count the number you start from.
Watch out
Watch out: a box on the left is still a missing number. Check your answer: 6 + 4 = 10 is true.
Exam tip
Grown-up tip. Put 6 counters on the table and ask: “How many more do we need to make 10?” Let your child add the counters one at a time, then write the sentence together.
Exercise 2E Missing numbers
Non-calculatorKey words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 2. Count on until you reach 5. The number of counts is the missing number.
- Start at 2, the number we know. Put your finger on it.Start: 2
- Count on to 5. Say each number as you count on.3, 4, 5
- Count how many numbers you said. That many is the missing number.3 numbers
- Write the missing number. 3
Check. 2 + 3 = 5. ✓
Watch out. Count the numbers after 2, not 2 itself.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 3. Count on until you reach 7. The number of counts is the missing number.
- Start at 3, the number we know. Put your finger on it.Start: 3
- Count on to 7. Say each number as you count on.4, 5, 6, 7
- Count how many numbers you said. That many is the missing number.4 numbers
- Write the missing number. 4
Check. 3 + 4 = 7. ✓
Watch out. Count the numbers after 3, not 3 itself.
Key words. The box is the number we take away.
Method. Start at 5. Count back until you reach 2. The number of steps is the missing number.
- Start at 5. That is the number we begin with.Start: 5
- Count back to 2. Each step back takes one away.4, 3, 2
- Count how many steps you took. The steps are the number taken away.3 steps
- Write the missing number. 3
Check. 5 − 3 = 2. ✓
Watch out. Count the steps back. Do not count the number you start from.
Key words. Adding undoes taking away.
Method. Undo the take away. Put back the number that was taken away.
- Look at the answer, 6. The answer is what is left after taking away.Answer: 6
- Add 2 back on. Adding undoes taking away.6 + 2 = 8
- Write the missing number. 8
Check. 8 − 2 = 6. ✓
Watch out. Do not take the number away again. Put it back on instead.
Key words. Adding undoes taking away.
Method. Undo the take away. Put back the number that was taken away.
- Look at the answer, 7. The answer is what is left after taking away.Answer: 7
- Add 2 back on. Adding undoes taking away.7 + 2 = 9
- Write the missing number. 9
Check. 9 − 2 = 7. ✓
Watch out. Do not take the number away again. Put it back on instead.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 5. Count on until you reach 8. The number of counts is the missing number.
- Start at 5, the number we know. Put your finger on it.Start: 5
- Count on to 8. Say each number as you count on.6, 7, 8
- Count how many numbers you said. That many is the missing number.3 numbers
- Write the missing number. 3
Check. 5 + 3 = 8. ✓
Watch out. Count the numbers after 5, not 5 itself.
Key words. The box is the number we take away.
Method. Start at 6. Count back until you reach 2. The number of steps is the missing number.
- Start at 6. That is the number we begin with.Start: 6
- Count back to 2. Each step back takes one away.5, 4, 3, 2
- Count how many steps you took. The steps are the number taken away.4 steps
- Write the missing number. 4
Check. 6 − 4 = 2. ✓
Watch out. Count the steps back. Do not count the number you start from.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 4. Count on until you reach 9. The number of counts is the missing number.
- Start at 4, the number we know. Put your finger on it.Start: 4
- Count on to 9. Say each number as you count on.5, 6, 7, 8, 9
- Count how many numbers you said. That many is the missing number.5 numbers
- Write the missing number. 5
Check. 4 + 5 = 9. ✓
Watch out. Count the numbers after 4, not 4 itself.
Key words. True means it is right. False means it is not right.
Method. Work out the sum, then check if the sentence is true.
- Work out 4 + 3. Count on from the bigger number.4 + 3 = 7
- Compare with the other side of the = sign. True means both sides are the same.7 and 8
- Write the answer. False
Check. Count all the things: 4 + 3 = 7. ✓
Watch out. The answer is False if the two sides are not the same.
Key words. The box is the number we take away.
Method. Start at 9. Count back until you reach 4. The number of steps is the missing number.
- Start at 9. That is the number we begin with.Start: 9
- Count back to 4. Each step back takes one away.8, 7, 6, 5, 4
- Count how many steps you took. The steps are the number taken away.5 steps
- Write the missing number. 5
Check. 9 − 5 = 4. ✓
Watch out. Count the steps back. Do not count the number you start from.
Key words. A pair is two numbers that go together.
Method. Find two different pairs that make 6. Any correct pair is fine.
- Try 1 and 5. Count on from the bigger number.1 + 5 = 6
- Try 2 and 4. A different pair that also makes the total.2 + 4 = 6
- Write the answer. Both pairs make the same total.1 + 5 = 6 or 2 + 4 = 6
Check. Count on to check each pair. Both give 6. ✓
Watch out. Make sure both numbers in your pair are different from the other pair.
Zero and one-step problems
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Zero means none. We write it as 0. It can be tricky when we add or take away.
Add zero: 5 + 0 = 5. Nothing is added, so 5 stays 5.
Take away zero: 5 − 0 = 5. Nothing is taken away, so 5 stays 5.
Take away all: 5 − 5 = 0. Nothing is left.
A one-step problem is a short story with one sum to work out. First, decide: are things joining together, or going away? Then write one number sentence.
Key ideas
- Zero means none.
- Adding zero does not change the number.
- Taking away zero does not change the number.
- Taking away all of them leaves zero.
- In a story, ask: are things joining together, or going away?
Key words. Zero means none at all. We write it as 0.
Method. Adding zero means adding nothing, so the number stays the same.
- Start with 5. This is the number we begin with.5
- Add zero. Nothing is added. Zero means none, so no new things are counted.5 + 0
- Write the answer. The total is the same as the start.5
Check. Count 5 things and add none. You still have 5. ✓
Watch out. Zero means none. Do not change the number when you add zero.
Key words. When nothing is left, the answer is zero, which we write as 0.
Method. Taking away all of the things leaves none.
- Start with 5. This is the number we begin with.5
- Take away all 5. Every thing goes.5 − 5
- Count what is left. Nothing is left.Nothing left
- Write the answer. Zero means none.0
Check. Add back 5 to zero: 0 + 5 = 5. ✓
Watch out. When you take away all of them, the answer is 0, not the number you started with.
Key words. Take away means some things go away. The − sign shows it.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. Start with the number we had.7 and 3
- Decide: add or take away? Things going away means take away.Going away, so we take away
- Write the number sentence. The sentence shows the story.7 − 3 = 4
- Write the answer. Say what the number is for.4 children
Check. Add back the 3 that went: 4 + 3 = 7. ✓
Watch out. Start with the number you had at the beginning, not the number that went away.
Watch out
Watch out: when you take away all of them, the answer is 0, not the number you started with. 5 − 5 = 0.
Exam tip
Grown-up tip. Use a bag with 5 buttons. Take all 5 out and ask: “How many are left in the bag?” Then take none out and ask again. Zero is the answer when nothing is left.
Exercise 2F Zero and one-step problems
Non-calculatorKey words. Zero means none at all. We write it as 0.
Method. Adding zero means adding nothing, so the number stays the same.
- Start with 6. This is the number we begin with.6
- Add zero. Nothing is added. Zero means none, so no new things are counted.6 + 0
- Write the answer. The total is the same as the start.6
Check. Count 6 things and add none. You still have 6. ✓
Watch out. Zero means none. Do not change the number when you add zero.
Key words. Zero means none at all.
Method. Start with zero things. Then add the things.
- Start with zero. Zero means there are no things yet.0
- Add 8. Now there are 8 things.0 + 8
- Write the answer. The total is the number you added.8
Check. Count 8 things. ✓
Watch out. Zero on the left still means none. The answer is the other number.
Key words. Zero means none. The − sign means take away.
Method. Taking away zero means taking nothing away, so the number stays the same.
- Start with 4. This is the number we begin with.4
- Take away zero. Nothing is taken away. Zero means none, so nothing goes.4 − 0
- Write the answer. Everything is still there.4
Check. Count 4 things. None were taken away, so 4 are left. ✓
Watch out. Taking away zero does not change the number.
Key words. When nothing is left, the answer is zero, which we write as 0.
Method. Taking away all of the things leaves none.
- Start with 7. This is the number we begin with.7
- Take away all 7. Every thing goes.7 − 7
- Count what is left. Nothing is left.Nothing left
- Write the answer. Zero means none.0
Check. Add back 7 to zero: 0 + 7 = 7. ✓
Watch out. When you take away all of them, the answer is 0, not the number you started with.
Key words. Zero means none at all.
Method. Start with zero things. Then add the things.
- Start with zero. Zero means there are no things yet.0
- Add 6. Now there are 6 things.0 + 6
- Write the answer. The total is the number you added.6
Check. Count 6 things. ✓
Watch out. Zero on the left still means none. The answer is the other number.
Key words. Zero means none at all. We write it as 0.
Method. Adding zero means adding nothing, so the number stays the same.
- Start with 3. This is the number we begin with.3
- Add zero. Nothing is added. Zero means none, so no new things are counted.3 + 0
- Write the answer. The total is the same as the start.3
Check. Count 3 things and add none. You still have 3. ✓
Watch out. Zero means none. Do not change the number when you add zero.
Key words. Zero means none. The − sign means take away.
Method. Taking away zero means taking nothing away, so the number stays the same.
- Start with 8. This is the number we begin with.8
- Take away zero. Nothing is taken away. Zero means none, so nothing goes.8 − 0
- Write the answer. Everything is still there.8
Check. Count 8 things. None were taken away, so 8 are left. ✓
Watch out. Taking away zero does not change the number.
Key words. Zero means none at all. We write it as 0.
Method. Adding zero means adding nothing, so the number stays the same.
- Start with 4. This is the number we begin with.4
- Add zero. Nothing is added. Zero means none, so no new things are counted.4 + 0
- Write the answer. The total is the same as the start.4
Check. Count 4 things and add none. You still have 4. ✓
Watch out. Zero means none. Do not change the number when you add zero.
Key words. A story sum is a short problem told as a story.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. The numbers tell us how many.0 and 4
- Decide: add or take away? Things joining together means add.Joining, so we add
- Write the number sentence. The sentence shows the story.0 + 4 = 4
- Write the answer. Say what the number is for.4 stickers
Check. Count 4 stickers in total. ✓
Watch out. Ask: are things joining together, or going away?
Key words. Take away means some things go away. The − sign shows it.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. Start with the number we had.9 and 2
- Decide: add or take away? Things going away means take away.Going away, so we take away
- Write the number sentence. The sentence shows the story.9 − 2 = 7
- Write the answer. Say what the number is for.7 birds
Check. Add back the 2 that went: 7 + 2 = 9. ✓
Watch out. Start with the number you had at the beginning, not the number that went away.
Key words. A story sum is a short problem told as a story.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. The numbers tell us how many.6 and 3
- Decide: add or take away? Things joining together means add.Joining, so we add
- Write the number sentence. The sentence shows the story.6 + 3 = 9
- Write the answer. Say what the number is for.9 beads
Check. Count 9 beads in total. ✓
Watch out. Ask: are things joining together, or going away?
Key words. Take away means some things go away. The − sign shows it.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. Start with the number we had.10 and 4
- Decide: add or take away? Things going away means take away.Going away, so we take away
- Write the number sentence. The sentence shows the story.10 − 4 = 6
- Write the answer. Say what the number is for.6 children
Check. Add back the 4 that went: 6 + 4 = 10. ✓
Watch out. Start with the number you had at the beginning, not the number that went away.
Key words. The − sign means take away. The answer is after the = sign.
Method. Start with the whole. Take away the part that goes. Write the sentence.
- Start with the whole. Count everything at the start.Start: 5
- Take away the part that goes. The − sign means take away.5 − 5
- Count what is left and write the sentence. The answer goes after the = sign.5 − 5 = 0
- Write the answer. 5 − 5 = 0
Check. Add back to check: 0 + 5 = 5. ✓
Watch out. The sign is a minus, not a plus. Taking away makes the number smaller.
Chapter summary
| Skill | Method |
|---|---|
| Add (put together) | Start at the bigger number and count on the smaller number. 5 + 2 = 7. |
| Subtract (take away) | Start with the whole, take away, then count what is left. Or count back: 8 − 3 = 5. |
| Part-whole and number bonds | The parts add up to the whole. 3 and 7 are a number bond to 10: 3 + 7 = 10. |
| Fact families | Use the same three numbers to make two addition and two subtraction sentences. |
| Missing numbers | Find the number that makes the sentence true. Count on or count back. |
| Zero | Adding zero or taking away zero leaves the number. Taking away all of them leaves 0. |
Can you…?
- I can put groups together and count on to add
- I can take away and count back to subtract
- I can use the part-whole model and number bonds to 10
- I can read and write + , − and = number sentences
- I can write a fact family from three numbers
- I can find a missing number in a sentence
- I can use zero when adding and taking away
- I can solve a one-step problem with pictures
Key terms
- add
- to put groups together, or to make a total bigger
- subtract
- to take away, or to find how many are left
- count on
- start at one number and keep going up, one step at a time
- count back
- start at one number and go down, one step at a time
- whole
- the total, which the parts make together
- part
- one of the smaller numbers that make up the whole
- number bond
- two numbers that make a total, such as 3 and 7 make 10
- fact family
- number sentences that use the same three numbers
- missing number
- a number we need to find, shown with a box
- zero
- none at all; written as 0
Exercise 2Z Check-up
Non-calculatorKey words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 4. It is quicker to start with the bigger number.Start: 4
- Count on 3 more. Say one number for each step on.4, then 5, 6, 7
- Write the total. The last number you say is the total.7
Check. Count all 7 things one at a time. You get 7 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 9 on the number line. Put your finger on the start number.Start: 9
- Count back 5. Each step back is one less than the number before.8, 7, 6, 5, 4
- Write the number you land on. The last number you say is the answer.4
Check. Count on from 4 to 9: that is 5 steps. ✓
Watch out. Do not count the starting number as your first step back.
Key words. Take away means remove some. The − sign means take away.
Method. Start with all the things. Cross out the ones taken away, then count what is left.
- Start with all the things. Count the whole group first.Start: 6
- Take away (cross out) the ones that go. Taking away means removing some.6 − 2
- Count what is left. Count only the things that are not crossed out.4 left
- Write the answer. 4
Check. Add back what you took away: 4 + 2 = 6. ✓
Watch out. Count only the things that are left. Do not count the crossed-out ones.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 6. Count on until you reach 10. The number of counts is the missing number.
- Start at 6, the number we know. Put your finger on it.Start: 6
- Count on to 10. Say each number as you count on.7, 8, 9, 10
- Count how many numbers you said. That many is the missing number.4 numbers
- Write the missing number. 4
Check. 6 + 4 = 10. ✓
Watch out. Count the numbers after 6, not 6 itself.
Key words. The + sign means add. The = sign means the answer is.
Method. Count each group. Then join them with a + sign and write the total after an = sign.
- Count the first group. Say how many there are.3
- Count the second group. Say how many there are in the other group.5
- Join the groups with the + sign. The + sign shows that we put them together.3 + 5
- Write the whole sentence. The = sign comes before the total.3 + 5 = 8
Check. Count all the things in both groups: 8. ✓
Watch out. Put the + sign between the two groups, and the = sign before the total.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 6. Count on until you reach 9. The number of counts is the missing number.
- Start at 6, the number we know. Put your finger on it.Start: 6
- Count on to 9. Say each number as you count on.7, 8, 9
- Count how many numbers you said. That many is the missing number.3 numbers
- Write the missing number. 3
Check. 6 + 3 = 9. ✓
Watch out. Count the numbers after 6, not 6 itself.
Key words. Adding undoes taking away.
Method. Undo the take away. Put back the number that was taken away.
- Look at the answer, 8. The answer is what is left after taking away.Answer: 8
- Add 2 back on. Adding undoes taking away.8 + 2 = 10
- Write the missing number. 10
Check. 10 − 2 = 8. ✓
Watch out. Do not take the number away again. Put it back on instead.
Key words. Zero means none at all.
Method. Start with zero things. Then add the things.
- Start with zero. Zero means there are no things yet.0
- Add 5. Now there are 5 things.0 + 5
- Write the answer. The total is the number you added.5
Check. Count 5 things. ✓
Watch out. Zero on the left still means none. The answer is the other number.
Key words. Take away means some things go away. The − sign shows it.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. Start with the number we had.7 and 3
- Decide: add or take away? Things going away means take away.Going away, so we take away
- Write the number sentence. The sentence shows the story.7 − 3 = 4
- Write the answer. Say what the number is for.4 cars
Check. Add back the 3 that went: 4 + 3 = 7. ✓
Watch out. Start with the number you had at the beginning, not the number that went away.
Key words. A fact family is a set of sentences that use the same three numbers.
Method. Use the same three numbers. Swap the parts for the second addition. Take each part away from the whole for the subtractions.
- Find the whole and the two parts. The whole is the biggest number.Whole 9, parts 2 and 7
- Write the two addition sentences. Swap the parts round for the second one.2 + 7 = 9 and 7 + 2 = 9
- Write the two subtraction sentences. Take each part away from the whole.9 − 2 = 7 and 9 − 7 = 2
- Write the whole family. 2 + 7 = 9, 7 + 2 = 9, 9 − 2 = 7, 9 − 7 = 2
Check. Check: 2 + 7 = 9 and 9 − 7 = 2. ✓
Watch out. In a subtraction sentence the whole always comes first.
Total 14 marks. Allow about 14 minutes.
Exercise 2X End-of-chapter quiz
Non-calculatorKey words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 6. It is quicker to start with the bigger number.Start: 6
- Count on 2 more. Say one number for each step on.6, then 7, 8
- Write the total. The last number you say is the total.8
Check. Count all 8 things one at a time. You get 8 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. To count back is to go down one number at a time.
Method. Start at the bigger number. Count back one at a time. The number you land on is the answer.
- Start at 10 on the number line. Put your finger on the start number.Start: 10
- Count back 3. Each step back is one less than the number before.9, 8, 7
- Write the number you land on. The last number you say is the answer.7
Check. Count on from 7 to 10: that is 3 steps. ✓
Watch out. Do not count the starting number as your first step back.
Key words. To add is to put groups together. Count on means keep going up from a number.
Method. Start at the bigger number, then count on the smaller number.
- Start at the bigger number, 4. It is quicker to start with the bigger number.Start: 4
- Count on 3 more. Say one number for each step on.4, then 5, 6, 7
- Write the total. The last number you say is the total.7
Check. Count all 7 things one at a time. You get 7 again. ✓
Watch out. Do not say the starting number again. Start with the next number after it.
Key words. The − sign means take away. The answer is after the = sign.
Method. Start with the whole. Take away the part that goes. Write the sentence.
- Start with the whole. Count everything at the start.Start: 5
- Take away the part that goes. The − sign means take away.5 − 2
- Count what is left and write the sentence. The answer goes after the = sign.5 − 2 = 3
- Write the answer. 5 − 2 = 3
Check. Add back to check: 3 + 2 = 5. ✓
Watch out. The sign is a minus, not a plus. Taking away makes the number smaller.
Key words. A missing number is shown by a box. Find the number that makes the sentence true.
Method. Start at 4. Count on until you reach 10. The number of counts is the missing number.
- Start at 4, the number we know. Put your finger on it.Start: 4
- Count on to 10. Say each number as you count on.5, 6, 7, 8, 9, 10
- Count how many numbers you said. That many is the missing number.6 numbers
- Write the missing number. 6
Check. 4 + 6 = 10. ✓
Watch out. Count the numbers after 4, not 4 itself.
Key words. Adding undoes taking away.
Method. Undo the take away. Put back the number that was taken away.
- Look at the answer, 4. The answer is what is left after taking away.Answer: 4
- Add 3 back on. Adding undoes taking away.4 + 3 = 7
- Write the missing number. 7
Check. 7 − 3 = 4. ✓
Watch out. Do not take the number away again. Put it back on instead.
Key words. A fact family is a set of sentences that use the same three numbers.
Method. Use the same three numbers. Swap the parts for the second addition. Take each part away from the whole for the subtractions.
- Find the whole and the two parts. The whole is the biggest number.Whole 7, parts 3 and 4
- Write the two addition sentences. Swap the parts round for the second one.3 + 4 = 7 and 4 + 3 = 7
- Write the two subtraction sentences. Take each part away from the whole.7 − 3 = 4 and 7 − 4 = 3
- Write the whole family. 3 + 4 = 7, 4 + 3 = 7, 7 − 3 = 4, 7 − 4 = 3
Check. Check: 3 + 4 = 7 and 7 − 4 = 3. ✓
Watch out. In a subtraction sentence the whole always comes first.
Key words. The = sign means the two sides are the same amount.
Method. Work out 4 + 3, then check it against the number that was said.
- Work out 4 + 3. Start at the bigger number and count on.Start at 4, count on 3: 7
- Compare with what was said. Is the total the same as the number in the sentence?7 and 6
- Write the answer. No. 4 + 3 = 7.
Check. Count all the things: 4 + 3 = 7. ✓
Watch out. Work out the total first. Do not guess from the numbers you can see.
Key words. A story sum is a short problem told as a story.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. The numbers tell us how many.3 and 4
- Decide: add or take away? Things joining together means add.Joining, so we add
- Write the number sentence. The sentence shows the story.3 + 4 = 7
- Write the answer. Say what the number is for.7 stickers
Check. Count 7 stickers in total. ✓
Watch out. Ask: are things joining together, or going away?
Key words. Take away means some things go away. The − sign shows it.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. Start with the number we had.9 and 4
- Decide: add or take away? Things going away means take away.Going away, so we take away
- Write the number sentence. The sentence shows the story.9 − 4 = 5
- Write the answer. Say what the number is for.5 ducks
Check. Add back the 4 that went: 5 + 4 = 9. ✓
Watch out. Start with the number you had at the beginning, not the number that went away.