Year 2 maths · Key Stage 1 · Number – addition and subtraction
Year 2 adding and subtracting to 100: a guide for parents
In Year 2 children build on the number bonds they learned in Year 1 and begin to add and subtract two-digit numbers in their heads, supported by number lines, objects and quick jottings. They use facts they already know to work out new ones, learn that addition can be done in any order but subtraction cannot, and use the opposite operation to check answers and find missing numbers.
Adding and subtracting to 100, explained
The foundation is knowing addition and subtraction facts within 20 so well that they come without counting on fingers: 8 + 7 = 15, and 15 − 7 = 8. Year 2 children then stretch these facts up to 100. If they know that 3 + 7 = 10, they can work out that 30 + 70 = 100, and if they know 9 − 4 = 5, then 90 − 40 = 50 follows. The idea is that tens behave just like ones, so one fact can unlock many.
Mental methods depend on the kind of numbers involved. To add ones to a two-digit number, such as 47 + 6, children “bridge” a ten: 47 + 3 makes 50, and 3 more makes 53. To add tens, such as 47 + 20, only the tens digit changes, so the answer is 67. To add two two-digit numbers, they usually partition the second number and add it in chunks: 47 + 36 becomes 47 + 30, then + 6. Adding three one-digit numbers is easier if they look for two that make 10 or a double first, so 6 + 4 + 7 is 10 + 7.
Your child will see these ideas on number lines, with base 10 equipment (rods for tens, small cubes for ones), in part-whole diagrams and in picture bars. Many teachers also write numbers in tens and ones columns. The formal column method is a Year 3 objective, although some schools introduce it in Year 2. Either way, setting numbers out in columns helps children see place value and prepares them for written methods with larger numbers.
Two big ideas run through the year. First, addition can be done in either order (3 + 9 = 9 + 3), so it is often quicker to start with the bigger number, but subtraction cannot be swapped: 9 − 3 is not the same as 3 − 9. Second, addition and subtraction are inverses, which means they undo each other. If 36 + 47 = 83, then 83 − 47 = 36 and 83 − 36 = 47. Children use this to check their work and to solve missing number problems such as 36 + ? = 83.
Language matters too. The sum is the total of an addition, and the difference is how far apart two numbers are, which can be found by counting up as well as by taking away. Word problems use phrases such as “altogether”, “how many more” and “how many fewer”, set in contexts like sweets, stickers, money and lengths. Children are encouraged to draw or build the problem first, then choose a method.
Words your child will hear
- Sum
- The total when numbers are added. The sum of 40 and 25 is 65.
- Difference
- How far apart two numbers are. The difference between 25 and 40 is 15.
- Number bond
- Two numbers that make a given total, such as 6 and 4 for 10, or 30 and 70 for 100.
- Partition
- Split a number into parts, such as 36 = 30 + 6, to make a calculation easier.
- Inverse
- The opposite operation. Subtraction is the inverse of addition, so 83 − 36 undoes 36 + 47.
- Commutative
- The order doesn’t change the answer. Addition is commutative; subtraction is not.
- Fact family
- The set of related facts from three numbers, such as 36 + 47 = 83, 47 + 36 = 83, 83 − 36 = 47 and 83 − 47 = 36.
What the National Curriculum says
In Year 2, pupils should be taught to:
- Solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures; and applying their increasing knowledge of mental and written methods
- Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
- Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and 1s; a two-digit number and 10s; 2 two-digit numbers; and adding 3 one-digit numbers
- Show that addition of 2 numbers can be done in any order (commutative) and subtraction of 1 number from another cannot
- Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems
Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.
A worked example
Work out 47 + 36 in your head, then use the inverse to check.
- Partition the second number into tens and ones: 36 is 30 and 6. Keep 47 whole.
- Add the tens first. Four tens and three tens make seven tens, so 47 + 30 = 77. Only the tens digit has changed.
47 + 30 = 77
- Now add the 6 ones by bridging the next ten. From 77, add 3 to reach 80, then add the 3 that are left over.
47 --+30--> 77 --+3--> 80 --+3--> 83
- Check with the inverse. Take 36 away from 83 in the same way: 83 − 30 = 53, then 53 − 6 = 47. That is the number we started with, so the answer is right.
83 − 30 = 53 53 − 6 = 47
47 + 36 = 83. The checks 83 − 36 = 47 and 83 − 47 = 36 both agree.
Common mistakes and how to help
Taking the smaller digit from the larger one: 52 − 17 = 45
Working from 7 and 2, a child does 7 − 2 = 5, and 5 − 1 = 4, because it feels wrong to take a bigger number from a smaller one. They have treated subtraction as if the order didn’t matter.
What helps: Remind them that 52 − 17 starts with 52 and takes 17 away. Count up instead: from 17 to 20 is 3, from 20 to 50 is 30, and from 50 to 52 is 2, so the difference is 35. Estimate first: 52 is about 50 and 17 is about 20, so the answer should be about 30.
Counting on and including the number they started from
To work out 47 + 6, a child says “47, 48, 49, 50, 51, 52” and answers 52. The starting number has been counted as the first jump, so the answer is one too small.
What helps: Say the starting number, then count the six jumps on fingers or a number line: 48 is one, 49 is two, up to 53. Better still, move away from counting in ones by bridging ten: 47 + 3 = 50, then 3 more.
Adding every time they see the word “more”
In “Tom has 24 stickers, which is 9 more than Amy”, the word more suggests addition, so the child writes 24 + 9 = 33. In fact Tom has more, so Amy has fewer, and the answer is 24 − 9 = 15.
What helps: Draw two bars, one longer than the other, and mark what is known. Ask who has the most, then check the answer fits: Amy should have fewer than Tom.
Treating the equals sign as “the answer comes next”
With 7 + ? = 15, a child writes 22 because they see the numbers 7 and 15 and add them. They read the sign as an instruction to work out something rather than as meaning “is the same as”.
What helps: Read it aloud as “7 and what makes 15?” and use the inverse: 15 − 7. Also write number sentences the other way round, such as 15 = 7 + ?, so the equals sign isn’t always followed by an answer.
How to help at home
- Make 10 and 100 quickly. Call out a number from 0 to 10 and ask for its partner that makes 10, then repeat with tens: if you say 30, your child says 70. A few minutes in the car or while cooking is plenty.
- Play shop with real coins. Price a few items between 10p and 50p and ask how much two cost together. Paying from a larger amount and working out the change by counting up is a natural way to practise adding and subtracting.
- Roll three dice. Add the three numbers, looking for pairs that make 10 or doubles before adding the last one. Then ask how they did it, because explaining the method is what makes it stick.
- Build fact families. Pick three numbers such as 20, 35 and 55 and ask for all four facts they make. Ask which fact you could use to check the others.
Related topics
Builds on
- Year 1: Adding and subtracting within 20
Leads on to
- Year 3: Column addition and subtraction
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