**Addition & Subtraction**

The National Curriculum aims to make sure that children are fluent in the maths necessary for everyday life. A good understanding of addition and subtraction, and how they relate to each other, is essential for solving all sorts of calculations and problems.

At the end of primary school, children will need to apply their addition and subtraction skills in Arithmetic and Reasoning tests. This may seem a bit daunting, but don’t worry – your child will build up their skills gradually, from simple number bonds to written and mental methods that involve increasingly large numbers.

There are lots of things you can do at home to support your child’s developing addition and subtraction skills.

## What your child will learn

Follow the links below for an overview of each year, with lots of information, support, and practice activities:

#### Addition & subtraction in Year 1 (age 5–6)

In Year 1, your child will be expected to be able to read, write, and understand mathematical ideas using addition (+), subtraction (–) and equals (=) signs. This includes:

- making and using number bonds to 10 and then to 20
- adding and subtracting one-digit and two-digit numbers to 20, including 0
- solving simple problems using objects, drawings, diagrams and symbols, including missing number problems such as 7 = ? – 9.

#### Addition & subtraction in Year 2 (age 6–7)

In Year 2, your child will be expected to be able to solve addition and subtraction problems using numbers with one and two digits. This includes:

- knowing and using addition and subtraction facts up to 20 and working out related addition and subtraction facts up to 100
- adding and subtracting using objects, pictures, and drawings, and also solving problems mentally
- understanding that addition and subtraction have an inverse relationship (i.e. they undo each other), and using this to check calculations.

#### Addition & subtraction in Year 3 (age 7–8)

In Year 3, your child will be expected to use a range of strategies to solve problems mentally, and to learn formal written methods for column addition and column subtraction. This includes:

- adding and subtracting numbers with up to three digits
- estimating answers to problems before working them out accurately and checking using the inverse operation (i.e. using addition to check subtraction and vice versa)
- explaining how they have solved a problem and why they chose a particular method.

#### Addition & subtraction in Year 4 (age 8–9)

In Year 4, your child will be expected to be able to solve addition and subtraction problems involving numbers up to four digits. This includes:

- choosing from a variety of methods, including mental calculations, using objects, diagrams and drawings such as number lines, the area/grid method, and written column addition and subtraction
- estimating answers before calculating accurately and checking answers by understanding that addition and subtraction are inverse operations
- solving two-step word problems that require them to solve two different calculations to get the answer.

#### Addition & subtraction in Year 5 (age 9–10)

In Year 5, your child will be expected to be able to solve addition and subtraction problems involving numbers with more than four digits. This includes:

- practising a range of mental calculation strategies and a variety of formal calculation methods, like using objects, diagrams and drawings such as number lines, the area/grid method, and written column addition and subtraction
- using rounding to estimate answers and checking that their answers are sensible and accurate
- solving multi-step word problems that involve multiple calculations before coming to the final answer.

#### Calculation in Year 6 (age 10–11)

In Year 6, your child will be expected to be able to solve problems, including multi-step word problems, involving adding, taking away, multiplying, and dividing with large numbers. This includes:

- choosing efficient methods to solve problems and checking their answer using a different method
- exploring the order of operations using brackets
- rounding answers to a specified degree of accuracy (for example, to the nearest 10, 20, 50, and so on).

**How to help at home**

You don’t need to be an expert to support your child with maths! Here are three simple but effective ways to help your child develop their addition and subtraction skills.

**1. Use the language of addition and subtraction**

Encourage your child to use mathematical language when talking about calculations, such as *add*,* altogether*,* more*,* plus*,* total*,* sum *for addition and *take away*, *subtract*, *minus*, *less*, *fewer, difference* for subtraction. For example, 7 – 3 = 4 can be read as ‘the difference between 7 and 3 is 4’.

### Activity: Addition

Practise adding numbers with these counters.

### 2. Go shopping

Shopping provides great opportunities to practise skills. When buying items, ask your child to round prices to the nearest pound before adding mentally.

Challenge your child to check shopping totals using subtraction. Encourage them to estimate, for example:

I have £15. We need chicken for £4.50, vegetables costing £4.75, and the bus is £3.50. Will I have enough?

**3. Explore different methods**

When adding or subtracting, ask your child to explain each stage of their sum and why they chose that method.

They might partition numbers into hundreds, tens, and ones, draw pictures to represent how they added or subtracted, use number lines, use objects, or try written column methods. Encourage them to check with a different strategy.

### Video: Early maths skills: addition

### Video: Early maths skills: subtraction

## Maths glossary

Use these quick links or explore our education glossary for definitions and examples of mathematical terms.

- The area/grid method method is a way of visualising multiplication, as part of formal calculations. It involves breaking numbers up and multiplying their parts separately in a grid, before adding them back together.
- Inverse operations are operations that can ‘undo’ each other. Addition is the inverse of subtraction.
- Number bonds are pairs that make up a total. For example, the number bonds for 4 are 0 + 4, 1 + 3, and 2 + 2.
- Number lines are images used to help children grasp number relationships. You can use them to count on or back to solve addition or subtraction problems.
- Partitioning means to split a number into smaller chunks. It is often used to break down larger numbers to make calculations easier.