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# Number & place value

Understanding what numbers mean is essential for learning maths. This is because knowing what each digit in a number is worth – place value – is the basis of our entire number system.

At the end of primary school, your child will sit mandatory tests in arithmetic and mathematical reasoning. Although this might seem a bit daunting, children build up their maths skills gradually. Your child will progress from simple counting in Year 1 all the way up to algebra in Year 6.

There are a variety of simple things you can do at home to help your child understand number and place value.

## What your child will learn

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

#### Number and place value in Year 1 (age 5–6)

In Year 1, children will work with numbers up to 100, counting on or back from any number in steps of 1, 2, 5, or 10. This includes:

• reading and writing numerals to 100 and number names to 20 in words
• using objects and number lines to represent numbers
• finding one more and one less than any number.

#### Number and place value in Year 2 (age 6–7)

In Year 2, children will recognise tens and ones in two-digit numbers (for example, ’23’ has 2 tens and 3 ones) and will be able to order numbers up to 100. This includes:

• counting in steps of 1, 2, 3, 5 and 10
• using more than (>), less than (<), and equals (=) symbols to compare numbers
• using place value and number facts to solve problems.

#### Number and place value in Year 3 (age 7–8)

In Year 3, children will recognise hundreds, tens, and ones in three-digit numbers (for example, ‘423’ has 4 hundreds, 2 tens, and 3 ones). This includes:

• counting in steps of 4, 8, 50, and 100
• reading, writing, comparing, and ordering numbers to 1000
• finding 10 or 100 more or less than a number.

#### Number and place value in Year 4 (age 8–9)

In Year 4, children will order and compare numbers beyond 1000 using place value in four-digit numbers (for example, ‘1428’ has 1 thousand, 4 hundreds, 2 tens, and 8 ones). This includes:

• counting in steps of 6, 7, 9, 25, and 1000
• counting backwards through zero to include negative numbers
• rounding any number to the nearest 10, 100, or 1000.

#### Number ad place value in Year 5 (age 9–10)

In Year 5, children will read, write, compare, and order numbers up to 1,000,000, recognising the place value of each digit. This includes:

• counting forwards and backwards with positive and negative numbers
• rounding numbers up to one million to the nearest 10, 100, 1000, 10,000 and 100,000
• recognising Roman numerals I, V, X, L, C, D, and M to read numbers and years.

#### Number and place value in Year 6 (age 10–11)

In Year 6, children will read, write, compare, order, and round numbers up to 10,000,000 and begin to learn about algebra, ratio, and proportion. This includes:

• using number lines to add and subtract negative numbers
• using simple formulae and following rules such as 2n + 3 to find numbers in a sequence
• solving problems involving place value, ratio, scale factors, and equations expressed.

## 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 understanding of number and place value.

### 1. Play counting games

Board games often show ordered numbers on tracks or grids. Make sure to put out these numbers, and count out loud as you progress. This will help your child quickly get a sense of what the numbers mean.

Dice can also help your child recognise number patterns quickly. For example, a pair of dice is a great way of showing your child doubles, or what it means for a number to be 1 bigger than another number.

Action games like ‘What’s the time, Mr Wolf?’ and songs like ‘Ten Green Bottles’ can help build early counting skills.

### Activity: Three Little Frogs rhyme Sing this fun action rhyme with your child.

### 2. Break down numbers

Look for numbers in the world around you and encourage your child to break them into parts. Breaking numbers up like this is called partitioning.

Point out a number and ask your child how many ones/tens/hundreds/thousands it has. Lots of children find this easier with physical objects, like stones or sticks. For example, they could group sticks into groups of ten.

### 3. Have counting races

Choose a starting number and a multiple to count up by. For example, you could start at 12 and count in steps of 4.

Take turns to say the next number in the sequence (12, 16, 20, 24, 28, …). Set a timer and see what number you can reach in one minute. This kind of game could also work as a bit of healthy competition between siblings or friends!

## Video support

### What is number?

Get a simple definition of the concept of number and the difference between cardinal, ordinal, and nominal numbers with this fun animation.

### What is place value?

Watch our fun animation for a simple definition of this early maths skill.

## Maths glossary

Use these quick links or explore our jargon buster for simple definitions and examples of mathematical terms.

• Hundred squares (or number squares) are visual images used to help children grasp the concept of number and place value.
• Number lines are visual images used to help children grasp the basic number relationships. Children will use number lines to count forwards and backwards, in, for example, 1s, 2s and 10s, depending on the scale of the number line.
• Partitioning means to split a number into smaller chunks, for example 58 = 50 + 8. It is often used to make calculating easier.
• Place value is the value of a digit depending on its position within a number, for example in 378, there are 3 hundreds, 7 tens and 8 ones.

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