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

In Year 4, your child will start using negative numbers and will learn how to round numbers. They will also use numbers well into the 1000s, and will start reading and writing Roman numerals.

The key words for this section are number and place value.

## What your child will learn

Take a look at the National Curriculum expectations for number and place value in Year 4 (ages 8–9):

#### Count in multiples of 6, 7, 9, 25, and 1000

Your child will count forwards and backwards from 0 in multiples of 6, 7, 9, 25, and 1000, on top of all the multiples they have learned in previous years.

Your child will learn to recognise patterns when counting in multiples. For example, when counting in multiples of 9, the digits always add up to 9. Finding these patterns can be very exciting and motivating for some children!

#### Find 1000 more or less than a given number

Your child will be able to count up or down in 1000s, starting from any number from 0 to 10,000. For example:

365, 1365, 2365, 3365.

#### Count backwards into negative numbers

Your child will be introduced to negative numbers. They will be expected to include negative numbers as they count forwards and backwards. For example, counting back in 2s:

6, 4, 2, 0, ⁻2, ⁻4, ⁻6, and so on.

#### Recognise the place value of four-digit numbers

Your child will learn that the position of the digit in a number tells us the value of the digit, up to numbers with four-digits.

Your child will be expected to know how many thousands, hundreds, tens, and ones there are in any four-digit number. For example:

In the number

1423, the 1 represents one thousand, the 4 represents four hundreds, the 2 represents two tens and the 3 represents three ones.

Note that children will use the word *ones* and not *units *when talking about place value.

#### Order and compare numbers beyond 1000

Your child will compare numbers beyond 1000 by saying which number is bigger or smaller than the other. They will also be able to order numbers beyond 1000:

6274, 2977, 952, 53, 8, 3009 in order from smallest to largest is 8, 53, 952, 2977, 3009, 6274.

Children will use words like *more*, *less*, *fewer*, *more than*, *less than*, *equal to*, *equivalent*, and *the same value as* when comparing numbers. They will use the more than (>), less than (<), and equals (=) symbols correctly.

#### Identify, represent, and estimate numbers shown in different ways

Your child will use numerals, words, objects, drawings, diagrams, pictures, and symbols to represent numbers. This includes using number lines and number squares.

#### Round any number to the nearest 10, 100, or 1000

Your child will round numbers up or down to the nearest 10, 100, or 1000. This means figuring out which value of 10, 100, or 1000 any given number is nearest to.

6527 rounded to the nearest 10 is 6530.

6527 rounded to the nearest 100 is 6500.

6527 rounded to the nearest 1000 is 7000.

It is worth noting that numbers in the exact middle of a range are rounded up. For example, 249 rounded to the nearest 100 is 200, but 250 rounded to the nearest 100 is 300.

#### Solve increasingly complex number problems

- counting
- ordering
- comparing
- rounding
- negative numbers
- large positive numbers.

Their knowledge of place value will be very useful for this. They will use physical objects, drawings, diagrams, and mathematical symbols to visualise problems.

#### Read and understand Roman numerals

Your child will be introduced to Roman numerals from 1 to 100 (or I to C). They will learn how and why our number system has changed over time. For example, they will see that Roman numerals do not use place value, and they do not use the concept of ‘0’ in the same way our number system does.

## How to help at home

There are lots of ways you can help your child to understand number and place value. Here are just a few ideas:

### 1. Use place value charts

Place value charts can be a great way to help your child represent numbers. These charts will help your child to read, write, and compare numbers, as well as to understand zero as a placeholder. For example, in the number 6203, your child will be able to see that we write the 0 to represent that there are no tens.

### 2. Compare and order numbers

When comparing numbers beyond 1000, your child should look at the digit with the largest value first. For example, if your child is comparing the numbers 2765 and 3276, they would first need to look at the digit with the largest value, i.e. the thousands digit:

2765 has 2 thousands, and 3276 has 3 thousands, so 2765 is less than 3276.

However, if we compare the numbers 7565 and 7654, they both have the same number of thousands. Therefore, we now need to look at the hundreds digit:

7565 has 5 hundreds, and 7654 has 6 hundreds, so 7565 is less than 7654.

Try this game to practise comparing numbers. Write twenty two- and three-digit numbers and the ‘>’ and ‘<’ symbols on separate pieces of paper. Deal your child two numbers, face down. Ask them to turn over the pieces of paper and to use the ‘>’ and ‘<’ symbols to show which number is bigger or smaller.

Why not try again with a timer? How many pairs can they order correctly in 30 seconds?

3. Learn multiplication fact pairs

By the end of Year 4, your child should be able to recall all multiplication facts up to 12 × 12. Your child will be tested on their times tables in the Year 4 multiplication tables check.

You can help your child to practise their multiplication facts by playing pairs. Write out 12 multiplication questions (for example, 8 × 5) on small cards or pieces of paper. Then write out the corresponding multiplication answers (in this case, 40) on more cards.

Lay them all out on the floor or table at random, face down. Ask your child to turn any two cards over. Are they a matching question and answer? If they are, your child should keep them. If not, they should turn them back over. Take it in turns and keep going until all the pairs have been found.

### Activity: Times tables

Beat the clock! How many questions can you answer in one minute?

### Video: What are multiples?

Find out all about multiples.

### 4. Use temperature to explore negative numbers

To help build your child’s familiarity with negative numbers, look for them in the real world. Vertical number lines like those seen on thermometers can help your child grasp the concept of negative numbers. In winter, your child could keep a weather diary and record the daily temperatures. They could then create a graph or chart to show the changes in temperature. Then you could then ask all sorts of questions about their data. For example:

‘What was the difference in temperature between Monday and Wednesday?’

‘What is the difference between the highest temperature and the lowest temperature?’

‘Did the temperature ever drop below 0°C?’

If it’s not a cold winter and the temperatures don’t drop below zero, your child could research countries around the world (including some cold ones!) and record their weather. Talk about the differences in temperatures together.

### 5. Learn Roman numerals

Point out Roman numerals in the modern world, like at the end of some TV programmes or in the introductions of some books. Help your child to understand that our number system has changed over time and that it now includes the concepts of zero and place value. You could investigate with your child why we changed from the Roman numeral system to our current Arabic number system.

Have a Roman numeral challenge. Can your child write the Roman numerals for key numbers, such as the number of the day they were born on, or their age? If your child has already started learning Roman numerals and you don’t know them, maybe they can help teach you!