Year 4 maths · Key Stage 2 · Number – number and place value

Year 4 place value: thousands, negative numbers and counting

In Year 4 children’s understanding of number grows beyond 1,000. They read, write and compare four-digit numbers, find 1,000 more or less than any number, count in multiples of 6, 7, 9, 25 and 1,000, and count backwards through zero into negative numbers, for example when reading a thermometer on a frosty morning.

Thousands and negative numbers, explained

In a four-digit number the digits have values of thousands, hundreds, tens and ones. In 5,284 the 5 is worth 5 thousands (5,000), the 2 is worth 2 hundreds (200), the 8 is worth 8 tens (80) and the 4 is worth 4 ones. Schools use base 10 blocks, place value counters and place value charts so that children can see that ten hundreds make one thousand. A comma separates the thousands, and a zero acts as a placeholder: 4,050 has no hundreds, and if that zero is left out the number becomes 450.

Children find 1,000 more or less than a number by changing only the thousands digit: 1,000 more than 3,206 is 4,206, and 1,000 less is 2,206. They also count in tens and hundreds, noticing which digits change and which stay the same. To compare and order numbers beyond 1,000, children start at the left, comparing the thousands first, then the hundreds, tens and ones until the numbers differ. They show the result with the signs < and >. They also begin to place the fractions and decimals they meet in other topics on the same number line as whole numbers.

Counting in multiples is a regular part of the year. Counting in 6s, 7s and 9s is the same as saying the times tables, which supports the tables work that leads to the Multiplication Tables Check in June. Counting in 25s (25, 50, 75, 100, 125…) links with money, as four lots of 25p make £1. Counting in 1,000s (1,000, 2,000, 3,000…) reinforces the thousands column. Children count both forwards and backwards.

Negative numbers are numbers below zero. The number line carries on to the left of zero, so counting back from 3 goes 3, 2, 1, 0, −1, −2, −3, and children say “minus 1” or “negative 1”. The most familiar context is temperature: on a thermometer, −3 °C is three degrees below freezing. Children read negative numbers on a number line, compare them, and count steps up and down, for example finding the temperature after a fall of 5 degrees from 3 °C, which is −2 °C.

Words your child will hear

Thousands: The fourth place from the right in a number. In 5,284 the 5 is worth 5,000.
Multiple: A number in a times table or counting sequence. 63 is a multiple of 9.
Placeholder: A zero that keeps the other digits in the correct columns, as in 4,050.
Negative number: A number less than zero, written with a minus sign, such as −4.
Ascending: Going up in order, from smallest to largest.
Descending: Going down in order, from largest to smallest.
Compare: Decide which number is greater or smaller, using words or the signs < and >.

What the National Curriculum says

In Year 4, pupils should be taught to:

Count in multiples of 6, 7, 9, 25 and 1,000
Find 1,000 more or less than a given number
Count backwards through 0 to include negative numbers
Recognise the place value of each digit in a four-digit number (1,000s, 100s, 10s, and 1s)
Order and compare numbers beyond 1,000

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Put these numbers in order, smallest first: 3,085, 3,508, 3,058, 3,850.

Write the numbers in a place value table so the thousands line up under thousands, the hundreds under hundreds, and so on.
```
Number   Th   H   T   O
3,085     3   0   8   5
3,508     3   5   0   8
3,058     3   0   5   8
3,850     3   8   5   0
```
Compare the thousands. All four numbers have 3 thousands, so they can’t be separated yet. Move to the hundreds.
Look at the hundreds. 3,085 and 3,058 have 0 hundreds, 3,508 has 5 hundreds and 3,850 has 8 hundreds. So 3,085 and 3,058 are the two smallest, then 3,508, then 3,850.
Separate the two with 0 hundreds by looking at the tens. 3,058 has 5 tens and 3,085 has 8 tens, so 3,058 is smaller.
Write the order using the sign: 3,058 < 3,085 < 3,508 < 3,850. Check by estimating roughly where each sits on a number line from 3,000 to 4,000: the order makes sense.

3,058, 3,085, 3,508, 3,850

Common mistakes and how to help

Changing the wrong digit for 1,000 more or less

Children used to adding 10 or 100 may change the tens or hundreds digit, so 1,000 less than 5,206 becomes 5,106.

What helps: Count aloud in 1,000s from a start number: 5,206, 4,206, 3,206. Only the thousands digit moves. Place value counters make it clear which counters you are removing.

Writing numbers as they sound

Hearing “four thousand and fifty”, a child writes 400050 or 450, because the number sounds like 4000 followed by 50.

What helps: Say the value of each place and fill the columns from the left: 4 thousands, 0 hundreds, 5 tens, 0 ones. Every whole number from 1,000 to 9,999 has exactly four digits.

Thinking that −5 is greater than −2

5 is greater than 2, and children carry that idea over to the digits and ignore the minus sign.

What helps: Use a thermometer. −5 °C is colder than −2 °C, so it is the smaller number. Numbers further to the left on a number line are always smaller.

Losing the pattern when counting back through zero

Counting back from 3 may go 3, 2, 1, 0, 1, 2, because the numbers below zero haven’t yet been given their own names and the child repeats the ones already said.

What helps: Count back along a number line, saying “minus” each time after zero: 1, 0, minus 1, minus 2. Temperature, lift buttons and floors below ground level are useful real examples.

How to help at home

Count in awkward steps. On a walk or at the table, count in 6s, 7s or 9s, then count back. If your child stalls, say the next number and carry on. Counting in 25s links to money: 25p, 50p, 75p, £1.
Check the winter temperature. When the forecast shows temperatures near freezing, ask “What is the temperature if it falls by 4 degrees?” and “Is −2 colder or warmer than −5?” Real weather makes negative numbers meaningful.
Make numbers with digit cards. Write digits 0 to 9 on small pieces of paper. Pick four and make the biggest number, the smallest number, and the number closest to 5,000. Say each number out loud in words.
Use big numbers from the real world. The heights of many mountains in metres, the year stamped on a coin and the number of people at a local event can all give four-digit numbers. Ask “What is 1,000 more?” or “Which is higher, and by how much?”

Builds on

Year 3: Place value to 1,000

Leads on to

Year 5: Numbers to 1,000,000