KeyStage

Year 5 maths · Key Stage 2 · Number – number and place value

Year 5 place value: numbers to 1,000,000 and Roman numerals

In Year 5 children extend their understanding of place value to numbers up to one million and beyond. They read, write, order and round large numbers, count in powers of ten, count through zero into negative numbers, and learn to read Roman numerals up to 1,000, including years written in Roman numerals.

Numbers to 1,000,000, explained

The place value system works the same way at every size: each place is worth ten times the place to its right. The places in a six-digit number, from the right, are ones, tens, hundreds, thousands, ten thousands and hundred thousands, and ten hundred thousands make one million, written 1,000,000. In 463,582 the 4 is worth 400,000, the 6 is worth 60,000, the 3 is worth 3,000, the 5 is worth 500, the 8 is worth 80 and the 2 is worth 2. Children read and write these numbers in digits and in words, put them in order, compare them with < and >, and say what each digit is worth. Place value charts and place value counters are still used, and numbers are often written with commas, or small spaces, to separate each group of three digits.

Counting in powers of ten means counting in steps of 10, 100, 1,000, 10,000 or 100,000 from any starting number, forwards or backwards. From 365,000, counting on in 10,000s gives 375,000, 385,000, 395,000, 405,000. Only one digit changes in each step, apart from when the count crosses a boundary: from 395,000 to 405,000 the hundred thousands digit changes too. Children also look at sequences that increase by fractions or decimals, such as 3, 3 1/2, 4, 4 1/2, and describe the rule in words, for example “add 1/2 each time”.

Negative numbers are numbers below zero. Children meet them in real contexts, such as temperatures in winter, floors below ground level in a lift, or an overdrawn bank balance. They use a number line or thermometer scale to count forwards and backwards through zero in whole numbers, for example counting on from −3 to 4, and say what a reading such as −5°C means. Calculating the size of a gap across zero becomes a separate objective in Year 6.

Rounding gives an approximate number that is easier to work with. Children round to the nearest 10, 100, 1,000, 10,000 and 100,000 by looking at the digit one place to the right of the one they are rounding to: 5 or more rounds up, and 4 or less rounds down. They use rounding when solving number problems, such as estimating the attendance at a match. Finally, children learn to read Roman numerals up to 1,000. The letters are I (1), V (5), X (10), L (50), C (100), D (500) and M (1,000). They are written largest to smallest and added, except where a smaller letter comes just before a larger one and is subtracted, so IV is 4, XC is 90 and CM is 900. A year such as MMXXVI is 2026.

Words your child will hear

Place value
What a digit is worth because of where it sits in a number.
Power of ten
10, 100, 1,000, 10,000 and so on, each ten times the one before.
Negative number
A number below zero, written with a minus sign, such as −5.
Round
Swap a number for a nearby simpler one, such as 463,582 to 460,000.
Approximate
Close to the exact value but not exactly equal to it.
Roman numerals
An ancient number system that uses letters, such as I, V, X, L, C, D and M.
Term-to-term rule
The rule that takes you from one number in a sequence to the next.

What the National Curriculum says

In Year 5, pupils should be taught to:

  • Read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit
  • Count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000
  • Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0
  • Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
  • Solve number problems and practical problems that involve all of the above
  • Read Roman numerals to 1,000 (M) and recognise years written in Roman numerals

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

A worked example

Round 463,582 to the nearest 10, 100, 1,000, 10,000 and 100,000.

  1. Write the number in a place value chart so each digit’s value is clear. For each rounding, find the digit being rounded to, then look at the digit to its right.
    HTh TTh Th  H  T  O
  4   6  3  5  8  2
  2. Nearest 10: the tens digit is 8 and the ones digit is 2. 2 is less than 5, so round down. Nearest 100: the hundreds digit is 5 and the tens digit is 8. 8 is 5 or more, so round up.
    463,582 → 463,580 (10)
463,582 → 463,600 (100)
  3. Nearest 1,000: the thousands digit is 3 and the hundreds digit is 5. A 5 rounds up, so 463 thousand becomes 464 thousand.
    463,582 → 464,000 (1,000)
  4. Nearest 10,000: the ten thousands digit is 6 and the thousands digit is 3. 3 is less than 5, so round down. Nearest 100,000: the hundred thousands digit is 4 and the ten thousands digit is 6, so round up.
    463,582 → 460,000 (10,000)
463,582 → 500,000 (100,000)
  5. Check each answer on a number line. 463,582 is nearer to 460,000 than to 470,000, and nearer to 500,000 than to 400,000. Each rounded number should sit close to the original.

463,580 (nearest 10), 463,600 (100), 464,000 (1,000), 460,000 (10,000) and 500,000 (100,000).

Common mistakes and how to help

Writing large numbers as they sound, so “two hundred and fifty thousand and six” becomes 250,0006 or 2506 instead of 250,006

Children write the parts they hear one after another, and zeros that are not spoken, such as the empty hundreds and tens, get left out.

What helps: Say the number in groups of three digits and use a place value chart. 250,006 has 250 thousands and 6 ones, so the tens and hundreds hold zeros.

Thinking −8 is bigger than −2 because 8 is bigger than 2

Children are used to larger digits meaning larger numbers, and the minus sign is easy to ignore.

What helps: Use a thermometer or number line. −8°C is colder than −2°C, and numbers further left on the line are smaller. So −8 < −2.

Rounding down when the digit is 5, or looking at the wrong digit

Some children round on the digit they are rounding to, not the one to its right. Others see a lone 5 as “half” and are unsure which way it should go.

What helps: Use a number line with a marked halfway point. For 463,582 to the nearest 1,000, the halfway point is 463,500, and 463,582 is past it.

Writing IIII for 4 or IC for 99 in Roman numerals

Children think of Roman numerals as simple adding, or subtract any small letter from any larger one. In fact only I, X and C are put in front to subtract, and only from the next two letters up: I from V and X, X from L and C, and C from D and M. So 99 is not IC.

What helps: Practise reading numbers in pieces: XCIX is XC (90) and IX (9), which makes 99. Look for Roman numerals on clocks and buildings and read them together, though many clock faces show 4 as IIII by tradition.

How to help at home

  • Read big numbers out loud. Find large numbers in the news, on sports pages or on a map, such as a population or a stadium capacity. Practise saying them aloud and ask what each digit is worth.
  • Round a total for an estimate. Take the populations of two towns or the distance in metres of a long journey and round each one, then work out an estimate. Ask what level of accuracy is useful for a quick answer.
  • Count in tens of thousands. Start at 120,000 and count on in 10,000s, then back again. Try another start number, then count through a boundary such as 95,000, 105,000.
  • Use a thermometer. Look at the temperature on an outdoor thermometer in winter and compare it with the previous day. Ask how many degrees warmer or colder it is, and how far from zero.
  • Spot Roman numerals. Look at clock faces, film or book copyright dates and building plaques. Read them together and work out the year, for example MCMXCIX is 1999.

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