Represent Numbers
Representing numbers means showing the same mathematical value in different forms — as digits, words, pictures, or symbols. The number 47 can appear as the numeral 47, the word 'forty-seven', or as 4 tens rods plus 7 ones cubes in base-10 blocks. Each representation conveys identical mathematical meaning whilst serving different purposes in learning and problem-solving.
Why it matters
Number representation skills underpin all mathematical learning from Reception through GCSE level. In everyday life, children encounter numbers in multiple forms — reading '£15' on a price tag, hearing 'fifteen pounds' spoken aloud, or counting 15 one-pound coins. These foundational skills support place value understanding, essential for addition and subtraction algorithms in Year 2 and beyond. Base-10 block representations help visualise regrouping in calculations like 47 + 28, where 4 tens become 5 tens and 15 ones become 7 tens and 5 ones. Tally marks appear in data handling from Year 1 onwards, whilst expanded form (80 + 7 = 87) builds conceptual understanding for mental arithmetic strategies taught throughout primary school.
How to solve represent numbers
Representing Numbers
- Numbers can be shown as digits, words, or on a number line.
- Use base-10 blocks: hundreds squares, tens rods, ones cubes.
- Tally marks: groups of 5 (four lines crossed by a fifth).
- Match each representation to the same value.
Example: The number 23: two tens rods + three ones cubes.
Worked examples
How many tally marks? ||||| ||||| |
Answer: 11
- Count the tally marks → 11 — Each group of ||||| = 5. Count the groups and add any extras: 11.
Write 12 as a word.
Answer: twelve
- Write the number as a word → twelve — 12 written as a word is "twelve".
Write 81 in expanded form.
Answer: 80 + 1
- Find the value of the tens digit → 8 x 10 = 80 — The digit 8 is in the tens place, so its value is 80.
- Find the value of the ones digit → 1 x 1 = 1 — The digit 1 is in the ones place, so its value is 1.
- Write in expanded form → 80 + 1 — 81 = 80 + 1.
Common mistakes
- Writing tally marks incorrectly, such as |||||| for 6 instead of ||||| | — the fifth mark should cross diagonally through the first four to form groups of 5
- Confusing digit names with number names, writing 'forty-three' as 403 instead of 43, misunderstanding that 'forty' means 4 tens, not 4 hundreds
- In expanded form, writing 52 as 50 + 20 instead of 50 + 2, adding the digit value rather than the place value of each position