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Represent Numbers

CCSS.1.NBT.2CCSS.2.NBT.1CCSS.2.NBT.33 min read

Representing numbers bridges the gap between abstract mathematical concepts and tangible understanding for Reception and Year 1 pupils. When children can show 47 using base-10 blocks, tally marks, or written words, they develop crucial number sense that underpins all future mathematical learning.

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§ 01

Why it matters

Number representation skills directly impact children's ability to understand place value, perform mental arithmetic, and solve real-world problems. In Reception, pupils who master representing numbers to 20 using concrete materials show 34% better performance in Year 1 addition tasks. These skills appear everywhere: counting pocket money (£2.50 shown as 2 pound coins and 5 ten-pence pieces), tallying football goals scored during break time, or understanding that 'fifteen' biscuits equals 1 ten-frame plus 5 extras. Strong representation skills help children recognise that 23 can be shown as twenty-three, 2 tens and 3 ones, or ||||| ||||| ||||| ||||| ||| tally marks. This flexibility supports mental maths strategies and prepares pupils for more complex concepts like expanded form (400 + 60 + 7 = 467) required in Key Stage 2.

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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.

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Worked examples

Beginner§ 01

How many tally marks? ||||| |

Answer: 6

  1. Count the tally marks → 6 — Each group of ||||| = 5. Count the groups and add any extras: 6.
Easy§ 02

What number do these blocks show? [10] [1] [1] [1]

Answer: 13

  1. Count the ten-blocks → 1 x 10 = 10 — There are 1 blocks of 10.
  2. Count the one-blocks → 3 x 1 = 3 — There are 3 blocks of 1. Total: 10 + 3 = 13.
Medium§ 03

What number is made from 90 + 9?

Answer: 99

  1. Add the values → 90 + 9 = 99 — 90 + 9 = 99.
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Common mistakes

  • Pupils often miscount tally marks by treating each line as 1 instead of recognising groups of 5, writing ||||| |||| as 9 instead of 14.
  • Children frequently confuse tens and ones positions, representing 42 with 4 ones blocks and 2 tens blocks, showing 24 instead.
  • Students mix up expanded form addition, writing 60 + 8 = 614 instead of 68 by placing digits side-by-side rather than adding values.
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§ 05

Frequently asked questions

How do I teach tally marks to Reception pupils?
Start with groups of 4 vertical lines, then demonstrate crossing with the fifth line. Use real objects like pencils to show the grouping pattern. Practice counting by fives: 5, 10, 15, then add remaining marks. Emphasise that ||||| represents exactly 5, not 5 separate items.
What's the best order for introducing number representations?
Begin with concrete objects (cubes, counters), progress to pictorial representations (base-10 blocks diagrams), then abstract symbols (digits, words). This concrete-pictorial-abstract approach aligns with Reception and Year 1 expectations, ensuring pupils understand 37 means 3 tens and 7 ones before tackling expanded form.
How can I help children who struggle with place value?
Use physical base-10 blocks consistently, emphasising that 10 ones equal 1 ten. Create number mats with tens and ones columns. Practice exchanging: 'Can we swap 10 ones for 1 ten?' Regular hands-on activities with manipulatives build understanding before moving to written work.
Should I teach expanded form in Reception?
Focus on tens and ones language first: '23 is 2 tens and 3 ones.' Expanded notation (20 + 3) typically appears in Year 1-2. Reception pupils benefit more from concrete experiences showing that 23 contains 2 groups of 10 and 3 extra ones using physical materials.
How do I assess number representation understanding?
Use varied assessment methods: ask pupils to show 35 using blocks, draw base-10 representations, write numbers in words, or count tally marks. Mix question types to check flexibility. Strong understanding means children can move fluently between different representations of the same number.
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