Number and Place Value

Number and place value is the foundation of all mathematics. Understanding what digits mean, how numbers are ordered, and how our number system works gives children the tools they need for every other area of maths.

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What This Topic Covers

The National Curriculum for Key Stage 1 develops children's number sense in two stages:

• Year 1: Counting to 100, reading and writing numbers, counting in 2s, 5s and 10s, finding 1 more and 1 less
• Year 2: Counting in steps of 2, 3 and 5; understanding tens and ones; comparing numbers using < > =; reading and writing numbers to 100 in words

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Year 1: Building Number Sense

Counting to 100

Children learn to count forwards and backwards to and across 100, starting from any number — not just from 1.

Examples:

• Count forwards from 47: 47, 48, 49, 50, 51...
• Count backwards from 62: 62, 61, 60, 59, 58...
• Count from 0 in 2s: 0, 2, 4, 6, 8, 10...
• Count from 0 in 5s: 0, 5, 10, 15, 20, 25...
• Count from 0 in 10s: 0, 10, 20, 30, 40, 50...

Reading and Writing Numbers to 100

Children read and write numbers in numerals and in words up to 20, and in numerals up to 100.

Numeral	Word
1	one
2	two
5	five
10	ten
11	eleven
12	twelve
13	thirteen
20	twenty

Note: Numbers 11-19 have irregular names that children must memorise. "Eleven" and "twelve" give no clues about their value — unlike "twenty-one" which clearly shows 2 tens and 1 one.

1 More and 1 Less

Given any number, children should be able to find one more and one less quickly and confidently.

Number	1 less	1 more
10	9	11
29	28	30
49	48	50
99	98	100

Teaching tip: Pay extra attention to numbers that cross a tens boundary (e.g. 1 more than 39 is 40, not 310).

The Number Line

Children represent and locate numbers on a number line. This helps them visualise the relationship between numbers.

0   10   20   30   40   50   60   70   80   90   100
|----|----|----|----|----|----|----|----|----|----|

Language to use: equal to, more than, less than, fewer, most, least

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Year 2: Place Value and Comparing Numbers

Tens and Ones

In Year 2, children formally learn that every two-digit number is made up of tens and ones (also called units).

Number	Tens	Ones
23	2	3
45	4	5
70	7	0
9	0	9

Partitioning:

• 23 = 20 + 3 (standard partition)
• 23 = 10 + 13 (non-standard partition — useful for subtraction)

Understanding place value is crucial. The digit 3 in 30 means 3 tens (= 30), while the digit 3 in 13 means 3 ones (= 3). Same digit, very different value!

Comparing Numbers: < > =

Children use the symbols < (less than), > (greater than) and = (equal to) to compare numbers.

Symbol	Meaning	Example
<	less than	34 < 56
>	greater than	72 > 27
=	equal to	40 = 40

Memory trick: The open end of the symbol always faces the bigger number. Think of it as a hungry crocodile — it always eats the larger number!

Counting in Steps

Count in	Example sequence
2s	0, 2, 4, 6, 8, 10, 12...
3s	0, 3, 6, 9, 12, 15...
5s	0, 5, 10, 15, 20, 25...
10s from any number	7, 17, 27, 37, 47...

Counting in 3s prepares children for understanding a third (1/3) in fractions.

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Key Vocabulary

Term	Meaning
digit	A single number symbol (0-9)
numeral	A written number (e.g. 47)
place value	The value of a digit based on its position
tens	Groups of ten
ones / units	Single values
partition	Split a number into parts (e.g. 45 = 40 + 5)
estimate	Make a sensible guess at a value
more than / greater than	Larger in value
less than / fewer than	Smaller in value
equal to	The same value

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Common Misconceptions

• "Bigger digits always mean bigger numbers" — The number 91 is greater than 19, even though both contain the same digits.
• "Counting always starts at 1" — Children need to practise counting from any starting number, including 0.
• "You always count in 1s" — Fluency in counting in 2s, 3s, 5s and 10s is explicitly required by the end of Year 2.
• "Place value only matters for big numbers" — Even the number 13 has place value: 1 ten and 3 ones.