Children are encouraged to develop a mental picture of the number system in their heads to use for calculation.

They develop ways of recording calculations using pictures etc.

Bead strings or bead bars can be used to illustrate subtraction.

They use numberlines and practical resources to support calculation. Teachers *demonstrate* the use of the numberline.

Bead strings or bead bars can be used to illustrate subtraction including bridging through ten by counting back 3 then counting back 2.

Children then begin to use numbered lines to support their own calculations - using a numbered line to count back in ones.

The numberline should also be used to show that 6 - 3 means the ‘difference between 6 and 3’ or ‘the difference between 3 and 6’ and how many jumps they are apart.

Children will also begin to represent and use number bonds to 10 and related subtraction facts.

Children will begin to use empty number lines to support calculations.

**Counting back:**

- First counting back in tens and ones.

- Then helping children to become more efficient by subtracting the units in one jump (by using the known fact 7 – 3 = 4).

- Subtracting the tens in one jump and the units in one jump.

- Bridging through ten can help children become more efficient.

Counting on:

The number line should still show 0 so children can cross out the section from 0 to the smallest number. They then associate this method with ‘taking away’.

Children will continue to use empty number lines with increasingly large numbers.

Children will begin to use informal pencil and paper methods (jottings).

Where the numbers are involved in the calculation are close together or near to multiples of 10, 100 etc counting on using a number line should be used.

**Decomposition - Exchange tens for ones**

*Children should :*

*be able to subtract numbers with different numbers of digits;**using this method, children should also begin to find the difference between two 3-digit sums of money, with or without 'adjustment' from the pence to the pounds;**know that decimal points should line up under each other.*

Where the numbers involved in the calculation are close together or near to multiples of 10, 100 etc, counting on using a number line should be used.

**Decomposition - Exchange tens for units**

*Children should :*

*be able to subtract numbers with different numbers of digits;**begin to find the difference between two decimal fractions with up to three digits and the same number of decimal places;**know that decimal points should line up under each other.*

**Decomposition and exchange**

*Children should :*

*be able to subtract numbers with different numbers of digits;**be able to subtract two or more decimal fractions with up to three digits and either one or two decimal places;**know that decimal points should line up under each other.*

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