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 addition.

Children also use numberlines and practical resources to support calculation and teachers *demonstrate* the use of the numberline.

Bead strings or bead bars can be used to illustrate addition including bridging through ten e.g. in the below case by counting on 2 then counting on 3 when performing the calculation 8 + 5 = 13.

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

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

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

Children will begin to use ‘empty number lines’ themselves starting with the larger number and counting on.

- First counting on in tens and ones.

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

- Followed by adding the tens in one jump and the units in one jump.

- Bridging through ten can help children become more efficient.

Children will continue to use empty number lines with increasingly large numbers, including compensation where appropriate.

They will count on from the largest number irrespective of the order of the calculation.

Compensation is used, where you add an easy number such as a multiple of ten and then subtract a small number.

Children will begin to use informal pencil and paper methods (jottings) to support, record and explain partial mental methods building on existing mental strategies.

Adding the least significant digits first

Children will carry below the line in column addition.

*Using similar methods, children will:*

*add several numbers with different numbers of digits;**begin to add two or more three-digit sums of money, with or without adjustment from the pence to the pounds;**know that the decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g. £3.59 + 78p*.

Children should extend the carrying method to numbers with at least four digits.

*Using similar methods, children will:*

*add several numbers with different numbers of digits;**begin to add two or more decimal fractions with up to three digits and the same number of decimal places;*

*know that decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g. 3.2 m – 280 cm.*

Children should extend the carrying method to number with any number of digits.

*Using similar methods, children will*

*add several numbers with different numbers of digits;**begin to add two or more decimal fractions with up to four digits and either one or two decimal places;*

*know that decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g. 401.2 + 26.85 + 0.71.*