Addition 

Stage 4 - Column method 

In this method, recording is reduced further. Carry digits are recorded below the line, using the words 'carry ten' or 'carry one hundred', not 'carry one'.

Later, extend to adding three-two digit numbers, two three-digit numbers and number with different numbers of digits 

Subtraction

Stage 2 - Partition

Subtraction can be recorded using partitioning to write equivalent calculations that can be carried mentally. This requires children to subtract a single-digit number or a multiple of 10 from a two-digit number mentally. The method of recording links to counting back on the number line. 

Stage 3- Expanded layout, leading to the column method.

Partitioning the numbers into tens and ones and writing one und the other mirrors the column method, where ones are placed under ones and tens under tens. 

This does not link directly to mental method of counting back or up but parallels the partitioning method for addition. It also relies on secure mental skills. 

Multiplication

Stage 3-Expanded short multiplication

The next step is to represent the method of recording in a column format, but showing the working. Draw attention to the links with the grid method above. Children should describe what they do by referring to the actual values of the digits in the column.

Stage 4- Short multiplication

The recording is reduced further by carrying digits recorded below the line. If, after practice, children cannot use the compact method without making errors, they should return to the expanded format of stage 3. 

Division

Stage 3- 'Expanded' method for HTU ÷ U

This method is based on subtracting multiples of the divisor from the number to be divided, the dividend. This method often referred to as 'chunking' is based on subtracting multiples of the divisor, or 'chunks' and is a useful reminder of the link between division and repeated subtraction. 

Stage 4- Short division of HTU ÷ U 

Short division of a three-digit number can be introduced to children who are confident with multiplication and division facts with subtracting multiples of 10 mentally, and whose understanding of partitioning and place value is sound.