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
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.
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.
Stage 5- Two-digit by two-digit products
Extend to TU x TU, asking children to estimate first. Starting with the grid method. The partial products in each row are added, and then the two sums at the end of each row are added to find the total product.
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.