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
Column Addition- No Exchange
Column Addition- With Exchange
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.
Column Subtraction- With Exchange
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 6 - Three-digit by two-digit products
Extend to HTU x TU asking children to estimate first. Children need to be secure with multiplication for TU x U and TU x TU before using the same method for HTU x TU. Again, the carry digits in the partial products are usually carried mentally.
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.
Stage 5- Long division
The next step is to tackle HTU ÷ TU. The layout, which links to chunking, is, in essence, the 'long division' method. Recording the build-up to the quotient on the left of the calculation keeps the links with 'chunking' and reduced the errors that tend to occur with the positioning of the first digit of the quotient.