Multiplication Methods
Please note that all guidance below is the minimum expectations for the teaching within each year group. It is expectated that many children will move through these steps faster (although understanding of all prerequisit steps is essential before moving to abstract calculations.
Previous steps (Pre-Prep)
CONCRETE
Children have been taught to double by adding an identical amount.
ABSTRACT
They have also been taught to double by partitioning numbers into 10s and 1s and doubling each part before recombining.
ABSTRACT
The children used a counting stick to add repeatedly for their 2x, 5x and 10x tables. They will have recited the sequences forwards and backwards.
CONCRETE
The children represented multiplication using manipulatives like cubes. This 'array' shows 2x5 or 5x2.
CONCRETE
Previously, the children will have looked at finding multiplication and division facts for a number by creating multiply arrays. Here are 3 examples for the number 12 (12x1,6x2,4x3)
CONCRETE
Children used manipulatives to create EQUAL groups when multiplying
CONCRETE
Children used different objects to add equal groups
PICTORIAL
Children used number lines and repeated addition to complete multiplication calculations
ABSTRACT
Children began to use multiplication fact triangles. Here, you can derrive 4 x 2 = 8, 2 x 4 = 8, 8 ÷ 4 = 2 and 8 ÷ 2 = 4. These are known as multiplication fact families
Year 3 and 4
Grid methods for multiplication
CONCRETE
Starting with counters and moving on to Dienes, children represent calculations using arrays. They start by counting individual cubes but progress to counting in repeated jumps. The example shows 13 x 4 = 52
PICTORIAL
Children draw the counters to show different amounts or just use the circles in the different columns to show their thinking as shown above.
ABSTRACT
Pupils start with multiplying by one digit numbers and showing the clear addition alongside the grid. This method is a stepping stone to written multiplication - the product of two 2-digit numbers is not effectively solved using this method
Formal methods for multiplication (short multiplication)
ABSTRACT
Children should progress to short multiplication (calculations with only 1-digit multipliers).
Year 5 and 6
ABSTRACT
When multiplying decimals, the multiplier is placed in the furthest right column, regardless of value. The decimal points must be lined up in the question and the answer.
ABSTRACT
Children move on to long multiplication (calculations with at least two 2-digit numbers). Muliplication of the 1s column (blue in the example) is completed first. A zero (red) is placed in the column before calculating the 10s column. Digits are carried below the line of calculation.