Progression in Multiplication and Division Phase 2 (draft) 2014
Multiplication
Division
Linking multiplication and division
To develop the link between multiplication and division, when counting in equal steps for example tens stop regularly and ask the
following questions orally and in writing:
• how many tens in 40? 10 x Δ = 40 and 40 ÷ 10 = Δ
• what is 4 tens? 10 x 4 = Δ and Δ = 10 x 4
• what is 4 lots of ten? 10 x 4 = Δ and Δ = 10 x 4
• what is 40 divided by 10? 40 ÷ 10 = Δ
• 40 is how many groups of ten? 40 = 10 x Δ
• what is 10 multiplied by 4? 10 x 4 = Δ
• what is 40 divided into tens? 40 ÷ 10 = Δ
The bead bar also shows multiplying and dividing by 5 very clearly
When dividing using the bead bar it can help to separate groups using pegs. This is important as the bead bar provides a link to the
number line, which can be used as a jotting for both multiplication and division. E.g. 35 ÷ 7
Progression in Multiplication and Division Phase 2 (draft) 2014
Children will develop their understanding of division and use jottings to support calculation
Children will develop their understanding of multiplication and use jottings to support
calculation:
Repeated addition
3 times 5 is 5 + 5 + 5 = 15
Sharing equally
6 sweets shared between 2 people, how many do they each get?
or 3 lots of 5 or 5 x3
Repeated addition on a number line:
Grouping or repeated subtraction
There are 6 sweets, how many people can have 2 sweets each?
and on a bead bar:
Repeated subtraction using a number line or bead bar
12 ÷ 3 = 4
Commutativity
Children will know that 3 x 5 has the same answer as 5 x 3. This can also be shown on the
number line.
Progression in Multiplication and Division Phase 2 (draft) 2014
Arrays
Children will be able to model a multiplication calculation using an array. (This knowledge will
support with the development of the grid method in Year 4.)
Repeated subtraction
using a number line
Repeated addition
4 times 6 is 6 + 6 + 6 + 6 = 24 or 4 lots of 6 or 6 x 4
Children will use number lines or bead bars to support their understanding.
Children will also move onto calculations involving remainders.
Inverse
Arrays
Children will model a multiplication calculation using an array. (This knowledge will
support with the development of the grid method in Year 4)
Inverse
Children will apply the inverse operation (division) to solve multiplication
calculations.
Children will apply the inverse operation (multiplication) to solve division calculations.
Progression in Multiplication and Division Phase 2 (draft) 2014