Progression in Multiplication and Division Phase 3 (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 3 (draft) 2014

The number line jotting for division is an important stage before learning about standard division methods (short and long division). E.g. 42 ÷ 3

Remainders The image of division on the bead bar can be extended to include remainders. E.g. 45 ÷ 10 = 4 remainder 5 or 4½ or 4.5

Progression in Multiplication and Division Phase 3 (draft) 2014

This shows clearly that there are 6 and a half groups of ten in 65 Other remainders are also clearly shown on the bead bar. e.g. 50 ÷ 8 = 6 remainder 2 or 6¼ or 6.25 The incomplete jump can be seen as part/fraction of a whole jump.

Understanding how the array supports a more formal method for multiplying is important Partitioning 38 x 5 = (30 x 5) + (8 x 5) = 150 + 40 = 190 Grid method TU x U (Short multiplication – multiplication by a single digit) 23 x 8 Children will approximate first 23 x 8 is approximately 25 x 8 = 200

A key understanding within phase 3 is that when we divide we are finding a fraction – sometimes it iseasier to consider our calculation as a fraction eg 288 divided by 4 would be a lengthy calculation if we base it on our knowledge of 4 x 10 being 40, however if we know that when we divide by 4 we are finding a quarter then we may more easily half and half again. Children will develop their use of repeated subtraction to be able to subtract multiples of the divisor. Initially, these should be multiples of 10s, 5s, 2s and 1s – numbers with which the children are more familiar.

continuing to build links between the array and division will be an important image to use

Progression in Multiplication and Division Phase 3 (draft) 2014

Grid method HTU x U (Short multiplication – multiplication by a single digit) 346 x 9 Children will approximate first 346 x 9 is approximately 350 x 10 = 3500

TU x TU (Long multiplication – multiplication by more than a single digit) 72 x 38 Children will approximate first 72 x 38 is approximately 70 x 40 = 2800

Using similar methods, they will be able to multiply decimals with one decimal place by a single digit number, approximating first. They should know that the decimal points line up under each other. e.g. 4.9 x 3 Children will approximate first 4.9 x 3 is approximately 5 x 3 = 15

Long Multiplication Method

is also 36 divided into rows of 9, or columns of 4 Understanding how mental methods can support division is vital – Tool Box is key for children having a sense of their own knowledge supporting their calculating. Eve if children cannot reach the answer have they got some facts that might help to reach the answer eg 136 divided by 9….I know that 10 nines is 90 so the answer must be more than 10.

develop chunking idea, using number line to model the chunks, and moving on to more

formal methods below.

97 ÷ 9

Progression in Multiplication and Division Phase 3 (draft) 2014

4346 x 8 34768 2 3 4

4.92 x 3 14.76 2

372 x 24 1488 + 7440 8928 1