Stage 2 -Multiply with concrete objects and pictorial representations

Transcription

1 Multiplication Policy The links between doubling and multiplication are closely linked and although they are grouped into stages here, they might be taught in a different order depending on the maturity of the child. Stage 1 Pre multiplication skills Practical counting Using beads, counters etc to make patterns- e.g. 2 red- 2 blue Matching e.g. Can you get everyone 2 biscuits, laying a table Using songs to count e.g Cherries on a Plate, Sausages in a pan, Noah s ark. Stage 2 -Multiply with concrete objects and pictorial representations Step 1. Counting with Concrete objects Children will need to regularly practise counting in 2s, 5s and 10s. so that they know them by rote or by heart. Give children experience of counting equal groups of objects in 2s, 5s and 10s. Counting in 2s e.g. counting socks, shoes, animal s legs Counting in 5s e.g. counting fingers, fingers in gloves, toes Counting in 10s e.g. fingers, toes

2 Step 2 Doubling up to 12 ( This is the first stage of scaling, which is an important aspect of multiplication- Twice as many). Doubling numbers up to 5 using fingers 3 and 3 is 6 Matching numicon- Double 5 is 10 Dominoes which are doubles? Step 3 Repeated addition- counting groups of the same size Counting with numicon- repeated addition = = 20 Problem solving How many legs will 3 teddies have? =

3 There are 3 sweets in 1 bag. How many sweets are there in 5 bags altogether? Key vocabulary: groups of, lots of, times, altogether, multiply, count Stage 3 Linking counting in 2s, 5s and 10s to multiplication Step 1 Doubling numbers to 20 - Using fingers to count in 2 s Each finger is 2s How How many fingers have you held up? Yes, eight 2 s are 16. Dropping 2p s in to a tin-, 2p, 4p, 6p, 8p How many coins did I drop in the tin? Yes four 2p s is 8p. Using simple arrays 8x 2 =

4 Again children will need to think about Scaling Up using the term twice as many. I have 8 apples, my brother has twice as many. How many does my brother have? Step 2 As above but with 5s and 10s. 10p + 10p + 10p +10p + 10p is the same as 5 lots of 10p or 5 x 10p. How many fingers are you holding up?(each finger is worth five). Yes, 8 lots of 5 is 40 8 x 5 = 40 This stage needs to be completed in many practical ways, lots of rote counting and emphasis on language. Concrete apparatus such as, tens apparatus, coins and numicon, and making arrays will need to be used to reinforce that it is sets of, groups of or lots of. Once the children have got this they will be able to apply it to other times tables- for example A triangle has 3 sides, how many sides will 4 triangles have? x Again remember scaling up. I have built a tower that is 4 bricks tall. Can you make a tower that is 3 times as big?

5 Step 3 Reinforcement of the 2 s, 5 s and 10 s times tables. Knowing that multiplication can be done in any order. Step 1 arrays Looking at columns Looking at rows groups of 2 2 groups of 3 3 x 2 = 6 2 x 3 = 6 Children should be shown how to build up tables using arrays. Use arrays to help teach children to understand the commutative law of multiplication, and give examples such as 3 x 2 = 6 so 2 x 3 = 6 Step 4 Use mental recall, investigation and jottings Children should begin to recall multiplication facts for 2, 5 and 10 times tables through practice in counting and understanding of the operation. They will then be able to use this to explore patterns and other multiplication tables. 4 x 3 =

6 By learning to count by rote in 3 s, 4 s and so on, children will be able to use their fingers to quickly work out the answers to more tricky multiplication facts. Using jottings to work out the multiplications is also good practice. Maybe getting children to draw squares to make up a bar. 4 x 3 = Use 100 square to find multiples of a number and then work out the times tables. 4 x 5 = Which numbers are multiples of 3? How many 3s in 27? What patterns can you see? Can you predict the next numbers? Would 103 be in the pattern?

7 6 x 3 = Key vocabulary: groups of, lots of, times, array, altogether, multiply, count, multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times as big as, once, twice, three times... Stage 4 Using partitioning to multiply numbers Step 1 Doubling 10,20, Using fingers, 10p s, tens apparatus or numicon as before. Relate to doubling numbers to = 6 double 3 = 6 2x 3 = = 60 double 30 = 60 2x 30 = 60 Step 2 Doubling easy numbers to 50 e.g. 24, 32,44 - where no digit goes over the boundary = double 23 2 x 23 Always show the links = 46 This can also be done as egg maths see addition section.

8 Step 3 - Doubling numbers to 50 e.g. 26, 38, - where the units digit does go over the boundary double 26 2x ( 10+2) = 52 This can also be done as egg maths see addition section. Step 4 Doubling 60, 70, 80, 90 and 100 These are tricky and have to be learnt. Coins, numicon and tens apparatus can be used. Children can count their fingers twice, touching them on their nose as they go. For example, show 8 fingers for 80, and then count them a second time. They should also know the link between simple doubling and doubling multiples of 10. For example, 8+8= =160. Step 5 Doubling easy numbers to 100 where the units do not go over the boundary Double x X This can also be done as egg maths or condensed in to a grid method, depending on the ability of the child.

9 Step 6 Doubling any number to 100 Double x Optional line = 156 This can be done as egg maths or can be condensed in to a grid method, depending on the ability of the child. X Step 7 Confirming the relationship between multiplying 2 single digit numbers and multiplying a single digit with a multiple of 10 Children will need to be able to multiply a multiple of 10 by any number For example if 2 x 5 = 10 then 2 x 50 = x 3 = 6 then 2 x 30 = x 3 = 9 then 3 x 30= 90 This will need to be linked to place value. They will need to be able to work out multiplications of multiples of 10s with answers into the hundreds. Tens apparatus and coins are good for this. 8 x 20

10 Step 8 - Using partitioning methods to multiply 2 digit numbers by 3, 4 and 5. Using a grid method 32x 3= X x 3 2 x 3 Children will be able to sketch quick arrays to help them partition the numbers and then recombine them for the answer. Key vocabulary: groups of, lots of, times, array, altogether, multiply, count, multiplied by, repeated ad-dition, column, row, commutative, sets of, equal groups, times, _times as big as, once, twice, three times..., partition, grid method, multiple, product, tens, units, value