Multiplication Year 1

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1 Multiplication Year 1 A range of concrete and pictorial representations should be used with teacher support. Examples: Using songs/rhythms to begin counting in 2 s, 5 s and 10 s Using pictures of shoes/socks to count in 2 s Using fingers/gloves to count in 5 s Using coins to count up in 2's (2p coins), 5 s (5p coins) and 10 s (10p coins).

2 Multiplication Year 2 Continue using a range of concrete and pictorial representation should be used as well as physical representations of sharing, grouping, arrays and patterns. Examples: Practical problem solving activities involving equal groups of 2, 5 and 10 objects e.g. 3 groups/lots of 2 cars is 6 cars Concrete representations of grouping Using bead strings to model groups of a certain number Counting repeated groups of a certain amount Using arrays

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5 Multiplication Year 3 Teach informal methods before moving onto the formal written method. Partitioning Example: = (2 0 5) + (4 5) = = 1 2 0

6 Multiplication Year 3 Grid Method Example: = 315

7 Multiplication Year 4 Use the formal written method, short multiplication to multiply a 2/3 digit number by a 1-digit number.

8 Expanded Column Method Line up the ones and the tens Multiply the ones (by 6 in this example). Multiply the tens (by 6 in this example). Add the amounts together.

9 Multiplication Year 5 Use the formal written method, long multiplication to multiply a 3/4 digit number by a 2-digit number. Example 2

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12 Multiplication Year 6 Use the formal written method, long multiplication to multiply up to 4- digit numbers by a 2-digit number, including money and decimals. Example = Multiply 4.02 by 100 = 402 Work out 402 x 73 using long multiplication = Divide the answer by =

13 Division Year 1 Practical hands-on activities with a high profile given to developing mathematical language together with visual images, concrete and pictorial representations of sharing, grouping, arrays and patterns. Examples: Sorting objects given into equal groups. Counting repeated groups of the same size Understand division as sharing Practical problem solving activities involving combining groups of 2 s, 5 s and 10 s Using practical objects to answer questions such as: How many 2 s make 12? Using bead strings to model grouping

14 Division Year 2 A range of concrete and pictorial representation should be used as well as physical representations of sharing, grouping, arrays and patterns. Examples: Grouping objects into groups Using sorting trays, asking children to sort objects into groups including 3 s. Using bead strings to model grouping Using repeated subtraction as a form of grouping Using practical objects to pose questions such as, How many groups of 5 can I make with 20 counters?

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16 Division Year 3 Repeated subtraction involving remainders.

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19 Division Year 4 Use the formal written method of short division to divide a 2-digit number by a 1-digit number and a 3-digit number by a 1-digit number. Children to write remainders as whole numbers.

20 Division Year 5 Use the formal written method of short division to divide up to 4-digit numbers by a one-digit number, giving the answer with a remainder or as a fraction. Example: = remainder remainder divisor divisor

21 Division Year 6 Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division and interpret remainders as whole number remainders, fractions or by rounding as appropriate for the context. Example: =

22 422 children need to travel by mini bus for a school trip. Each mini bus can hold 15 pupils. How many mini buses are needed? Round answer up to 29 mini buses.

23 Pupils are also expected to show remainders as a decimal. 0 5 Continue until there are no remainders left or give the answer to the nearest decimal place e.g (to 1 d.p).

24 Multiplying and Dividing by 10, 100 and 1000 When multiplying or dividing by 10, 100 or 1000, the children need to use their knowledge of place value to understand the digits move, not the decimal point.

25 36 x 10 = = one space to the left 3 6 one space to the right

26 3.6 x 1000 = = three spaces to the left two spaces to the right

27 Multiplication Tables In Year 2 pupils should be taught to recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers. In Year 3 pupils should be taught to recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables. In Year 4 pupils should recall multiplication and division facts for multiplication tables up to

28 Multiplication Tables Knowing multiplication facts and their corresponding division facts is key for so many other mathematical areas Mental calculations such as 400 x 8 = 3200 knowing 4 x 8 = 32 and then multiplying by 100 Mental calculations such as = 0.8 knowing 64 8 = 8 and then dividing by 10 Word problems i.e. converting measures to solve a word problem e.g. A ribbon is 2m long, it is cut into 4 pieces, how long is each piece of ribbon, in centimetres? 1. Convert 2m into cm [2 x 100 = 200cm] 2. Divide 200 by 4 = 50 because 20 4 = 5 then multiply the answer by cm Finding equivalent fractions x3 x3 3 Problems involving ratio and proportion A bag contains red, blue and green balls. How many blue balls will there be if there are 60 green balls? x12 blue : green 7 : 5? : 60 x12 7 x 12 = 84 blue balls

29 Strategies to learn Multiplication Tables at home Flash cards (multiplication on one side, the answers on the other) Commutative law 8 x 5 = 40 so 5 x 8 = 40 also. Missing number questions x 6 = 42 Knowing corresponding division facts 42 6 = 7 because 6 x 7 = 42 If you know 8 x 9 = 72, what other facts do you know? 90 x 8 = x 8 = x 90 = = = = 9