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Methods of Multiplication

Methods of Multiplication. Heatherside Junior School. Multiplication. x x x x x x x x x x x x x x x. x x x x x x x x. x x x x x x x. 2 x x x x x x x. 2 x x x x x x x. lots of . times. groups of. repeated addition. array. product of. multiply. multiple of.

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Methods of Multiplication

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  1. Methods of Multiplication Heatherside Junior School

  2. Multiplication x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 2 x x x x x x x 2 x x x x x x x lots of times groups of repeated addition array product of multiply multiple of double x x x x x x x x x x x x x x x x

  3. Step 1 – Multiplication as arrays Recognising that 3x2 gives the same answer as 2x3 2 x 3 = 6 3 x 2 = 6 2 + 2 + 2 = 6 3 + 3 = 6 Understanding that multiplication is repeated addition

  4. Step 2 – Knowing tables facts is key ‘Learn Its’ – a progressive approach 3 facts 5 minutes 3 weeks Stage 1: counting in 10s, 5s, and 2s Stage 2 (by the end of Year 2): x10, x5, x2 Stage 3 (by the end of Year 3): x3, x4, x9 Stage 4 (by the end of Year 4): x6, x7, x8

  5. ‘Learn Its’ vocabulary FACTS SWITCHERS FACT FAMILIES 9 ÷ 3 = 3 12 ÷ 3 = 4 15 ÷ 3 = 5 3 X 3 = 9 4 X 3 = 12 5 X 3 = 15 3 X 4 = 12 3 X 5 = 15

  6. Step 3 - Partitioning This method helps show the value of each digit in a number. Children develop a greater understanding of the reasonableness of an answer and they are able to apply known facts. 23 x 8 = 20 3

  7. Step 4 - The Grid Method 23 x 8 = 160 + 24 = 184 • The number is partitioned and placed on the grid. • The total is added to calculate the final answer.

  8. Step 5The Expanded Column Method The question is… 38 x 7 = The number is partitioned… 38 x 7 30 8 x 7 30 + 8 x 7 56 (7 x 8) +210 (7 x 30) 266

  9. 38 x 7 = 38 x 7 = 266 We aim for children to begin to be able to use short multiplication for TU x U by the end of Year 4. The short method 38 x 7 266 5 Step 6 ….This is then reduced to Short Multiplication

  10. Remember to partition the numbers using known facts first. 63 x 42 = Using the Grid Method for TU x TU 2400 + 120 = 2520 120 + 6 = 126 2520 + 126 = 2646

  11. Moving from the Gridto Column Method for TU x TU 56 x 27 42 (7x6) 350 (7x50) 120 (20x6) + 1000 (20x50) 1512 1 The question is 56 x 27 =

  12. The Grid Method for larger numbers 89 x 123 First partition each number 89x123 [80 9] [100 20 3] This is then shown on a grid like this…

  13. Multiplying using the grid method Firstly, multiply each column and row and record the answer in the correct box 8000 900 1600 180 240 27

  14. Completing the calculation Now total up all the yellow numbers. = 8900 = 1780 = 267 = 10,947 Add all the totals to get the final answer

  15. 256 x 28 48 (8x6) 400 (8x50) 1600 (8x200) 120 (20x6) 1000 (20x50) +4000 (20x200) 7168 If children are very secure at Level 5 they may go on to use the compact method, where 0 is used to denote the multiple of 10. 56 x 27 392 4 + 1120 1 1512 1 Step 7 - Long Multiplication

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