1. Multiplication and Division Calculating efficiently and accurately

2. Objectives To explore the knowledge, skills and understanding required for children to multiply / divide efficiently and accurately To explore the progression in recording and (some of) the teaching approaches used Self-esteem

3. The Four Rules Understanding Mental calculations Rapid recall Efficient written methods Models, images & concrete materials Stories / rhymes Problem solving and role play Use of ICT

4. Counting Doubles / halves / near doubles Multiplication as repeated addition, describing an array and scaling Division as grouping and sharing Recall of multiplication / division facts for 2, 3, 4, 5, 10 times tables and beyond Multiply two / three-digit numbers by 10 / 100 Understand that multiplication and division are inverses Progression in knowledge and understanding for x / ÷

5. Counting and estimation There are 5 principles of counting: 1. The stable order principle - understanding that the number names must be used in that particular order when counting 2. The one-to-one principle - understanding and ensuring that the next item in a count corresponds to the next number 3. The cardinal principle - knowing that the final number represents the size of the set 4. The abstraction principle - knowing that counting can be applied to any collection, real or imagined 5. The order irrelevance principle - knowing that the order in which the items are counted is not relevant to the total value

6. Counting in context How many 10p coins are here? How many 10p coins are here? How much money is that? How many toes are there on 2 feet? How many gloves in 3 pairs? How many gloves in 3 pairs? If Sarah counts in 2s and Nigel counts in 5s, when will they reach the same number? How many lengths of 10m can you cut from 80m of rope? How many lengths of 10m can you cut from 80m of rope? Mr Noah

7. Doubling and halving in context There are 8 raisins. Take half of them. There are 8 raisins. Take half of them. How many have you taken? One snake is 20cm long. Another snake is double that length. How long is the longer snake? I double a number and then double the answer. I double a number and then double the answer. I now have the number 32. What number did I start with? Doubling machineChip the chopper

8. 9465483071 2836569732 1224518219 7763445328 6096751743

9. 1263282032 2480562740 308421816 4870154535 725410906 2 3 4 5 6 7 8 9 10 Three in a row Choose two numbers from the row of numbers above the grid. Multiply them together. If the answer is on the grid, cover that number with a counter.

10. 430612 209525 721510 360508 1 2 3 4 5 10 15 18 20 24 30 60 100 Three in a row Choose two numbers from the row of numbers above the grid. Divide the larger number by the smaller number. If the answer is on the grid, cover that number with a counter.

11. 2 x 3 or 3 x 2 3 plates, 2 cakes on each plate (Children could draw a picture to help them work out the answer) 2 x 3 or 3 x 2 3 plates, 2 cakes on each plate (Children could use dots or tally marks to represent objects – quicker than drawing a picture) Multiplication pictures symbols

12. Number tracks / number lines (modelled using bead strings) 2 x 3 or 3 x 2 4 620 [two, three times] or [three groups of two]

13. Arrays 5 x 3 or 3 x 5 14 x 2 = 28 x 104 2208 Array creator

14. X 103 4 X 3 4 4012 Answer = 52 13 x 4 = 52

15. 43 x 6 258 1 40 x 6 = 240 3 x 6 = 18 X403 6 24018 43 x 6 ( 3 x 6) 18 (40 x 6) 240 258 43 x 6

16. 27 x 34

17. Multiplication grid ITP Approximation: Answer lies between 600 (20 x 30) and 1200 (30 x 40) or 30 x 30 = 900 27 x 34 28 ( 7 x 4) 80 (20 x 4) 210 ( 7 x 30) 600 (20 x 30) 918 27 x 34 108 (27 x 4) 810 (27 x 30) 918 Extend to HTU x U, U.t x U and HTU x TU 27 x 34

18. 6 ÷ 2 6 cakes shared between 2 6 cakes put into groups of 2 (Children could draw a picture to help them work out the answer) pictures Division

19. 6 ÷ 2 6 cakes shared between 2 6 cakes put into groups of 2 (Children could use dots or tally marks to represent objects – quicker than drawing a picture) symbols

20. Number tracks / number lines - grouping (modelled using bead strings) 8 ÷ 2 = 4 6 ÷ 2 = 3 0 2 4 6

21. Number lines / Arrays 15 ÷ 5 = 3 0 5 10 15 Grouping ITP

22. 06096 (6 x 10) (6 x 6) Starting from 0 Number dial ITP 96 ÷ 6 = 16 96 ÷ 6 6 x 10 = 60 6 x 6 = 36

23. Efficient methods.... Answer = 125 r 4 Approximation: Answer lies between 100 (600 ÷ 6) and 150 (900 ÷ 6) 754 - 600 (6 x 100) 154 - 120 (6 x 20) 34 - 30 (6 x 5) 4 Extend to U.t ÷ U and HTU ÷ TU 754 ÷ 6

24. Efficient methods.... Short division 291 ÷ 3 = 97 Estimate: 270 ÷ 3 = 90 3 291 97 2 7 43.4 6.2 1 43.4 ÷ 7 = 6.2 Estimate: 42 ÷ 7 = 6