Multiplication and Division Calculating efficiently and accurately

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

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

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 / ÷

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

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

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

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.

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.

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

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

Arrays 5 x 3 or 3 x 5 14 x 2 = 28 x Array creator

X X Answer = x 4 = 52

43 x x 6 = x 6 = 18 X x 6 ( 3 x 6) 18 (40 x 6) x 6

27 x 34

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

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

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

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

Number lines / Arrays 15 ÷ 5 = Grouping ITP

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

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

Efficient methods.... Short division 291 ÷ 3 = 97 Estimate: 270 ÷ 3 = ÷ 7 = 6.2 Estimate: 42 ÷ 7 = 6