Multiplication

Multiplication facts Children should be reasonably comfortable with multiplying single digit numbers by single digit numbers (they might not have instant recall of multiplication facts but should be able to derive some facts reasonably quickly). Initially children should know their 2, 5 and 10 x tables, then their 3 and 4. Finally they should master their 6, 7, 8 and 9 x tables. Children should understand that multiplication facts can be done in any order; 8 x 5 is the same as 5 x 8 etc.

Multiplying by 10 and 100 Th H T U 6 3 5 4 Children will be taught how to multiply by 10 and 100. They need to understand the value of 0 as a place holder. The process of moving/sliding digits along is reinforced – not ‘knocking it off the end’! X by 10 – 1 space to the left X by 100 – 2 spaces to the left 6 x 10 = 60 35 x 10 = 350 54 x 100 = 5400 Th H T U 6 3 5 4

Repeated addition 4 x 3 = 3 + 3 + 3 + 3 = 12 Children will be shown the link between addition and multiplication. Mental strategies will support repeated addition with units multiplied by units. 4 x 3 = 3 + 3 + 3 + 3 = 12 5 x 7 7 + 7 + 7 + 7 + 7 = 35

Partitioning When beginning TU X U we partition the larger number. 17 x 5 = 10 x 5 = 50 7 x 5 = 35 85 This method reinforces place value – the 1 represents 1 ten and the 7 represents 7 units.

Grid method Grid method is used at different stages of multiplication to reinforce place value and demonstrate the processes you go through to reach an answer. Again we partition the largest number. 23 x 8 = (20 x 8 then 3 x 8 then add the 2 numbers together) x 20 3 8 160 24 = 184

Short Multiplication x 7 161 23 x 7 = 23 x 7 161 U x U then T x U The grid method for TU X U then transfers into the ‘column method’. 23 x 7 = U x U then T x U 23 x 7 (3 x 7) 21 (20 x 7) 140 161 This then condenses and ‘carries’ are introduced. 23 x 7 161 2 The ‘20’ from 3 x 7 hangs below the line ready to be added to the tens from 20 x 7.

Grid method Grid method is then used to solve HTU x U problems. Children work strategically to solve; H x U, T x U then U x U 346 x 9 ( 300 x 9, 40 x 9, 6 x 9 then add the 3 numbers together) X 300 40 6 9 2700 360 54 = 3114

Grid method This method is then extended to TU x TU 32 x 18 = x 30 2 (30 x 10, 2 x 10 then 30 x 8, 2 x 8) Total the rows then add the 2 numbers together. x 30 2 10 300 20 = 320 8 240 16 = 256 576

Have a go! Have a go at these questions using the grid method! 126 x 4

Long multiplication The grid method for TU X TU is then taken on to the column method. 28 x 23 = U x U, U x T, T x U then T x T 28 x 23 24 (8 x 3) 160 (8 x 20) 60 (20 x 3) 400 (20 x 20) 644 1 This method can then be condensed: 28 x 23 = 28 x 3 then 28 x 20 28 x 23 84 (28 x 3) 2 560 (28 x 20) 1 644

Multiplication of decimals This can be done 2 ways: Multiply the number by 10 or 100 to reach a whole number before starting, solve the problem then divide the answer by 10 or 100 at the end. 4.5 x 16 = (4.5 x 10 = 45) 45 x 16 270 (45 x 6) 3 450 (45 x 10) 720 1 720 ÷ 10 = 72 2. Multiply then divide by 10 or 100 mentally as you go along at each stage. 4.5 x 16 = 72 4.5 x 16 27.0 (4.5 x 6) 45.0 (4.5 x 10) 72.0 1

Multiplication Whichever method your child is learning in school it is essential that they have a good grasp of relevant multiplication tables in order to make good progress.