Multiplication Here are some words your child might use or come across when multiplying. Methods we use for multiplying! Drawing pictures Counting in 2s Counting in 5s Counting in 10s Questions to practise e.g. There are five sweets in one bag. How many sweets are there in 3 bags? Repeated Addition 5 x 3 is the same as 5+5+5 This can be shown on a number line: 5 x 3 = 15 +5 +5 +5 ____________________________________________________________ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Multiplying in Any Order e.g. Understanding 3 x 4 is the same as 4 x 3 We can show this works by using a number line. Example 1: 5 x 3 = 15 is the same as 3 x 5 = 15 +5 +5 +5 ____________________________________________________________ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 +3 +3 +3 +3 Example 2: 2 x 6 = 12 is the same as 6 x 2 = 12 +2 +2 +2 +2 +2 +2 _________________________________________________ 0 1 2 3 4 5 6 7 8 9 10 11 12 +6 +6 +3 Arrays (When objects are arranged in rows and columns) Any multiplication can be drawn as an array: Example 1: Example 2: 5 x 3 = 15 6 x 2 = 12 2 x 6 = 12 3 x 5 = 15 Learning Times Tables It is vital that as children begin to understand the steps above that they start to learn their times tables. If they do not learn these by heart it will make it very difficult for the children to complete the methods we will move onto next. This means being able to: Recite e.g: 1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 6 5 x 2 = 10 6 x 2 = 12 7 x 2 = 14 8 x 2 = 16 9 x 2 = 18 10 x 2 = 20 11 x 2 = 22 12 x 2 = 24 Quick recall e.g: 5 x 2 = ? AND 11 x 2 = ? Partitioning (Multiplying the tens and units of the start number separately) As a number sentence: 14 x 5 = 70 This can be shown as an array: 14 x 5 = (10 x 5) + (4 x 5) = 50 + 20 = 70 10 5 Grid Method for TU X U (Continues Partitioning) Example 1: 23 x 8 = Step 1: (partition the start number and multiply each part) X 20 3 8 160 24 Step 2: (add the two answers) Example 2: 58 x 7 = 406 Step 1: (partition the start number and multiply each part) X 50 8 7 350 56 Step 2: (add the two answers) 4 Grid Method for HTU X U 357 x 6 = 2142 X 300 50 7 6 1800 300 42 Grid Method for TU X TU 72 x 38 = 2736 X 70 2 30 2100 60 8 560 16 Grid Method for ThHTU X U 4356 x 8 = 34848 X 4000 300 50 6 8 32000 2400 400 48 Short Multiplication TU X U (used for multiplying by 1 digit numbers) 14 x 8 = 112 (For ALL Short Multiplication work from right to left) This is how children will set this method out. (The pictures below shows the steps of what is happening.) Step 1: Step 2: Step 3: Start with the units column e.g. 4 x 8 = 32 The 3 tens in 32 are carried to the next column. Move to the next column (right to left) e.g. 1x8=8 However, we already have 3 in this column from step 1 so we need to add these together i.e. 8 + 3 = 11 More examples of Short Multiplication (used for multiplying by 1 digit numbers) Example 1: Example 2: Example 3: Short Multiplication involving decimals (used for multiplying by 1 digit numbers) Example 1: 35.6 x 8 = 284.8 Step 1: Calculate as if there are no decimal places i.e. Example 2: 29.43 x 3 = 88.29 Step 1: Calculate as if there are no decimal places i.e. Step 2: Put the decimal places into the answer e.g. In this question there was one decimal place in 35.6 so we need to put 1 decimal place into the answer i.e. 2848 becomes 284.8 Step 2: Put the decimal places into the answer e.g. In this question there were two decimal places in 29.43 so we need to put 2 decimal places into the answer i.e. 8829 becomes 88.29 Long Multiplication (used for multiplying by numbers with more than 1 digit) Example 1: 72 x 38 = 2736 (For ALL Long Multiplication work from right to left) This is how children will set this method out. (The pictures below shows the steps of what is happening.) Step 1: Start with the units column e.g. 72 x 8 = 576 Follow the same process as for short multiplication. (Do not worry about the 3 in the tens column at this stage.) Example 2: Step 2: Move to the next column (right to left) e.g. 72 x 3 = 216 We put a 0 in the units column because it is actually 72 x 30 which is ten times bigger than 72 x 3. Example 3: Step 3: We then add the two answers together. Example 4: It is very important that children remember that when they add their working out together they do not add any of the small digits used for carrying in their multiplication. However, they must include any digits involved in carrying for addition. Here the small digits used for carrying in addition have been coloured red to show this. Long Multiplication involving Decimals (used for multiplying by numbers with more than 1 digit) Example 1: 3.57 x 24 = 85.68 Step 1: Calculate as if there are no decimal places i.e. Example 2: 1 decimal place in 6.8 so 1 decimal place in the answer - 29620.8 Step 2: Put the decimal places into the answer e.g. In this question there were two decimal places in 3.57 so we need to put 2 decimal places into the answer i.e. 8568 becomes 85.68 Example 3: Example 4: 2 decimal places in 9.43 AND 1 decimal place in 25.3 which is 3 decimal places altogether. 2 decimal places in 243.56 AND 3 decimal places in 7.253 which is 5 decimal places altogether. So we need 3 decimal places in the answer 238.579 So we need 5 decimal places in the answer 1766.54068