1. Tuesday 26 th February 2013 Minishant Primary School Parental Workshop Class 1 Mental Maths and Decomposition

2. Mental Maths The ability to calculate ‘in your head’ is an important part of mathematics and an important part of coping with maths in everyday situations.

3. MENTAL STRATEGIES FOR ADDITION AND SUBTRACTION There are many different ways of adding and subtracting; to do both efficiently ‘in our head’, children need to be able to use and apply the following strategies: Counting forward and backwards Reordering Partitioning Bridging Compensating Using doubles and near doubles Number bonds

4. Counting forward and backwards The image of a number-line helps children to appreciate the idea of counting forward and back, it allows them to recognise patterns and relationships too. E.g. Count up in one’s from 8 to 28 Count up in three’s from 0 to 30 Count up in five’s from 5 to 55 Count back in one’s from 100 to 77 Count back in two’s from 40 to 20 Count back in ten’s from 80 to 10

5. Partitioning It is essential for children to know that numbers can be partitioned into, for example, hundreds, tens and units. In this way numbers are seen as wholes rather than a collection of single digits in columns. E.g. 30+ 47 = 30 + 40 + 7 78 - 40 = 70 – 40 - 8

6. Bridging Addition For example: 8 + 7 How many more are needed to make 10? 2 If the 2 is taken from the 7, how many are left over? 5 So, 8 + 7 is 10 + 5 56 + 17 - The ten from 17 is added to 56 to make 66 Then from 66 the 7 units are added = 73

7. Bridging Subtraction: For example: 63 – 37 First subtract the 3 tens 63- 30 = 33 Then subtract the 7 units in 2 sections 33 – 3 = 30 30 – 4 = 26 7

8. Compensating Compensation is one of several efficient written methods for addition of larger numbers. It involves adding too much and then taking the extra off that you have added. For example: 744 + 86 Round 86 up to the nearest 100: 86 → 100 744 + 100 = 844 We have added 14 too many (100 - 86 = 14) so we must take it away 844 - 14 = 830 744 + 86 = 830

9. Decomposition Consider the following subtraction: TU 56 -12 __ When subtracting one number from another, we start with the units in the right hand column and then move on to the tens in the left hand column. In each column we subtract the bottom number from the top number and write the result below. In this sum, we subtract 2 from 6 in the units column to get 4. 56 -12 4 Now we move along to the tens column and subtract 1 from 5 to get 4. 56 -12 44 This is an easy sum because each number in the bottom row is smaller than the number in the top row. What happens if that’s not the case, as in the following example?

10. Decomposition 34 -19 ___ The problem is that we can’t take 9 from 4 in the units column. If you have only 4 apples, your friend can’t take 9 away from you. What we need here is something called decomposition. Decomposition happens when we borrow an amount from the number on the left to give it to the number on the right. We only do this in the top row.

11. Decomposition What this means here is that we can’t take 9 from 4 so we exchange a ten from the next column along (the 3). We will take 10 off the left hand number (3) and give it to the right hand number (4). The 3 is in the tens column, so it represents 30. Taking 10 off 30 leaves 20 (2) and adding 10 to 4 gives 14.

12. Decomposition We can now subtract 9 from 14 in the units column to get 5. Next, we subtract 1 from 2 in the tens column to get 1. And that’s the answer: 34 – 19 = 15.

13. Task Now it is your turn to have a go, using decomposition. W.A.L.T.: To subtract tens and units, using decomposition.