Addition and subtraction

1. Explaining how we teach mathematics, and what you can do to help your child become a confident mathematician. Addition and subtraction

2. What are we going to talk about this afternoon? • Number: Place value, partitioning, ordering, comparing, sequencing, rounding, estimating • Calculations: Addition and subtraction • Vocabulary, and ability to explain methods • Using and applying • We use a consistent, progressive approach • KS1 – Focus on mental calculation strategies • KS2 - Informal written method leading to a standard written method • Primary strategy web site

3. Place value and partitioning • A vital skill. • It is understanding that what each digit is worth is dependent on its position in a number. • Visually supported with use of arrow cards, digit cards and base blocks. Using base blocks 572 is partitioned into 500 and 70 and 2 500 70 2

4. Place value grid http://www.primaryresources.co.uk/online/numberboard2.swf or PV Chart v8.exe • Then adding and subtracting 1, 10 and 100. • e.g. 1 or 10 more or less bingo spreadsheet

5. Hundred square

6. Ordering Being able to put numbers in order and place them on a number line. 10 8 6 12 Ordering numbers: Number line 112 165 178 125 194 143

7. Comparing numbers Which number is bigger? Which number is smaller? Using the symbols: is smaller than < is greater than >

8. Sequencing Identifying the sequence and adding to it. • This includes completing dot to dot pictures and making patterns with coloured beads then goes on to completing number sequences such as: • a) 2 4 6 ___ 10 12 ___ • 43 38 33 ___ 23 18 ___ ___ • 4.3 3.8 3.3 ___ 2.3 1.8 ___ • Children also need to be able to explain what the sequence/pattern is e.g. a) adding 2, b) subtracting 5 c) subtracting 0.5 We use a counting stick to practise counting in sequences.

9. Rounding Need to know the multiples of 10 and 100 Multiples of 10 are: 0 10 20 30 40 50 60 70 80 90 100 110 etc. Post box sorting 65 Which multiple of 10 is 65 between? Which multiple of 10 is 65 nearest? 60 61 62 63 64 6566 67 68 69 70 65 rounds to 70

10. Estimating How many sweets? How many shells? Rounding to estimate what the answer will be near. 64 + 57 rounds to 60 + 60 = 120 so the answer must be near 120

11. Adding 4 + 7 Key stage 1: Start with the biggest number first Count on Use a number line Any written work is done horizontally 7 + 4 = 11 7 + 4 1 2 3 4 7 8 9 10 11

12. Number bonds We can’t emphasise enough the need for children to confidently know their number facts before they progress to more formal written methods. Triangular cards • addition and subtraction bonds for totals up to 10 • addition and subtraction bonds for totals up to 20 Hit the button • doubles of all numbers up to 10 and then 20 • addition and subtraction bonds with multiples of 10 for totals up to 100 • addition and subtraction bonds with multiples of 5 for totals up to 100 These facts will enable them to carry out the more formal methods of addition and subtraction with confidence.

13. Adding two digit numbers using • informal methods • 23 + 32 = (20 + 30) + (3 + 2) • 50 + 5 = 55 • Easy sums: 20 + 30 = 50 • Then 20 + 32 = (20 + 30) + 2 • 50 + 2 = 52 • and finally 25 + 37 = (20 + 30) + (5 + 7) • 50 + 12 = 62 • The aim is that, eventually children will be able to add two 2 digit numbers mentally. Adding with arrow cards

14. We introduce more formal written methods in stages. First this:23 + 32 = 20 3 + 30 2 50 + 5 = 55 35 + 39 = 30 5 + 30 9 60 + 14 = 74 Then this: 3 5 + 3 9 1 4 6 0 7 4 Then this: 3 5 3 9 7 4 1 3 5 2 + 1 8 9 5 4 1 1 1 Expanded addition

15. Subtracting Key stage 1: Any written work is done horizontally Count back Use a number line The difference between 7 and 4 is 3 7 – 4 = 3 4 3 2 1 3 4 5 6 7 3 2 1 4 5 6 7

16. Subtraction After lots of visual, practical and mental subtraction work with single digit numbers including use of a number line and use of relevant language such as difference between, minus, how many less is?... how many less than?..., subtract, take, take away etc. children learn to subtract larger numbers. We begin to teach more formal methods using partitioning. 67 – 23 = 60 7 - 20 3 40 4 = 44

17. 63 - 27 Decomposition Finally we move to the more compact method, when we feel children are ready for this. For some children the final compact method will be difficult and they will continue to use informal methods into year 6. This compact method is known as 'decomposition‘. They will progress to using bigger numbers and decimals.

18. Thank you for reading this. We hope you find it useful. Wizard number What is the Number?