How we teach calculation at Gospel Oak

1. How we teach calculation at Gospel Oak A guide for Parents and Carers

2. Aims • To explain how we teach your children +, -, x and ÷. • To explain why we use these methods. • To give you some ideas as to how you can support your children at home.

3. Why is maths taught differently now? • When I was at school, maths lessons involved teaching rules of how to do things. We didn't question and often we didn't understand why we were "carrying ten" or "borrowing one". • This meant that I was fine as long as I remembered the rules and as long as the type of question didn’t change, but I had no clear understanding of what I was doing and why it worked. • Activities like this were probably okay for the children who ‘got’ maths, but not for those who struggled or were uninspired by the work on offer.

4. By the end of Key Stage 2, we want your children to: • Recall key number facts e.g. all +/- facts for each number to 10, times tables, number bonds etc. • Have a good understanding of the 4 operations (+ - x ÷). • Have an efficient, reliable method of calculation for each operation. • Apply their understanding to problems and real life situations. • Use a calculator effectively.

5. Children need: • To be taught the specific skills needed for calculation. • To understand what they are doing and why. • To understand why maths is important in a real life context. • To leave education with a solid understanding of maths in order to help them in adult life. • And most of all... to enjoy maths.

6. Our methods • All our calculation methods are based on developing an understanding of the number system and building on existing mental strategies. • We want children to develop a mathematical understanding, a feel for the value of number, NOT just to learn a mechanical method that is prone to error. • Once they fully understand what they are doing, they can move to more compact methods.

7. Please remember that each child is an individual and all children develop their mathematical understanding at a different pace.

8. Addition

9. Addition vocabulary • Add/adding/addition • Plus • Sum • And • Altogether/together • Increase • More • Total

10. Mental strategies for addition • Recall of number bonds. • Using near doubles. • Partitioning (splitting a number up) and recombining (putting it back together again). • Counting on and counting back in steps of 1, 10, 100 or 1000. • Adding the nearest multiple of 10, 100 or 1000 and adjusting e.g. add 10 then take away 1 in order to add 9 to a number. • Using the relationship between addition and subtraction.

11. Overview of progression in addition • R/Y1 - children are encouraged to develop a mental picture of the number system in their heads. • Y2 - children use empty number lines to count on from the larger number. • Y3 - children continue to use empty number lines with increasingly large numbers, and begin to use informal paper and pencil methods. • Y4 - children begin to carry below the line. • Y5 - children extend the carrying method to numbers with at least four digits. • Y6 - children extend the carrying method to numbers with any number of digits.

12. subtraction

13. Subtraction vocabulary • Subtract/subtraction • Minus • Take away • Take from • Fewer • Decrease • Difference between • Reduce

14. Mental strategies for subtraction • Recall of addition and subtraction facts. • Finding a small difference by counting up. • Partitioning (splitting a number up) and recombining (putting it back together again). • Counting on and counting back in steps of 1, 10, 100 or 1000. • Subtracting the nearest multiple of 10, 100 or 1000 and adjusting e.g. take away 10 then add 1 in order to take away 9 from a number. • Using the relationship between addition and subtraction.

15. Overview of progression in subtraction • R/Y1 - children are encouraged to develop a mental picture of the number system in their heads. • Y2 - children use empty number lines to count on and count back. • Y3 - children continue to use empty number lines with increasingly large numbers, and begin to use informal paper and pencil methods. • Y4 - children extend their use of written methods. • Y5 - children extend the decomposition method to larger numbers and to decimal numbers. • Y6 - children extend the decomposition method to more complex numbers.

16. Multiplication

17. Multiplication vocabulary • Multiply/multiplication/multiplied by • Times • Times table • Product • Groups of • Lots of

18. Mental strategies for multiplication • Using knowledge of doubling and halving. • Using recall of times tables facts. • Using closely related facts e.g. 13 x 11 = (13 x 10) + (13 x 1). • Multiplying by 10, 100 or 1000. • Partitioning numbers e.g. 23 x 4 = (20 x 4) + (3 x 4). • Using knowledge of factors.

19. Overview of progression in multiplication • R/Y1 - children will experience equal groups of objects and will count in 2s and 10s and begin to count in 5s. • Y2 - children will extend their understanding of multiplication. • Y3 - children continue to use repeated addition, numberlines and arrays, and begin to use informal paper and pencil methods. • Y4 - children will continue to use arrays, leading into the grid method of multiplication. • Y5 - children extend their use of the grid method to larger numbers and decimals. • Y6 - children extend their use of the grid method to larger numbers and decimals.

20. division

21. Division vocabulary • Divide/division/divided by • Divisible by • Share/share equally • Group

22. Mental strategies for division • Using knowledge of doubling and halving. • Using times tables facts to find division facts e.g. 3 x 5 = 15 so 15 ÷ 5 = 3. • Using closely related facts e.g. 21 ÷ 7 = 3 so 210 ÷ 7 = 30, 210 ÷ 70 = 3, 2.1 ÷ 7 = 0.3 etc. • Dividing by 10, 100 or 1000. • Using knowledge of factors.

23. Overview of progression in division • R/Y1 - children will understand equal groups and share items out in play and problem solving. • Y2 - children will extend their understanding of division. • Y3 - children continue to use repeated subtraction and numberlines. • Y4 - children will develop their use of repeated subtraction, and begin to use informal paper and pencil methods. • Y5 - children will continue to use a written method to solve division questions. • Y6 - children will continue to use a written method to solve division questions.

24. How you can support your child • Look for and talk about numbers in the environment • Play games • Shopping • Counting on/back • Number bonds • Doubles/halves • Times tables • Division facts