Progression in Calculation St James RC Primary School 31 st January 2013

1. 1 2 3 4 5 6 7 8 9 10 11 12 400 30 2 Progression in CalculationSt James RC Primary School31st January 2013

2. Objectives • To demonstrate the need for clear and appropriate progression in mathematics. • To highlight the importance of mental strategies. • To know how best to support your children at home.

3. What mathematics have you done today?

4. Our Aim By the end of key Stage 2, all children should be able to use an efficient written method for each operation with confidence and understanding.

5. Prior Knowledge Oral and mental work in mathematics is essential, particularly so in calculation. Early practical, oral and mental work must lay the foundations by providing children with a good understanding of how the four operations build on efficient counting strategies and a secure knowledge of place value and number facts.

6. Number Facts

8. Learning times tables • Say the multiples (just the answers) • Chant the tables (the old fashioned way!) • Test children on times table facts (not in order) • Learn the ‘fact family’. (two multiplication and two division calculations that use the same numbers)

9. Place Value Th H T U.th hth

10. 400 30 2 How to help your child at home • Dice Measuring • Playing cards Board games • Car number plates Door numbers • Money Timetables • Cooking Dominoes • Multiplication and division facts • Countdown Time Please don’t introduce your child to compact written methods before they are ready!

11. Progression towards a compact (formal) written method 1 Establish mental methods, based on a good understanding of place value in numbers. 2 Solve calculations in a horizontal format. 3 Children set out written calculations, initially using expanded layouts that record their mental methods. 4 As children become more confident, they refine the written record into a more compact and efficient method. 5 Extend to larger numbers and to decimals. (Children may initially need to return to a more expanded layout.)

12. 400 30 2 1 2 3 4 5 6 7 8 9 10 11 12

13. Addition Stage 1 – numbered lines counting on in ones. Stage 2 – Empty number lines • Bridging to ten • Partitioning • Adding larger numbers Stage 3 – Partitioning (‘exploding’ number sentences) Stage 4 – expanded notation in columns Stage 5 – compact column method

14. Subtraction Stage 1 – Numbered lines counting back in ones. Stage 2 – empty number lines • Bridging to ten • Partitioning • Subtracting larger numbers Stage 3 – Use number line to count up (useful for ‘find the difference’ and finding change). Stage 4 – Expanded partitioning Stage 5 – compact decomposition

15. Multiplication Stage 1 – Repeat addition on a number line. Stage 2 – Partitioning using known facts. Stage 3 – Grid method. Stage 4 – Expanded layout. Stage 5 – compact method.

16. Division Stage 1 – Repeat subtraction on a number line. Stage 2 – repeat subtraction on a number line finding remainders. Stage 3 – Partitioning into ‘known’ facts. Stage 4 – Chunking. Stage 5 – Bus stop.

17. ‘Build on what pupils already know, understand and can do. Pupils should not be taught to use a compact method if their understanding and recording of mental methods is not secure. When a ‘taught’ method does not build on pupils’ previous understanding, then the various stages of the calculation will be difficult to reproduce and errors will result’ Key Stage 3 Strategy

18. Key Messages • Consistency of approach is crucial to children’s understanding of written calculations • If children are introduced to compact methods before their understanding is developed they will not be successful

19. Division is mathematics where you get two numbers then you put one of the numbers into the other number and you write how many can go into that number. Then you multiply the number on top with the number on the side and you get the answer. Put it on the bottom and subtract it with the number in the middle. However many is left you put a ‘r’ on the top then the number by the ‘r’ that stands as the reminder.Emily