1. Progression through the teaching of calculation Year 5 - 6

2. Aim of Progression Maths has changed!! The maths work your child is doing at school may look very different to the kind of ‘sums’ you remember. This is because children are encouraged to work mentally, where possible, using personal jottings to help support their thinking. ‘Formal’ calculations are introduced from Year 3 onwards. Even then children are encouraged to use these methods for calculations they cannot solve in their heads.

3. Calculation When faced with a problem, we want children to ask themselves…. Can I do this in my head? Could I do this in my head using drawings or jottings to help me? Do I need to use a written method? Should I use a calculator?

4. Addition + THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF CHILDREN TO ACHIEVE. Year 5 Following formal addition methods with carrying above the line being introduced at Year 4, children should at Year 5 should then extend the carrying method to numbers with at least four digits. 587 3587 + 475 + 675 1 1 _ 1 1 1___ 1062 4262

5. Addition + Using similar methods, children will: Add several numbers with different numbers of digits Begin to add two or more decimal fractions with up to three digits and the same number of decimal points Know that decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g 3.2m – 280cm

6. Addition + Year 6 Children should extend the carrying method to number with any number of digits. 7648 6584 + 1486 + 5848 1 11_ 111_ 9134 12432 Using similar methods, children will: Add several numbers with different numbers of digits Begin to add two or more decimal fractions with up to four digits and either one or two decimal places Know that decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g 401.2 + 26.85 + 0.71

7. Subtraction - Year 5 The teaching of subtraction continues from Year 4 where an expanded method will have been introduced. This expanded method uses partitioning Step 1: 754 = 700 + 50 + 4 - 286 200 + 80 + 6 Step 2: 700 + 40 + 14 (adjusting from T to U) - 200 + 80 + 6 Step 3: 600 + 140 + 14 (adjusting from H to T) - 200 + 80 + 6 400 + 60 + 8 = 468

8. Subtraction - Decomposition 614 1 754 (as in your booklet, as the borrowing between the tens - 286 and the hundreds takes place, the 5 and the 7 will be 468 crossed out) Children should: Be able to subtract numbers with different numbers of digits Begin to find the number between two decimal fractions with up to three digits and the same number of decimal places Know that decimal points should line up under each other.

9. Subtraction - Year 6 If children are able by the end of year 5 to cope with decomposition then they will continue with this method into Year 6 513 1 6467 - 2684 3783 Children should: Be able to subtract numbers with different numbers of digits Be able to subtract two or more decimal fractions with up to three digits and either one or two decimal places Know that decimal points should line up under each other.

10. Multiplication X Year 5 As in Year 4, Year 5 children when being introduced to multiplication will be using the Grid Method Year 5 children will begin with HTU x U 369 x 9 Children are expected to approximate first 369 x 9 is approximately 370 x 10 – 3700 x 300 60 9 2700 9 + 540 81 1 1___ 3321 270054081

11. Multiplication X TU x TU 72 x 38 Again children are expected to approximate first 72 x 38 is approximately 70 x 40 = 2800 x 70 2 2100 30 + 560 8 60 16 1____ 2736 210060 56016

12. Multiplication X Using similar methods, children will be expected to multiply decimals with one decimal place. They should know that decimal points line up under each other. e.g 4.9 x 3 Approximating first 4.9 x 3 is approximately 5 x 3 = 15 x 4 0.9 12 3 + 2.7 14.7 122.7

13. Year 6 ThHTU x U 4346 x 8 Approximate first 4346 x 8 is approximately 4346 x 10 = 43460 x 4000 300 40 8 32000 8 + 2400 320 48 34768 Multiplication X 32000240032048

14. Multiplication X Year 6 HTU x TU 372 x 24 Approximate first 372 x 24 is approximately 400 x 25 = 10000 X 300 70 2 6000 20 + 1400 4 1200 280 40 8 _ 1__ 8928 6000140040 6001408

15. Multiplication x Using similar methods, Year 6 pupils will be expected to multiply decimals with up to two decimal places by a single digit and then by two digits. 4.92 x 3 Approximate first 4.92 x 3 is approximately 5 x 3 = 15 X 4 0.9 0.02 12 3 + 0.7 _0.06 12.76 122.70.06

16. Multiplication X Year 6 For the higher attainers who have grasped the concept of multiplication in Year 5, the short method of multiplication will be taught. 365 x 9 5 4_ 3285

17. Division  Year 5 In Year 4, a method of division called ‘Chunking’ will be introduced as a written method. This method is carried over into Year 5 where children will use the method to solve short division questions such as TU  U Example: 196  6 32 r 4 6 ) 196 - 180 (30x) 16 - 12 (2x) 4 Answer: 32 reminder 4 or 32r4

18. Division  Year 6 Children will continue to use this method into Year 6 where they will extend it to solving HTU  U and HTU  TU HTU  TU Example: 972  36 27 36 ) 972 - 360 (10x) 612 - 360 (10x) 252 - 180 (5x) 72 - 72 (2x) Answer 27

19. Division  Year 6 Division using the ‘chunking’ method will be extended to solving division with decimals up to two decimal places. 87.5  7 12.5 7 )87.5 - 70.0 (10X) 17.5 - 14.0 (2X) 3.5 - 3.5 (0.5X) 0 Answer: 12.5

20. Division  A short method of division will be introduced to those children who can fully understand the chunking method. This will only be used for division of HTU by U or TU by U. 4 1 369  9 = 3 9)369

21. By the end of Year 6, all children will have a range of calculation methods, mental and written. Selection will depend upon the numbers involved. Children should not be made to go onto the next stage if: * they are not ready * they are not confident Children should be encouraged to approximate their answers before calcualting and should be encouraged to check their answers after calculation. Children should also be encouraged to consider first before they attempt the question, whether a mental calculation would be appropriate.

22. Time for you to have a go!! Try to use the methods explained tonight to solve each of the following questions: 1. 1654 + 465 = 2. 6854 - 798 = 3. 965  30 = 4. 374 X 24 =