1. Calculation Policy Guidance on progression of written methods.

2. Main Menu Aims Expectations Addition & subtraction Multiplication Division Place value Fractions

3. Introduction This policy is to provide parents with a clear guide to how written calculations are taught in Valley Gardens Middle School so they may confidently support their children at home. Currently only formal written methods are covered, but the policy will be extended to the progression of mental methods and strategies. This is a working document and will be updated throughout the year.

4. Addition & Subtraction Mental methods Column Addition Column Subtraction Column methods (decimals)

5. Addition & Subtraction Mental methods Refer to the NCETM Calculation Policy (“Year” corresponds to the “stages” in the VGMS assessment system)

6. Addition & Subtraction Column Addition Notes: EXPANDED: Can be supported using place value counters or Dienes: e.g. showing 70 + 80 = 15 tens, exchanged to 1 hundred and 5 tens) COMPACT: All exchanges written at the bottom and in the correct column (not in- between columns). (expanded) column method(compact) column method

7. Addition & Subtraction Column Subtraction Notes: All exchanges written carefully next to the number (e.g. since the 1 in the units column actually represents 10 units, not 1 unit).

8. Addition & Subtraction Column methods (decimals) Notes: Decimal points in line, fill in any spaces with “0”s. All exchanges written at the bottom and in the correct column (not in-between columns). Subtraction: all the same points apply.

9. Multiplication Mental methods Grid multiplication (HTU x U) Column multiplication (HTU x U) Grid multiplication (HTU x TU) Column multiplication (HTU x TU) Column multiplication (decimals)

10. Multiplication Mental methods Refer to the NCETM Calculation Policy (“Year” corresponds to the “stages” in the VGMS assessment system)

11. Multiplication Grid multiplication (HTU x U) Notes: Set out the grid as a rectangle split into sections (this links in with previous work on arrays – see mental methods).

12. Multiplication Column multiplication (HTU x U) Notes: The link between column method and grid method should be made clear. All exchanges written at the bottom and in the correct column (not in-between columns).

13. Multiplication Grid multiplication (HTU x U) Notes: Set out the grid as a rectangle split into sections (this links in with previous work on arrays – see mental methods).

14. Multiplication Column multiplication (HTU x TU) (expanded) column method(compact) column method Notes: All exchanges written at the bottom and in the correct column (not in-between columns). Refer to place value when multiplying by 10 / 100 etc. HTU labels above each column Calculation labels (right hand side) may be included when first learning, but dropped when confident.

15. Multiplication Column multiplication (decimals) Notes: Use of correct place value should be stressed here (as opposed to counting the number of digits after the decimal point, which misses the understanding of what is really happening).

16. Division Mental methods Simple chunking Short division Short division (continued) Long division (by one-digit divisor) Long division (by two-digit divisor) Division (decimals)

17. Division Mental Methods Refer to the NCETM Calculation Policy (“Year” corresponds to the “stages” in the VGMS assessment system)

18. Division Simple chunking Notes: Underline how many “lots of” to make it clear which numbers add together to make the answer.

19. Division Short Division Notes: This method can be built up using place value counters or Dienes (video to follow).

20. Division Short Division (continued) Notes: The correct form of remainder should be used as appropriate to the question. E.g. money questions would usually require a decimal answer. (with decimal answer) (with fraction answer)

21. Division Long Division (by one-digit divisor) Notes: Links should be made with the short division method. This is presented as an intermediate step towards long division with a 2 (or more) digit divisor.

22. Division Long Division (by two-digit divisor) Notes: Writing out a short list of multiples (e.g. the 18 times table) helps to avoid mistakes in an already complicated method. … by a double digit number

23. Division Dividing by decimals Notes: First adjust the divisor to be a whole number Finally the correct place value for the answer can be obtained either through: a) estimation: 24.9 ÷ 5.9 = 4 (roughly) b) equivalent fractions: 24.9/5.9 = 249/59 (examples to follow)

24. Place Value (this page to follow)

25. Fractions Fractions of an amount Improper fractions Equivalent fractions Adding / subtracting fractions Multiplying fractions Dividing fractions

26. Fractions Fractions of an amount Notes: “Bar modelling” approach shown here. The “bracket” at the top represents the whole.

27. Fractions Improper fractions Notes: A mixture of bars, fractions circles and other shapes should be used so pupils remain flexible in their understanding.

28. Fractions Equivalent fractions Notes: Some possible visual representations shown here.

29. Fractions Adding / subtracting fractions Notes: Using two 3 by 5 grids for adding thirds and fifths (to show equivalence). Subtraction would work the same but taking away squares at the final stage.

30. Fractions Multiplying fractions Notes: Again using a 3 by 5 grid and the fact that multiplying by a fraction is the same as finding that fraction of the first number. This can give pupils a clear understanding of where the “rule” comes from (multiply the numerators and the denominators).

31. Fractions Dividing fractions Notes: One possible approach using Cuisenaire rods: First establish the “name” of each fraction and what represents the “whole”. Next see how many of the fraction fit into the “whole”. Any parts are just fractions of that block.