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Threshfield Primary School

Threshfield Primary School. WHOLE SCHOOL PROGRESSION IN CALCULATION STRATEGIES IN MATHEMATICS. GUIDANCE FOR PARENTS & FAMILIES Monday 22 nd September 2014. ADDITION. Stage 1: Use of practical apparatus to find the total . Recording and developing mental pictures. and. 2 + 3 = 5.

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Threshfield Primary School

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  1. Threshfield Primary School WHOLE SCHOOL PROGRESSION IN CALCULATION STRATEGIES IN MATHEMATICS GUIDANCE FOR PARENTS & FAMILIES Monday 22nd September 2014

  2. ADDITION

  3. Stage 1: Use of practical apparatus to find the total. Recording and developing mental pictures. and 2 + 3 = 5

  4. Stage 2: Progression in the use of a number line 8 + 5 = 13

  5. Stage 3: The empty number line as a representation of a mental strategy. 34 + 23 = 57

  6. Stage 4: Partitioning into tens and ones to lead to a formal written method. 25 + 47 = 72

  7. Written partitioning:- 47 + 25 40 + 20 = 60 and7 + 5 = 12 60 + 12 = 72 Or 47 + 20 = 67 67 + 5 = 72

  8. Stage 5 Using Dienes apparatus / place value counters alongside columnar written method. 25 + 47 =

  9. Stage 6: Compact column method

  10. SUBTRACTION

  11. Stage 1: Use of practical apparatus to take away or find how many more. Recording and developing mental pictures.

  12. Stage 2: Progression in the use of a number line. 8 – 3 = 5

  13. Additional ‘number lines’ - the bead string and hundred square

  14. Stage 3: The empty number line as a representation of a mental strategy. Finding an answer by COUNTING BACK – representing taking away. 15 – 7 = 8

  15. 74 – 27 = 47 “Take away 20” “Take away 7”

  16. Finding an answer by COUNTING ON – representing the “difference between”.

  17. Stage 4: Practical equipment using exchange to ‘take away’. 72 – 47 72 – 47 = 25

  18. Stage 5: Making the link between the practical and columnar subtraction. 72 - 47

  19. Stage 6: Compact method

  20. MULTIPLICATION

  21. Stage 1: Use of practical apparatus to find the total of groups of the same size. Recording and developing mental images. 2 + 2 + 2 + 2 + 2 = 10 5 + 5 + 5 + 5 + 5 + 5 = 30 6 x 5 = 30

  22. 3 lots of 4 are 12 4 lots of 3 are 12

  23. Stage 2: The bead string, number line and hundred square.

  24. Stage 3: Arrays

  25. Stage 4: The Grid Method 7 x 8 = 25 + 15 + 10 + 6 = 56

  26. 4 x13 = 52 This then becomes: 40 + 12 = 52

  27. 18 x 13 100 + 80 = 180 30 + 24 = 54 180 + 54 = 234

  28. 53 x 16 Estimate 50 x 20 = 1000 • Adding the rows is the most efficient calculation: • 500 + 300 = 800 • 30 + 18 = 48 • So 800 + 48 = 848

  29. Stage 5: Expanded short multiplication 38 x 7 30 + 8 X 7 56 (7 x 8) 210 (7 x 30) 266

  30. Stage 6: Short multiplication for up to TU x 12

  31. 53 x 16 53 x 16 18 (6 x 3) 300 (6 x 50) 30 (10 x 3) 500 (10 x 50) 848

  32. DIVISION

  33. Stage 1: Use of practical apparatus to SHARE and put into EQUAL-SIZED GROUPS. Recording and developing mental images

  34. Stage 2: Bead strings, number lines and simple multiples. 15 eggs are placed in baskets, with 3 in each basket. How many baskets are needed?

  35. Counting on a labelled and then blank number lines. 15 ÷ 3 = 5

  36. Stage 3: Arrays for division 56 ÷ 7 Dividend (56) ÷ divisor (7) = Quotient (8)

  37. Stage 4: Short division Just as multiplication is repeated addition, so division is repeated subtraction, i.e. taking away the same number repeatedly. 432 ÷ 5 432 200 (40 x 5) 232 200 (40 x 5) 32 30 (6 x 5) 2 How many 5s have been subtracted in total? Answer = 86, with 2 remaining. “CHUNKING” – initially, this could be done on an open number line.

  38. Stage 5 Long division

  39. Notes: • We teach the children to ask themselves 4 questions – in steps - about the calculations they are doing:- • Is it a calculation you can do in your head (mentally)? If yes, then do it mentally. If not, then … • Is it a calculation you can do with jottings? If yes, then do it using jottings. If no, then … • Is it calculation where you need a more formal written method? If yes, then choose the appropriate method. If no, then … • Is it a calculation where you need a calculator? If yes, then use a calculator.

  40. There are 7 strands of mathematical learning:- • Using & applying maths • Counting & understanding number • Knowing & using number facts • Calculating • Understanding shape • Measuring • Handling data • Calculating is just one of those strands

  41. Using & Applying Maths Calculating Knowing number facts Understanding place value

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