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Richmond Primary School

Richmond Primary School. Maths Calculations Policy. This is intended to give a broad overview of the methods we use for teaching maths throughout the school. It is hoped that it may help you to support your child with their maths at home.

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Richmond Primary School

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  1. Richmond Primary School Maths Calculations Policy

  2. This is intended to give a broad overview of the methods we use for teaching maths throughout the school. It is hoped that it may help you to support your child with their maths at home. If you have any questions about it, please do not hesitate to contact either your child’s class teacher or Miss Dottie, who will be happy to help.

  3. Development of Addition Pictures are used to illustrate what is happening to the numbers. Year One Lisa has 5 lollies and Tim has 2 lollies. How many lollies do they have altogether?

  4. The children would then progress to using marks to represent the number, rather than drawings of the items themselves. Lisa has 5 lollies and Tim has 2 lollies. How many lollies do they have altogether? Year One

  5. 0 1 2 3 4 5 6 7 8 9 10 The next step would be using a number line (with numbers already marked on it) 5 + 2 = 7 Year One Children would progress to drawing or completing their own number line to help solve a problem.

  6. Pictures to represent number of items • Marks to represent number of items • Number lines to show steps added Children may be encouraged to draw their own number line with markers of their own choosing, e.g. Year Two 61 + 14 = 75 +10 +4 61 71 75

  7. As children begin to work with Tens and Units, they may add by partitioning one (or both) of the numbers. 23 + 12 = 23 + 10 + 2 Year Two = 33 + 2 = 35 At this stage the children may still need to jot these numbers down in this way, but this method provides the children with a strategy for adding pairs of 2 digit numbers mentally.

  8. I added 17 and 3 to get to 20, then 20 more to get to 40. • Number lines to show steps added • Partitioning one or both numbers Children may be given several numbers to add, and are encouraged to do this by finding pairs that make 10, or 20 4 + 8 + 16 + 2 = Year Three 20 + 10 = 30 Children will begin to explain their calculations verbally and in writing. 23+17 = 40

  9. Number lines to show steps added • Partitioning one or both numbers Children may be encouraged to break down the numbers they are adding, according to their value Year Four E.g. 358 + 73 = 300 + 50 + 8 70 + 3 300+120+ 11 = 431

  10. 3587 + 675 4262 By this stage, a lot of addition will be performed mentally, using various strategies – adding near doubles and adjusting, adding near numbers and adjusting, adding pairs that “bond”, adding Tens first, then Units. Children will also be working with larger numbers, of 4 digits or more. They will be encouraged to use the vertical method of adding, for speed, unless they need an expanded method to help them. Year Five Children will begin to use this same method to add simple decimal numbers and to add several numbers together.

  11. Mum is buying a new carpet. The carpet costs £480 but Mum must add on 12.5% to the price to have it fitted. How much does it cost to have the carpet fitted? Children will add using the same methods as Year 5 (although some children might still need the support of more visual methods taught further down the school). Although the methods remain the same, the range of whole numbers and decimal numbers they work with will become more complex, as will the nature of the addition problems they are asked to solve. Year Six

  12. Development of Subtraction Again, pictures are used to illustrate what is happening to the numbers. Sam spent 4p. What was his change from 10p? Year One

  13. The next step in subtracting would be using a marked number line. Year One 0 1 2 3 4 5 6 7 8 9 10 What is the difference between 3 and 8?

  14. Children in Year Two continue to use pictures or marks to represent subtraction problems. They also use number lines; beginning with numbered lines they progress to partly-numbered lines, using them to “count up” from the smaller number to the larger one. Year Two 43 – 28 = 15 +2 +10 +3 40 43 28 30

  15. Until children are able to perform these calculations mentally, they will record their thinking in the form of number lines or jottings. Children will also be encouraged to develop strategies for subtracting numbers mentally: • Subtract by partitioning 37 – 12 = 37 – 10 (=27) – 2 = 25 Year Two • Subtract by rounding and compensating 34 – 9 = 34 – 10 (=24) + 1 = 25

  16. I did 50 – 30 then added 1 back on. By Year Three, children will generally be using numbers too large for pictures to be efficient, but they will be using the same methods taught previously, and often using a number line. • Counting up • Partitioning • Compensating Year Three By this stage children will also be expected to explain the strategies they have used. 50 – 29 = 21

  17. 0.5 – 0.31 = ? Subtraction in Years 4, 5 and 6 will be based on the same principles taught previously, but will be applied to higher numbers and more complex problems. There will also be more emphasis on the importance of applying these strategies to solve problems mentally. Years 4 5 6 • Counting up • Partitioning • Compensating

  18. Development of Multiplication Pictures and marks will be used to represent the problem. Year One There are 3 sweets in each bag. How many sweets are there in 5 bags?

  19. In addition to using pictures and marks to represent the problem, children will use number lines – numbered at first, progressing to empty ones of their own. 2 x 4 = 8 Year Two 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Children may also calculate multiplication as repeated addition: 2 x 4 = 2 + 2 + 2 + 2 = 8

  20. 0 Instead of pictures, children will use “arrays” – a simple form of diagram to represent the calculation. 4 x 3 = 12 Year Three Children may also continue to calculate multiplication as repeated addition, and to use partially numbered lines: 3 x 6= 18 6 12 18

  21. 161 x 20 3 7 161 By Year 4, written multiplication will be taught using the “grid method”, which children will continue to use throughout the school. 23 x 7 = Year Four 140 21 140 + 21 =

  22. x 70 2 • 8 In Years 5 and 6, the grid method will be extended for use with larger numbers (as well as development of mental calculations. The expectation is that children will be able to recall multiplication facts up to 10 x 10, quickly.) 72 x 38 = Years 5 and 6 2100 + 60 = 2160 560 + 16 = 576 2160 + 576 = 2100 60 560 16 Children will increasingly be expected to estimate the size of their answers before calculating. 2736

  23. Development of Division Pictures and marks will be used to represent the problem. Year One 12 children get into teams of 4 to play a game. How many teams are there?

  24. 0 1 2 3 4 5 6 7 8 Again, pictures will develop into simpler marks used to represent the problem. 6 eggs fit into a box. How many boxes would you need to pack 24 eggs? Children may use prepared number lines, or draw their own, jumping in steps and counting how many jumps they have used. (This clearly demonstrates the link between multiplication and division.) Year Two 8 ÷ 2 = 4

  25. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 As for the other areas of Maths, children will need to be able to explain how they have solved problems. I know that 23 and 23 is 46, so 46 ÷ 2 must be 23. In Year 3, children will use the same methods, but may encounter “remainders” with their answers. 13 ÷ 3 = 4 r1 8 children can travel in a minibus. How many minibuses would be needed to take 29 children to a football match? Year Three

  26. Year 4 children will continue to calculate division by sharing and grouping. They may also calculate division by using their repeated addition strategies. 72 ÷ 5 = 5 +5 +5 +5 +5 +5 +5 +5 +5 +5 +5 +5 +5 +5 (=70) 14 r 2 Year Four They may still use arrays and other jottings to help them. 16 ÷ 4 = 4

  27. 0 Children are now encouraged to use faster methods of division to cope with larger numbers. 198 ÷ 6 = 33 10 groups 10 groups 10 groups 3 groups 60 120 180 198 Years 5 and 6 They will also begin to write the remainders as either a fraction or a decimal. 27 ÷ 4 = 6¾ or 6.75

  28. Useful maths websites: • http://mathsblog.co.uk/ • http://www.bbc.co.uk/schools/websites/4_11/site/numeracy.shtml • http://nrich.maths.org • http://www.leics.gov.uk/index/education/support_for_schools/sips/aandi-supportteams/ais-primaryimprovementstrategy/ais-numeracy/lgfl_numeracy/lgfl_numeracy_parents.htm

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