1. Downton C of E Primary School Maths Calculation Policy

2. POLICY FOR CALCULATIONS Document Purpose This policy reflects the values and philosophy of Downton Primary School in relation to the teaching and learning of Calculations in Mathematics. It sets out a framework within which all staff, both teaching and non-teaching, work. It gives guidance on planning, teaching and assessment. Audience This policy, having been presented to and agreed upon by the teaching staff and the Governing Body, is for the use of all teaching staff and parents. Introduction Each of the four operations build on mental skills which provide the foundations for jottings and informal written methods of recording. Skills need to be taught, practised and reviewed constantly. These skills lead on to more compact written methods of calculation. Children need to build up a repertoire of increasing complexity. When teaching a new strategy, it is important to start with numbers that the child can easily manipulate so that they understand the concept. The transition between stages should not be hurried as not all children will be ready to move on to the next stage at the same time. Therefore the progression in this document is outlined in stages, which are not necessarily fixed to particular year groups. Previous stages may need to be revisited to consolidate understanding when introducing a new strategy. It is far better that children understand how to use an expanded method than are rushed into using a contracted method. A sound understanding of the number system is essential for children to carry out calculations Strategies for calculation need to be supported by familiar models and images to reinforce understanding.

3. Addition Mental Skills Recognise the size and position of numbers Count on in ones and tens Know number bonds to 10 and 20 Add multiples of 10 to any number Partition and recombine numbers Bridge through 10 Models and Images Counting apparatus Place value apparatus Number lines Empty number lines Counting stick Bead string ITPs–Number Facts, Ordering Numbers, Number Grid, Counting on and back in ones and tens Vocabulary Add, addition, plus, and, count on, more than, sum, total, altogether, increase one more, ten more, Early Experiences Combine two sets of objects practically, using cubes/counters etc. Draw objects Number sentence with objects drawn. Partition numbers to 10. Record: 5=3+2 2+2 +1=5 Nb. number lines are not appropriate here It is important that the children have a good understanding of place value and partitioning using real objects, resources and visual images to support calculations

4. Stage 1 Know by heart all pairs of numbers with a total of 10 (number bonds to 10 Put the biggest number first and count on. 8 + 7 = 15 Stage 2 (Know number bonds to 20) Add 3 or more single digit numbers. 8 + 7 + 3 = Partition two digit numbers using tens and ones. Jump along marked and then empty number lines (start by counting on in 10s and then progress to multiples of 10. Or use 100 squares.

5. Stage 3 Partitioning method 48+36= 40 + 30 + 8 + 6 40 + 30 = 70 8 + 6 = 14 70 + 14 = 84 40+ 8 30+ 6 70+14 = 84 48 +36 70 14 84 Eventually this will lead to the standard written method Stage 4 3 or more digit numbers This can now be extended to larger numbers It is far better that children work using the expanded method they understand rather than a more formal standard written method that they can not explain to you. 762 +453 = 700 +400 = 1100 60 + 50 = 110 2 + 3 = 5 1215 Standard written method 8462 + 753 9215 1 1

6. Stage 5 Children then use their chosen method to work with decimal numbers efficiently and accurately. 24.2 + 16.7 = 20 + 10 = 30 4 + 6 = 10 0. 2 + 0.7 = 0.9 40.9 Mental Skills Recognise the size and position of numbers Count back in ones and tens Know number facts for all numbers to 20 Subtract multiples of 10 from any number Models and Images Counting apparatus Place value apparatus Number lines Empty number lines. Counting stick Bead strings ITPs–Number Facts, Counting on and back in ones and tens, Difference Vocabulary take away, how many left? How many fewer than? How many more to make… count back, less than, fewer, difference between, subtract, minus, subtraction, decrease, Subtraction Early Experiences  Begin to count backwards  Practical taking away from a set of objects  Draw objects and cross out number taken away.  Number sentence with objects drawn.  Group of cubes on a tray, part of them covered and need children visualise the calculation.  Compare lengths of objects ready to find the difference

7. It is important that the children have a good understanding of place value and partitioning using real objects, resources and visual images to support calculation. Stage 1 Use the language ‘less than’. Stage 2 N.B. Help children decide whether to count on or back depending on the size of the difference. E.g. 56 – 7…count back. 85 – 62…count on. Count back in ones and then tens. Know by heart subtraction facts for numbers up to ten and 20. Big Maths means subtraction facts are learned by rote from KS2 Subtract single digit numbers often bridging through 10 Subtract multiples of 10 mentally but also show how to record using a number line.

8. Begin to find the difference by comparing 2 lines Find a small difference by counting up from the smallest number Find the difference by counting on. 32 – 26 = 6 Extend the size of numbers Jump along the empty number line using boundary numbers or multiples of 10. 74-27= 47 Stage 3 Optional Additional method (for children working in upper KS2 at level 3 and above)

9. 7 4 4 2 8 6 1316 4 5 8 Leading to: Created by the school staff on December 3 rd 2012

10. Multiplication Mental Skills Recognise the size and position of numbers Count on in different steps 2s, 5s, 10s Double numbers up to 10 Recognise multiplication as repeated addition Quick recall of multiplication and division facts/ fact families Multiplying by 10, 100, 1000 and understanding the effect Multiplying by multiples of 10 Resources, Models and Images Counting apparatus Place value apparatus Arrays e.g. egg boxes, windows drawer units. Multiplication squares Number lines Counting stick Bead strings ITPs–Multiplication grid, Number Dials, Multiplication Facts, Array Creator Squared paper lino or wallpaper with squares on- for grid method.. Vocabulary lots of, groups of, multiply, multiplication, multiple, product, once, twice, three times, array, row, column, double, repeated addition, times, 10 times as big/long/high etc. Fact families, switcher, smile multiplication Stage 1 Counting in 2s, 5s and 10s

11. Stage 2 Repeated addition 4 lots of 2 make 8 Stage 3a Multiplication as an array Number line Arrays Grouping Children are taught fact families- they understand Inverses and that 3x4 = 4x3 Stage 3b Introducing the Grid Method: X 4 103 4012 40 + 12 = 52

12. Stage 4 Multiplying TU x U This depends on the ability to multiply multiples of 10 together mentally 23 x 4 80 + 12 = 92 X203 48012 Stage 5a Multiplying TU x TU 14 x 33 X303 10 4 30030 12012

13. Stage 5b Standard Written Method This is best when the numbers get bigger but the example shows 14x33 so that you can see where the numbers in the standard method come from. Extends to: Stage 6 This can now be extended to multiplying 3 digit numbers by 2 digit numbers and multiplication of whole numbers by decimals. Division Vocabulary lots of, equal groups of, shared equally, group, halve, half, divide, division, divided into, divided by, remainder, factor, quotient, divisible by, inverse Mental Skills Recognize the size and position of numbers Count back in different steps 2s, 5s, 10s Halve numbers to 20 Recognize division as repeated subtraction Quick recall of division facts Use known multiplication facts to derive associated division facts Divide by 10, 100, 1000 and understand the effect Divide by multiples of 10 Models and Images Counting apparatus Arrays Number lines Empty number lines. Multiplication squares ITPs–Multiplication grid, Number Dials, Grouping, Remainders 4 x 2 = 8 2 x 4 = 8 8 ÷ 2 = 4 8 ÷ 4 = 2 Stage 1 Practical sharing of objects with vocabulary of sharing not grouping. This may include a ‘leftover’

14. Stage 2 Understand division as grouping Link grouping to arrays Stage 3 Using a number line to record grouping up and to find any remainders. E.g. 18 ÷ 3 19 ÷ 3 Stage 4 Chunking This involves taking away known amounts of the divisor until the division is completed. Writing out a fact box for the divisor will help. e.g. 68 ÷ 5 5 68 Take away 50 (10 x 5) 18 Take away 15 (3 x 5) 3 Answer = 10 + 3 = 13 r 3 Fact box 1 x 5 = 5 2 x 5 = 10 5 x 5 = 25 10 x 5 = 50 20 x 5 = 100 50 x 5 = 250 Stage 5 This can now be extended to larger numbers (HTU by TU) and decimals divided by a single digit. Many children will be able to use the standard written ‘Bus shelter’ method. 5 6 8 1 1 3 r3