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2 This policy contains the progression in calculation procedures that are taught throughout Busbridge Infant School. It emphasises the importance in calculating mentally as well as focusing on writing procedures. Mental calculation is complementary to written recording as in every written method there is an element of mental processing. Written recording helps the children clarify their thinking. The understanding of the number system starts with counting. It is a tool for calculation strategies. The key aspects of number are ‘nominal’ (number as labels), ‘ordinal’ (order of numbers and 1 to 1 correspondence) and ‘cardinal’ (the final number is how many in a set). Each of the four operations (addition, subtraction, multiplication and division) builds on mental skills e.g. number bonds, doubles, counting in different steps etc, which provide the foundation for jottings and informal written methods of recording. Strategies for calculation need to be supported by familiar models, images and practical activities to reinforce understanding. A sound understanding of the number system is essential for children to carry out calculations efficiently and accurately. The long term aim is for children to be able to select the most efficient method that is appropriate for a given task. Introduction

11, 12, 13, 14, 15… there are 16 teddies Say some number names in familiar contexts; such as nursery rhymes Count reliably up to 20 everyday objects Order and write numbers up to 10 then up to 20 Recognise the numerals 1 – 9 then Say number names in order 5 currant buns… Count reliably up to 10 everyday objects 1, 2, 3… there are 3 teddies Numbers as Labels and for Counting Uses developing mathematical ideas and methods to solve practical problems There are 5 spots on this side and 5 on the other. They are the same!

Calculating Responds to the vocabulary involved in addition and subtraction in rhymes and games 5 little men in a flying saucer… Recognises the differences in quantity when comparing sets of objects This set has more Finds 1 more or one less from a group of up to 5 objects If 1 get 1 more cube then there will be 1,2,3,4…4 cubes Relates addition by combining two groups Relates subtraction to taking away Three teddies take away two teddies leaves one teddy

Calculating In practical activities begins to use the vocabulary involved in adding and subtracting We need 3 milks. We have 4 so I need to take one away Finds one more or one less than a number to 10 Uses developing mathematical ideas and methods to solve practical problems including sharing and halving There are 10 bricks. 5 for you and 5 for me Use a range of strategies for addition and subtraction including some mental recall of number bonds Look 5 and 5 make 10.

Progression in Teaching 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 using place value Bridge through 10 Doubles and halves Models, Images and apparatus Place value apparatus - Dienes Arrow/ place value cards Number tracks Numbered number lines Marked but unnumbered number lines Empty number lines Hundred square Counting stick Bead string Models and Images charts Key Vocabulary add addition plus and count on more sum total altogether increase 408

7 1, 2, 3, 4, 5, 6 … there are 6 cubes Read and write numbers from 0 to 20 then to at least 100 in numerals and in words Count reliably up to 10 then 20 everyday objects Find one more/one less than a number One more than three is four Begin to relate addition to combining two groups of objects Count in ones and tens Begin to use the + and = signs to record mental calculations in a number sentence = = 5 Count along a number line to add numbers together

8 Know doubles of numbers Put the biggest number first and count on Know by heart all pairs of numbers with a total of Begin to partition numbers in order to add

9 Know which digit changes when adding 1s or 10s to any number = = = Adding two two-digit numbers Counting in tens and ones Partitioning and recombining = Know by heart all pairs of numbers with a total of and how many more make 20?

10 Add near multiples of 10 to a 2 digit number by adding 10 and adjusting = =46 Adding two two-digit numbers (bridging through tens boundary) Using an empty number line OR Using place value cards and Dienes to partition numbers and recombine = = = = = = = = =15 Add two single-digit numbers that bridge 10

11 Progression in Teaching Subtraction Mental Skills Recognise the size and position of numbers Count back in ones and tens Know number bonds for all numbers to 20 and related subtraction facts Use the inverse of addition Subtract multiples of 10 from any number Partition and recombine numbers (only partition the number to be subtracted) Bridge through 10 Doubles and halves Models, Images and apparatus Place value apparatus - Dienes Arrow/place value cards Number tracks Numbered number lines Marked but unnumbered lines Hundred square Empty number lines Counting stick Bead strings Models and Images Charts Key Vocabulary Subtract Take away Minus Count back Less Fewer Difference between 408

12 Begin to count backwards in familiar contexts such as number rhymes or stories Continue the count back in ones from any given number Begin to relate subtraction to ‘ taking away ’ Find one less than a number Count back in tens Ten green bottles hanging on the wall … Five fat sausages frying in a pan … Three cubes take away two cubes leaves one cube Begin to use the – and = signs to record a number sentence using numbers up to 10 whilst still using practical resources = 2

13 Compare 2 sets to find numerical difference The difference between 8 and 5 is Maria had six sweets and she ate four. How many did she have left? Understand the operation of subtraction and use related vocab. Subtract numbers when solving problems involving up to 10 objects in a range of contexts = 2 Within the range say 1 or 10 less than any number Know by heart subtraction facts for numbers up to – 10 = 13 – 1 = 7 – 2 = 5

14 Begin to find the difference by counting up from the smallest number Subtract 10 from a two- digit number Subtract multiples of 10 from any number Begin to partition numbers in order to take away – – 43 – 20 = – 3 =

= 47 Count back Partition the number to be subtracted bridging through 10 Subtract single digit numbers bridging through = =10 10=2= = = =47 Decide whether to count up from the smaller number or count back depending on the difference between the two numbers = 7 Count up Subtract mentally a near multiple of 10 from a 2 digit number 56 – 21 = = =35 Know by heart subtraction facts for numbers up to 20

16 Progression in Teaching Multiplication Mental Skills Recognise the size and position of numbers Count on in different steps 2s, 5s and 10s Double numbers to 10 Recognise multiplication as repeated addition Represent multiplication as arrays Quick recall of multiplication facts in the 2, 5 and 10 times tables Use known facts to derive associated facts Multiplying by multiples of 10 Models, Images and apparatus Place value apparatus Arrays 100 squares Number tracks Numbered number lines Marked but unnumbered lines Empty number lines Multiplication squares Counting stick Models and Images charts Vocabulary Lots of Groups of Times Multiply Multiplication Multiple Product Once, twice, three times Array, row, column Double Repeated addition 408

17 Count in tens from zero Count in twos from zero Count in fives from zero Know doubles and corresponding halves to

18 Understand multiplication as repeated addition = 8 4 x 2 = 10 2 multiplied by 4 4 lots of 2 Understand multiplication as an array Understand how to represent arrays on a number line as repeated addition Know by heart facts for the 2,5 & 10 multiplication tables Tables spider x 5 6 x 5 = 302 x 5 = 10 8 x 5 = 40 3 x 5 = 15 4 x 5 = x 5 = 50 5 x 5 = 25

19 Use known facts to work out new ones Use known facts and place value to carry out mentally simple x calculations 7 x 2=14 2 x 7=14 Know that multiplication of two numbers can be done in any order Use place value apparatus to support the multiplication of U x TU 4 x 13=52 4x10=40 4x3= = Use place value apparatus to support the multiplication of U x TU alongside the grid method 4 x = 52

20 Progression in Teaching Division Mental Skills Recognise the size and position of numbers Count back in different steps 2s, 5s, 10s Halve numbers to 20 Recognise division as repeated subtraction Understand division as grouping or sharing Quick recall of division facts for the 2, 5 and 10 times tables Use the inverse of multiplication Use known facts to derive associated facts Divide by multiples of 10 Models, Images and apparatus Counting apparatus Arrays 100 squares Number tracks Numbered number lines Marked but unnumbered lines Empty number lines Multiplication squares Models and Images charts Vocabulary Lots of Groups of Share Shared between Group Divide Divide into Division Divided by Remainder Factor Quotient Divisible ÷ ÷ ÷ 408

21 Count back in tens Count back in twos Count back in fives ? Solve problems by sharing objects in a practical or role play context Give every bear a sweet – how many sweets do we need? Solving practical problems by sharing into equal groups Give each bear 2 sweets – how many sweets do we need?

22 Understand division as sharing Understand division as grouping Know halves to 20 and other simple fraction of numbers, objects and quantities Half of 6 is 3 ½ of 6 = 3 Quarter of 8 is 2 ¼ of 8 = etc…. 1,2,3,4,5 6,7,8,9,10 etc Represent ‘groups’ for division as repeated subtraction on a number line using apparatus alongside the line to include remainders 18 divided into groups of 3 18  3 =  3 =