+

Gorse Ride Schools Calculation Policy

ADDITION

SUBTRACTION

MULTIPLICATION

DIVISION

Children are given many opportunities to practise using given resources and strategies and will not be moved on to new methods until they are fluent in current ones. They also revisit previous strategies as and when appropriate. It is important that children experience a range of concrete materials such as Numicon, pictures, toys, to help them understand a concept before moving onto a more abstract format, such as number lines and 100 squares. OBJECTIVES  Children count reliably with numbers from one to 20, place them in order and say which number is one more than a given number.  Using quantities and objects, they add two single-digit numbers and count on to find the answer. STRATEGIES/RESOURCES 

OBJECTIVES  Children count reliably with numbers from one to 20,place them in order and say which number is one less than a given number.  Using quantities and objects, subtract two single-digit numbers and count STRATEGIES/RESOURCES  Take away a number from a group and count what is left.

Counting two groups by counting ALL.

Foundation Stage



Counting two groups by counting ON from the larger number.



Numicon



Counting objects



Counting objects



Subtraction facts up to and including 10



Singing number rhymes & songs

OBJECTIVES  They solve problems, including doubling, halving and sharing. STRATEGIES/RESOURCES 

Singing number rhymes & songs



Doubling and sharing in games and role play

+

Gorse Ride Schools Calculation Policy



Year 1



Number bonds up to and including 10



Singing number rhymes & songs



Addition in games and role play

OBJECTIVES  given a number, identify one more  identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, most,  read, write and interpret mathematical statements involving addition (+) and equals (=) signs  add one-digit and two-digit numbers to 20, including zero  represent and use number bonds and

Subtraction in games and role play

OBJECTIVES  given a number, identify one less  identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, less than (fewer), least  read, write and interpret mathematical statements involving subtraction (–) and equals (=) signs  subtract one-digit and two-digit numbers to 20, including zero

OBJECTIVES  solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher. STRATEGIES/RESOURCES 

Counting on in 2s, 5s, 10s.

+

Gorse Ride Schools Calculation Policy related subtraction facts within 20 solve one-step problems that involve addition using concrete objects and pictorial representations, and missing number problems such as 7 = – 9.



STRATEGIES/RESOURCES  Start with larger number and count on





Find biggest number on number line and move on the correct number of jumps.

 

represent and use number bonds and related subtraction facts within 20 solve one-step problems that involve subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = – 9.

STRATEGIES/RESOURCES  Start with larger number and count back (moving on to bridging 10)



Jumping on in 2s, 5s, 10s on number track/ 100 square



Model multiplication with a range of practical, real life resources



Number stories



Recall of doubles and halves to 10.

Using prepared number lines 



Use resources to ‘take away’ from the larger number

Beadstrings



Mental recall of number bonds up to and including 20.



Number stories (problems)



Numicon to represent calculations

 Counting ON to find the difference 12 – 9 =



Numicon to represent calculations

+

Gorse Ride Schools Calculation Policy

ADDITION

Year 2

OBJECTIVES  applying their increasing knowledge of mental and written methods  recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100  add and subtract numbers using concrete objects, pictorial representations, and mentally, including: -a two-digit number and ones -a two-digit number and tens -two two-digit numbers -adding three one-digit numbers  show that addition of two numbers can be done in any order (commutative)  recognise and use the inverse relationship between addition and subtraction and use this

SUBTRACTION



Division as sharing in real life contexts



Division as grouping in real life contexts

MULTIPLICATION

DIVISION

OBJECTIVES  recall and use multiplication facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers  calculate mathematical statements for multiplication within the multiplication tables and write them using the multiplication (×) and equals (=) signs  show that multiplication of two numbers can be done in any order (commutative)  solve problems involving multiplication, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

OBJECTIVES  recall and use division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers  calculate mathematical statements for division within the multiplication tables and write them using the division (÷) and equals (=) signs  show that division of one number by another cannot be done in any order  solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts. STRATEGIES/ RESOURCES  Sharing equally

+

Gorse Ride Schools Calculation Policy to check calculations and solve missing number problems. STRATEGIES/ RESOURCES  Using prepared number lines



Using a partially prepared or empty number line, e.g. 9 + 5

-to count on in 1s, 10s, multiples of 10, bridging 10



Partition 2 digit numbers to add. (only crossing the tens when ready) 34 + 15 = 30 + 10 = 40 4+5=9 40 + 9 = 49 

Use 100 square to

OBJECTIVES  applying their increasing knowledge of mental and written methods  recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100  add and subtract numbers using concrete objects, pictorial representations, and mentally, including: -a two-digit number and ones -a two-digit number and tens -two two-digit numbers  show that subtraction of one number from another cannot (be done in any order)  recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. STRATEGIES/ RESOURCES  Using prepared, partially prepared and empty number lines -to count back in 10s and ones

-to count 10s and ones in one jump

STRATEGIES/ RESOURCES  Repeated addition (on number line, 100 square, bead string etc)



Arrays



Grouping



Repeated subtraction

+

Gorse Ride Schools Calculation Policy consolidate 

Concrete resources (Numicon, counters, etc) available.

-to bridge through 10

-to count on/ up 23 – 18 =

Children continue to learn using resources and models and images in Lower and Upper KS2 to help develop conceptual understanding

Year 3

Consolidation of mental methods

Consolidation of mental methods

Expanded column addition for TU + TU, HTU + TU and HTU + HTU where necessary .

Expanded column subtraction with decomposition for HTU – TU and HTU – HTU where necessary

458 + 373 700 120 11 831

457 – 226 = 231 400 + 50 + 7 200 + 20 + 6 200 + 30 + 1 =231

Using objects and other models and images including arrays and number lines to multiply and its relation to scaling. Consolidation of mental methods including using knowledge of number facts to derive related facts of TU x U : If 2 x 3 = 6 then 2 x 30 = 60

Consolidation of mental methods including using knowledge of number facts to derive related facts of TU ÷ U: For example, using 3 × 2 = 6 and 6 ÷ 3 = 2 to derive related facts (for example, 30 × 2 = 60 and 60 ÷ 3 = 20) Use number lines to calculate TU ÷ U where appropriate (including remainders) by asking “How many groups of U are in TU?” and chunking on in groups of U (inverse – repeated addition)

+

Gorse Ride Schools Calculation Policy Consolidation of mental methods

Consolidation of mental methods

Column addition up to 4 digits

Expanded column subtraction with decomposition up to 4 digits

1458 + 3473 2931

Year 4

2457 – 1229 =

11

40

Consolidation of mental methods Grid multiplication (using arrays as starting point) for HTU x U and TU x U and TU x TU Grid method - 72 x 38 is approximately 70 x 40 = 2800

1

2000 + 400 + 50 + 7 1000 + 200 + 20 + 9 1000 + 200 + 20 + 8

x 30 8

Use number lines to calculate TU÷U or HTU ÷U using chunks of 10 30 ÷ 6 can be modelled as: grouping – groups of 6 taken away and the number of groups counted e.g.

70 2 2100 60 560 16

= 1228

Year 5

Consolidation of mental methods

sharing – sharing among 6, the number given to each person

Consolidation of mental methods

Consolidation of mental methods

Consolidation of mental methods Consolidate grid method

Compact column addition including: Numbers up to 5 digits Same number of decimal places Different number of decimal places

Column subtraction with decomposition for subtracting whole numbers and numbers with the same decimal places

Consolidate using number lines to Short multiplication for multiplying chunk groups on a number line for numbers up to 4 digits with U TU÷U

2457.6 – 1229.8 = 14584 +34734 293 18 1 1

3 4 6. 6 7 + 4 2 3. 4 7 7 0. 0 7 1

1

40

16 1

2000 + 400 + 50 + 7 . 6 1000 + 200 + 20 + 9 . 8 1000 + 200 + 20 + 7 . 8 = 1227.8

Grid method - 372 x 24 is approximately 400 x 20 = 8000

x 20 4

300 70 2 6000 1400 40 1200 280 8

1223 × 5 6115 1 1 1

Consolidation of mental methods

Short division for TU ÷ U Calculations with no “carrying” (e.g. 96 ÷ 3) Calculations with “carrying” (e.g. 72 ÷ 3) Calculations with “carrying” and remainders (e.g. 5309 ÷ 8) 2 42 3 712 6

+

Gorse Ride Schools Calculation Policy Consolidation of mental methods Compact column addition to add several numbers of increasing complexity

Year 6

Consolidation of mental methods Compact column subtraction with decomposition to subtract numbers of increasing complexity including numbers with different number of decimal places

4 1 2 4. 9 2 3 1 6. 8 9 + 2 2 1. 2 5 6 6 6 5. 0 4 1

2

Consolidation of mental methods Short multiplication to multiply numbers with up to 2 d.p by U

1223.65 × 5 6118.25 1 1 1 3

19457.6 – 5229.8 = 16

15 1

59457.60 - 25229. 85 3 4 2 3 7 .7 5

Consolidation of mental methods Consolidate short division Long division for the higher achievers with TU as divisors

2

Long multiplication for multiplying numbers up to 4 digits and numbers up to 2 decimal places by TU

×

= 34237.75

1223.65 25 6118.25 1 1 1 3

2

244 73.00 1 1

=

30591 .25

Appendix 1 – Mental Strategies

Foundation Stage

ADDITION

SUBTRACTION

MULTIPLICATION

DIVISION

Children are encouraged to develop a mental picture of the number system through activities such as: 1. Counting – forwards from zero and/or on from a given number 2. Comparing two numbers to find one more 3. Ordering numbers from smallest to largest 4. Combining two groups of objects (or two single digit numbers) to find how many altogether; counting all, counting

Children are encouraged to develop a mental picture of the number system through activities such as: 1. Counting – backwards to zero and/or back from a given number 2. Comparing two numbers to find one less 3. Ordering numbers from largest to smallest 4. Taking a group of objects from a given set to find how many are left; counting out

Children are encouraged to develop a mental picture of the number system through activities such as: 1. Counting – in ones, twos, fives and tens 2. Sharing objects into equal groups and then counting how many in each group 3. Using and discussing the vocabulary involved in multiplication

Children are encouraged to develop a mental picture of the number system through activities such as: 1. Counting – in ones, twos, fives and tens 2. Sharing objects into equal groups and then counting how many in each group 3. Using and discussing the vocabulary involved in

+

Gorse Ride Schools Calculation Policy

5.

Year 1

on from the first number, counting on from the biggest number Observing number relationships and patterns in the environment to help derive facts

Children should be able to use the following strategies, as appropriate, for mental calculations: 1. Counting forwards: 4 + 8 count on in ones from 4 or 8 13 + 4 count on from 13 2. Reorder numbers in a calculation: 2+7=7+2 1+6=6+1 3. Begin to bridge through 10, when adding a single digit number: 9+5= 8+4= 4. Use known number facts and place value to add pairs of single digit numbers: 3+2=6+4= 5. Add 9 to a single digit number by adding 10,then subtracting 1(compensating): 4 + 9 = 4 + 10 – 1 = 6. Identify near doubles, using doubles already known: 4 + 3 = (3 + 3) + 1 5 + 6 = (5 + 5) + 1 Children need to know that doubling is adding the same number to itself 7. Use patterns of similar calculations: 4+2= 14 + 2 = 24 + 2 =

5.

Observing number relationships and patterns in the environment to help derive facts

Children should be able to use the following strategies, as appropriate, for mental calculations: 1. Counting backwards: 7 - 3 count back in ones from 7 (a given number) 15 - 3 count back in ones to 3 (a given number) 18 – 6 count back in twos 2. Reorder numbers in a calculation: It is important for children to know when numbers can be reordered (e.g. 2 + 5 + 8 = 8 + 2 + 5 and when they cannot (e.g. 8 – 5 ≠ 5 – 8). 3. Find a small difference by counting up (on) from the smaller to the larger number: 25 – 19 = 17 – 14 = 4. Use known number facts and place value to subtract pairs of single digit numbers: 6-4= 9–3= 5. Add 9 to a single digit number by adding 10, then subtracting 1: 6 + 9 = 6 + 10 – 1 = 6. Identify near doubles, using doubles already known: 12 + 11 = 11 + 11 + 1 or 12 + 12 - 1 7. Use patterns of similar calculations: 10 – 0 = 10 10 – 1 = 9 10 – 2 = 8

4.

Observing number relationships and patterns in the environment to help derive facts

Children should be able to use the following strategies, as appropriate, for mental calculations: 1. Counting forwards: Count in twos – 2, 4, 6, 8, …to 20 Count in fives – 5, 10, 15, 20, … to 20 or more Count in tens – 10, 20, 30, … to 50 or more 2. Doubling: 7 + 7 is double 7 Double 7 = 14

division 4. Observing number relationships and patterns in the environment to help derive facts Children should be able to use the following strategies, as appropriate, for mental calculations: 1. Counting backwards: In twos – 10, 8, 6, … 0 In tens – 50, 40, 30, … 0 2. Halving: 10 shared by 2 is 5 Half 10 = 5

+

Gorse Ride Schools Calculation Policy

Year 2

Children should be able to use the following strategies, as appropriate, for mental calculations: 1. Count on in ones or tens: 15 + 4 = 5 + 30 = 2. Reorder numbers in a calculation: 2 + 15 = 15 + 2 4 + 13 = 13 + 4 3. Add three small numbers by putting the larger number first and/or finding a pair totalling 10: 4+8+2=8+2+4 7+6+3=7+3+6 4. Partition additions into 10’s and ones then recombine: 23 + 14 = 20 + 10 = 30, 3 + 4 = 7, 30 + 7 = 37 5. Bridge through 10 or 20: 6+5= 16 + 7 = 6. Use known number facts and place value to add pairs of numbers: 42 + 3 = ? + 4 = 34 7. Partition into ‘5 and a bit’ when adding 6, 7, 8, 9, then recombine: 25 + 8 = 25 + 5 + 3 = 33 8. Add 9, 19, 11, 21, by rounding up and compensating: 23 + 9 = 23 + 10 – 1 34 + 11 = 34 + 10 + 1 6 9. Identify near doubles: 8 + 9 = (8 + 8) + 1 11 + 12 = (11 + 11) + 1 10. Use patterns of similar calculations: 4+3=7 40 + 30 = 70 400 + 300 = 700 11. Use the relationship between addition and subtraction (Inverse): 15 + 4 = 19

Children should be able to use the following strategies, as appropriate, for mental calculations: 1. Counting on / backwards: 27 – 4 count on or back in ones from any two digit number 18 – 4 count back in twos from 18 46 – 30 count back in tens from 46 2. Find a small difference by counting up (on) from the smaller to the larger number: 33 - 28 = 74 – 68 = 3. Reorder numbers in a calculation: It is important for children to know when numbers can be reordered (e.g. 2 + 36 = 36 + 2 and when they cannot (e.g. 36 – 2 ≠ 2 – 36). 4. Partition subtractions into 10’s and ones and then recombine: 78 – 40 = 70 - 40 + 8 5. Bridge through 10 or 20: 14 - 6 = 28 - 9 = 6. Use known number facts and place value to subtract pairs of numbers: 20 - 16 = 20 - ? = 16 7. Subtract 9, 19, 11, 21, by rounding up and compensating: 42 - 19 = 42 - 20 + 1 64 - 21 = 64 - 20 – 1 8. Identify near doubles: 13 + 14 = Double 14 and subtract 1 or double 13 and add 1 40 + 39 = Double 40 and subtract 1 9. Use patterns of similar calculations: 4 - 3 =1 14 - 3 =11 24 - 3 =23 7 10. Use the relationship between addition and subtraction (Inverse): 27 - 13 = 14

Children should be able to use the following strategies, as appropriate, for mental calculations: 1. Counting on forwards: Count in fives – 5, 10, 15, 20… The 2 times table up to 2 x 10 The 10 times table up to 10 x 10 2. Use knowledge of number facts and place value to multiply by 2, 5 or 10: 3x2= 4x5= 5 x 10 = 3. Doubling: 7 + 7 = 7 x 2 Children need to understand that doubling is multiplying by 2

Children should be able to use the following strategies, as appropriate, for mental calculations: 1. Counting backwards: In fives – 30, 25, 20, … 0 Division facts for the 2, 5 and 10 times tables 2. Use knowledge of number facts and place value to multiply and divide by 2, 5 or 10: 9 x 2 = 4 x 5 = 7 x 10 = 18 ÷ 2 = 20 ÷ 5 = 70 ÷ 10 = 3. Use doubles and halves and halving as the inverse of doubling: 7 + 7 = 7 x 2 half of 14 is 7 14 ÷ 2 Children need to understand that halving is dividing by 2

+

Gorse Ride Schools Calculation Policy 19 – 4 = 15 12. Use doubles and halves, and halving as the inverse of doubling: Double 12 (12 + 12) = 24, therefore what is half of 24? 13. Bridging through 60 to calculate a time interval: What will be the time 20 minutes after 8.50? (not 8.70) 8.50 + 10 minutes = 9.00 9.00 + 10 minutes = 9.10

14 + 13 = 27 11. Use doubles and halves, and halving as the inverse of doubling: Double 16 (16 + 16) = 32, therefore what is half of 32?