1. Mental Strategies in Key Stage 1
Wednesday 27th February 2019

2. Essential skill
The ability to calculate mentally is an essential skill, but, as with written methods of calculation, children need to be taught. It can make reaching the answer to a difficult question or problem much quicker.

3. Questions the children must ask themselves
Children should be taught and encouraged to ask themselves the following questions when faced with a calculation:
Do I know the answer?
Can I work it out in my head?
Do I need to do a jotting/drawing?
Do I need to use a written method?

4. Which method is best?
A feature of mental calculation is that a type of calculation can often be worked out in several different ways. Which method is best will depend on the numbers involved, the age of the children and the range of methods that they are confident with.

5. Addition and subtraction
It is important that children understand the relevant concepts, in that addition is:
Combining two or more groups to give a total or sum
Increasing an amount
and subtraction is:
removal of an amount from a larger group (take away)
Comparison of two amounts (difference)

6. Principles Addition and subtraction are inverses
Addition is commutative i.e = 3 + 5
Subtraction is NOT commutative i.e. 5 – 3 is not the same as 3 – 5
Addition is associative i.e = 5 + (3 + 7) but subtraction is not i.e. 10 – 3 – 2 is not the same as 10 – (3 – 2)
Commutativity and associativity means that calculations can be rearranged

7. YEAR 1 - addition and subtraction
Children in Year 1 should be taught strategies through progression of the following method: Concrete  Model Abstract

8. Rapid recall in Year 1 Children should be able to:
Represent and use number bonds and related subtraction facts within 20
Double numbers to 10
Know the corresponding halves of numbers up to 20
This will ensure some mental calculations can be solved much quicker

9. Addition
7 + 3 = 10 Concrete – counters Model – beadstring Abstract – number line Mental – 7 in your head and count on 3 more OR use their knowledge of number bonds and already know that the answer is 10

10. Addition
8 + 5 = 13 Concrete – counters Model – beadstring Abstract – number line Mental – put 8 in your head and count on 5 more

11. Subtraction
5 – 2 = 3 Concrete – counters – touch count and remove the number to be taken away, in this case 2 then touch count to find the number that remains Model – beadstring – slide along the number to be taken away and count the remaining beads

12. Continued…
Abstract – number line – count back along the number line to land on the answer Mental – put 5 in your head and count back 2

13. Subtraction
13 – 5 = 8 Concrete – counters Model – beadstring Abstract – number line Mental – put 13 in your head and count back 5

14. Reorder numbers in a calculation
Children in year 1 need to recognise that they can rearrange an addition, but not a subtraction. They also need to understand that the principle behind reordering a calculation is to make it more efficient, particularly when utilising a counting on strategy. Children need to be encouraged, through teaching, which calculations should be reordered and those that are already in the most efficient format.

15. Examples
8 + 3 – doesn’t need reordering as the greater number is first – reorder to – reorder to – doesn’t need reordering as the greater number is first

16. YEAR 2 – addition and subtraction
Again, children should be taught the skills using the progression steps: Concrete  Model Abstract

17. YEAR 2 - rapid recall Children should be able to:
Recall and use addition and subtraction facts to 20 fluently
Derive and use related facts up to 100

18. Addition
= 37 Concrete – base 10 Model – beadstring Abstract – number line Mental – put 34 in your head and count on 3 more

19. Addition
= 54 Concrete – base 10 Model – beadstring Abstract – blank number line Mental – = = 54 (counting on in 10s from any number)

20. Adding three 1 digit numbers
= 12 Children should recognise that two of the numbers in this number sentence make 10 (4+6) so therefore 10 + the remaining 2 is = 16 Same with this calculation – 2+8 make 10

21. Subtraction
47 – 4 = 43 Concrete – base 10 Model – beadstring Abstract – blank number line Mental – 47 in your head and count back 4

22. Subtraction
66 – 23 = 43 Concrete – base 10 Model – beadstring Abstract – blank number line Mental 1. split the numbers into tens and units 60 – 20 = 40 6 – 3 = = Count back in tens then units 66 – 20 = – 3 = 43

23. Multiplication and Division
In developing a progression through mental calculation strategies for multiplication and division, it is important that children understand the relevant concepts, in that multiplication is:
Repeated addition
and division is:
Repeated subtraction (grouping)
Related to finding a fraction of a number (sharing)

24. Multiplication and Division
Children also need to understand that:
Multiplication and division are inverses
Multiplication is commutative i.e. 3 x 5 = 5 x 3 but division is NOT i.e. 15  3 is not the same as 3  15

25. YEAR 1 – rapid recall Children should be able to:
Count in multiples of twos, fives and tens
Recall and use doubles of all numbers to 10 and corresponding halves

26. YEAR 1 - multiplication
In Year 1, children will begin to solve multiplication number sentences using arrays and practical equipment. E.g. baking trays, egg boxes, wrapping paper etc. The children will learn that multiplication is repeated addition. They should also learn that if you multiply a number by 2, it is the same as doubling.

27. Multiplication 4 x 5 = 20 Arrays to represent the number sentence
 4

28. Continued…
2. Repeated addition Multiplication 4 x 5 or 5 x 4 4. Mental strategy Count in fives 4 times

29. YEAR 1 - division
In Year 1, children will use practical equipment and jottings to solve division calculations. The children will learn that division is grouping and sharing. Children should also learn that if you divide a number by 2, it’s the same as halving.

30. Division
12  2 = 6 1. Practical equipment e.g. 12 sweets and 2 children – share them out equally 2. Jottings Draw 12 peas and 2 plates – share them out equally 3. Mental 12  2 is the same as half of 12

31. YEAR 2 – rapid recall Children should be able to:
Count in steps of 2, 3 and 5 from 0
Recall and use multiplication facts for the 2, 5 and 10 times tables
Derive and use doubles of simple two-digit numbers (numbers in which the ones total less than 10)
Derive and use halves of simple two-digit numbers (numbers in which the tens are even)
Recognise odd and even numbers

32. YEAR 2 - multiplication
There should be consolidation of multiplication being repeated addition through a range of methods.
Practical equipment
Arrays
Jottings
Beadstring
Number line

33. Which method?
Examples: 5 x 4 – using commutativity to identify a recalled fact (changing it into 4 x 5) 3 x 10 – recalled fact 7 x 3 – using a representation from the methods previously discussed 2 x 9 – using knowledge that multiplying by 2 is doubling 6 x 6 – using a representation from the methods previously discussed

34. YEAR 2 - division
There should be consolidation of division being repeated subtraction through a range of methods:
Practical equipment
Arrays
Jottings
Beadstring
Number line

35. Which method?
Examples: 16  4 – using a representation from the methods previously discussed 20  5 – recalled fact 40  10 – recalled fact 18  3 – using a representation from the methods previously discussed 12  2 – using knowledge that dividing by 2 is halving

36. How can you support your child at home?
Use the mental strategies covered this evening
Copies of the mental strategies policies are on the school website for your own viewing
Learn the 2, 5 and 10 times tables by heart (3 times tables if they already know these)
Practise number bonds to 10 and 20
Learn doubles and corresponding halves of numbers up to 20

37. Continued…
Give your child a number and ask them to make it in as many ways as possible using the four operations (+, -, x and )
Encourage your children to use maths wherever they are – shopping, clocks on walls, weighing when baking, different 2D and 3D shapes are all around us – maths is everywhere!
Have a positive attitude towards maths and tell your child that they CAN solve a problem or a calculation.