Mental Strategies in Key Stage 1 Wednesday 27th February 2019

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.

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?

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.

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)

Principles Addition and subtraction are inverses Addition is commutative i.e. 5 + 3 = 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 = 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

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

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

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

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

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

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

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

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.

Examples 8 + 3 – doesn’t need reordering as the greater number is first 2 + 7 – reorder to 7 + 2 5 + 13 – reorder to 13 + 5 11 + 6 – doesn’t need reordering as the greater number is first

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

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

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

Addition 34 + 20 = 54 Concrete – base 10 Model – beadstring Abstract – blank number line Mental – 34 + 10 = 44 + 10 = 54 (counting on in 10s from any number)

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

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

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 = 3 40 + 3 = 43 2. Count back in tens then units 66 – 20 = 46 46 – 3 = 43

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)

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

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

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.

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

Continued… 2. Repeated addition 4 + 4 + 4 + 4 + 4 5 + 5 + 5 + 5 3. Multiplication 4 x 5 or 5 x 4 4. Mental strategy Count in fives 4 times

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.

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

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

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

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

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

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

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

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.