Parent/Carer Workshop Lower KS2 – Mental Strategies February 2019

With any calculation, children should be taught to ask themselves: Do I just know the answer? Can I work it out in my head? Do I need a jotting? Do I need to use a written method? When using a jotting, there is no requirement to follow a particular method of recording

Addition and Subtraction Addition is: combining two or more amounts to give a total or a sum (the word ‘sum’ should only be used to refer to addition and not any calculation) Increasing an amount Subtraction is: Removal of an amount from a larger group (take away) Comparison of two amounts (finding difference)

Children also need to know that: Addition and subtraction are inverses Addition is commutative ie 5 add 3 is the same as 3 add 5 but subtraction is not so 5-3 is not the same as 3-5 Please remember that formal column addition and subtraction is not taught until Year 3

Addition and Subtraction End of Y3 objective – To add and subtract numbers mentally, including a three-digit number and ones, a three-digit number and tens and a three-digit number and hundreds End of Y4 objective – Add and subtract numbers mentally, including a three- digit number to or from a three-digit multiple of tens Partitioning of numbers is a core strategy for adding and subtracting pairs of numbers. They can either partition both of the numbers or keep the first number the same and partition the second number

For example, 37+16 30+10 is 40 7+6 is 13 so 40 +13 = 53 526+200 encourage counting on in hundreds 137+40 encourage counting on in tens 693-7 encourage counting back in ones 42-25 42-20 is 22 then 22 take 5 which is 17 Children can also subtract by counting on – this encourages knowledge of difference. It is useful for calculating change, time duration and efficient to use when numbers are close together such as 104-95 Empty number lines are useful to help children with these calculations (53-38=15) In order to use these strategies, children need a firm understanding of place value

Examples of calculations: 23+54 54+23 – put larger number first In Y3, children need to build on their knowledge gained in Y2 and continue to reorder calculations to make them more efficient. Efficiency is a crucial skill for children to learn and practise Examples of calculations: 23+54 54+23 – put larger number first 12+19+12 12+12+19 – use knowledge of doubles 6+8+4 6+4+8 – use number bonds to 10 70+50+30 70+50+30 – use knowledge of number bonds to 100

Adding and Subtracting by compensating and rounding Examples of calculations: 34+29 – see it as 34 +30 -1 96-39 – see it as 96-40 then add 1 273-59 – see it as 273-60 then add 1

In Y4, children need to build on the knowledge gained in Y3 to reorder to improve efficiency further Examples of calculations 18+6-8 should be reordered to 18-8+6 They should also see 150+270 as 15+27 then make it ten times bigger so 42 to 420

Finding differences by counting on Examples of calculations: 80-43 count on in tens from 43 then ones 504-180 count on in hundreds then tens then ones Children could use empty number lines to record this – this would be a mental jotting

Multiplication and Division It is important that children know: Multiplication is repeated addition Division is repeated subtraction (grouping) and related to finding a fraction of a number (sharing) They also need to know that multiplication and division are inverses and multiplication is commutative (so 3x5 is same as 5x3) but division is not

Lower KS2 Multiplication and Division objectives: End of Y3 objective: Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know End of Y4 objective: Use place value, known and derived facts to multiply and divide mentally, including: Multiplying by 1 and 0 Dividing by 1 Multiplying together three numbers

Year 3 and Year 4 Children should initially be using base 10 equipment to multiply by 10 and 100 They should then put the numbers into HTU columns and notice that each digit has moved one place to the left ie. Become ten times bigger, if multiplying by 10 We never say ‘ just add a zero’ as that is mathematically incorrect. Division is modelled in the same way except the numbers move one place to the right when dividing by 10 and two places to the right when dividing by 100

Dividing and Multiplying by 1 Children should realise, through investigation, that a calculating process is not necessary when dividing by 1. Any number that is divided by 1 will result in the number itself so 542 divided by 1 is 542 because any number shared into one group will result in that group having the whole quantity in it. Similarly, any number multiplied by 1 will be itself

Within known tables, use related facts to multiply and divide TO (ones) by a one-digit number – multiplication trios

Examples of calculations 7x8= 56 56 divided by 8 is 7 56 divided by 7 is 8 70x8 is 560 70x80 is 5600 700x800 is 560000 This encourages mental calculation and efficiency

Y4 – using related facts to multiply To multiply by 5, multiply by 10 then halve To multiply by 4, double then double again To multiply by 20, double then multiply by 10 They should develop this skill further by including decimals Example of calculation Double 7.6 would be double 7 then 0.6 to 1.2 then add to get 15.2

Multiply together three numbers 2x3x4 Start practically, for example, using counters 2 x 3 four times Once the child understands how the calculation works practically or pictorially, they should then be encouraged to choose an appropriate order for calculating based on the numbers involved. So 6 (2x3) x 4 = 24

Using partitioning to multiply TU by one-digit number Use the grid method – make the calculation using squared paper then they can become more abstract and calculate mentally using a grid Example of Calculation: 30x4=120 31x4=124 36x6 so 30x6 is 180 and 6x6 is 36 then add 180 and 36 to get 216

Use compensation to multiply by 19 Encourage the child to multiply by 20 then take off one ‘lot’ of the number (or more) Example of calculations 19x4 Calculate 20x4 then subtract 1x4 19x8 Calculate 20x4 then subtract 2x4

Doubling through partitioning Doubling is also x2 Double 76 Partition 76 into 70 and 6 Double 70 to get 140 Double 6 to get 12 Add together 140 and 12 to get 152 Halving can be done the same way so half of 146, halve 140 to get 70 then halve 6 to get 3 then add 70 and 3 to get 73

How to support your child at home Use the mental strategies covered this evening Copies of the mental strategies policy are on the school’s website Learn times tables appropriate to the year group that they are in (they should know all times tables up to 12x12 by the end of Year 4 – test to be introduced summer 2020) Practise number bonds (two numbers added together) to all numbers up to 100 (and 1000 if you can) Give your child a number and ask them to make it as many different ways as they can using addition, subtraction, multiplication and division Encourage your child to use maths everywhere – reading clocks, train timetables, prices in the supermarket, weighing cake ingredients – maths is all around us everyday. Have a positive attitude towards maths yourself and tell your children that they CAN do it