Mathematics Workshop Calculation KS2 Parents

Amy Lee Mathematics Subject Leader

January, 2014

Why is mental calculation Important?

2000 -102

This is most sensibly done by counting back, not by decomposition

25 x 8

z  Children relying on written procedures forget

how much they can do mentally

25 x 8 is double 25 x 4

The calculating continuum

Mental Recall

Mental Calculations with jottings

Informal Methods

Expanded Written

Methods

Standard Written

Methods

Calculator

Addition & Subtraction

Mental Calculation Strategies

Calculation Strategies Counting on and Back (with partitioning)

z  Counting on and back -count on or back by partitioning the second number

z  Complementary Addition (find a difference)

Calculation Strategies Partitioning

z  Requires a secure understanding of place value 26 + 32 = 20 + 6 + 30 + 2 = 6 + 2 = 8 20 + 30 = 50 8 + 50 = 58

Counting On/Back

960 – 500 count back in hundreds from 960 3.2 + 0.6 count on in tenths 1.7 + 0.55 count on in tenths and hundredths All of these can be represented using the number line model.

Your Turn…

Use the strategy of counting on/back or complimentary addition to solve the following. 1. 322 - 112

2. 7. 6 + 0.55

How could you check? Get ready to explain how you solved it or model to the class.

Re-ordering

3 + 8 + 7 + 6 + 2 as 3 + 7 + 8 + 2 + 6 Why re-order? 180 + 650 as 650 + 180 (thinking of 180 as 150 and 30) 4.7 + 5.6 – 0.7 as 4.7 – 0.7 + 5.6 = 4 + 5.6

Bridging

z  Knowing how close a number is to the next or previous multiple of 10. 16 + 7 = 16 + 4 + 3 = 23

Bridging

1.4 + 1.7 as 1.4 + 0.6 + 1.1 0.8 + 0.35 as 0.8 + 0.2 + 0.15 8.3 – 2.8 as 2.8 + 0.2 + 5.3 Again, the number-line model provides visual representation for pupils.

Bridging – Your Turn

Solve these by representing the strategy of bridging on a number - line. 0.6 + 0.52

1.4 - 0. 6

Calculation Strategies Compensation

z  Good for adding or subtracting numbers close to a multiple of 10, such as numbers that end in 1, 2, 8 or 9

36 + 28 = 36 + 30 – 2 = 64

Calculation Strategies Compensation

z  Good for adding or subtracting numbers close to a multiple of 10, such as numbers that end in 1, 2, 8 or 9

36 + 28 = 36 + 30 – 2 = 64

Compensation

138 + 69 as 138 + 70 – 1 2 ½ + 1 ¾ as 2 ½ + 2 – ¼ 5.7 + 3.9 as 5.7 + 4.0 – 0.1 6.8 – 4.9 as 6.8 – 5.0 + 0.1

Your Turn - Compensation

Choose one of the following to solve. Use compensation as your strategy. 1. 11.5 - 8. 9 2. 5.7 + 4.2

Calculation Strategies Number lines & Time

z  The time is 10:36am. How long will it be until 11:15am?

Multiplication & Division

Calculation Strategies

Multiplication & Division Strategies

z  Number facts and multiplication tables should

be learnt ‘by heart’. Resorting to a basic counting strategy can distract learners from thinking about the calculation strategy they are trying to use.

z  Division and multiplication are inverse operations. They should also be able to recall quickly the corresponding division facts.

Multiplication & Division Strategies

z  Use known facts derive answers to multiplication and division problems 4 x 8 = 2 x 16 = 32 (doubling and halving) 9 x 6 is (10 x 6) – 6 = 54

(rounding and compensating) 63÷7= 9 because 9 x 7=63 (reversibility)

Multiplication & Division Strategies

z  Partitioning 24 x 6 = 20 x 6 + 4 x 6 = ���

z  Rounding and compensating

24 x 6 = 25 x 6 - 6

Your Turn…

Use partitioning or rounding and compensating 1. 19 x 5 2. 1.8 x 3

Grid Method

z  Used to ensure pupils move from mental strategies to expanded written method to standard written methods.

Grid Method - Multiplication

Grid Method - Division

Standard Written Method

z  Addition, subtraction, multiplication, division z  Policies available on school website (click

‘Learning’ tab and then ‘Mathematics Resources’)

z  These show step by step procedures

Remember, fluency in mental calculation should come first!