Year 5/6 Mathematical Strategies Progression in written calculation methods.

Aims 1. Increase knowledge of how we teach written methods for addition, subtraction, multiplication and division. 2. Share helpful ideas and resources that will allow you to support your child at home.

Our approach at Hillside  Develop children’s understanding of number and give them a firm basis to build on.  Constant reinforcement of key skills.  Ensure the children receive daily mental maths strategies to help build confidence and knowledge.

Vocabulary includes; add, addition, more, plus, increase, make, sum, altogether, score, how many more…..? How many more is … than ….?

=

Horizontal Method

Either partition both numbers or just the second number = = = 177 OR = = = = 177

Expanded Vertical Method

Can be done using either the largest or the smallest digit first. Partial sums are added mentally. Year 5 Year 6

Compact Method

Vertical layout, contracting the working to a compact efficient form: First without any carrying: HTU

Vertical layout, contracting the working to a compact efficient form: ThHTU Then including carrying: Emphasis is always on place value… 140 not 14

Vocabulary includes; subtract, subtraction, take away, minus, leave, how many are left/left over? Difference between, how many fewer is… than….? How much less is….? Difference between.

=

23 – 14 is not the same as 14 – 23!! Never swap your numbers around! All ages need to be reminded:

Complimentary Addition - Subtraction by adding on

= (to 200) 300 (to 500) (to 502)2 304

Compact Method

Year 5 HTU Year 6 ThHTU Method 1 -Without decomposition

Method 2: with decomposition Year 5 HTU Year 6 ThHTU

Decimals – Compact method Year 5 Year 6 H T U. t Th H T U. t h

Vocabulary includes; lots of, groups of, times, multiply, multiplication, multiplied by, multiple of, product, repeated addition, array.

734 x 23=

Grid Method

Year x x 3

Year 6 As for Year 5 plus 3 digit x 2 digit x 25

Expanded Method

1 3 4 x x x Year 6 Year 5

Decimal Expanded method – Year x

Compact Method

1 7 x x Year x Year 5

Decimal Compact method – Year x

Vocabulary includes; halve, share, share equally, group in pairs, equal groups of, divide, division, factor, quotient, divisible by.

357 divided by 17 =

Vertical Chunking Method

(10 x 7) (10 x 7) (10 x 7) (5 x 7) 11 7 (1 x 7) (30 x 7) (6 x 7) divided by 7 = 36 r divided by 7 = 36 r 4 Year 5 division – 3 digit divided by 1 digit. Year 6 division – 3 digit divided by 2 digit

Compact Method

5) divided by 5 is 9. 9 There are 4 tens left over. There is no remainder. 9 tens divided by 5 is 1 ten. Year 5:

4) divided by 4 is 3. 3 There is 1 ten left over. There is a remainder of 2. 9 tens divided by 4 is 2 tens units divided by 4 is Year 6:

Long Division

839 ÷ 27= Method (27 x 10 = 270) (27 x 1 = 27) = 31

839 ÷ 27 Method 2 27 ) Don’t forget the remainder! r 2