Maths Information Evening

Welcome to our maths calculation evening Do I need jottings ?

Can I do it in my head?

Shall I use a pencil and paper method?

Do I need to use a calculator?

Aims of this evening • To look at progression through calculation methods from YR to Y6; • To find out what you can do to help your child in maths at home; • To develop confidence in supporting your child in maths at home.

DfEE 1999 ‘Parents who are confident about maths tend to have children who are also confident, and these children are ready to tackle and assimilate new ideas in a way that is impossible for children who feel uncertain about, or even fear, maths.’

How is maths taught?

Daily mathematics lesson; Emphasis on mental calculations; Interactive whole class and group teaching; Enjoyable practical approaches, including the use of ICT and games; • Application of maths skills in problemsolving.

• • • •

Calculations The aim is that children will always be able to recognise when calculations can be done ‘in their heads’ and choose effective and efficient strategies to work out the answers.

KS1 In the beginning ‌ Children use practical resources to learn to count and to carry out simple calculations involving addition, subtraction, multiplication and sharing/grouping (division).

Children start to use jottings to record their calculations.

When they are ready, children use Base 10 equipment to support addition and subtraction and they start to record it using drawings.

Using number lines Number lines are introduced in KS1 and continue to be used throughout KS2 when appropriate.

Using number lines for addition and subtraction:  we add by ‘counting on’;  we subtract by either ‘counting on’ or ‘counting back’ depending on the numbers involved;

Have a go!

Imagine you are showing your child how to use a number line. What would you do for these: •22 – 5 = •145 – 94 = •The bus is due to arrive at 7.35am but is 46 minutes late. What time does it arrive?

•Sally wants to buy a CD that costs £15.60. She only has £13.45. How much more money does Sally

Summary so far …

In KS1 the emphasis is on: working practically; working mentally;

using models and images, including number lines to support calculations. calculations recorded in horizontal number sentences (14 + 23 = 37);

In KS2, more formal written methods of calculation are introduced but children are still encouraged to use mental methods and jottings where appropriate.

Number lines continue to be used for some calculations across KS2.

Addition- Progression Foundation: learning number bonds to 10, 20 and 100; 1) Mental calculation supported by: - Modelling of method by teacher - Jottings - Number lines 2) Step-by-step using base 10 equipment 3) Compact ‘carrying’ method

Lancashire Mathematics Team

The next slide shows how the understanding that has developed using base 10 equipment in KS1, can be transferred into the early stages of formal column addition (Y3):

This becomes the compact column addition method No ‘Carrying’ 4 1 + 2 6 6 7

‘Carrying’ 4 7 + 7 6 1 2 3 1

1

In year 4, this is applied to 4-digit numbers and decimals.

Year 5

Year 6

Have a go ‌

2435 + 486

27.55 + 100.9 + 68.08

By the end of year 6, children should be able to add whole numbers and decimals, using formal compact methods.

They should also be able to add: - several numbers with different numbers of digits, understanding the place value;

- decimals with up to two decimal places (with mixed numbers of decimal places), knowing that the decimal points line up under one another.

- amounts of money and measures.

Subtraction - Progression Foundation: learning number bonds to 10, 20 and 100.

1) Mental calculations supported by: - Modelling of method by teacher - Jottings - Number line 2) Expanded decomposition using partitioning 3) Compact decomposition Lancashire Mathematics Team

Expanded decomposition using partitioning 89 - 57

71 - 46

71 - 46

83 – 26 70

-

80 20 50

  

13 6 7 = 57

When children are ready, this leads to the compact method of decomposition (subtraction) and can be applied to 4-digit number and decimals:

Have a go …

378 – 212

254 – 137 45.4 – 26.15

By the end of year 6, children should be able to subtract whole numbers and decimals using the formal compact method. They should also be subtracting: -numbers with different numbers of digits, understanding place value; -decimals with up to 2 decimal places (with mixed numbers of decimal places), knowing that the decimal points line up under one another; -amounts of money and measures.

Multiplication - Progression Foundation: knowledge of multiplication and division facts up to 12 x 12.

1) Mental calculation supported by: - Jottings - Number lines - Modelling of method by teacher 2) Understanding of multiplication as: - repeated addition - an array 3) Grid method Lancashire Mathematics Team

Knowing multiplication facts It is vital that children know their times tables – as children progress through school, much of their maths work depends upon their knowledge of multiplication and division facts.

Tables should be practised at least 2-3 times a week at home.

Expectations: Year 2 2 times table 5 times table 10 times table Year 3

2 times table 3 times table 4 times table 5 times table 8 times table 10 times table

Years 4, 5, 6 Derive and recall all multiplication and division facts up to 12 x 12 (5 second recall).

First, children will develop their understanding of multiplication and use jottings to support calculation: Repeated addition 3 times 5

is

5 + 5 + 5 = 15

or 3 lots of 5 or 5 x 3

Repeated addition can be shown easily on a number line: 5x3=5+5+5 and on a bead bar: 5

5x3=5+5+5 5

5

Lancashire Mathematics Team

Arrays In year 2 children start to model a multiplication calculation using an array.

This knowledge will support the introduction of the grid method in Y3.

5X3

3X5

Grid method of multiplication 10

3

60 + 18 = 78

6

6 x 13 = 78 Lancashire Mathematics Team

Grid method – have a go: TU x U (Short multiplication - multiplication by a single digit) 23 x 8

X

HTU x U (Short multiplication - multiplication by a single digit) 346 x 9 X

Long Multiplication ( where both numbers have 2 or more digits) TU x TU

72 x 38 X

70

2

30

2100

60

8

560

16

2100 + 560 + 60 + 16 2736

HTU x TU

372 x 24

X

300

70

2

20

6000

1400

40

4

1200

280

8

6000 + 1400 + 1200 + 280 + 40 + 8 8928

During year 5, the grid method for short multiplication may be reduced to the compact method shown below:

By the end of year 6, children should be able to: - multiply numbers with up to 4 digits by a two-digit whole number using the grid method of long multiplication; - multiply numbers with up to two decimal places by whole numbers using the grid method.

Division - Progression

Foundation: knowledge of multiplication and division facts up to 12 x 12.

1) Mental calculations supported by: - Jottings - Number lines - Modelling of method by teacher 2) Understanding division as sharing and grouping.

3) Visualising division using: - arrays - repeated subtraction 4) Using ‘chunking’ Lancashire Mathematics Team

Y2

Children use practical equipment to represent division calculations as grouping and use jottings to support their calculation.

12 รท 3 =

This child has used a strategy of grouping tallies to find the answer.

Lancashire Mathematics Team

Y3 – Practical equipment to number line Stage 1 48 ÷ 4 = 12 (groups of 4)

Stage 2 48 ÷ 4 = 10 (groups of 4) + 2 (groups of 4) = 12 (groups of 4)

48

48

44 40 36 32 28

10 groups

24 20 16 12 8 4 0

8 2 groups 0

Y4 – will Number to their formal written method (known Children continue toline develop use of grouping (repeated subtraction) to beas able‘chunking’) to subtract multiples of the divisor, moving on to the use of the 'chunking' method.

48 12 4 48 - 40 10x 8 - 8 2x 0

10 groups

Answer: 12

2 groups

8 0

The ‘chunking’ method Short division (TU ÷ U, HTU ÷ U)

6

72 - 60 x 10 12 - 6 x1 6 - 6 x1 0 Answer = 12

Long division (HTU ÷ TU)

15

12

432 - 150 282 - 150 132 - 60 72 - 60 12

15 432 - 300

x 10 x 10 x4 x4

Answer = 28 r 12

-

x 20 132 120 x8 12 Answer = 28 r

Have a go …

138 ÷ 6

204 ÷ 12

PROGRESSING THROUGH THE STAGES By the end of year 6, children have a range of calculation methods, mental and written. Selection depends upon the numbers involved.

Children do not move onto the next stage if: 1) 2)

they are not ready. they are not confident.

Children are encouraged to consider if a mental calculation would be appropriate before using written methods.

Some practical suggestions for home‌

•Count with your child; •Practise number bonds and times tables; •Play number games; • Use the Abacus Active learn website; •Involve children when taking measurements or weighing items; • Take note of numbers in real life e.g. telephone numbers, bus numbers etc; •Give children opportunities to use money to shop, check change etc; •When helping your children calculate, use the method that they have been taught.

Thank you for attending our maths calculations evening!