Maths

Maths How do we teach it? Why do we teach it like that? What do the written methods look

like? What can you do at home to help?

How do our children learn in Maths lessons at

Orleans? Encouraged to use mental calculation methods Practise recall of number facts to become

quicker and more accurate They are more aware of the strategies they

use to calculate Focus on correct use of vocabulary and talk for

learning Real-life, contextual learning Practical and engaging lessons – fascinators!

CB's

‘I hear and I forget. I see and I remember. I do and I understand.’

(A Chinese proverb)

‘It just doesn’t look like it did in my day.’

Until fairly recently, maths was taught using Victorian era methods.

Were you one of the lucky ones?

Logical and strong with numbers?

Vast numbers of clerks to perform calculations every day.

Victorian Times

Today, calculators and spreadsheets can do this car quicker, so the need for everybody to be able to do big calculations by hand has largely disappeared

That’s not to say we don’t need strong number skills!

We are inundated by numbers all the time…

Probably not…but we do need to know that:

27 x 43 is roughly 30 x 40 and…

that this is roughly 1,200

It's partly the need to have a good feel for numbers that is behind the modern methods.

Do we all need to be able to work out 27 x 43 precisely with a pen and paper?

National Numeracy Strategy 1999

• The revolution in the teaching of maths at primary school kicked in with this strategy.

• The emphasis moved away from blindly following rules (remember borrowing one from the next column and paying back?) towards techniques a child understood

The Aim for children to do mathematics in

their heads, and if the numbers are too large, to use pencil and paper to avoid losing track.

To do this children need to learn quick and efficient methods, including mental methods and appropriate written methods.

Mathematics is foremost an activity of the mind; written calculations are an

aid to that mental activity.

Learning written methods is not

the ultimate aim.

We want children to ask themselves:

1. Can I do this in my head?

2. Can I do this in my head with the help of drawings or jottings?

3. Do I need to use an expanded or compact written method?

4. Do I need a calculator?

A sledgehammer to crack a nut!

1 0 0 0- 7 9 9 3

10 1199

16- 9

7

01

97x 100

00000

970097007 5 65

0 80

Addition

• Y3 Programme:• To add mentally combinations of 1-digit and 2-

digit numbers• Develop written methods to record, support or

explain addition of 2-digit and 3-digit numbers

• Y4 Programme:• To add mentally pairs of 2-digit numbers• To refine and use efficient written methods to

add 2-digit and 3-digit numbers and £.p

Addition – progression

How would you solve these?

● 25 + 42● 25 + 27● 25 + 49● 145 +127

Partitioning

48 + 33 40 8 30 3

70 + 11 = 81

Number line

242 + 136 = 378

242 342

+ 100

+ 30 +6 372

378

+ 10 26

+1 36

+1

37 38

26 + 12 =38

Use the number line to work these out…

242 + 136 = 378

242 342 + 100 + 30 +6

372 378

• 67 + 48 = • 346 + 237 = • 3241 + 1471 =

Column Method

358 + 33 11 80300391

Leading to391

358 + 33

1

Expanded Compact

Subtraction

Subtraction - progression Y3 Programme: To subtract mentally combinations of 1-digit and 2-

digit numbers Develop written methods to record, support or

explain subtraction of 2-digit and 3-digit numbers

Y4 Programme: To subtract mentally pairs of 2-digit numbers To refine and use efficient written methods to

subtract 2-digit and 3-digit numbers and £.p

• 67 - 45● 67 – 59● 178 - 99● 3241 - 2167

How would you solve these?

Number line• Subtraction as taking away

30 – 17 = 13

3015 20- 5 - 10- 2

13

5 12

Difference

• Subtraction as finding the difference

Number line• Subtraction as finding the difference

• Jump to next multiple of 10• Count the jumps

10 + 4 + 2 = 16

34 – 18 =

3418 20 30+2 + 10 + 4

Column Method

547 134 413

82 - 57 25

7 1

Use the number line to work these out…

• 48 – 31 = • 256 - 167 =

3418 20 30+2 + 10 + 4

Multiplication

Y3 Programme:•Multiply one digit and two digit numbers by 10 or 100 and describe the effect;•Derive and recall multiplication facts for the 2, 3, 4, 5, 6, and 10 times tables;•Use informal and practical methods to multiply two digit numbers e.g. 13 x 3.

Y4 Programme:•Multiply numbers to 1000 by 10 and then 100 and describe the effect;•Derive and recall multiplication facts up to 10 x 10;•Use written methods to multiply a two digit number by a one digit number e.g. 15 x 9.

Multiplication - progression

How would you solve these?

● 24 50● 24 4● 24 15● 136 9

Number lineMultiplication as repeated addition

4 x 2 = 2 + 2 + 2 + 2So, 2 x 4 = 8

0 2 4

4 x 2

6 8

+2

+2

+2

+2

Arrays

3 x 6

Add the dots

Or

What multiplication are

these arrays showing?

Partitioning

24 x 5

20 x 5 = 100 4 x 5 = 20

100 + 20 = 120

Grid Method24 x 5

20 4 x 5 100 20

100 + 20 = 120BBC News Video Link

Expanded Multiplication

38x 7

210 56 266

(30 x 7)(8 x 7)

Use the grid method to work these out:

24 x 5

20 4 x 5 100 20

100 + 20 = 120

24 x 7

142 x 3

Division

Y3 Programme: Use practical and informal written methods to

divide two-digit numbers (e.g. 50 ÷ 4);

Y4 Programme: Develop and use written methods to record,

support and explain division of two-digit numbers by a one-digit number, including division with remainders (e.g. 98 ÷ 6) 

Division - progression

How would you solve these?

● 123 3● 165 10● 325 25● 623 24

Division

Arrays First group

of 3

12 ÷ 3 = 4

Repeated subtraction

0 3 6 9 12

- 3 - 3 - 3 - 3

12 - 3 – 3 – 3 – 3

12÷ 3 = 4

Counting in steps

0 3 6 9 12

12÷ 3 = 4 Add the jumps

Fingers“6 “9 “1

2”“3”

+ 3

+ 3

+ 3

+ 3

Chunking

25 75- 50 (10 x 5) 25- 25 (5 x 5) 0 75 ÷ 5 = 15

75 ÷ 5

0 75

10 x 5

5 x 5

Need to know

tables!BBC News Video Link