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Maths the Modern Way!!

- Multiplication and Division
- St Teresas Primary School
- Paul Hargreaves
- Primary Strategy Consultant Mathematics
- Essex County Council

Mental Starter Bunny Ears

Total Recall!

- Select pairs of numbers from the target board on
- your table. Add these using one of the methods
- from last session. Will you use a number line?

Will - you partition and add mentally? Do you need to
- make jottings?
- BE BRAVE try to avoid using the standard
- method!
- Now try with three numbers! Or try pairs of
- numbers and carry out a subtraction!

The Primary National Strategy

- Basis of teaching since 1999 based on extensive

research and proven success - Daily entitlement to maths lesson
- Key features
- Progression carefully set out
- Interactivity use of models, images, games,

practical activities - Focus on mental skills as well as written
- Vocabulary, problem solving, communication,

explanation and reasoning

There is no right way to work!!

- Children exposed to a range of methods.
- Methods selected will depend upon the situation

and the numbers involved, including when to use

calculators. - Children make decisions about methods and draw on

a range of strategies and approaches when

applying Maths is context. - Children in same class could be using different

methods to others depending on their ability,

confidence and stage of mathematical development.

Describing Shapes

The Importance of Vocabulary

- Key to success in mathematics
- Can be confusion between school and home
- Children need opportunities in class and in

homework to use mathematical vocabulary games,

collaborative work, open ended investigations

Mathematical Vocabulary Booklet

- Guide to which words and phrases are introduced

to each year group - Schools many make decisions regarding vocabulary
- It is not a checklist
- Check with children and teachers if there are

unfamiliar words

Multiplication

- Calculate the answer to this
- 5 6
- x 3

Did you do this?

- 5 6
- x 3
- 1 6 8
- 1

Or did you use a mental method?Why did you

choose the method you used?

Repeated Addition (Year 2/3)

- 5 added to 5 added to 5
- 5 5 5
- 3 lots of 5
- 5 x 3
- 3 x 5
- Lots of practical experiences and use of number

lines. Children will begin to use x and signs.

Multiplication as an Array

2 x 4 8 4 lots of 2 8

4 x 2 8 2 lots of 4 8

Arrays are quite common ice cube trays, egg

boxes, chocolate boxes, medicine wrapping, tiles

etc.

Multiplication by 10

- 7 x 10 70

Multiplication by 10

- 7 x 10 70

Multiplication by 10

- 7 x 10 70
- BUT WE DIDNT JUST ADD A 0!

Multiplication by 10

- 7 x 10 70
- BUT WE DIDNT JUST ADD A 0!
- 7
- 7.0
- Both of these numbers are worth the same!
- 7 add a 0 is 7 0 7
- We havent multiplied here!

Multiplication by 10

- H T U

Multiplication by 10

- H T U
- 7

Multiplication by 10

- H T U
- 7
- 7

Multiplication by 10

- H T U
- 7
- 7 0

Partitioning

- 15 x 5

Partitioning

This is 10 x 5 and 5 x 5 added together. 10 x 5

50 5 x 5 25 50 25 75

- 15 x 5

Partitioning

- 36 x 4

Partitioning

- 36 x 4

36 x 4 is 30 x 4 and 6 x 4 added together. I know

that 30 is three lots of 10, so 30 x 4 is 10 x 4

added to 10 x 4 added to 10 x 4. 10 x 4 40 10 x

4 40 10 x 4 40 6 x 4 24 40 40 40 24

144

Partitioning

- 36 x 4

36 x 4 is 30 x 4 added to 6 x 4 I know that 30 x

4 is 10 times bigger than 3 x 4 3 x 4 12, so 30

x 4 120 6 x 4 24 120 24 144

Grid Method

- 23 x 8

Grid Method

- 23 x 8

20

3

x

8

Grid Method

- 23 x 8

20

3

x

160

8

Grid Method

- 23 x 8

20

3

x

160

24

8

Grid Method

- 23 x 8

20

3

x

160

24

160

24

8

184

Have a Go!!

- 26 x 5
- 32 x 4

Grid Method

- 26 x 5

20

6

x

100

30

100

30

5

130

Grid Method

- 32 x 4

30

2

x

120

8

120

8

4

128

Grid Method

- 346 x 4

x

300

40

6

4

Grid Method

- 346 x 4

x

300

40

6

4

1200

Grid Method

- 346 x 4

x

300

40

6

4

1200

160

Grid Method

- 346 x 4

x

300

40

6

4

24

160

1200

Grid Method

- 346 x 4

x

300

40

6

1200

160

4

24

160

1200

24

1384

Grid Method

- 72 x 38

70

2

x

30

8

Grid Method

- 72 x 38

70

2

x

2100

560

2100

60

30

60

16

2736

560

16

8

Standard Method

- 23 x 8

20

3

x

160

24

160

24

8

184

Standard Method

- 23 x 8

2 3

x 8

20 x 8

1 6 0

3 x 8

2 4

1 8 4

Standard Method

- 23 x 8

20 x 8

1 6 0

4

3 x 8

2 4

2

1 8 4

Standard Method

- 23 x 8

20 x 8

1 6 0

1 8 4

3 x 8

2 4

2

1 8 4

Why Not Just Teach the Standard Method?

Why Not Just Teach the Standard Method?

0 0 0 2 1

Why Not Just Teach the Standard Method?

5 6

x 4 2

0 0 0 2 1

- 2
- 2 0

3 2

Squashy Boxes

Division

- Share 8 sweets between two children.

Division

- Share 8 sweets between two children.

Division

- Share 8 sweets between two children.

Division

- Share 8 sweets between two children.

Division

- Share 8 sweets between two children.

Division

- Share 8 sweets between two children.

Division

- Share 8 sweets between two children.

Division

- Share 8 sweets between two children.

Division

- Share 8 sweets between two children.

Division

- Share 8 sweets between two children.

4 sweets in each pile

Repeated Subtraction (Grouping)

- 8 ? 2 can be thought of as
- 8 2 6
- 6 2 4
- 4 2 2
- 2 2 0

Ive taken 2 away 4 times, so the answer is 4!!

-2

-2

-2

-2

0

2

4

6

8

- 13 ? 3
- 13 3 10
- 10 3 7
- 7 3 4
- 4 3 1

I cannot make anymore groups of 3 out of 1, so

there is one left over.

- 13 ? 3 4 r 1
- 13 3 10
- 10 3 7
- 7 3 4
- 4 3 1

I cannot make any more groups of 3 out of 1, so

there is one left over.

- 72 ? 5
- 72 5 67 37 5 32
- 67 5 62 32 5 27
- 62 5 57 27 5 22
- 57 5 52 22 5 17
- 52 5 47 17 5 12
- 47 5 42 12 5 7
- 42 5 37 7 5 2

- 72 ? 5
- 72 5 67 37 5 32
- 67 5 62 32 5 27
- 62 5 57 27 5 22
- 57 5 52 22 5 17
- 52 5 47 17 5 12
- 47 5 42 12 5 7
- 42 5 37 7 5 2

Too long winded!!!!

- 72
- - 50 (10 x 5)
- 22
- - 5 (1 x 5)
- 17
- - 5 (1 x 5)
- 12
- - 5 (1 x 5)
- 7
- 5 (1 x 5)
- 2

72 ? 5 14 r 2

14 r 2

- 72
- - 50 (10 x 5)
- 22
- - 5 (1 x 5)
- 17
- - 5 (1 x 5)
- 12
- - 5 (1 x 5)
- 7
- 5 (1 x 5)
- 2

5 )

72 ? 5 14 r 2

14 r 2

- 72
- - 50 (10 x 5)
- 22
- - 20 ( 4 x 5)
- 2

5 )

72 ? 5 14 r 2

Try it!!!

- 93 ? 4 256 ? 7

Why not use the way that we were taught?

The method that we are used to looks like this

- 6 ) 1 3 3

The method that we are used to looks like this

- 6 ) 1 3 3

0

1

The method that we are used to looks like this

- 6 ) 1 3 3

0 2

1

1

The method that we are used to looks like this

- 6 ) 1 3 3

0 2 2 r 1

1

1

It does work, but many children make the

following errors

The method that we are used to looks like this

- 6 ) 1 3 3

Hmmm! I cant make any groups of 6 out of 1, so

The method that we are used to looks like this

- 6 ) 1 3 3

0

Hmmm! I cant make any groups of 6 out of 3, so

The method that we are used to looks like this

- 6 ) 1 3 3

0 0

Hmmm! I cant make any groups of 6 out of 3, so

The method that we are used to looks like this

- 6 ) 1 3 3

0 0 0

Hmmm! I cant make any groups of 6 out of 3, so

The method that we are used to looks like this

- 6 ) 1 3 3

0 0 0

Great! The answer is 0!

The method that we are used to looks like this

- 6 ) 1 3 3

OK 6s into 1 dont go, so..

The method that we are used to looks like this

- 6 ) 1 3 3

1

The method that we are used to looks like this

- 6 ) 1 3 3

1

Now, 6s into 13. I know that two 6s are 12 and

Ill have 1 left over.

The method that we are used to looks like this

- 6 ) 1 3 3

12

1

1

The method that we are used to looks like this

- 6 ) 1 3 3

12

1

1

Oh, look! 6s into 13 again! I know that!

The method that we are used to looks like this

- 6 ) 1 3 3

12

12 r 1

1

1

The method that we are used to looks like this

- 6 ) 1 3 3

12

12 r 1

1

1

The answer is 1212 r 1!

The method that we are used to looks like this

- 18 )1 1 0

The method that we are used to looks like this

- 18 )1 1 0

0

1

The method that we are used to looks like this

- 18 )1 1 0

0 0

1

11

The method that we are used to looks like this

- 18 )1 1 0

0 0

1

11

Back to square one! Lots more learning and

understanding is needed here. To successfully

tackle this problem, you need to know how to use

repeated subtraction!

Multiplication Tables

- Year 1 begin to learn 2x, 5x and 10x
- Year 2 know 2x, 5x and 10x.
- Year 3 know 2x, 3x, 4x, 5x, 6x and 10x.
- Year 4 know all facts to 10 x 10

Multiplication Tables

- Three for free!
- If you know 3 x 5 15, you also know
- 5 x 3 15
- 15 ? 5 3
- 15 ? 3 5

Maths the Modern Way!!

- Multiplication and Division
- St Teresas Primary School
- Paul Hargreaves
- Primary Strategy Consultant Mathematics
- Essex County Council