Maths the Modern Way!!

1
Maths the Modern Way!!

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

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Mental Starter Bunny Ears
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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!

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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

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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.

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Describing Shapes
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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

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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

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Multiplication

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

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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?
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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.

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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.
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Multiplication by 10

• 7 x 10 70

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Multiplication by 10

• 7 x 10 70

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Multiplication by 10

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

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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!

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Multiplication by 10

• H T U

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Multiplication by 10

• H T U
• 7

19
Multiplication by 10

• H T U
• 7
• 7

20
Multiplication by 10

• H T U
• 7
• 7 0

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Partitioning

• 15 x 5

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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

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Partitioning

• 36 x 4

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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
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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
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Grid Method

• 23 x 8

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Grid Method

• 23 x 8

20
3
x
8
28
Grid Method

• 23 x 8

20
3
x
160
8
29
Grid Method

• 23 x 8

20
3
x
160
24
8
30
Grid Method

• 23 x 8

20
3
x
160
24
160
24
8
184
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Have a Go!!

• 26 x 5
• 32 x 4

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Grid Method

• 26 x 5

20
6
x
100
30
100
30
5
130
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Grid Method

• 32 x 4

30
2
x
120
8
120
8
4
128
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Grid Method

• 346 x 4

x
300
40
6
4
35
Grid Method

• 346 x 4

x
300
40
6
4
1200
36
Grid Method

• 346 x 4

x
300
40
6
4
1200
160
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Grid Method

• 346 x 4

x
300
40
6
4
24
160
1200
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Grid Method

• 346 x 4

x
300
40
6
1200
160
4
24
160
1200
24
1384
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Grid Method

• 72 x 38

70
2
x
30
8
40
Grid Method

• 72 x 38

70
2
x
2100
560
2100
60
30
60
16
2736
560
16
8
41
Standard Method

• 23 x 8

20
3
x
160
24
160
24
8
184
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Standard Method

• 23 x 8

2 3
x 8
20 x 8
1 6 0
3 x 8
2 4
1 8 4
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Standard Method

• 23 x 8

20 x 8
1 6 0
4
3 x 8
2 4
2
1 8 4
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Standard Method

• 23 x 8

20 x 8
1 6 0
1 8 4
3 x 8
2 4
2
1 8 4
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Why Not Just Teach the Standard Method?
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Why Not Just Teach the Standard Method?
0 0 0 2 1
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Why Not Just Teach the Standard Method?
5 6
x 4 2
0 0 0 2 1

• 2
• 2 0

3 2
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Squashy Boxes
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Division

• Share 8 sweets between two children.

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Division

• Share 8 sweets between two children.

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Division

• Share 8 sweets between two children.

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Division

• Share 8 sweets between two children.

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Division

• Share 8 sweets between two children.

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Division

• Share 8 sweets between two children.

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Division

• Share 8 sweets between two children.

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Division

• Share 8 sweets between two children.

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Division

• Share 8 sweets between two children.

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Division

• Share 8 sweets between two children.

4 sweets in each pile
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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
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• 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.
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• 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.
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• 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

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• 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!!!!
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• 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
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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
66
14 r 2

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

5 )
72 ? 5 14 r 2
67
Try it!!!

• 93 ? 4 256 ? 7

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Why not use the way that we were taught?
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The method that we are used to looks like this

• 6 ) 1 3 3

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The method that we are used to looks like this

• 6 ) 1 3 3

0
1
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The method that we are used to looks like this

• 6 ) 1 3 3

0 2
1
1
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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
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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
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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
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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
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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
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The method that we are used to looks like this

• 6 ) 1 3 3

0 0 0
Great! The answer is 0!
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The method that we are used to looks like this

• 6 ) 1 3 3

OK 6s into 1 dont go, so..
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The method that we are used to looks like this

• 6 ) 1 3 3

1
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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.
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The method that we are used to looks like this

• 6 ) 1 3 3

12
1
1
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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!
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The method that we are used to looks like this

• 6 ) 1 3 3

12
12 r 1
1
1
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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!
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The method that we are used to looks like this

• 18 )1 1 0

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The method that we are used to looks like this

• 18 )1 1 0

0
1
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The method that we are used to looks like this

• 18 )1 1 0

0 0
1
11
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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!
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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

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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

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Maths the Modern Way!!

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