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Maths the Modern Way!!

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Maths the Modern Way!! Multiplication and Division St Teresa s Primary School Paul Hargreaves Primary Strategy Consultant Mathematics Essex County Council – PowerPoint PPT presentation

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Title: 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

2
Mental Starter Bunny Ears
3
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!

4
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

5
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.

6
Describing Shapes
7
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

8
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

9
Multiplication
  • Calculate the answer to this
  • 5 6
  • x 3

10
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?
11
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.

12
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.
13
Multiplication by 10
  • 7 x 10 70

14
Multiplication by 10
  • 7 x 10 70

15
Multiplication by 10
  • 7 x 10 70
  • BUT WE DIDNT JUST ADD A 0!

16
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!

17
Multiplication by 10
  • H T U

18
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

21
Partitioning
  • 15 x 5

22
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

23
Partitioning
  • 36 x 4

24
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
25
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
26
Grid Method
  • 23 x 8

27
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
31
Have a Go!!
  • 26 x 5
  • 32 x 4

32
Grid Method
  • 26 x 5

20
6
x
100
30
100
30
5
130
33
Grid Method
  • 32 x 4

30
2
x
120
8
120
8
4
128
34
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
37
Grid Method
  • 346 x 4

x
300
40
6
4
24
160
1200
38
Grid Method
  • 346 x 4

x
300
40
6
1200
160
4
24
160
1200
24
1384
39
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
42
Standard Method
  • 23 x 8

2 3
x 8
20 x 8
1 6 0
3 x 8
2 4
1 8 4
43
Standard Method
  • 23 x 8

20 x 8
1 6 0
4
3 x 8
2 4
2
1 8 4
44
Standard Method
  • 23 x 8

20 x 8
1 6 0
1 8 4
3 x 8
2 4
2
1 8 4
45
Why Not Just Teach the Standard Method?
46
Why Not Just Teach the Standard Method?
0 0 0 2 1
47
Why Not Just Teach the Standard Method?
5 6
x 4 2
0 0 0 2 1
  • 2
  • 2 0

3 2
48
Squashy Boxes
49
Division
  • Share 8 sweets between two children.

50
Division
  • Share 8 sweets between two children.

51
Division
  • Share 8 sweets between two children.

52
Division
  • Share 8 sweets between two children.

53
Division
  • Share 8 sweets between two children.

54
Division
  • Share 8 sweets between two children.

55
Division
  • Share 8 sweets between two children.

56
Division
  • Share 8 sweets between two children.

57
Division
  • Share 8 sweets between two children.

58
Division
  • Share 8 sweets between two children.

4 sweets in each pile
59
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
60
  • 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.
61
  • 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.
62
  • 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

63
  • 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!!!!
64
  • 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
65
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

68
Why not use the way that we were taught?
69
The method that we are used to looks like this
  • 6 ) 1 3 3

70
The method that we are used to looks like this
  • 6 ) 1 3 3

0
1
71
The method that we are used to looks like this
  • 6 ) 1 3 3

0 2
1
1
72
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
73
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
74
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
75
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
76
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
77
The method that we are used to looks like this
  • 6 ) 1 3 3

0 0 0
Great! The answer is 0!
78
The method that we are used to looks like this
  • 6 ) 1 3 3

OK 6s into 1 dont go, so..
79
The method that we are used to looks like this
  • 6 ) 1 3 3

1
80
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.
81
The method that we are used to looks like this
  • 6 ) 1 3 3

12
1
1
82
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!
83
The method that we are used to looks like this
  • 6 ) 1 3 3

12
12 r 1
1
1
84
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!
85
The method that we are used to looks like this
  • 18 )1 1 0

86
The method that we are used to looks like this
  • 18 )1 1 0

0
1
87
The method that we are used to looks like this
  • 18 )1 1 0

0 0
1
11
88
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!
89
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

90
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

91
Maths the Modern Way!!
  • Multiplication and Division
  • St Teresas Primary School
  • Paul Hargreaves
  • Primary Strategy Consultant Mathematics
  • Essex County Council
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