Maths the Modern Way!!
Download
Report
Transcript Maths the Modern Way!!
Maths the Modern Way!!
Multiplication and Division
St Teresa’s Primary School
with
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
5x3
3x5
Lots of practical experiences and use of number
lines. Children will begin to use x and = signs.
Multiplication as an Array
2x4=8
4 lots of 2 = 8
4x2=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 DIDN’T JUST ADD A 0!
Multiplication by 10
7 x 10 = 70
BUT WE DIDN’T JUST ADD A 0!
7
7.0
Both of these numbers are worth the same!
7 add a 0 is 7 + 0 = 7
We haven’t multiplied here!
Multiplication by 10
H
T
U
Multiplication by 10
H
T
U
7
Multiplication by 10
H
T
7
U
7
Multiplication by 10
H
T
7
U
7
0
Partitioning
15 x 5
Partitioning
15 x 5
This is 10 x 5 and
5 x 5 added
together.
10 x 5 = 50
5 x 5 = 25
50 + 25 = 75
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
x
8
20
3
Grid Method
23 x 8
x
20
8
160
3
Grid Method
23 x 8
x
20
3
8
160
24
Grid Method
23 x 8
x
20
3
160
+ 24
8
160
24
184
Have a Go!!
26 x 5
32 x 4
Grid Method
26 x 5
x
20
6
100
+ 30
5
100
30
130
Grid Method
32 x 4
x
30
2
120
+ 8
4
120
8
128
Grid Method
346 x 4
x
4
300
40
6
Grid Method
346 x 4
x
300
4
1200
40
6
Grid Method
346 x 4
x
300
40
4
1200
160
6
Grid Method
346 x 4
x
300
40
6
4
1200
160
24
Grid Method
346 x 4
x
300
40
6
4
1200
160
24
1200
160
+
24
1384
Grid Method
72 x 38
x
30
8
70
2
Grid Method
72 x 38
x
70
2
30
2100
60
8
560
16
2100
560
60
+ 16
2736
Standard Method
23 x 8
x
20
3
160
+ 24
8
160
24
184
Standard Method
23 x 8
23
x 8
160
20 x 8
24
3x8
184
Standard Method
23 x 8
23
x 8
23
x 8
160
20 x 8
24
3x8
184
4
2
Standard Method
23 x 8
23
x 8
23
x 8
160
20 x 8
24
3x8
184
184
2
Why Not Just Teach the Standard
Method?
10007
x
3
5 6
x 4 2
Why Not Just Teach the Standard
Method?
10007
x
3
00021
5 6
x 4 2
Why Not Just Teach the Standard
Method?
10007
x
3
00021
5 6
x 4 2
12
20
32
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
8
6
4
2
–
–
–
–
2
2
2
2
2
can be thought of as
=6
I’ve taken 2
=4
away 4 times, so
the answer is 4!!
=2
=0
-2
0
-2
2
-2
4
-2
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
67
62
57
52
47
42
–
–
–
–
–
–
–
5
5
5
5
5
5
5
=
=
=
=
=
=
=
67
62
57
52
47
42
37
37 – 5 = 32
32 – 5 = 27
27 – 5 = 22
22 – 5 = 17
17 – 5 = 12
12 – 5 = 7
7–5= 2
72 5
72
67
62
57
52
47
42
–
–
–
–
–
–
–
5
5
5
5
5
5
5
=
=
=
=
=
=
=
67
62
57
52
47
42
37
37 – 5 = 32
32 – 5 = 27
27 – 5 = 22
22 – 5 = 17
17 – 5 = 12
12 – 5 = 7
7–5= 2
Too long
winded!!!!
-
72 5 = 14 r 2
-
72
50
22
5
17
5
12
5
7
5
2
(10 x 5)
(1 x 5)
(1 x 5)
(1 x 5)
(1 x 5)
72 5 = 14 r 2
14 r
5 ) 72
- 50
22
5
17
5
12
5
7
5
2
2
(10 x 5)
(1 x 5)
(1 x 5)
(1 x 5)
(1 x 5)
72 5 = 14 r 2
14 r 2
5 ) 72
- 50 (10 x 5)
22
- 20 ( 4 x 5)
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…
0
6)1 3 3
1
The method that we are used to
looks like this…
0 2
6)1 3 3
1
1
The method that we are used to
looks like this…
0 2 2r1
6)1 3 3
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 can’t make any
groups of 6 out of 1, so…
The method that we are used to
looks like this…
0
6)1 3 3
Hmmm! I can’t make any
groups of 6 out of 3, so…
The method that we are used to
looks like this…
0 0
6)1 3 3
Hmmm! I can’t make any
groups of 6 out of 3, so…
The method that we are used to
looks like this…
0 0 0
6)1 3 3
Hmmm! I can’t make any
groups of 6 out of 3, so…
The method that we are used to
looks like this…
0 0 0
6)1 3 3
Great! The answer is 0!
The method that we are used to
looks like this…
6)1 3 3
OK – 6s into 1 don’t
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 I’ll have 1 left
over.
The method that we are used to
looks like this…
12
6)1 3 3
1
1
The method that we are used to
looks like this…
12
6)1 3 3
1
1
Oh, look! 6s into 13
again! I know that!
The method that we are used to
looks like this…
12 12 r 1
6)1 3 3
1
1
The method that we are used to
looks like this…
12 12 r 1
6)1 3 3
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…
0
18 )1 1 0
1
The method that we are used to
looks like this…
0 0
18 )1 1 0
1
11
The method that we are used to
looks like this…
0 0
18 )1 1 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
Year
Year
Year
1
2
3
4
–
–
–
–
begin to learn 2x, 5x and 10x
know 2x, 5x and 10x.
know 2x, 3x, 4x, 5x, 6x and 10x.
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 Teresa’s Primary School
with
Essex County Council