Transcript Multiplication and Division - Hadnall CofE Primary School

Multiplication
The children begin to recognize repetitive
addition in groups of the same size.
How many wheels do we need for
these 3 bikes?
2
+
2
+
2
The children will learn counting in steps of 2, 5
and 10
eg 2, 4, 6, 8, 10, 12 etc
10, 20, 30, 40, 50, 60 etc
1
2
3
4
5
6
7
8
9 10 11 12
The children will represent multiplication in
groups and record pictorially as repeated
additions.
5, 10, 15, 20,
25, 30, 35, 40
They will begin to use number lines to represent
repeated additions.
I have got three 5p coins. How much money do
I have altogether?
0 1
2
3
4
5
6
7
8
9
10
11 12 13 14 15
They will also record repeated additions as
equations
5 + 5 + 5 = 15
Children continue to use a number line to record
repeated addition eg
How many sides do 3 squares have?
The
multiplication
sign is
introduced
4 + 4 + 4 =12 or
3 x 4 = 12
+4
+4
+4
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
We begin to understand multiplication as an
array.
2x3=6
3x2=6
Can you see any examples of arrays around you?
Here are some the children came up with earlier!
4 x 3 = 12
3 x 4 = 12
Once we know this ................
We can find out this...........
How many children will Vicar Rob fit in church on
Sunday? How many adults can visit? What if there is a
mixture of adults and children?
Children then use their knowledge of multiplication
as arrays as an introduction to the grid method.
Apples come in bags of 15. How many apples are
there in 4 bags?
10
4
5
15 x 4
10 x 4 = 40
5 x 4 = 20
40 + 20 = 60
As you can see learning and knowing times tables
becomes very important!
Children are introduced to the grid layout for
multiplication:
There are 8 classes in a school. Each class has 27
children. How many children are there altogether?
x
20
8
160
7
56
160
+56
216
When children are confident using the grid
method, they are introduced to a vertical
layout.
They begin with the least significant digit
first i.e. the units:
27
X 8
56
160
216
8x7
8 x 20
From here the children gain confidence with both
methods and with calculating larger numbers
e.g 78 x 42
Grid method
x
70
Vertical method
8
40
2800
320
3120
2
140
16
+ 156
3276
78
x 42
16
140
320
2800
3276
2x8
2x70
40x8
40x70
Children continue with vertical layout, more
able may compact the working.
381
x 24
381
4x1
4
X 24
3
4
x
80
320
1524
1
4
x
300
1200
7620
1
20 x 1
20
9144
20 x 80
1600
20 x 300
6000
9144
Children are encouraged to estimate before calculating
and use informal paper and pencil methods to support
multiplication.
Progression into decimal calculations.
Ideal contexts are money and measures.
£4 . 65 x 9
£
4 . 65
x
9
0 . 45
5 . 40
36
. 00
1
41.85
£
9 x 0 . 05
9 x 0 . 60
9 x 4 . 00
4 . 65
x5 4 9
41 . 85
Division
The children will start their work on division with
many opportunities of role play and working in
context.
eg in the café, the children will be asked to
share the 6 biscuits between 2 plates.
Can you share the 40 straws between 8
children? How many straws do they have each?
Children will represent division pictorially and using
a number line eg
12 ÷ 4 = 3
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
By changing the arrays they met in multiplication,
children develop understanding of division as
grouping or sharing and reinforce understanding
division as the inverse of multiplication.
ie
2x3=6
6÷3=2
3x2=6
6÷2=3
We now use some of the methods taught to solve
problems with remainders, rounding up or down
depending on the context.
23 people are travelling to the cinema. Each car can
carry 5 people. How many cars are needed?
r3
0
5
10
23 ÷ 5 = 4 r3 or 5 cars
15
20
23
I can buy a book with 3 tokens. I have 14 tokens.
How many books can I buy?
14 ÷ 3 = 4 r2 or 4 books as I have to keep the
other tokens for later.
r2
0
3
6
9
12
14
At this stage we begin to introduce the idea of
partial tables in order to gain children’s
confidence when making larger jumps of the
divisor e.g 4x table
1
1
4
2
2
8
4
4
16
10
10
40
5
5
20
Division using the complimentary multiplication
written method
Partial tables are used to support the calculation
e.g. 89 ÷ 6 =
60
24
84
1
6
2
12
4
24
10
60
5
30
(10x6)
(4x6)
(14x6)
so 89 ÷ 6 = 14 r 5
A child may also be using a number line along with
partial tables.
If children are ready, they will be
introduced to the short (or bus stop)
method of division
e.g. 98 ÷ 7 = 14
14
7
2
98
It is important that children use mental
facts to give an estimate of an answer
Partial tables are then developed to include
larger numbers e.g. 196 ÷ 6 using 6x table
120
60
180
12
192
10
60
20
120
40
240
100
600
50
300
(20x6)
(10x6)
(2x6)
(32x6)
196 ÷ 6 = 32r4
180 (30x6)
12 ( 2x6)
192(32x6)
196 ÷ 6 = 32r4
We now consolidate short division for 2
digit divided by 1 digit then extend to
3 digit divided by 1 digit
e.g. 430 ÷ 5
86
4 3
5 430
Continue to use partial tables to support
calculation
We then make sure that children are
interpreting remainders correctly
e.g. 432 ÷ 5
86 r 2
5
43
432
Division is extended to 4 digits divided
by 1 digit
We now express remainders as a
fraction
e.g. 496 ÷ 11
45 r 1
11
4 5
496
Answer with a fraction is 451/11
We now move on to long division for
numbers up to 4 digits divided by 2 digits
e.g. 432 ÷ 15
15
28 r 12
432
30
132
120
12
Express fraction in lowest term:
12/15 = 4/5
So answer is 284/5 or 28.8
Continue to use partial tables if needed
The next step is to move into decimals
using money or measures alongside partial
tables if necessary
e.g. 87.5 ÷ 7
1
7
2
14
4
28
10
70
5
35
0.5
3.5
12.5
1
3
7 87.5
Thank you everyone for coming along to
our Maths Calculation evening.
We hope it has been useful for you.
This presentation will now be placed on
the School Website
www.hadnallcofeprimary.org.uk