Transcript WAVE 3 Conference Numeracy

Multiplication
and Division
Calculating efficiently
and accurately
Objectives


To explore the knowledge, skills and
understanding required for children to
multiply / divide efficiently and accurately
To explore the progression in recording and
(some of) the teaching approaches used
Self-esteem
Rapid recall
Models, images &
concrete materials
Understanding
Use of ICT
The Four
Rules
Problem solving
and role play
Mental
calculations
Stories / rhymes
Efficient
written methods
Progression in knowledge
and understanding for x / ÷
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Counting
Doubles / halves / near doubles
Multiplication as repeated addition, describing an array and
scaling
Division as grouping and sharing
Recall of multiplication / division facts for 2, 3, 4, 5, 10
times tables and beyond
Multiply two / three-digit numbers by 10 / 100
Understand that multiplication and division are inverses
Counting and estimation
There are 5 principles of counting:
1.
The stable order principle - understanding that the
number names must be used in that particular order when
counting
2.
The one-to-one principle - understanding and ensuring
that the next item in a count corresponds to the next
number
3.
The cardinal principle - knowing that the final number
represents the size of the set
4.
The abstraction principle - knowing that counting can
be applied to any collection, real or imagined
5.
The order irrelevance principle - knowing that the
order in which the items are counted is not relevant to the
total value
Counting in context

How many 10p coins are here?
How much money is that?

How many toes are there on 2 feet?

How many gloves in 3 pairs?
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If Sarah counts in 2s and Nigel counts in 5s, when
will they reach the same number?
How many lengths of 10m can you cut from 80m of
rope?
Mr Noah
Doubling and halving in context
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There are 8 raisins. Take half of them.
How many have you taken?
One snake is 20cm long.
Another snake is double that length.
How long is the longer snake?
I double a number and then double the answer.
I now have the number 32.
What number did I start with?
Chip the chopper
Doubling machine
94
65
48
30
71
28
36
56
97
32
12
24
51
82
19
77
63
44
53
28
60
96
75
17
43
Three in a
row
Choose two
numbers from
the row of
numbers
above the
grid.
Multiply them
together.
If the answer
is on the grid,
cover that
number with a
counter.
2 3 4 5 6 7 8 9 10
12
24
30
48
72
63
80
8
70
54
28
56
42
15
10
20
27
18
45
90
32
40
16
35
6
Three in a row
Choose two
numbers from
the row of
numbers above
the grid.
Divide the
larger number
by the smaller
number.
If the answer is
on the grid,
cover that
number with a
counter.
1
2
20
3
24
4
30
5
60
10
15 18
100
4 30 6 12
20 9
7
5 25
2 15 10
3 60 50 8
2 x 3 or 3 x 2
Multiplication
3 plates, 2 cakes on each plate
pictures
(Children could draw a picture to help them work out the answer)
2 x 3 or 3 x 2
3 plates, 2 cakes on each plate
symbols
(Children could use dots or tally marks to represent objects – quicker than drawing a
picture)
Number tracks / number lines
(modelled using bead strings)
2 x 3 or 3 x 2
[two, three times] or [three groups of two]
0
2
4
6
Arrays
5 x 3 or 3 x 5
14 x 2 = 28
x
2
10
20
4
8
Array creator
13 x 4 = 52
X
10
3
4
Answer = 52
X
10
3
4
40
12
43 x 6
X
40
3
6
240
18
( 3 x 6)
(40 x 6)
43
x 6
18
240
258
40 x 6 = 240
3 x 6 = 18
43
x 6
258
1
27 x 34
27 x 34
Approximation:
Answer lies between 600 (20 x 30) and 1200 (30 x 40)
or 30 x 30 = 900
27
x 34
28
80
210
600
918
( 7 x 4)
(20 x 4)
( 7 x 30)
(20 x 30)
Extend to HTU x U, U.t x U and HTU x TU
27
x 34
108 (27 x 4)
810 (27 x 30)
918
Multiplication
grid ITP
6÷2
Division
6 cakes shared between 2
pictures
6 cakes put into groups of 2
(Children could draw a picture to help them work out the answer)
6÷2
6 cakes shared between 2
symbols
6 cakes put into groups of 2
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Number tracks / number lines - grouping
(modelled using bead strings)
8÷2=4
6÷2=3
0
2
4
6
Number lines / Arrays
15 ÷ 5 = 3
0
5
10
15
Grouping
ITP
96 ÷ 6 = 16
(6 x 10)
(6 x 6)
Starting
from 0
0
60
96 ÷ 6
6 x 10 = 60
6 x 6 = 36
Number dial ITP
96
Efficient methods . . . .
754 ÷ 6
Approximation:
Answer lies between
100 (600 ÷ 6) and 150 (900 ÷ 6)
Answer = 125 r 4
754
- 600
154
- 120
34
- 30
4
(6 x 100)
(6 x 20)
(6 x
Extend to U.t ÷ U and HTU ÷ TU
5)
Efficient methods . . . .
Short division
291 ÷ 3 = 97
Estimate: 270 ÷ 3 = 90
97
3
291
2
43.4 ÷ 7 = 6.2
6.2
Estimate: 42 ÷ 7 = 6
7
43.4
1