Transcript presentation

Progression in Teaching
Multiplication and Division
(NNS recommendations)
Prior Experience Required
Before children are introduced to multiplication and division they should:

Be able to count securely

Understand basic addition and subtraction

Be able to form groupings
I can count to
one hundred.
Listen to me. . . 1,
2, 3 , 4 . . .99,
100!!!
Two add
three
makes
five!
I have grouped my
counters into threes!
Stage 1: Mental Counting and Counting Objects
(Years 2 and 3)
Let’s all count in multiples of
two. Are you ready? Two,
four, six . . .
Altogether I have
123, 456, 789, 1011
12 counters!
Stage 2: Early mental calculations and
learning number facts with recording.
(Years 2 and 3)
Gemma W
What is six times 2?
12
Yes, that’s right!
2 x 6 = 12
6 x 2 = 12
12 ÷ 2 = 6
12 ÷ 6 = 2
Stage 3: Working with larger numbers and
informal jottings (Years 2, 3 and 4)
24 x 8. Let’s see that’s . . . 20 x 8 which is 2 x 8 x
10 . . . 160. 4 x 8 is 32. So 24 x 8 is 160 + 32
which is 60 + 32 + 100 which is 192!
24 x 8 . Let’s see. . . 6 x 8 = 48 so double 6
gives 12 x 8, so that’s 96. Then double 12 is
24 so double 96. Double 100 is 200 take away
double 4 which is 8 gives 192!
Stage 4: Non-standard expanded written
methods begin in Year 4, first with whole
numbers.
Grid method for 38 x 7
Expanded vertical recording
38
x 7
210 (30 x 7)
56 (8 x 7)
266
x
30
8
7
210
56
266
Stage 5: Standard written methods for
whole numbers then for decimals (beginning
in Year 4 and extending through to Year 6.)
203
x
57
10150
1421
11571
458 ÷3 by chunking
3 4158
458
- 300
(100 x 3)
23.75
x
3
Compact short multiplication
158
- 150
(50 x 3)
6
(2 x 3)
2
Answer 152 rem 2
71.25
Compact short multiplication of decimals
28
15 432
8
Compact long multiplication
152 rem 2
300
132
120
12
Answer 28 rem 12
Compact long multiplication
Stage 6: Use of calculators
(beginning in Year 5)
We’ve measured the playground and it is 23.75 metres
long and 18.55 metres wide. What is the area of the
playground?
It is 23.75 metres times 18.55 metres. I’ve worked it out on
my calculator. It’s 440.56 square metres to the nearest
centimetre!