Good Solid Teaching of Percentages
Vince Wright
The University of Waikato
Intended outcomes of the webinar:
1.
2.
3.
4.
Identify similarity of structure in percentage problems
Consider how numbers and co-ordination of steps make a difference
Use some useful representations
Relate these ideas to GST
An item costs $50.00 usually.
It is on sale at 25% discount.
What is the sale price?
0%
0
10
%
50
%
10
20
100
%
40
30
50
75
100
?
50
Part
Whole
50
½x
½x
75%
100
http://www.nzmaths.co.nz/sites/default/files/Numeracy/2007matmas/Bk7/MM%207_4.pdf
An item costs $60.00 usually.
It is on sale at 20% discount.
What is the sale price?
0%
0
10
%
20
%
10
50
%
20
30
80
%
40
100
%
50
60
80
100
?
60
Part
Whole
60
x6
x6
8
10
÷ 10
÷ 10
80
100
240 cows give birth to 180 calves.
What is the calving percentage?
?
100
240
180
calves
cows
cows
240
calves
180
÷ 10
÷ 10
24
18
÷6
÷6
4
3
x 25
x 25
100
140 ewes give birth to 245 lambs.
What is the lambing percentage?
100%
140
ewes
lambs
140
245
÷5
÷5
28
49
÷7
÷7
4
x 25
100
7
x 25
27 out of 45 kiwi chicks survive.
What is the survival rate as a percentage?
survivors
27
chicks
x
3/
÷9
3
45
÷9
5
5
x 3 /5
X 20
X 20
60
100
Goods and Services Tax
GST exclusive price
GST inclusive price
GST
GST exclusive price
10 %
GST inclusive price
0%
100% 110%
GST exclusive price
12.5 %
GST inclusive price
0%
100%
112.5%
GST exclusive price
15 %
GST inclusive price
0%
100%
115%
The GST exclusive price of an item is $86.00
Work out the GST inclusive price.
5%
10%
15 %
GST inclusive price
Percentage
Amount
100%
$86.00
10%
$8.60
5%
$4.30
115%
$98.90
The GST inclusive price of an item is $345.00
Work out the GST inclusive price.
15 %
GST inclusive price
Percentage
115%
Amount
$345
÷ 115
÷ 115
1%
$3
x 15
x 15
15%
$45
x 100
x 100
100%
$450
Where does the multiply by 3 then divide by 23 rule come from?
Take any multiple of 4.
Divide by 4.
Now multiply the number by 3.
What fraction of the number did you find?
Take any multiple of 4.
Multiply the number by 3.
Now divide by 4.
What fraction of the number did you find?
Multiplying by 3 then dividing by 23 is finding
3/
23 of the amount.
You need
to know
this
15 %
GST inclusive price
You
know
this
3 lots of
5%
20 lots of
5%
15 %
GST inclusive price
23 lots
of 5%
Good Solid Teaching of percentages means:
1. Using representations to show learners how the part-whole or wholewhole relationships work
2. Connecting understanding with calculation proficiency
vince@waikato.ac.nz