Good Solid Teaching of Percentages
Vince WrightThe University of Waikato
Intended outcomes of the webinar:
1.Identify similarity of structure in percentage problems2.Consider how numbers and co-ordination of steps make a difference3.Use some useful representations4.Relate these ideas to GST
An item costs $50.00 usually.It is on sale at 25% discount.What is the sale price?
75 100
? 50
10% 50% 100%
0%
0 2010 30 40 50
Part Whole
75% 100
50
½ x ½ x
10%
20%
50%
80%
100%
0%
0 2010 30 40 50 60
An item costs $60.00 usually.It is on sale at 20% discount.What is the sale price?
80 100
? 60
http://www.nzmaths.co.nz/sites/default/files/Numeracy/2007matmas/Bk7/MM%207_4.pdf
Part Whole
80 100
60
8 10
÷ 10÷ 10
x 6x 6
240 cows give birth to 180 calves.What is the calving percentage?
? 100
180
240
calves cows
calvescows
100
180240
1824
34
÷ 10÷ 10
÷ 6÷ 6
x 25x 25
140 ewes give birth to 245 lambs.What is the lambing percentage?
100%
140
ewes lambs
100
245140
4928
74
÷ 5÷ 5
÷ 7÷ 7
x 25x 25
27 out of 45 kiwi chicks survive.What is the survival rate as a percentage?
survivors chicks
4527
53
10060
÷ 9÷ 9
X 20X 20
x 3/5
x 3/5
Goods and Services Tax
GST exclusive price GST
GST inclusive price
GST exclusive price 10 %
GST inclusive price
100% 110%0%
GST exclusive price 12.5 %
GST inclusive price
100% 112.5%0%
GST exclusive price 15 %
GST inclusive price
100% 115%0%
The GST exclusive price of an item is $86.00Work out the GST inclusive price.
15 %
GST inclusive price
10%5%
Percentage Amount
$86.00100%
115%
$8.6010%
$4.305%
$98.90
The GST inclusive price of an item is $345.00Work out the GST inclusive price.
15 %
GST inclusive price
Percentage Amount
100%
115% $345
1% $3
15% $45
$450
÷ 115÷ 115
x 15x 15
x 100x 100
Where does the multiply by 3 then divide by 23 rule come from?
Take any multiple of 4.
Multiply the number by 3.
Now divide by 4.
What fraction of the number did you find?
Take any multiple of 4.
Divide by 4.
Now multiply the number by 3.
What fraction of the number did you find?
15 %
GST inclusive price
You know this
You need to know
this
Multiplying by 3 then dividing by 23 is finding 3/23 of the amount.
15 %
GST inclusive price
3 lots of 5%
20 lots of 5%
23 lots of 5%
Good Solid Teaching of percentages means:
1.Using representations to show learners how the part-whole or whole-whole relationships work2.Connecting understanding with calculation proficiency