G ood S olid T eaching of Percentages

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

vince@waikato.ac.nz