The aim of the session is to reinforce methods of
teaching the following topics across the curriculum
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Calculating a percentage of a quantity 7.N10, 8.N10
How to increase/decrease a quantity by a
percentage 8.N10
Calculating a percentage increase or decrease
9.N10a
Expressing one quantity as a percentage of another
9.N10
The equivalence of fractions, percentages and
decimals 8.N9
7.N10, 8.N10 Calculate percentages of quantities
using non-calculator methods where appropriate
Example –
Sam plants 320 seeds. If 40% of all seeds germinate how
many seeds will germinate?
Non Calculator Method
40% of 320
10% = 320 = 32
10
40% = 32 x 4 = 128
Try this one –
We would like 70% of all pupils to achieve a grade C or
above in the Maths exam. If 160 pupils are sitting the
exam, how many pupils will need a C or above?
10 % = 160 = 16
10
70% = 16 x 7 = 112 pupils
Calculator Method
Find 69% of £825
69 x 825
100
= 569.25
Try this one –
Approximately 14% of all pupils travel to school by car. If
there are 1225 pupils in the school, how many travel to
school in a car?
14 ÷ 100 x 1225 = 171.5
≈ 172 pupils
8.N10 Calculate the outcome of a given percentage
increase/decrease
The number of smokers in Wales decreased by 15% last
year. If at the beginning of last year there were
approximately 300,000 smokers in Wales how many
smokers were there at the end of the year?
We find 15% of 300,000 and then decrease (subtract) the
answer from the 300,000.
10% = 300000 ÷ 10 = 30,000
5% = 30,000 ÷ 2 = 15,000
15 % = 30, 000 + 15, 000 = 45, 000 decrease
At the end of the year there were
300,000 – 45,000 = 255,000 smokers in Wales.
If you are increasing by a certain percentage you add on
the answer.
Try this one.
The director of a small shop expect the sales of tablet
computers to increase by 35% this Christmas. If they sold
1400 last year, how many will they expect to sell this year?
Find 35% of 1400
10% = 1400 ÷ 10 = 140
30 % = 140 x 3 = 420
5% = 140 ÷ 2 = 70
35% = 420 + 70 = 490
Expected sales = 1400 + 490 = 1890 tablet computers.
Calculator Method
35 x 1400 = 490
Expected Sales = 1400 + 490 = 1890
100
9.N10a
Calculate a percentage increase/decrease
Sales of a certain magazine increases from 4000 to 6500
in a three month period. Work out the percentage
increase of the magazine sales.
The formula that is taught in maths is
Percentage Increase = Increase x 100%
Original
Increase = 6500 – 4000 = 2500
Percentage Increase = 2500 x 100% = 62.5%
4000
Try this one
The value of a car decreases from £18000 to
£12500 in one year. Work out the percentage decrease of
the car in that year.
Decrease = 18000 – 12500 = 5500
Percentage Decrease = 5500 x 100% = 30.55555555%
18000
= 30.6% to 1 decimal place
9NS5 Express one quantity as a percentage of
another
Daniel achieved 18 out of 20 in a test, write this as a
percentage
18 x 100% = 90%
20
Non calculator method means we would cancel down 20
and 100, then multiply 18 x 5
Try this one
12 out of every 40 pupils have brown hair, write
this as a percentage
12 x 100% = 30%
40
7.N9
Use the equivalence of fractions, percentages
and decimals to compare proportions.
The pupils should know the basic conversions of
½ = 0.5 = 50%
¼ = 0.25 = 25% 1/10 = 0.1 = 10%
To compare fractions, percentages and decimals
pupils need to be able to convert all of the
quantities to the same unit.
Change 3/10 into a percentage
3 x 100% = 30%
10
Change 0.3 into a percentage
0.3 x 100% = 30%
Change 37% into a decimal
37% = 37 = 0.37
100
Convert 65% into a fraction
65% = 65 = 13
100 20