Dŵr y Felin Comprehensive School
Percentages
Methodology
Booklet
Percentages
.
Key Teaching Point
The pupils should know that per – cent means ‘out of 100’
In Year 8 pupils are mainly taught non-calculator methods for working out
percentages.
Percentage of a Quantity.
Examples
Non Calculator Methods
For non calculator methods pupils are taught always to start with 10%. From
experience some pupils favour the method of ‘breaking the percentage down’
and will revert to this even with a calculator.
Find 10% of 130
Find 40% of 340
10% = 130 = 13
10
Step 1 Step 2 -
Find 60% of 397
Step 1 Step 2 -
10% = 340 = 34
10
40% = 34 x 4 = 136
10% = 397 = 39.7
10
60% = 39.7
x 6
238.2
5
Find 35% of 240
Step 1 Step 2 Step 3 Step 4 -
Find 42% of 60
Step 1 Step 2 Step 3 Step 4 Step 5 -
Multiply the
10% answer by
4
4
Divide the 10%
10% = 240 = 24
answer by 2
10
30% = 24 x 3 = 72
5% = 24 ÷ 2 = 12
30% + 5% = 72 + 12 = 84
10% = 60 = 6
10
40% = 6 x 4 = 24
1% = 6 = 0.6
10
2% = 0.6 x 2 = 1.2
42% = 24 + 1.2 = 25.2
Divide the
10% answer
by 10
Add the 40%
and the 2%
answers.
Calculator Method
Example
Find 34% of 456 = 34 x 456 = 155.04
100
Common Misconceptions
• Errors in basic mental addition
• Errors in setting the sum out correctly
• In more complex questions (42% etc) confusion about which answers
to add together.
Finding One Number As A Percentage of Another.
Example
Find 36 as a percentage of 50.
2
36 x 100% = 72%
50 1
Common Misconceptions
• Errors in basic numeracy
• Pupils unable to ‘cancel down’ correctly
Percentage Increase / Decrease
Percentage Increase = Increase x 100%
Original
Percentage Decrease = Decrease x 100%
Original
Example
The sales of ice cream increased from 40 to 48 per day. Work out the
percentage increase.
Increase = 48 – 40 = 8
5
% Increase = 8 x 100% = 40 = 20%
40 2
2
Common Misconceptions
• Errors in basic numeracy
• Pupils unable to recall the formulae