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What do students need to be able to do before we solve percentage problems?Have a knowledge of percentages
Know common factors & multiples
Recall of multiplication and
division facts
Fabulous Folding The first step might be to…..
Using a piece of paper, fold it and mark the fold lines.
What is the meaning of the denominator and numerator? FIO Number Level 2-3 Page 18. (Teacher guide - notes)Purpose - build up 2 double no lines
21
0 1
To find the fraction of a quantity..
0 41
21
43
1
eg. one quarter of the class of 32 students travel to school by bus,
how many of the class travel by bus?
32168
So 8 students travel by bus
24
These lines can be simplified toThese lines can be simplified to
41
0 8 32
What stage do students need to be to do this?Multiplicative?
0 1
0% 20% 100%
20% of 150 is
Question (in context)
The local dairy farmer is selling 20% of his herd of 150 cows. How many is he selling? Rewrite in
maths language
150
How do we use the lines to get the answer?
0% 20% 100%
150
20 x 5 = 100
150 divided by 5 = 30
0% 20% 100%
150
Find 10% : 150 divided by 10
So 10% = 15
So 20% =30
There are 30 students in Room 16. 40% are girls. How many girls are there in the class?
What is the maths? (Mathematize it)
How do we use the lines to get the answer?
0% 20% 40% 100%
30
20 x 5 = 100
20% = 6
So 40% = 12
30 divided by 5 = 6
0% 20% 40% 100%
30Find 20% : 30 divided by 5
20% = 6 so 40% =12
30% of the swimming team are girls. If there are 18 girls . How many are in the team altogether?
18 is 30% of
Sarah went shopping for a new bike which cost $350. When she got to town there was a sale and she got 20% off the price. What did she pay?
Did she pay more or less?
How much less?
So instead of paying 100% she only paid?
Show all this on the number lines
0% 80% 100%
$350
40
32
80
31
120
× 3 or add to 80 = 120
Don’t forget to use “reverse” Don’t forget to use “reverse” problems. problems. Jim watched 2 thirds of a DVD. If he watched for 80 Jim watched 2 thirds of a DVD. If he watched for 80 minutes, how long was the DVD?minutes, how long was the DVD?
The value of a $400 antique vase has been increased by 20%. What is its value now?
What questions do we ask?120% of 400 is
Or divide 400 by 10 (to get 10%) and multiply by 12.
X 4 X 40% 120%100%
$400
After an increase in his weekly wage of 20% Joe has $540.What was his wage before the increase?
$540 is 120% of
0% 100% 120%
$540
How about looking at GST?
Problem A plasma TV costs $1 200 before GST. How much GST will have to be paid on this?
What is the maths?
112.5% of $1 200 = $1 200 + 12.5% of $1 200 =
0 100% 112.5% 8 x 12.5% 9 x12.5%
1200
8 x 150 9 x 150
Will you pay more or less?
When GST is raised to 15%, how much more will you pay?
Moving to number properties20% of 150 is ?
Now is time to link what they know about % with decimal fractions.
How else can we write this?
What does 20% actually mean?
How could we do this without the number line?
For some students this stage will be a long time coming! For others they will tell you.
Now might be the time to bring in a calculator and some more “awkward” q’s
Teaching progression
Materials
Images
Knowledge
Start by:Using materials, diagrams to illustrate and solve the problemProgress to:Developing mental images to help solve the problemExtend to:Working abstractly with the number property
Sian has 2 packs of sweets, each with the same number of sweets. She eats 6 sweets and has 14 left. How many sweets are in a pack?
Don’t forget to always use “reverse” problems
Jim watched 2/3 of a DVD. If he watched for 80 minutes how long was the DVD?
40
32
80
31
120
× 3 or add to 80 = 120
Ameeta has 3 packs of biscuits, and 4 extra loose biscuits. Sam has one pack of biscuits and 16 loose biscuits. If they both have the same number of biscuits, how many biscuits are in a pack?
Can you draw a picture to show the problem?