1. Created by Mr. Lafferty Maths Dept.
Proportion
Proportional Division
Proportion per item
Direct Proportion
Graph of Direct Proportion
Inverse (Indirect) Proportion
23-Feb-19
Created by Mr. Lafferty Maths Dept.

2. Created by Mr. Lafferty Maths Dept.
Starter Questions 9 8 6
23-Feb-19
Created by Mr. Lafferty Maths Dept.

3. Created by Mr. Lafferty Maths Dept.
Proportion
Proportional Division
Learning Intention
Success Criteria
1. Be able to find total shares.
1. We are learning to calculate proportional division by using shares.
2. Find fractional share.
3. Solve problems using appropriate working.
23-Feb-19
Created by Mr. Lafferty Maths Dept.

4. Proportion www.mathsrevision.com Proportional Division
Example : Jack and Victor share a raffle win of £500
in the ratio 2:3. How much does each get ?
Are we expecting more or less
Make smaller fraction
Total number of shares :
2 + 3 = 5 shares
No. of shares £
5 → 500
Jack
2 →
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Created by Mr. Lafferty Maths Dept.

5. Proportion www.mathsrevision.com Check : £200 + £300 = £500
Make smaller fraction
Are we expecting more or less
Proportion
Proportional Division
No. of shares £
5 → 500
Victor
3 →
Check :
£200 + £300 = £500
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Created by Mr. Lafferty Maths Dept.

6. Proportion www.mathsrevision.com Proportional Division
Ex : Ryan, Ross and Ben share 24 cakes in the ratio
1 : 2 : 3. How many cakes does each get ?
Are we expecting more or less
Make smaller fraction
Total number of shares :
= 6 shares
No. of shares Cakes
6 → 24
Ryan
1 →
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23-Feb-19
Created by Mr. Lafferty Maths Dept.

7. Proportion www.mathsrevision.com Are we expecting more or less
Make smaller fraction
Proportion
Proportional Division
No. of shares Cakes
6 → 24
Ross
2 →
23-Feb-19
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Created by Mr. Lafferty Maths Dept.

8. Proportion www.mathsrevision.com Check : 4 + 8 + 12 = 24
Make smaller fraction
Are we expecting more or less
Proportion
Proportional Division
No. of shares Cakes
6 → 24
Ben
3 →
Check :
= 24
23-Feb-19
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Created by Mr. Lafferty Maths Dept.

9. Created by Mr. Lafferty Maths Dept.
Proportion
Now try TJ4+
Ex 15.1
Ch15 (page 111)
23-Feb-19
Created by Mr. Lafferty Maths Dept.

10. Created by Mr. Lafferty Maths Dept.
Starter Questions
23-Feb-19
Created by Mr. Lafferty Maths Dept.

11. Created by Mr. Lafferty Maths Dept.
Proportion
Proportion
Learning Intention
Success Criteria
Understand the term
per item.
1 We are learning the value of one item using proportion.
2. Solve simple proportional problems.
23-Feb-19
Created by Mr. Lafferty Maths Dept.

12. Proportion www.mathsrevision.com Proportion
If you know the total cost of several items, you can
easily find the cost per item ( cost for 1 ).
Are we expecting more or less
Make smaller fraction
Example : The cost of 5 chocolate bars is £8.00.
Find the cost of one.
No. of Bars £
5 → 8.00
Per item
1 →
23-Feb-19
Created by Mr. Lafferty Maths Dept.

13. Created by Mr. Lafferty Maths Dept.
Proportion
Now try TJ4+
Ex 15.2
Ch15 (page 112)
23-Feb-19
Created by Mr. Lafferty Maths Dept.

14. Created by Mr. Lafferty Maths Dept.
Starter Questions
23-Feb-19
Created by Mr. Lafferty Maths Dept.

15. Created by Mr. Lafferty Maths Dept.
Proportion
Direct Proportion
Learning Intention
Success Criteria
1. Understand the idea of Direct Proportion.
1. We are learning the term Direct Proportion.
2. Solve simple proportional problems.
23-Feb-19
Created by Mr. Lafferty Maths Dept.

16. Proportion www.mathsrevision.com Direct Proportion
Two quantities, (for example, number of cakes and total
cost) are said to be in DIRECT PROPORTION, if :
Are we expecting more or less
Make smaller fraction
“ .. When you double the number of cakes
you double the cost.”
Example : The cost of 6 cakes is £4.20.
Find the cost of 5 cakes.
No. of cakes £
6 → 4.20
5 →
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Created by Mr. Lafferty Maths Dept.

17. Proportion www.mathsrevision.com Direct Proportion
Example : On holiday I exchanged £30 for $45.
How many $ will I get for £50.
Are we expecting more or less
Make bigger fraction
£ $
30 → 45
50 →
23-Feb-19
Created by Mr. Lafferty Maths Dept.

18. Proportion www.mathsrevision.com Direct Proportion
Example : 300 pencils cost £6. How much will 200 cost.
Are we expecting more or less
Make smaller fraction
Pencil £
300 → 6
200 →
23-Feb-19
Created by Mr. Lafferty Maths Dept.

19. Created by Mr. Lafferty Maths Dept.
Proportion
Now try TJ4+
Ex 15.3
Ch15 (page 113)
23-Feb-19
Created by Mr. Lafferty Maths Dept.

20. Created by Mr. Lafferty Maths Dept.
Starter Questions
23-Feb-19
Created by Mr. Lafferty Maths Dept.

21. Created by Mr. Lafferty Maths Dept.
Proportion
Direct Proportion Graphs
Learning Intention
Success Criteria
1. Understand that Direct Proportion Graph is a straight line.
1. We are learning about Direct Proportion Graphs.
2. Construct Direct Proportion Graphs.
23-Feb-19
Created by Mr. Lafferty Maths Dept.

22. Created by Mr. Lafferty Maths Dept.
Proportion
Direct Proportion Graphs
The table below shows the cost of packets of “Pencilss”.
We can construct a graph to represent this data.
What type of graph do we expect ?
23-Feb-19
Created by Mr. Lafferty Maths Dept.

23. Direct Proportion Graphs
Notice that the points lie on a straight line passing through the origin
Direct Proportion Graphs
This is true for any two quantities which are in Direct Proportion.
23-Feb-19
Created by Mr. Lafferty Maths Dept.

24. Proportion KeyPoint Two quantities which are in DIRECT PROPORTION
Direct Proportion Graphs
KeyPoint
Two quantities which are in
DIRECT PROPORTION
always lie on a straight line
passing through the origin.
23-Feb-19
Created by Mr. Lafferty Maths Dept.

25. Proportion x 1 2 3 4 y 6 9 12 www.mathsrevision.com
Linear Patterns !
Can you find a formula connecting y and x
Proportion
Direct Proportion Graphs
Example : Plot the points in the table below.
Are they in direct proportion? x 1 2 3 4 y 6 9 12
We plot the points (1,3) , (2,6) , (3,19) , (4,12)
23-Feb-19
Created by Mr. Lafferty Maths Dept.

26. Proportion www.mathsrevision.com Direct Proportion Graphs y 12
Plotting the points
(1,3) , (2,6) , (3,9) , (4,12) 11 10 9 8 7
Since we have a straight line
passing through the origin
x and y are in
direct proportion. 6 5 4 3 2 1
23-Feb-19
Created by Mr. Lafferty Maths Dept. x 1 2 3 4

27. Created by Mr. Lafferty Maths Dept.
Proportion
Direct Proportion Graphs
Now try TJ4+
Ex 15.4
Ch15 (page 114)
23-Feb-19
Created by Mr. Lafferty Maths Dept.

28. Created by Mr. Lafferty Maths Dept.
Starter Questions y x x x x x x x x
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Created by Mr. Lafferty Maths Dept.

29. Created by Mr. Lafferty Maths Dept.
Ratio & Proportion
Inverse Proportion
Learning Intention
Success Criteria
1. Understand the idea of Inverse Proportion.
1. We are learning the term Inverse Proportion.
2. Solve simple inverse proportion problems.
23-Feb-19
Created by Mr. Lafferty Maths Dept.

30. Ratio & Proportion www.mathsrevision.com Inverse Proportion
Inverse proportion is when one quantity doubles
and the other halves. The two quantities are said
to be INVERSELY PROPORTIONAL
or (INDIRECTLY PROPORTIONAL) to each other.
Are we expecting more or less
Easier method
Workers Hours
3  8 4
Example : If it takes 3 workers 8 hours to build a wall.
How long will it take 4 men.
Men Hours
3  8
(less)
1  3 x 8 = 24 hours
4  24 ÷ 4 = 6 hours
23-Feb-19
Created by Mr. Lafferty Maths Dept.

31. Ratio & Proportion www.mathsrevision.com Inverse Proportion
Are we expecting more or less
Example : It takes 10 workers 12 months to build a house.
How long should it take 8 men.
Men Months
Easier method
Workers months
10  12 8
10  12
1  12 x 10 = 120
8  120 ÷ 8 = 15 months
(more)
23-Feb-19
Created by Mr. Lafferty Maths Dept.

32. Proportion Now try TJ4+ Ex 15.5 Ch15 (page 116) www.mathsrevision.com
Have you updated your Learning Log ?
Proportion
Direct Proportion Graphs
Now try TJ4+
Ex 15.5
Ch15 (page 116)
Are you on Target ?
I can ?
23-Feb-19
Created by Mr. Lafferty Maths Dept.