1. So it is useful to view percentages as hundredths.
Why calculate percentages?
It is a method of comparing fractions by giving both fractions a common denominator - hundredths.
So it is useful to view percentages as hundredths. =

2. Percentages At what stage are percentages introduced?
(knowledge and strategy)

3. Percentages AM (Stage 7: NC Level 4)
Solve fraction  decimal  percentage conversions for common fractions e.g. halves, thirds, quarters, fifths, and tenths
AP(Stage 8: NC Level 5)
Estimate and solve problems using a variety of strategies including using common factors, re-unitising of fractions, decimals and percentages, and finding relationships between and within ratios and simple rates.

4. What common fraction to percentage conversions should be known?
1/ / %
1/5 20/ %
1/ / %
1/4 25/ %

5. Ideas for teaching common fraction to percentage conversions
Equivalent fractions, decimals & percentages
(Book 8, page 21 and Material Master 4-28)
Using deci-mats to show: 1/10=10 /100 = 0.1= 10%
Bead strings and tags / slavonic abacus
Decipipes

6. Practice / Assess I have, Who Has Memory / Snap Dominoes Happy
Quick activities to practice and/or check common fraction to percentage conversions are known.
Practice / Assess
Memory / Snap
Headworks
(Brian Storey)
Bingo
I have, Who Has
Dominoes
Happy
Families

7. Types of Percentage Calculations
Applying Percentages
Types of Percentage Calculations
Finding percentages of amounts, e.g. 25% of $80
Expressing quantities as a percentage (for easy comparison), e.g. 18 out of 24 = ?%
Increase and decrease quantities by given percentages, including mark up, discount and GST e.g. A watch cost $20 after a 33% discount. - What was it’s original price?

8. E.g. Find 25% of $80 (easy!) 25% = 1/4 so 25% = 1/4 of 80 = $20
Mini Teaching Session 1
Estimate and find percentages of whole number amounts.
E.g. Find 25% of $80 (easy!)
25% = 1/4 so 25% = 1/4 of 80 = $20
E.g. Find 35% of $80 (harder!)
“Pondering Percentages” NS&AT 3-4.1(12-13)

9. Find 35% of $80
100%
$80
$80

10. Find 35% of $80
100%
$80
$80

11. Find 35% of $80
100%
$80

12. Find 35% of $80 $8
10%
100%
$80 $8
30%
$24 $4 5%
35%
$28

13. Now try this…
46% of $90

14. Is there an easier way to find 46%?
100%
10%
40% 5% 1% 6%
46%
$90 $9
$36
$4.50
$0.90
$5.40
$41.40
Is there an easier way to find 46%?

15. Estimating Percentages
Using Number Properties:
Explain how you would estimate 61% of a number?
Estimating Percentages
16% of 3961 TVs are found to be faulty at the factory and need repairs before they are sent for sale. About how many sets is that?
(book 8 p 26 - Number Sense)
About 600

16. Using Figure It Out
“Percents” Game (MM7-5)

17. Expressing quantities as a percentage
Mini Teaching Session 2
Expressing quantities as a percentage
(for easy comparison),
e.g.18 out of 24 = ?%
Hot Shots N3-4 (12)
Percentages N7/8 4.5 (22)
Laser Blazer PR3-4.2(12-13)

18. Calculating Percentages
Percentage strips help students to see that calculating percentages is like mapping a fraction onto a base of 100.
Leonne got 18 out of her 24 shots in.
What was her shooting percentage? 10 20 24

19. Leonne’s Percentage (18 out of 24)10 20 24
10%
20%
30%
40%
50%
60%
70%
80%
90%
100% 0%
So Leonne’s 18 out of 24 maps onto 75 out of 100 (75%).
How does this relate to how you would calculate 18/24 as a percentage?

20. Leonne’s Percentage (18 out of 24)
Using a double number line
Laser Blazer (FIO)
hits 0 24
100% 0% ? 18 1 75
18/24 = 3/4 %

21. Ratios and Rates Both are multiplicative relationships.
What is the difference between a ratio and a rate?
Both are multiplicative relationships.
A ratio is a relationship between to things that are measured by the same unit,
e.g. 4 shovels of sand to 1 shovel of cement.
A rate involves different measurement units,
e.g. 60 kilometres in 1 hour (60 km/hr)

22. Rates Nikki jogs 2.4km (6 laps) in 12 minutes
What other information can you get from this statement?
Write the questions only - you don’t have to solve them….yet!

23. Nikki jogs 24 laps in 12 minutes
How long did it take to run 1 lap?
How far can she run in 1 minute
Nikki jogs 24 laps in 12 minutes
How far will she have run in 1 hour (if the same pace is kept)
How long will it take to run 10 laps?

24. How long will it take to run 10 laps? 24 laps:12 min so 10 laps:? min
Key Idea: The key to proportional thinking is being able to see combinations of factors within numbers.

25. 24 laps:12 min so 10 laps:? min 24 : 12 10/24 = 5/12
Find the unit rate (there are always two unit rates)
1 lap: 0.5 min so multiply by or
2 laps : 1 min so multiply by 5
Relationship within the rates
24 : :1
the minutes taken are half the laps
2 : 1
Relationship between the rates
24 : 12
10/24 = 5/12
10 : ?

26. 24 laps:12 min so laps:? min
Using cubes
24:12
2:1
10:5

27. 24 laps:12 min so 10 laps:? min Using double lines 24 1 10 12
minutes
Laps
10/24 = 5/12 5

28. 24 laps:12 min so 10 laps:? min Minutes Laps Rate 1 24 12 Rate 2 10
Use ratio tables to identify the multiplicative relationships between the numbers involved.
Minutes
Laps
Rate 1 24 12
Rate 2 10
X 5/12
Note there are other relationships:
The difference between the height in toothpicks and the height in counters of each plant is x 1.5
The difference between Plant B and Plant A’s height (in counters or toothpicks) is x two-thirds.
÷ 2

29. Mei ling earns $40 in 16 weeks so how much will she have earn in 6 weeks? 16 weeks : $40 so 6 weeks : $?

30. 16 weeks : $40 so 6 weeks : $? Relationship within the rates
Find the unit rate (there are always two unit rates)
1 week : $ so multiply $2.50 by 6 or
0.4 week: $ so multiply $1 by 15
Relationship within the rates
16 : 40
16 : 40 = 2:5 so multiply 5 by 3
6 : ?
Relationship between the rates
16 : 40
6/16 = 3/8 so what is 3/8 of 40
6 : ?