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. =

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

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.

What common fraction to percentage conversions should be known? 1/10 10/10 0 10% 1/5 20/10 0 20% 1/2 50/10 0 50% 1/4 25/10 0 25%

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

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

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?

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)

Find 35% of $80 100% $80 $80

Find 35% of $80 100% $80 $80

Find 35% of $80 100% $80

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

Now try this… 46% of $90

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%?

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

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

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)

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

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?

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 %

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)

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!

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?

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.

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 10 or 2 laps : 1 min so multiply by 5 Relationship within the rates 24 : 12 2:1 the minutes taken are half the laps 2 : 1 Relationship between the rates 24 : 12 10/24 = 5/12 10 : ?

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

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

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

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

16 weeks : $40 so 6 weeks : $? Relationship within the rates Find the unit rate (there are always two unit rates) 1 week : $2.50 so multiply $2.50 by 6 or 0.4 week: $1 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 : ?