1. on dividing by 10 as you go to the right”, ‘deci is about ten’….). Write the percentage value beside the decimal numbers (10%, 1%, 23%, 50%, 99% and 0.1%) and have learners show this on a hundred board. Ask learners to focus on two number representations and record what they notice. For example: 0.1 is 1/10 and is 10/100 or 10%. Ask the learners in pairs to write their own definition of ‘percent’, and suggest why we use the word is ‘percent’ and the symbol %. Share and discuss their understandings eg A percentage is a way of expressing a fraction of 100, or another way of writing hundredths. Percent, from the Latin ‘per centum’ literally means out of (per) one hundred (cent). The symbol % is made up of the / per sign and the two zeros (00) from the number 100. Activity Process: Estimating Percentages Learning Intention: Understanding estimation as approximately not exactly. Discuss with learners their understanding of the word estimate. Create a definition of the word, for example Estimation is...... finding a number that is close enough to the right answer. You are not trying to get the exact right answer What you want is something that is an reasonable guess Everyday simple fractions can be used to estimate the percent of a number. Create a display of common fractions using a strip. Ask learners to estimate 17% of 46 by Finding the percent that it is closest to on the strip. 17% is about 20% Find the fractional equivalent of 20% on the strip, it is 1/5 Find a compatible number for the number for the number you are asked to find the percent of. 46 is about 50. Use the fraction strip to find the percent. 20% is equal to 1/5. 1/5 of 50 is 10 A reasonable guess is that 17% of 46 is about 10 (Learners might ask why 1/3 as 0.333… has dots after the decimal. Explain it is a recurring number) Australian Curriculum Year 6 Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies ACMNA132 Key Ideas Financial literacy. Percentages are commonly used in real life. Resources FISH Vocabulary Percent, percentages, Investigate, calculate, estimate, exact Activity Process: What is a percentage Learning Intention: Revision The word per cent comes from the Latin word per centum. This means out of a hundred and is represented by the symbol % Brainstorm on the group/class chart what learners know about decimals. Record their ideas. (for example: “there’s a decimal point between whole numbers and parts”, “there are tenths, hundredths, thousandths”, “with decimal numbers you keep Fraction 1/1001/201/101/51/41/21/33/41 Percent 1%5%10%20%25%50%33 1/3 %75 % 100% Decimal 0.10.50.100.200.250.500.333....0.7 5 1

2. numerator will be greater than 100 and the denominator will be 100. Any fraction with a numerator greater than its denominator is called improper for example 150 is 150% and 5 of 1000 is 0.5%. Repeat the groups of four using the FISH process to match the cards using the information in the table Some Calculations with Percentages and fraction strips previously used. Activity Process: Percentages and Money Many shops identify the amount of discount in a sale in terms of percentage off. Consider the example of a 25% off sale: An advert for a sale of children’s bikes could advertise a sale price which is 25% off the original price. The ordinary purchase price was $100 the sale price is 25% less. We have to ask the question. What % of the price is 25% The % sign tells us that it is 25/100 as a fraction which can be simplified to ¼ of the original price. We know that the denominator tells us there is 4 parts of the whole, so we can divide 100 by 4 to get 25. The bike sale price is $25 less than the original. Of’ means ‘multiplied by’. Percentages relate numbers to 100. So that 50% actually means 50 out of 100. This means that 50% of a quantity (say, 40) can be calculated by multiplying the quantity by 50/100 (say, 40 x 50/100). Learners are encourage the students to justify the reasonableness (Green FISH) of the answers that they get using the percentage key on the calculator to solve problems. Ask the learners if they know how to work out 25% of 28 using a calculator. If possible use a projected calculator so everyone can see and key in 28 x 25%. Challenge them to find 40% of 35 by first estimating (remind them that estimation is not exact but approximate) and then performing the operation on the calculator. Activity Process: Percentage Sort Learning Intention-To assist the development of computation skills when calculating and working with percentages. Play this game in two parts. Sort the number into those to 100 and those beyond. Find and print cards at http://www.schools.nsw.edu.au/learning/7-12assessments/naplan/teachstrategies/yr2011/images/nn_numb_frde_s4_worksheet4_3.pdf In groups of four using FISH process learners match the cards using the information in the table Some Calculations with Percentages and fraction strips previously used. As a whole class activity: FISH from selected groups explains the FISH process they used to complete the activity. The class as active listeners comment on and evaluate the effectiveness of strategies used by each group. Teacher as white FISH uses a selection of questions to elicit responses that will emphasise the effective relationships between the calculations, e.g. What strategies could I use? Activity Process: Percentage Sort Part Two-Percents Less Than 1 or Greater Than 100 It is possible to have over 100% and less than 1%. The fractional form of a percentage greater than 100 is always an improper fraction. A percentage is part of 100 so the

3. 0% 10% 25% 50% 100% 0 10 12.5 25 50 0% 20% 50% 100% 200% 0 2.5 12.5 25 50 0% 25% 50% 75% 100% Full Price Pose this problem: "Is 50% of 25 more, less, or the same as, 25% of 50?" Tell the students that you want them to explain their answers. Discuss the models students use to solve the problem: Examples include: use of equivalent fractions: 50% is 1/2, so 50% of 25 is one-half of 25; 25% is 1/4, so 25% of 50 is one-quarter of 50; Since 50 is twice as much as 25, and one-quarter is half of one-half, the answers must be equal. use of operational order: 50 x 25% gives the same result as 25 x 50% as only the order of the factors is changed. use of matching double number lines: Investigate: Tell the students that they can use a calculator for 50% of the problems,(all four must be completed) but suggest that thinking about each problem (FISH process) is a beneficial first step. 25% of what number is 12? (25% x ? = 12) (Answer: 25% of 48) 40% of what number is 14? (40% x ? = 14) (Answer: 40% of 35) What percentage of 28 is 21? (? % x 28 = 21) (Answer: 75% of 28) What percentage of 18 is 6? (? %x 18 = 6) (Answer: 33.33%of 18) Assessment: Option 1 (a) Choose an arrow that matches what you would pay in a 25% off sale. Justify the reasonableness of your answer Ask learners to share the strategies they used to solve these problems. Option 1 (b using a calculator) At the 25% off sale and item costs $34 at normal price. What does it cost at 25%, 50% and 75% off Option 2 (a) Using a shopping advertising brochure choose five articles to purchase. The store is having a 30% off sale and they must work out what the estimated discounted price will be. Using Yellow FISH strategies, model your answers Option 2 (b) Is 135% of 300 the same as 300 plus 35% of 300? Why? Why not? Using Green FISH thinking to explain your reasoning. Option 2 (c) 1. Look through a newspaper and find at least five places where money and/or percentages are used to communicate with the public. Write down what you find. 2. Work out approximately what percentage of the paper is used for advertising. 3. Describe how your reach your conclusions using the FISH strategies