What percent of Canadians do you think use the Internet regularly? PERCENTS. Aims for this unit: What does percent mean?

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1 PERCENTS What percent of Canadians do you think use the Internet regularly? Aims for this unit: I will be able to interpret, represent and use percents greater than 100% I will interpret, represent, and use percents between 0% and 1% I will relate percents to fractions and decimals I will solve problems involving percents What does percent mean? How is a percent like a fraction? How else could you write 68%? If every Canadian use the Internet regularly, what percent would that be? If no Canadian used the Internet regularly, what percent would that be?

2 What are the percent equivalents of some fractions you know? 1/4 is equal to % 1/2 is equal to % 3/4 is equal to % Hitchhiker's thumb Not hitchhiker's thumb 1/10 is equal to % About 25% of people have hitchhiker's thumb. Do more or less students in our class have hitchhiker's thumb?

3 With a partner, figure out the following: 1. What fraction does 25% represent? Draw a picture to show why. 2. In our class, how many people might we expect to have hitchhiker's thumb? 3. What multiplication or division could you do to answer #2? 4. About how many students in a school of 600 would you expect to have hitchhiker's thumb? Prove your thinking. 5. Find out how many students in our class actually have hitchhiker's thumb and compare that to your results from #2. 4 and 16 4 is 25% of 16 What do you think??? Agree or Disagree? 1. A percent of a number is always less than that number. 2. Every number is some percent of every other number % means one half. 4. To get 15% of a number, you can take 30% of the number's double. 9 and 20 9 is 45% of 20

4 Percents Greater than 100% Percents Greater than 100% Aim: I can represent and interpret percents greater than 100% Ivan is 160 cm tall. Taira is 152 cm tall. Both Ivan and Taira are 13 years old. An adult's height is normally 107% of his or her height at age 13. How tall are Ivan and Taira likely to be as adults?

5 Why is a 10 x 10 grid a good model for percents? How do you know how many squares to shade to show a particular percent? Because there are 100 squares, 1 square = 1 % If your height now is the whole grid, or 100%, how might you show your height when you are an adult? Part A We know that Ivan's height now is 160 cm. How many centimetres does each small square in the grid represent? How can you use this answer to figure out what 107% of Ivan's present height is?

6 Now, let's figure out Taira's height as an adult. She is currently 152cm. How tall will she grow to be? If 160cm = 100% of his current height, each square will represent 1.6 cm x 107 = cm or about 163 cm. 1.6 x 107 = Ivan's height as an adult. Figure out his future height cm

7 Let's look at 2 strategies to solve this problem: A bacon double cheeseburger, fries and a medium milkshake provide a Grade 8 student with 390% of the recommended daily grams of fat allowance for a person that age. Strategy #1: 100% of 20g = 20 g 400% of 20g = 4 x 20 = 80 grams 10% of 20 g = (20 10) = 2g 390% of 20g = (80-2)g = 78g 100% of something is the whole thing. 390% = 400% - 10% 400% is 4 times 100% To get 10%, divide 100% by 10. Calculate 390% by subtracting 10% from 400%. How many grams of fat are in the meal if the recommended daily allowance is 20 grams? With a partner solve this problem. Strategy #2: 100% = 20 gm 20/100 = x.20 = 78 grams If 100% of 20 is 20, then 1% of 20 will be 20 divided by 100 or x 0.20 will equal 78 grams

8 Pages 148, 149 Questions 5, 6, 7 and

9 Fractional Percents Aim: I can represent and interpret percents between 0% and 1% What percent does each square on a 10 by 10 grid represent? How do you know how many squares to shade in to show a certain percent? If we shade in part of a square, what does that represent?

10 You can taste sweetness if 0.5% of a sugar and water mixture is sugar. Why should 0.5% be less than 1%? Suppose the full grid represents 250 g of a sugar and water mixture. What is the least amount of sugar that must be in a 250 g sugar and water mixture for it to taste sweet? If the whole grid represents 250 g, each of the 100 squares represents 250 g / 100 or 2.5 g. So half of a square is 2.5 g / 2 or 1.25 grams

11 About 0.8% of the Canadian population is from Central or South America. If Canada's population is about 34 million, about how many of our citizens have come from Central or South America? One way to look at it is to think that 0.8% is the same as saying If we multiply the numerator and the denominator by 10 to get rid of the decimal, we can make an equivalent fraction = = We write 0.8% as a fraction, and then as a decimal x = There are about Canadian citizens who come from Central or South America.

12 Relating Percents to Decimals and Fractions Assignment: P 153 # 5c, 6, 8, 10 and 12 Aim: I can express a percent as an equivalent decimal or fraction, or a decimal or fraction as an equivalent percent. Critical thinking task: Write 74% as both a decimal and a fraction. Turn to your partner and compare your answers.

13 What portion of this circle is coloured in? 1/4 or 25% or 0.25 What is the ratio of the shaded portion to the whole circle? One pair of skis costs 150% of the cost of another pair of skis. What fraction of the price of the cheaper skis is the price of the more expensive skis? 1 : 4 or 1/4 25 : 100 or 25/100 Can you express this as a ratio and as a fraction? Write down how you would calculate this. How can you write a fraction as a decimal and a decimal as a percent?

14 100% represents the price of the cheaper skis. Grade 8 Grade 9 The ratio can be written as 150:100 and then changed to a fraction 150/100. Both the numerator and the denominator can be divided by 50, so the fraction is equal to 3/2 or 1 1/2. To write this as a decimal, the ratio 150:100 can be written as 150/100. Divide the numerator by the denominator, and 150% is equal to 1.5 Grade 7 This circle graph shows what fraction of the students in a school is in each grade. What percent of the students are in Grade 8?

15 Grade 8 Grade 9 Grade 7 5/12 are in Grade 8. Each section of the graph represents 1/12. 5/12 = = = 41.7% or about 42% A group sponsoring a contest says that 1 out of 16 tickets wins a prize. What percent of the tickets wins a prize?

16 Solving Problems Using a Proportion Today's assignment is: Page 157 #1-6, 8, 10, 11 Today's Aim (): I can solve a percent problem using an equivalent ratio

17 What do we know about proportion? A proportion compares two ratios. If three of the four terms are known, the proportion can be solved for the fourth term. Jock has a mass of 82.0 kg. After a season of football, his body fat was reduced from 18% of his total mass to 12.5% of his total mass, but his total mass did not change. How much body fat did Jock lose? With a partner, try and calculate how much body fat Jock lost? You have 5 minutes

18 18% % = 5.5% first, calculate the percent change 5.5% = 5.5 = = Then, set up a proportion to solve the problem. We need to solve for x. That means we need to get x alone on one side of the equation. To get x by itself, we need to 'undo' the division by 82. We 'undo' it by using the opposite operation. In this case, we need to multiply by 82. *Remember, whatever you do to one side of an equation, you must do to the other. = x Times 55 by 82, then divide by 1000: 55 x = 4.51 kg We call this "cross-multiply and divide".

19 Let's look at the original problem again. Jock has a mass of 82.0 kg. After a season of football, his body fat was reduced from 18% of his total mass to 12.5% of his total mass, but his total mass did not change. About 12% of the boys at Wilson Middle School play hockey. This is 30 boys. How many boys are at Wilson Middle School? How much body fat did Jock lose? We know from the previous slide that the answer to this problem was 4.51, so Jock lost 4.51 kg of body fat. With a partner, try and calculate how many boys are at Wilson? You have 3 minutes Hint: Cross Multiply = x You know what the 12% is. It's 30 boys, but you want to know what the 100% is.

20 We need to solve for x. Multiply both sides by 100. The body mass for muscle should be about 310% of the mass for fat. If Taylor's fat mass is 10.4 kg, what should his muscle mass be? Because x is currently a denominator, we need to multiply both sides by x so that it becomes a numerator. If muscle mass is 310%, then fat mass is 100%. We know Taylor's fat mass is 10.4 kg. That is equivalent to 100%. To get x by itself, we divide both sides by 12. = That means that there are 250 boys at WMS. x Or, 100 x = 250 With a partner, try and calculate how much muscle mass does Taylor have? You have 1 minute Hint: Cross Multiply

21 Assignment: Solving Percent Problems using Decimals Pages 161, 162 #3, 5, 8, 9, and 14 Lesson Aim: I can use the decimal representation of a percent to solve a problem.

22 How can you write the decimal equivalent of a percent? Let's briefly review how percents and decimals are related. Write each percent as a decimal and explain your thinking: 50% 0.50 You can divide the percent by % 8.5% You can move the decimal point two places to the left You can write the percent as an equivalent fraction with a denominator of 100, and then divide the numerator by the denominator.

23 About how many First Nations people in Alberta live in large towns and cities? In Alberta, more and more people are living in urban areas (large towns and cities). According to the 2006 census, about 5.78% of Alberta's population of was First Nations. About 55.6% of these First Nations people were living in urban areas. In Alberta, more and more people are living in urban areas (large towns and cities). According to the 2006 census, about 5.78% of Alberta's population of was First Nations. About 55.6% of these First Nations people were living in urban areas. What does 5.78% look like as a decimal? Move the decimal point 2 places to the left to become Take and multiply it by the population of Alberta. This will give you the approximate population of First Nations people in Alberta. About how many First Nations people in Alberta live in large towns and cities? x = Because we can't have part of a person, we will round this to So, about First Nations people live in Alberta.

24 The next part of the question asks how many of Alberta's First Nations people live in large towns and cities. We know our First Nations population is , and that 55.6% of the group of people lives in large towns and cities. How do we turn 55.6% into a decimal? Move the decimal point 2 places to the left. It now becomes Multiply x = We know that about First Nations people live in the large towns and cities of Alberta. On-line sales in Canada in 2009 were 135.7% of on-line sales in (Statistics are only gathered every 2 years). If Canadians placed 95 million orders in 2009, about how many orders did they place in 2007? Can you think of a strategy that would help you to find the answer? Work with your partner and discuss how you could figure this out.

25 135.7% = if you write it as a decimal x 2007 sales = 2009 sales x 2007 sales = 95 million sales Divide both sides by because dividing is the opposite of multiplication. Use a calculator to do the division. Try one more questions with a partner before you start working on your own. October: 500 hits on school blog. November: 112% of the number of October hits sales = 95 million = 70 million Canadians placed about 70 million online sales in In November, the number of hits on the school blog rose to 112% of the number in October. There were 500 visitors to the blog in October. How many hits were there in November?

26 Solve Problems by Changing Your Point of View Today's Assignment: Pages 166 and 167 Questions 3, 5, 7, 11 and 13 Today's Aim: I can solve problems by looking at situations in different ways.

27 Chris lives in British Columbia where the PST is 7%. He wants to buy a new guitar. He finds the guitar he wants on sale for 25% off the regular price of $ How can we solve this problem using related percents? How can Chris calculate the cost of the guitar including taxes? Remember, that in British Columbia, you not only pay PST, you also need to pay the GST of 5%. However, each tax is calculated on the actual cost of the item and then added together at the end. 1. Understand the problem The cost has two parts: Cost = discounted price + taxes 2. Make a PlanFirst, calculate the discounted price = original price 25% discount Then add 7% for the PST Then add 5% for the GST

28 3. Carry Out the Plan Original price is $ % of original price is = or0.25 x which equals $ Discounted price = = Calculate GST on a football that costs $58.50 Now we need to calculate the PST and the GST. Both sets of taxes will be based on the discounted price of $ PST= 7% of x = or $23.10 GST = 5% of $ x = or $16.50 The total cost of the guitar will be: $ $ $16.50 = $369.97

29 Zoey made a poster by enlarging a 10 cm by 5 cm picture to 380% of its size. What is the area of the poster? Using the strategies from the previous problem, find a solution with a partner. Today's Assignment: P 173 Question #s 3, 4, 5 and 7

30 Solving Percent Problems Using Fractions How did you find 25% of 96 using the decimal equivalent of the percent? 25% of 200? Aim: I can create and solve a percent problem using fractions. Multiply 96 by 0.25 Multiply 200 by 0.25 How can you find 25% of 96 using the fraction equivalent of the percent? 25% of 200 using the fraction equivalent? With a partner, find 25% of 96 and 25% of 200 using both decimal and fraction equivalents of 25% Discuss with your partner which way was easier. Multiply 96 by 1/4 Multiply 200 by 1/4 Remember that multiplying by 1/4 is the same as dividing by 4

31 12 boys were in a class. They made up 40% of the class. How big was the class? Now, turn over your chart paper and create a problem of your own. Create a problem involving percent that could be solved by taking 5/8 of a number. With a partner, use chart paper and markers to solve this problem. You are to do the following: 1. Make any decisions you feel are necessary to solve the problem. 2. Write out the main points of your solution on the chart paper. 3. Be prepared to communicate you solution process to the rest of the class. With a partner, use chart paper and markers to solve this problem. You are to do the following: 1. Make any decisions you feel are necessary to solve the problem. 2. Write out the main points of your solution on the chart paper. 3. Be prepared to communicate you solution process to the rest of the class.

32 combining percents Aim: I can use percents to solve problems involving two percentages. Bradyn wants to buy an android tablet. In a newspaper, he sees a tablet that regularly sells for $ It is advertised at 20% off, but, because he lives in British Columbia, he has to pay 5% GST and 7% PST. How much is the new tablet? With a partner, calculate if Bradyn has enough money to buy an android tablet.

33 Percent Change Aim: I can solve problems involving changes described as percents.

34 In 2008, the number of movie tickets sold in Canada increased 0.5% to million. Suppose it increased another 0.5% in 2009? How many tickets would have been sold in 2009? How many tickets would have been sold in 2007? Things to think about: A. Why can you describe the ticket sales in 2008 as 100.5% of the sales in 2007? B. How can you calculate the number of tickets for 2007 if you know the percent increases from 2007 to 2008, and from 2008 to 2009? C. Since the ticket sales increased from 2007 to 2008, ticket sales in 2008 must have been more than the ticket sales in D. Since ticket sales were higher in both 2008 and 2009, they must have been more than 100% of the 2007 sales. With a partner, spend the next 7-10 minutes finding a strategy to help you solve this problem.

35 In order to solve this problem, it will need to be broken down into 2 parts. First, we need to find how many tickets were sold in We know that 2007's sales represents 100% because 2008's sales were 0.5% higher. This means that 2007's sales will be less than million. Another strategy we can use is to change 100.5% into a decimal fraction. When we divide by 100, it becomes We will then divide million by Regardless of which strategy we use, the answer will be the same = million So, in 2007, Canadians purchased million movie tickets. One way we can set it up is as an equation. = We can use our cross multiply and divide strategy. (100 x 120.3) 100.5

36 In 2008, the number of movie tickets sold in Canada increased 0.5% to million. Suppose it increased another 0.5% in 2009? How many tickets would have been sold in 2009? How many tickets would have been sold in 2007? This year, Jasmine has 520 songs on her ipod. This has increased 45% from the number of songs she had last year. How many songs did she have last year? The original problem also asks you to find how many tickets were sold in In order to calculate this, the sales from 2008 (120.3 million tickets) now becomes the 100%. One strategy to solve this would be: million x 100.5% (1.005) = million. Hint! If her song library increased 45%, now it is 145% of what it was before.

37 assignment: Pages Jackson had $800 in his bank account. He withdrew $80 to buy a gift for a special friend. #3, 5, 7, 10, and 12 a. By what percent did his balance decrease? Hint!! To calculate the percent,compare the amount withdrawn to the original balance, not the new balance. b. What percent of the old balance is the new balance?

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