number ratio and chapter 6 percent -...

Chapter

Big IdeaRatio and percent help me describe relationships and solve problems.

Learning GoalsI can show my understanding of ratio using manipulatives.

I can show my understanding of ratio using drawings.

I can show my understanding of ratio symbolically.

I can show my understanding of percent using manipulatives.

I can show my understanding of percent using drawings.

I can show my understanding of percent symbolically.

Essential QuestionHow can I use ratios and percents to solve problems?

Important Wordspart-to-part ratiopart-to-whole ratiopercentratio

NUMBER

6Ratio and Percent

CHAPTER 6: Ratio and Percent124

Recognizing Ratios

Write ratios to compare different numbers using a colon (:), the word to, or a fraction.

Example:

Charles brought a dozen cinnamon buns to his friend’s house. Charles likes frosting, but his friend doesn’t, so he only frosted some of the cinnamon buns. Write the ratio of frosted cinnamon buns to unfrosted cinnamon buns.

There are three frosted cinnamon buns. There are nine unfrosted cinnamon buns. I can write the ratio of frosted to unfrosted cinnamon buns as 3 to 9, 3 : 9, or .

11. Two students are playing Xs and Os. Use their game board to answer the following.

a. Write the ratio of Xs to Os.

b. The next turn will be X. Write the ratio of Xs to Os if X wins.

c. Write the ratio of Xs to Os if O wins.

12. Use the sales poster below to answer the following questions.

a. Draw a picture to represent the ratio of flowers to the number of dollars.

b. Write a ratio to compare the number of flowers to the number of dollars.

A ratio compares two or more numbers.

3 flowers for

39

CHAPTER 6: Ratio and Percent 125

13. Use the alphabet to write the following part-to-whole ratios.

a. Vowels to total letters.

b. Consonants to total letters.

14. Use the pictures below to answer the following questions.

a. For each picture, write a ratio comparing the height of the tree to the number of soccer balls.

b. Explain how you can use the ratios to tell which tree is taller.

15. The school parking lot is shown below.

a. Write a part-to-whole ratio comparing the number of cars to the total number of vehicles.

b. Write a part-to-whole ratio comparing the number of SUVs to the total number of vehicles.

c. Write a part-to-part ratio comparing the number of cars to the number of SUVs.

d. Explain which ratio best shows the type of vehicle most teachers drive.

16. A class is made up of 20 girls and 10 boys.

a. Draw a picture or build a model to represent this class.

b. Write two equivalent ratios that compare the number of girls to the number of boys.

c. Write two equivalent ratios that compare the number of boys to the total number of students.

Recognizing Ratios (continued)

A part-to-whole ratio compares the number of items in one part of a group to the number of items in the

whole group.

A part-to-part ratio compares the number of items in one part of a group to the number of items in

another part of the group.


17. In a newspaper there are 12 pages of advertising and 15 pages of news.

a. Draw a picture or build a model to represent this newspaper.

b. Write two equivalent ratios that compare the number of pages of news to the number of pages of advertising.

c. Write two equivalent ratios that compare the number of pages of news to the total number of pages in the newspaper.

18. Pedro has 75¢ and Carlos has $1.25.

a. Draw a picture or build a model to represent the money each boy has.

b. An equivalent ratio to compare the amount of money Pedro has to the amount of money Carlos has is 3 to 5. What might this ratio mean?

19. Which team in each pair has more girls?

a.

b.

Recognizing Ratios (continued)

10. Describe the difference between part-to-part ratios and part-to- whole ratios.

11. Which of the ratios in your answers are part-to-part ratios? Which are part-to-whole ratios?

I can show my understanding of ratio using manipulatives.

I can show my understanding of ratio using drawings.

I can show my understanding of ratio symbolically.

The Stars The Moons

The Tops The Dreidels

or

or


Real World Ratios

Ratios can be used to compare quantities. Use ratios to solve problems by drawing, building, using patterns, or using equivalent ratios.

Example:

Addison can run three laps around the gym in two minutes. How many laps could she run in eight minutes?

Umar’s strategy:I drew 3 circles to show the laps and wrote the number 2 under this to show the time. 3 : 2 minutes

Then I drew the same thing again until I had enough to show 8 minutes. A ltogether, I counted 12 circles.

Addison could do 12 laps in 8 minutes.

Raghida’s strategy:I built a row of cubes that used three red cubes for the laps and two b lue cubes for the minutes. 3 to 2

Then I built new rows until I had enough b lue cubes to show eight minutes. 12 to 8


Franchesca’s strategy:I can skip count by 2s to eight for the minutes: 2, 4, 6, 8.

Then I skip count by 3s the same number of times for the laps: 3, 6, 9, 12.

= = =


2 2 2 2

2

23

46

69

812


Real World Ratios (continued)

Arian’s strategy:I wrote a ratio to compare the number of laps to the number of minutes.

Then I wrote a ratio with eight as the denominator because I want to know how many laps can be run in 8 minutes.

To make an equivalent ratio I multiply the 3 by 4. 3 x 4 = 12

An equivalent ratio is .

Addison can do 12 laps in 8 minutes.

11. The members of Joan’s soccer team, the parents, and the volunteers had to ride in minivans to an out-of-town game. Each minivan holds eight people. Twenty-four people are going to the game. How many minivans are needed?

a. Draw a picture to show the people in the minivans.

b. Write a ratio to compare the total number of people to the number of minivans.

12. Lucas is drawing rectangles for a hallway display. He wants all of the rectangles to have the same shape as the one shown on the right, but to be different sizes.

a. Write a ratio comparing the height of the rectangle to the length of the rectangle.

b. Draw a rectangle with a height of 20 cm and a length of 30 cm.

c. Write a ratio comparing the height of the rectangle you drew to the length of the rectangle you drew.

d. Compare the two ratios and explain what the ratios tell you about whether the rectangles are the same shape.

e. Draw three more rectangles that are the same shape but different sizes.

f. Explain what you notice about the height-to-length ratio of each rectangle.

?8

3 laps2 minutes

128


Real World Ratios (continued)

13. There are eight black hamsters in a cage. The ratio of black hamsters to tan hamsters is 2 : 3. How many tan hamsters are in the cage?

14. The football team ordered six pizzas for every four players. The soccer team ordered five pizzas for every three players to share. Which players will get more pizza to eat?

15. Professor Doolittle is mixing turtle food. The instructions say he should mix 500 g of lettuce with four scoops of sunflower seeds. He has a 750 g package of lettuce. How many scoops of sunflower seeds should he add to it?

16. Sandy’s football team uses five balls for every eight players during practice. How many balls will be needed if there are 40 players on the team?

17. Marilu has 36 stamps in her collection. On which letters is the ratio of Canadian stamps to American stamps the same?

a. b. c. d.

18. Adult and student tickets are available for the Edmonton Folk Festival. Last year, the ratio of adult tickets to student tickets was .

a. What is the ratio of adult tickets to total tickets?

b. If 320 student tickets were sold, how many adult tickets were sold?

19. The ratio of boys to girls in a Grade 6 class is 2 : 3. How many students might there be in the class?

10. Describe the strategies you used to solve these problems.

11. How do you think artists use ratios when drawing people?

I can use manipulatives to show my understanding of ratio.

I can use drawings to show my understanding of ratio.

I can use symbols to show my understanding of ratio.

52

CANADA CANADA

CANADA

CANADA

CANADA CANADA

CANADA

CANADACANADA

CANADA


Close Call

Use percents, fractions, decimals, and ratios to represent and compare amounts.

Example:

Moncton Stables has 40 horses. Twenty-six of the horses have been in horse shows. Use a fraction, a decimal and a percent to describe the horses that have been shown.

Boston’s strategy:

For the fraction, I wrote the number of horses that have been shown, over the total number of horses:

For the decimal I thought about writing a fraction with 100 on the bottom.

I coloured 26 out of 40 in a hundred

grid, twice. Then, for the last 20 squares

I only coloured in half of 26, or 13, because 20 is only half of 40.

Then I counted up the coloured squares.

26 + 26 + 13 = 65

is 65 hundredths or 0.65.

For the percent I used the fraction out of 100.

is 65% because % means out of 100.

11. Look at the Quebéc flag below. Estimate the percent of the flag that is:

a. blue.

b. white.

c. the fleur-de-lis symbols.

65100

2640

65100

Percent is a number that could be written as a fraction of 100.

40 40 20


Close Call (continued)

2. For each hundred grid shown below, write:

a. the percent shaded. b. the fraction shaded.

c. the decimal shaded. d. a ratio to compare the shaded portion to the whole.

13. Estimate the shaded portion of each picture as a percent.

i. ii. iii.

iv. v. vi.

a. b.

c. d.

e. f.



15. Use the strategy of your choice to estimate, then calculate, the percent equal to each fraction.

a. b.

c. d.

16. Use the strategy of your choice to calculate the percent equal to each decimal.

a. 0.75 b. 0.06 c. 0.4 d. 0.30

17. Describe and compare the strategies you used to write fractions as percents in question 5 to the strategies you used to write decimals as percents in question 6.

18. Give an example of when each of the following percents could be considered a small number.

a. 2% b. 50% c. 100%

19. Give an example of when each of the following percents could be considered a large number.

a. 1% b. 20% c. 80%

14. Match each fraction to the percent that most closely represents it.

a. b. c. d. e. f. g.

i. 65% ii. 1% iii. 33% iv. 50% v. 100% vi. 77% vii. 25%

71000

34

9801000

63100

24100

1430

13

35

146200

3040

750


10. There are 25 students in Mr. Singh’s class. He surveyed his students to find out their favourite sports. The results are shown in the table below.

a. Write a fraction to represent the number of students who like each sport.

b. Write a percent to represent the number of students who like each sport.

c. Write a decimal to represent the number of students who like each sport.

d. Write a ratio comparing the number of students who like each sport to the total number of students in the class.

e. Order the sports from least favourite to most favourite.

11. Describe whether you think each of the following statements is true or false.

a. Ice covers 20% of the Earth.

b. Left-handed people make up 50% of the population.

c. Thirty percent of people are female.

12. What strategies did you use to determine percents, fractions, decimals, and ratios?

13. How are fractions, decimals, percents, and ratios related?

I can use manipulatives to show my understanding of percent.

I can use drawings to show my understanding of percent.

I can use symbols to show my understanding of percent.


Sport Number of students

Football 5

Soccer 3

Basketball 2

Baseball 6

Jump rope 4

Skiing 5


Percent Problems

Represent percents by building, drawing, or writing a fraction or decimal to solve the following problems.

Example:

Water covers 72% of the surface of the Earth. What percent of the surface is land?

Caleb’s strategy:I covered a blank hundred grid with 72 bingo chips. Then I counted the squares that weren’t covered. There are 28 squares uncovered,

therefore 28% of the Earth’s surface is land.

Dameon’s strategy:I know that the whole Earth will be 100%. 100 - 72 = 28

Land covers 28% of the Earth’s surface.

Eli’s strategy:I know that the whole Earth is . I can compare

to . One whole less 72 hundredths is 28 hundredths because 100 - 72 = 28.

I know that of the Earth is covered by land .

Land covers 28% of the surface of the Earth.

Gage’s strategy:I shaded in 72 of the hundredths on a hundredths circle.

There are 28 hundredths, or 28%, left unshaded. Land covers 28% of the Earth’s surface.

100100

28100

72100

100100


Percent Problems (continued)

11. Isabela and Janna are playing a video game where they each start with 100% Star Power and use it as they play the game. Each girl’s screen is shown below.

a. Estimate, as a percent, the Star Power each girl has remaining.

b. Estimate, as a percent, the Star Power each girl has used.

c. Explain which girl you think is likely to win this game.

12. A new recreation facility is being built in Red Deer. Use a Hundredths Grid to design a recreation centre that meets the requirements below.

Swimming pool 35% of the facility area

Gymnasium 30% of the facility area

Boys’ change room 10% of the facility area

Girls’ change room 10% of the facility area

Cafeteria 15% of the facility area

13. Meteorologists describe the amount of the sky covered by clouds using the words in the table below.

a. For each description, write the percent of the sky covered by clouds.

b. Draw or build to show the percent of the sky covered by clouds in each description.

c. Write a weather report for today using one of these descriptions and the related fraction or percent.

110

910

510

510

910

110

Fraction of sky covered by clouds Description of cloud cover

or more Overcast

to Broken clouds

to Scattered clouds

or less Clear skies



14. The table below shows the percent of people who voted in four federal elections.

a. Choose a province. Show the data by building, drawing, and writing.

b. Explain what these percents tell you about the voters in the province you chose.

c. Explain why you think Statistics Canada chose to use percentages to show this data.

15. Mr. Radcliffe needs to arrange his science exams in order, from the lowest mark to the highest mark.

a. Explain two strategies you could use to order these exams.

b. Order the exams from the lowest mark to the highest mark.

16. Jeremy is planning a class picnic and has researched the forecast for the next week.

a. Order the days from the one on which it is most likely to rain to the one on which is it least likely to rain.

b. Explain on which day Jeremy should plan to have the picnic, and why.

910 98% 86% 65

100355056%

Day Forecast High (°C) Probability of Precipitation (%)

Monday 30 75

Tuesday 25 90

Wednesday 22 10

Thursday 28 50

Friday 25 40

2000 2004 2006 2008

Canada 61% 61% 65% 59%

Manitoba 62% 57% 63% 56%

Saskatchewan 62% 59% 65% 59%

Alberta 60% 59% 62% 52%

British Columbia 63% 63% 64% 60%



17. Explain how Chris most likely felt about the percentage in each of the following situations.

a. Chris earned 50% on his driving test.

b. Chris went to a 50%-off sale at the Sport Spot.

18. Jeffrey got his science test back with a score of 90/200. He told his friends he got 90% on the test. What do you think Jeffrey does not understand about percents?

19. The Parent Advisory Council of Westview Elementary raised $1000.00 last year. The list below shows the percent earned at each fundraiser.

28% from hot lunches

24% from the penny carnival

40% from popcorn sales

02% from movie nights

06% from wrapping paper sales

a. List the fundraisers in order, from the one that earned the most money to the one that earned the least money.

b. Explain which fundraisers you think the Parent Advisory Council should repeat this year, and why.

10. What are some advantages of using percentages to show information?





Pretty Percents

Find percents by building a model, drawing a picture, or finding an equivalent fraction.

Example:

Find 25% of 200.

Kailey’s strategy:I know 25% is . I tried to write a fraction that was equivalent to and had a denominator of 200 and looked like . I divided 200 by 4 to get 50.

=

25% of 200 is 50.

Lamees’s strategy:I drew a number line that went from 0% to 100% and marked 50% and 25% because 50% is half way between 100% and 0%, and 25% is half way between 0% and 50%.

Then I labelled the number line with 0 and 200 at the ends. I found the number half way between 0 and 200.

200 2 = 100

I wrote 100 below the 50% mark.

I found the number half way between 0 and 100.

100 2 = 50

I wrote 50 below the 25% mark.

25% of 200 is 50.

Malak’s strategy:I know 10% of 200 is 20. That means 20% of 200 must be 40. That also means 5% of 200 must be 10 because 5% is half of 10%.

40 + 10 = 50 must be 25%, because 20% + 5% = 25%

25% of 200 is 50.

14

50200

14

14

?200

0% 100%50%25%

0 20010050< >


Pretty Percents (continued)

11. Find each percent using the strategy of your choice.

a. 50% of 20 b. 50% of 400 c. 50% of 12

25% of 20 25% of 400 25% of 12

75% of 20 75% of 400 75% of 12

10% of 20 10% of 400 10% of 12

12. Explain how you could use one percent, such as 10%, to find another, such as 5% or 20%.

13. Use mental math strategies to find each of the following percents.

a. 50% of 6 b. 25% of 16 c. 75% of 120 d. 10% of 50

e. 50% of 130 f. 5% of 20 g. 75% of 1000 h. 20% of 200

14. Explain the mental math strategies you used in question 3.

15. Use as many strategies as you can to find 75% of 80. Compare strategies with a partner. How are they similar? different?

Naomi’s strategy:I put bingo chips on 25 squares in a hundredths grid to show 25%.

I imagined two grids because that would be 200. I doub led 25 to get 50.

25% of 200 is 50.

16. Explain how you used drawings or concrete materials to find one of the percents on this page.





Simply Solved

Find percents and numbers by building models, drawing pictures, or finding equivalent fractions.

Example:

When Jeff plays baseball he hits an average of 10 out of 50 pitches. What percent of the pitches does Jeff hit?

I can colour 10 out of 50 squares on a b lank hundred chart, then do it again. 20 squares are coloured in. That is 20%. Jeff hits 20% of the pitches.

If Jeff practises by having 100 balls pitched to him, how many will he likely hit?

He wil l l ike ly hit 20% or 20 out of 100 pitches.

In one game Jeff has 25 pitches thrown to him. How many hits is he likely to have?

is equivalent to . To find this out, I took half of each number.

50 2 = 25 and 10 2 = 5

In a game with 25 pitches, Jeff will l ike ly have 5 hits.

11. The percent symbol, %, means out of 100. If 20% of your classmates like chocolate, does that mean there are 100 people in your class? Explain.

12. The Ormsby Owls raised $2000 last year. The list below shows the percentage of the total earned at each fundraiser.

20% from the hot lunch 40% from cookie dough sales

25% from the car wash 15% from the pizza lunch

a. Explain how you can tell which fundraiser earned the most money without knowing the individual dollar amounts.

b. Calculate the amount the Owls earned at each individual fundraiser.

c. Describe how you could use the amount earned at the hot lunch to find the amount earned from cookie dough sales.

1050

525


Simply Solved (continued)

18. How did you use drawings or concrete materials to solve these problems?




13. On a test with 80 questions, Jasmin answered 70% correctly.

a. How many questions did Jasmin answer correctly?

b. How many questions did Jasmin answer incorrectly?

c. How could you use the number of questions Jasmin answered correctly to find the number she answered incorrectly?

14. The Grade 7 class at Hardisty School has 120 students. Girls make up 55% of that class.

a. How many girls are in Grade 7?

b. How many boys are in Grade 7?

c. What percent of the Grade 7 students are boys?

15. About 97% of the mass of a watermelon is water.

a. Estimate the mass of water in a 5000 g watermelon.

b. Calculate the mass of water in a 5000 g watermelon.

16. Calculate how much money you would save on each of the following items:

a. an $84 bicycle helmet with a 25% off coupon

b. a $500 bicycle on sale for 20% off

17. Explain why you save more on the bike in the previous question, even though the percent off is lower.

number ratio and chapter 6 percent -...

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