b. How many times more money did Amando earn than Henry?

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1 6.1 Independent Practice Name Put an A in the box next to the additive comparison, put an M in the box next to the multiplicative comparison, and record the answer to each question. 1. Amando earned $24 mowing lawns. Henry earned $8.00 sweeping out the garage. a. How much more money did Amando earn than Henry? b. How many times more money did Amando earn than Henry? 2. Compare the two sets of cubes Set #1 Set #2 a. using an additive comparison: b. using a multiplicative comparison: 3. A hare can jump 15 feet in a single bound. A red kangaroo can leap 30 feet in a single bound. How many times farther does a red kangaroo leap than a hare? 4. A ladder is 12 feet high. A step stool is 4 feet high. How many times higher is the ladder than the step stool? Thinking Multiplicatively

2 6.1 School-Home Connection Name Today we learned to solve tasks using multiplicative thinking. Put an A in the box next to the additive comparison, put an M in the box next to the multiplicative comparison, and record the answer to each question. 1. A deer can run 35 miles per hour. A cheetah can run 70 miles per hour at top speed. a. How many times faster can a cheetah run than a deer? b. How much faster does a cheetah run than a deer? 2. Compare the two stacks of cubes a. using an additive comparison: b. using a multiplicative comparison: Set #1 Set #2 3. A necklace has 45 black beads and 9 white beads. How many times more black beads are there than white beads? 4. Julie s cat weighs 8 pounds. Her dog weighs six times as much as her cat. How much does her dog weigh? Thinking Multiplicatively

3 6.2 Independent Practice Name Use ratio notation to represent the following situations: 1. The ratio of the number of squares to circles. 2. For every week there are 7 days. 3. The number of girls to the number of boys on an indoor soccer team is four to two. 4. For every 3 jobs Matt completes, his mom pays him $ There is one jump rope for every three children. 6. The ratio of blue beads to orange beads is six to four. Savannah mixes 1 cup of white paint with 4 cups of green paint. 1 cup white paint 1 cup green paint 1 cup green paint 1 cup green paint 1 cup green paint 7. Circle each of the following that describes Savannah s mixture. a. There is 1 cup of white paint for every 4 cups of green paint. b. The ratio of the number of cups of white paint to the number of cups of green paint is 4:1. c. The ratio of the number of cups of white paint to the number of cups of green paint is 1:4. d. There are 4 cups of green paint per 1 cup of white paint. e. There are four times as many cups of green paint as cups of white paint. f. The ratio of green paint to white paint is 4:1. g. For every cup of green paint there are 4 cups of white paint. 8. Describe a situation you would love that is in a ratio of 5:3. 9. Describe a situation you would dislike that is in a ratio of 2:6. What Is a Ratio?

4 6.2 School-Home Connection Name Today we learned to recognize, read, and write ratio relationships. Use ratio notation to represent the following situations: 1. The ratio of the number of stars to circles. 2. For every year there are 52 weeks. 3. June earns $7.00 for every 3 hours of babysitting. 4. There are 2 cups of flour for every 5 eggs. 5. For every 10 burritos purchased, 1 burrito is free minutes of break is allowed for every 50 minutes of work. Hardy s trail mix recipe calls for 3 cups of peanuts for every cup of raisins. 1 cup peanuts 1 cup peanuts 1 cup peanuts 1 cup raisins 7. Circle each of the following that describes Hardy s trail mix. a. There is 1 cup of peanuts for every 3 cups of raisins. b. The ratio of the number of cups of peanuts to the number of cups of raisins is 3:1. c. There are 3 cups of peanuts per cup of raisins. d. There are three times as many cups of raisins as cups of peanuts. e. The ratio of raisins to peanuts is 1:3. f. For every 1 cup of peanuts there are 3 cups of raisins. g. There are 1/3 as many cups of raisins as peanuts. 8. Describe a situation you would love that is in a ratio of 1:6. 9. Describe a situation you would dislike that is in a ratio of 8:3. What Is a Ratio?

5 6.3 Independent Practice Name Create a list of six different ratios for each scenario. 1. A class is made up of 14 girls and 15 boys. Ratio Written in Words Ratio Type of Ratio girls to boys part-to-part 14:29 boys to total whole-to-part 29:15 2. A painter is mixing colors to get the right shade of green. He uses 4 quarts of blue for every 5 quarts of yellow. Ratio Written in Words Ratio Type of Ratio Types of Ratios

6 6.3 Independent Practice Name 3. Jamie took the following pictures. What ratios can be seen in them? List four part-topart ratios and four part-to-total or total-to-part ratios in the table below. Vehicles Ratio Written in Words Ratio Type of Ratio part-to-part part-to-part part-to-part part-to-part part-to-total part-to-total total-to-part total-to-part 4. McCoy says that the ratio of motorcycles to trucks is 3:2. Is he correct? Explain why or why not. 5. What scenario would a ratio of 6:5 represent? Types of Ratios

7 6.3 School-Home Connection Name Today we compared ratios with the same unit in part-to-part and part-to-whole ratios. Complete the table to create a list of six different ratios for this scenario. 1. From his last paycheck, Lynn saved $400 and spent $800. Ratio Written in Words Ratio Type of Ratio money saved to money spent 800:400 part-to-whole 800:1200 total money to money saved total-to-part Complete the table to create six different ratios to describe the set of balls. Ratio Written in Words Ratio Type of Ratio part-to-part part-to-part part-to-whole part-to-whole whole-to-part whole-to-part 2. There were 6 days of rain and 25 days of sunshine in the month of May. Simon says that the ratio for May is 25:6, but Clarissa says that the ratio is 31:6. Who is correct? Why? Types of Ratios

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9 6.4 Independent Practice Name 1. a. Fill in the table for 5 iterations. The price of three 2-liter bottles of soda is $4. # of Iterations Bottles of Soda Price b. List one relationship or pattern evident on the the table above. c. What is the ratio of the bottles of soda to the price for 7 iterations? d. What is the original ratio of the bottles of soda to the price? e. What is the original ratio of the price to the bottles of soda? It takes 50 kg of cement and 10 L of water to make concrete. # of Iterations Kg of Cement L of Water a. Fill in the table for 5 iterations. b. List one relationship or pattern evident on the table above. c. What is the ratio of cement to water after 10 iterations? d. What is the original ratio of cement to water? e. What is the original ratio of water to cement? Equivalent Ratios: Iterating

10 6.4 School-Home Connection Name Today we recognized ratios in real-world situations and used iterations to generate equivalent ratios. Example: The ratio of sugar to flour is 1:3. The ratio of flour to sugar is 3:1. Each cake needs 1 cup of sugar for every 3 cups of flour. # of Cakes Cups of Sugar Cups of Flour Find a real-world example of a ratio at home and create a table for 5 iterations. Answer the questions about your ratio. a. List one relationship or pattern evident in the table above. b. Describe one of the ratios shown in the table. c. What would be the ratio of the 9th iteration? Equivalent Ratios: Iterating

11 6.5 Independent Practice Name 1. When building a house, code regulations require that for every 3 sheets of plywood the builder should use 84 nails. Use the table to make additional ratios for less than 3 sheets of plywood. Which ratio is in simplest form? 84 Nails 3 Sheets of Plywood 2. In the season, the local basketball team made 18 free throws for every 24 attempts. Use the table to make additional ratios for less than 24 attempts. Which ratio is in simplest form? Free Throws Made Free Throws Attempted 3. When watering a lawn, outdoor faucets use 20 gallons of water every 10 minutes. Use the table to make additional ratios for less than 10 minutes. Which ratio is in simplest form? Time (in minutes) Gallons of Water Equivalent Ratios: Partitioning & Simplest Form

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13 6.5 School-Home Connection Name Today we created equivalent ratios by partitioning a given ratio and recognizing a ratio in simplest form (the smallest whole number ratio when the greatest common factor between two terms is one). Example: Cans of Water Cans of Orange Concentrate Cans of Water Cans of Orange Concentrate original 4 2 original possible recipes for making less juice 1 1/2 1/2 1/4 possible recipes for making less juice 2/2 1/2 2/3 1/3 1/4 1/8 2/4 1/4 1. When Margo fills her car with 25 gallons of gas, she knows that she can go approximately 400 miles. Use the table to make additional ratios for less than 25 gallons. a. Which ratio is in simplest form? 25 Gallons of Gas 400 Miles Equivalent Ratios: Partitioning & Simplest Form

14 6.5 School-Home Connection Name 2. A gallon (16 cups) of coconut popcorn oil is mixed with 48 cups of unpopped popcorn kernels. Use the table to make additional ratios for less than 1 gallon of popcorn oil. a. Which ratio is in simplest form? Coconut Popcorn Oil Popcorn Kernels 3. During baseball season, Louis was at bat 30 times and had 18 hits. Use the table to make additional ratios for less than 18 hits. a. Which ratio is in simplest form? At Bat Hits 4. To purify water for drinking, add 5 teaspoons of bleach to 50 gallons of water. Use the table to make additional ratios for less than 50 gallons of water. a. Which ratio is in simplest form? Bleach Gallons Equivalent Ratios: Partitioning & Simplest Form

15 6.6 Independent Practice Name Represent the solution for each situation in more than one way. 1. There are 84 chocolate chips for every one dozen cookies. a. What is the ratio of the number of chocolate chips to the number of cookies? b. What is the value of the ratio? c. What is the unit rate? d. How many chocolate chips would be in 1 cookie? e. How many chocolate chips would be in 6 cookies? f. How many chocolate chips would be needed to make 3 dozen cookies? 2. A faucet drips 8 ounces for every 24 minutes that pass. a. What is the ratio of ounces of water to number of minutes? b. What is the value of the ratio? c. What is the unit ratio? d. How much time will it take for 26 ounces of water to drip? 3. A mixture of paint is made by combining 6 cans of yellow paint with every 4 cans of red. a. What is the ratio of yellow cans of paint to red cans of paint? b. What is the value of the ratio? c. What is the unit ratio? d. How many cans of red paint would be needed if 4 cans of yellow paint were used? Value of a Ratio and Unit Rates

16 6.6 School-Home Connection Name Today we learned to find the value and the unit rate of a ratio. Represent the solution for each situation in more than one way. 1. Papier-mâché is made by combining 9 parts glue with 3 parts water. a. What is the ratio of glue to water? b. What is the value of the ratio? c. What is the unit rate? d. How many gallons of glue would be needed to make 16 gallons of papier-mâché? 2. An air conditioner drips 7 ounces in 10 minutes. a. What is the ratio of ounces of water to minutes? b. What is the value of the ratio? c. What is the unit rate? d. How much water will drip in 1 hour? 3. There is a ratio of 10 cups of oatmeal to 4 cups of raisins in a granola recipe. a. What is the ratio of cups of oatmeal to cups of raisins? b. What is the value of the ratio? c. What is the unit rate? d. How many cups of raisins are needed for 40 cups of oatmeal? Value of a Ratio and Unit Rates

17 6.7 Independent Practice Name Solve each problem by drawing a model, creating a table, or using an equation, then verify the answers by locating and marking the answers on the multiplication table. A semi truck trailer has 2 axles. Each axle has 4 tires. 1. What is the ratio of the number of axles to the number of tires for 1 trailer? 2. What is the ratio of the number of axles to the number of tires for 9 trailers? What is the ratio of 1 trailer axle to the number of tires? 4. What is the ratio of the number of axles to the number of tires when there are 7 trailer axles? Equivalent Ratios on a Multiplication Table

18 6.7 School-Home Connection Name Solve each problem by drawing a model, creating a table, or using an equation, then verify the answers by locating and marking the answers on the multiplication table. The cab of a semi truck is called the tractor. The front axle has 2 tires. The two rear axles each have 4 tires. 1. What is the ratio of the number of axles to the number of tires for 1 tractor? 2. What is the ratio of the number of axles to the number of tires for 6 tractors? 3. What is the ratio of the number of axles to the number of tires for 10 tractors? Most semi truck engines are V-8s, meaning the engine has 8 cylinders. Fuel is burned inside each cylinder producing power to run the truck. What is the ratio of cylinders to trucks? 5. What is the ratio of the number of cylinders to 8 trucks? Equivalent Ratios on a Multiplication Table

19 6.8 Independent Practice Name Solve each problem using a tape diagram. Use the following context to answer the questions: In a triathlon, athletes compete in a race that includes swimming, biking, and running. Typically, the ratio of the biking distance to the running distance is 4:1, and the ratio of the swimming distance to the running distance is 3: A standard distance triathlon has a 40 km bike ride. How long is the run in a standard distance triathlon? 2. In a middle distance triathlon, the combined biking and running distance is 100 km. How long is the bike ride? How long is the run? 3. A standard distance triathlon has a 1500 m swim. How long is the run? 4. In a sprint distance triathlon, the combined swimming and running distance is 5750 m. How long is the swim? How long is the run? Tape Diagrams

20 6.8 School-Home Connection Name Today we learned how to solve ratio problems using a tape diagram. Solve each problem using a tape diagram. 1. In a school-wide survey, it was discovered that the students of West Elm Elementary preferred vanilla ice cream to chocolate ice cream in a 2:1 ratio. West Elm Elementary has 420 students. How many students prefer each type of ice cream? 2. Shaylee collects postcards from around the world. So far she has collected 90 postcards and divided them into the categories Northern Hemisphere and Southern Hemisphere. For every 3 cards from the northern hemisphere, Shaylee has 7 cards from the southern hemisphere. How many cards are in each category? 3. Secretariat was a famous American thoroughbred racehorse that had a stride length (the distance between steps) of 24 feet. When comparing the stride length of Secretariat to a cheetah (the world s fastest land animal), the ratio is 8:7. What is the stride length of a cheetah? Tape Diagrams

21 6.9 Independent Practice Name Solve each problem using a tape diagram. 1. At dinner, Malcom drinks both water and milk. For every 2 ounces of milk he drinks, he drinks 5 ounces of water. a. On Monday, he drinks 3 ounces of milk. How many ounces of water does he drink? b. On Tuesday, he drinks 8 ounces of water. How many ounces of milk does he drink? 2. According to a poll, the perfect ratio of salsa to tortilla chips is 16 fluid ounces of salsa to 12 ounces of tortilla chips. The Gecko restaurant plans to serve 100 ounces of tortilla chips during the dinner rush. How many fluid ounces of salsa should the chef make? 3. The painters mixed together 3 gallons of blue paint and 5 gallons of white paint to create the perfect color. How many cans of each paint should be mixed together so that the painters have a total of 15 gallons of paint? Tape Diagrams: Fractional Unit Values

22 6.9 School-Home Connection Name Today we learned how to solve ratio problems using a tape diagram. The recipe for the perfect lemonade is written in ratios. Use tape diagrams to solve each problem. 4 parts sugar 16 parts water 3 parts lemon juice 1. After squeezing all of your lemons, you measure the juice and have 1 cup of lemon juice. How much water will you need? 2. While preparing lemonade for a party, you know you ll want to make the recipe with 30 cups of water. How much sugar will this recipe need? 3. You are only making enough lemonade for yourself and have 1 ounce of lemon juice. How much sugar will you need? 4. When the water and lemon juice are mixed together, the mixture is 57 ounces. How much of the mixture is lemon juice and how much of the mixture is water? Tape Diagrams: Fractional Unit Values

23 6.10 Independent Practice Name Use a double number line to solve each word problem. Ratio of distance range (in miles) to charge time or gasoline fill-up time (in minutes). Gasoline Car Affordable Electric Car Luxury Electric Car 350:5 80: :60 1. A luxury electric car charges for 45 minutes. How many miles can it travel? 2. A gasoline car needs to travel 735 miles. How many minutes will it spend filling up with gasoline? 3. A luxury electric car travels 2,300 miles on a road trip. How long was the car charging during the road trip? 4. An affordable electric car is charged for 240 minutes. How many miles can it travel? 5. Each type of car is charged or filled with gas for a total of 15 minutes. How far can each car travel? Double Number Lines

24 6.10 School-Home Connection Name Today we learned how to solve ratio problems using double number lines. Use a double number line to solve the word problems. 1. Mike is making pizzas at home. He only works on one pizza at a time to ensure the best quality. It takes 2 minutes to assemble each pizza, 1 minute to load the pizza into the oven, 8 minutes to bake the pizza, and 1 minute to unload the pizza from the oven and slice it. a. How long does it take Mike to finish 1 pizza? What is the unit rate of the ratio of time to the number of pizzas? b. If Mike plans to make 8 pizzas for a party with his friends, how long will it take him to finish all of the pizzas at this rate? c. If Mike has 57 minutes, how many pizzas can he make? Explain your reasoning. d. If Mike has 90 minutes, how many pizzas can he make? Explain your reasoning. Double Number Lines

25 6.11 Independent Practice Name Use the information in the table to create additional ramps that have a ratio equivalent to a ramp with a base length of 6 and a height of 4 but are not identical to the original ramp. Record the dimensions and the ratios of the equivalent ramps in the table. Record two additional equivalent ratios of your choice in the empty columns at the right end of the table. The grid and white space below are provided as a workspace for creating ramps that are equivalent to the original ratio. Length of Base /2 9 Height Ratio 6:4 Equivalent Ratio Ramps

26 6.11 School-Home Connection Name Today we calculated equivalent ratios and modeled them by drawing ramps on a grid. Use the information in the table to create additional ramps that have a ratio equivalent to a ramp with a base length of 8 and a height of 10 but are not identical to the original ramp. Record the dimensions and the ratios of the equivalent ramps in the table. Record two additional equivalent ratios of your choice in the empty columns at the right end of the table. The grid and white space below are provided as a workspace for creating ramps that are equivalent to the original ratio. Length of Base Height / Ratio 8:10 Equivalent Ratio Ramps

27 6.12 Independent Practice Name As part of the answer for each situation below, complete the table of ratios and the corresponding table of ordered pairs. Plot at least 3 of the ordered pairs on the coordinate grid and label the graph appropriately. 1. Five students in my class have 3 apples to share between them. If this ratio is constant for my class of 30 students, how many apples are there? y Students 5 30 Apples 3 Ratio of Column Ratio Ordered Pair x 2. These same 5 students also have 2 oranges to share. How many oranges are there? Students 5 30 y Oranges Ratio of Column Ratio Ordered Pair x Graphing Equivalent Ratios

28 6.12 School-Home Connection Name Today we learned to plot pairs of values on a coordinate grid from a table of equivalent ratios. As part of the answer for each situation below, complete the table of ratios and the corresponding table of ordered pairs. Plot at least 3 of the ordered pairs on the coordinate grid and label the graph appropriately. 1. Everett buys e-books to read on his tablet. Each book costs $4.00. If Everett has $22.00 to spend, how many e-books can he buy? y E-book Cost Ratio of Column Ratio Ordered Pair x 2. There are 8 cars for every 10 people in the United States of America. Following this average, how many cars would there be in a town of 150 people? y Ratio of Column Ratio Ordered Pair x Graphing Equivalent Ratios

29 6.13 Independent Practice Name A community theater performs plays throughout the year. Tickets can be purchased online or at the box office. The theater has set a goal to increase their online ticket sales. Online Tickets Sold Box Office Tickets Sold Play Play Play Play Was the theater successful at increasing their online tickets sales from the first play to the second play? Why or why not? 2. Was the theater successful at increasing their online tickets sales from the second play to the third play? Why or why not? 3. Was the theater successful at increasing their online tickets sales from the first play to the third play? Why or why not? 4. Was the theater successful at increasing their online tickets sales from the first play to the fourth play? Why or why not? Comparing Ratios

30 6.13 School-Home Connection Name A theater sells snacks at a concession stand. They have a goal to increase their revenue by asking their employees to use a technique called upselling. Upselling is when an employee encourages a customer to upsize their order by buying an upgrade or an add-on in order to have a more profitable transaction. Cookies 1 for 50 3 for $1.00 Concession Stand Menu Popcorn Small (32 oz.) $3.75 Medium (46 oz.) $4.50 Large (64 oz.) $5.00 Theater Candy $2.00 each Buy 3 Get 1 Free Suppose a customer would like to buy a cookie; a clerk may encourage them to buy 3 cookies for $1.00 because it is a better value. The clerk may also point out that a large popcorn is double the serving of a small popcorn for less than double the price. Number of Transactions Sales Before the Play Intermission Sales 1 Cookie Cookies Small Popcorn Large Popcorn Box Theater Candy Boxes Theater Candy Compare the ratio of the number of sales for cookies, popcorn, and candy before the play to the number of sales during intermission. Is the theater more successful at upselling during intermission than they were before the show began? Why or why not? Comparing Ratios

31 6.14 Independent Practice Name gallons of gasoline cost $ a. What is the price for 1 gallon of gas? b. How much gas can you get for $1.00? 2. Max has a job screen printing T-shirts. In an 8-hour day, he can load, screen print, and fold 160 shirts. He works at a constant pace. a. How many T-shirts does he finish in 1 hour? b. How many minutes does it take to complete 1 shirt? More Practice With Unit Rates

32 6.14 School-Home Connection Name 1. Hallie has a job that pays $9.00 for every 1 hour that she works. a. How much money does she earn every minute? b. How much money does she lose if she clocks in 10 minutes late for work? c. How many minutes does she have to work to earn $1.00? d. Hallie gets a paid 15-minute break. How much money does she earn while on break? More Practice With Unit Rates

33 6.15 Independent Practice Name 1. If you had legs like a siren salamander... A siren salamander has a long body with two tiny forelegs (around 2 cm long) and no hind legs. The largest of the siren species is called the greater siren and can grow up to 90 cm long. Siren Human Body Forelegs 90 cm 54 in 2 cm a. What is the ratio of a siren salamander s body to its forelegs in simplest form? b. If you were 54 in tall, how long would your arms be using this same ratio? c. What could you do with arms that long? 2. If you could jump like a springhare... A springhare resembles a kangaroo but is the size of a rabbit measuring about 15 in long. This amazing animal has been known to jump as far as 30 ft (360 in) in a single bound. Springhare Human Body Length of Jump 15 in 54 in 360 in a. What is the ratio of a springhare s body to its jump in simplest form? b. If you were 54 in tall, how far could you jump using this same ratio? c. What could you do with a jump that size? Hop Like a Frog Tasks

34 6.15 School-Home Connection Name 1. If you drank nectar like a Madagascan hawk moth... A hawk moth in Madagascar has a proboscis that is used to extract nectar from flowers. A moth that is 9 cm long has a proboscis that is 27 cm long. Hawk Moth Human Body Proboscis/Tongue 9 cm 54 in 27 m a. What is the ratio of a hawk moth s body to its proboscis in simplest form? b. If you were 54 in tall, how long would your tongue be using this same ratio? c. What in your world is around the same length as your tongue would be? 2. If you had a claw like a male fiddler crab... This crab has a claw that is nearly the same size as its body. Crab Human Body Claw/Hand 2 in 54 in 2 in a. What is the ratio of a male fiddler crab s body to its claw in simplest form? b. If you were 54 in tall, how big would your hand be using this same ratio? c. What could you do with a hand that size? Hop Like a Frog Tasks

35 6.16 Independent Practice Name Florida supplies 70% of the citrus for the United States. 87% of the citrus produced in Florida is processed and sold as concentrate, and the remaining citrus is sold as fresh fruit. Answer the following questions when the whole is Shade the grid to show how Florida s citrus is sold. Concentrate Fresh Fruit Color Key 2. What percentage of Florida s citrus is made into concentrate? 3. What is the part to whole ratio for concentrate? 4. For every 100 pieces of fruit, how many pieces of fruit are made into concentrate? 5. What percentage of Florida s citrus is sold fresh? 6. What is the part to whole ratio for fresh citrus? 7. When there are 100 pieces of fruit, how many pieces are sold fresh? Answer the following questions when the whole is Use two colors to shade the grids to show the percentage of how Florida s citrus is sold. 9. What percentage of Florida s citrus is made into concentrate? 10. For every 400 pieces of fruit, how many pieces of fruit are made into concentrate? 11. What percentage of Florida s citrus is sold fresh? 12. For every 400 pieces of fruit, how many pieces are sold fresh? A Percent Is a Ratio per 100

36 6.16 School-Home Connection Name Utah s agriculture commodities consist of livestock, livestock products, and crops. Utah s Agriculture Commodities Percent Color Key Cattle and Calves 34% Dairy Products Hay 9% Other 37% Answer the following questions when the whole is Use color to shade the grid to represent Utah s agriculture commodities. 2. What percentage of Utah s agriculture commodities are dairy products? 3. What is the part to whole ratio for cattle and calves? 4. For every 100 commodities, what number of commodities is hay? Answer the following questions when the whole is Use color to shade the grids to represent Utah s agriculture commodities when the whole is What percentage of Utah s agriculture commodities are other? 7. What is the part to whole ratio for cattle and calves? 8. For every 300 commodities, what number of commodities are dairy products? A Percent Is a Ratio per 100

37 6.17 Independent Practice Name Note: Percent ratios are part-to-whole. What percentage of the grid is shaded? 1. Shade the grid with a 1:2 ratio. What percentage is shaded? 2. Shade the grid with a 5:50 ratio. What percentage is shaded? 3. What percentage of the number line is shaded? What percentage of the number line is shaded? What percentage of the following shapes are stars? Determine Percent Using Equivalent Ratios

38 6.17 School-Home Connection Name Note: Percent ratios are part-to-whole. Today we determined a percentage by creating an equivalent ratio with a denominator of 100. What percentage of the grid is shaded? 1. Shade the grid with a 4:20 ratio. What percentage is shaded? 2. Shade the grid with a 5:50 ratio. What percentage is shaded? 3. What percentage of the number line is shaded? What percentage of the number line is shaded? What percentage of the following shapes are stars? Determine Percent Using Equivalent Ratios

39 6.18 Independent Practice Name Solve each question in at least two different ways. The following are examples of strategies that could be used: grids, equivalent ratios, tables, double number lines, using money as a context, using mental math and explaining your reasoning, etc. (Note: solving a percent problem with a multiplication equation will be addressed in Lesson 6.19.) 1. What is 20% of 80? 2. What is 35% of 60? Use Ratio Reasoning to Solve Percent Problems

40 6.18 School-Home Connection Name Today we used equivalent ratios to determine a percentage of a whole. Solve each question in at least two different ways. The following are examples of strategies that could be used: grids, equivalent ratios, tables, double number lines, using money as a context, using mental math and explaining your reasoning, etc. (Note: solving a percent problem with a multiplication equation will be addressed in Lesson 6.19.) 1. What is 90% of 30? 2. What is 25% of 88? Use Ratio Reasoning to Solve Percent Problems

41 6.19 Independent Practice Name carat gold is composed of 58% gold, 14% copper, and 28% silver by weight. A jeweler is making one 14-carat gold ring weighing 30 grams and one 14-carat gold ring weighing 35 grams. How many grams of each metal is needed for each ring? Use Equations to Solve Percent Problems

42 6.19 School-Home Connection Name 1. White gold is 85% gold, 10% nickel, and 5% zinc by weight. A jeweler is making one white gold ring weighing 40 grams and one white gold ring weighing 42 grams. How many grams of each metal is needed for each ring? Use Equations to Solve Percent Problems

43 6.20 Independent Practice Name Solve. Show your work, or, if using mental math, explain your strategies % of what number is 80? 2. 10% of what number is 7? 3. 2% of what number is 1.5? 4. If 20 is 8% of a total, what is the total? 5. If 300 is 100% of a total, what is the total? Find the Whole Given a Part and a Percent

44 6.20 School-Home Connection Name Solve. Show your work, or, if using mental math, explain your strategies % of what number is 17? 2. 50% of what number is 550? 3. 1% of what number is 5? 4. If 114 is 38% of a total, what is the total? 5. If 48 is 80% of a total, what is the total? Find the Whole Given a Part and a Percent

45 6.21 Independent Practice Name Solve. Show your work, or, if using mental math, explain your strategies ounces is equal to how many pounds? (1 pound = 16 ounces) 2. How many cups are in 2 gallons? 4 (1 gallon = 16 cups) Carrie rode her bike 22 kilometers. Eli rode his bike 2,550 meters. Which person rode the farthest? (1 kilometer = 1,000 meters) Convert Measurement Units Within the Same System

46 6.21 School-Home Connection Name Solve. Show your work, or, if using mental math, explain your strategies. 1. How many tons are in 3,500 pounds? (1 ton = 2,000 pounds) 2. A movie has a playing time of 132 minutes. How long is the movie in hours? (1 hour = 60 minutes) 3. A dog tag pendant is 46 millimeters tall. How tall is this in centimeters? (1 millimeter = 0.01 centimeters) Convert Measurement Units Within the Same System

47 6.22 Independent Practice Name Solve. Show your work, or, if using mental math, explain your strategies. 1. Charlotte plans to drink 75 ounces of water in one day. She has a 1-liter water bottle and wonders, how many liters are in 75 ounces? (1 ounce = ) 2. How many gallons are in 40 liters of soda pop? (1 gallon = liters) 3. When 1 Canadian dollar is worth 77 cents of American money, how much is 50 Canadian dollars worth when exchanged for American money? Convert Measurement Units Between Systems

48 6.22 School-Home Connection Name Solve. Show your work, or, if using mental math, explain your strategies. 1. A typical home WiFi router has a range of 46 meters. How long is this distance in feet? (1 foot = meters) 2. A sign in Canada indicates that the speed limit is 120 kilometers per hour. What is the speed limit in miles per hour? (1 kilometer = miles) 3. Kim is 171 centimeters tall. Dan is 5 feet 9 inches tall. Who is taller? (1 inch 2.54 centimeters) Convert Measurement Units Between Systems