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Solve Ratio Problems Using Tape Diagrams and Double Number Lines

Engage with math problems requiring ratio and proportion-solving techniques. Learn how to utilize tape diagrams and double number lines to tackle various scenarios: from determining how far Travis drove in one hour to analyzing the cost per orange and calories per cracker. The exercises promote understanding of ratios in practical applications, such as fuel efficiency and cooking measurements. Everything culminates in independent practice, ensuring you can confidently apply these skills in real-life situations.

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Solve Ratio Problems Using Tape Diagrams and Double Number Lines

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  1. Warm Up Use a TAPE DIAGRAM to solve the problems below. Show your work! 1. Travis drove 129 miles in 3 hours. How many miles did he drive in 1 hour? 2. Six oranges cost $5.34. How much does 1 orange cost? 3. A bottle of body wash costs $2.88 and contains 12 ounces. How much does it cost per ounce? 4. A package of 5 crackers has 205 calories. How many calories are in 1 cracker?

  2. Representing Ratios – Part 2 Double Number Lines Tables

  3. Double Number Line • A double number line allows you to show two quantities at one time • A double number line works well when you are modeling a rate • Remember our example from yesterday with Sam? • That was a double number line! Miles _0___ 5___10_____20____40___ Hours _0__1/4__1/2____1_____2____

  4. Double Number Line Example 1 Ms. Lipman’s car gets 30 miles per gallon. Use a double number line to show this data and determine how many miles can be driven on three gallons. • Draw two lines – label the top miles and the bottom gallons • Divide the lines into 3 parts • Each part represents 30 miles on the top line and 1 gallon on the bottom • Label your lines with the correct values • What is the answer? Use your double number line to find: • How many miles can she drive on 2 gallons? __________ • How many miles can she drive on 4 gallons? __________

  5. Double Number Line Example 2 Ki-mon can run 1 lap in 6 minutes. How many laps can he run in 18 minutes? Use a double number line to find your answer. Minutes ______6_______12______18_____ Laps ______1_______2_______3______ How many laps can he run in 9 minutes?

  6. Tables • A table of ratios allows you to organize information efficiently! • Let’s look at our example of Sam’s bike riding: • Sam bikes 20 miles in 1 hour. Sam’s rate is the same no matter how long or short his bike ride is.

  7. Tables • Tables can also be constructed horizontally • Turn to a partner and share: • What do you think the advantages are to using a table to represent a ratio? • What is your preferred method of representing a ratio? Why? (tape diagram, concrete model, double number line, table)

  8. Tables – Example 1 • To make yellow icing, you mix 6 drops of yellow food coloring with 1 cup of white icing. How much yellow food coloring should you mix with 5 cups of white icing to get the same shade? • Use a table to find the answer.

  9. Tables – Example 2 • In a recent year, Joey Chestnut won a hotdog eating contest by eating nearly 66 hot dogs in 12 minutes. If he ate at a constant rate, determine about how many hot dogs he ate every 2 minutes. • Use a table to find the answer.

  10. Real World Application! • What are some of the places you go with friends? • What are some different modes of transportation you have used? • Has anyone ever been in a cab? • Has anyone ridden on the lightrail in Charlotte? • http://www.youtube.com/watch?v=6-SwGBBt5K0&safety_mode=true&persist_safety_mode=1

  11. The Movie that Wasn’t • You have 30 seconds to find your 7 o’clock partner and take a seat • Each pair will get a sheet with a scenario about going to the movies • Do your work on a separate sheet of paper • The first pair to thoroughly complete the activity will receive a ticket each! • Your activity must include: • Work shown for all three parts • Correct answers with written explanations

  12. Independent Practice • You have 10 minutes to complete the Independent Practice worksheet. • Raise your hand if you have questions or need help.

  13. Exit Ticket – Show your work! • Katniss from the Hunger Games can shoot 20 apples through the core in 30 seconds flat. (She’s super talented, right?). Use a double number line to find out how many apples can she shoot in 4 minutes. • To make cranberry jam, you need 12 cups of sugar for every 16 cups of cranberries. Find the amount of sugar needed for 4 cups of cranberries. Draw a table.

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