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? 1. 43 miles 2. $0.89 3. $0.24 per ounce 4. 41 calories

Representing Ratios – Part 2 Double Number Lines Tables One skill in a mathematician’s toolbox is the ability to represent numerical relationships in a variety of visual models. Yesterday we worked on two models: the tape diagram and concrete models. Today, we are going to learn how to represent ratios using a double number line.

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____

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? __________ I can use this information to complete a double number line which will help me uncover my answer. I know many of you can solve this mentally but the point of today is not necessarily getting an answer. Instead we’re working on something more difficult: modeling our work.

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?

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. Hours Miles 1 20 2 40 3 60

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) Hours 1 2 3 Miles 20 40 60

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. Drops of Yellow Cups of Icing 6 1 12 2 18 3 24 4 30 5 Since 1x5 = 5, multiply each quantity by 5. So, add 30 drops of yellow food coloring to 5 cups of icing.

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. Divide each quantity by one or more common factors until you reach a quantity of 2 minutes. Divide by 2, then divide by 3 So Chestnut ate about 11 hot dogs every 2 minutes Hot Dogs Time (minutes) 66 12 33 6 11 2

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

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

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

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.