Lesson 4.2.4 – Teacher Notes Standard: 7.RP.A.2a, b, c, d - Recognize and represent proportional relationships between quantities. Full mastery can be expected with the exception of problems relating to distance, rate, and time. Lesson Focus: The focus of the lesson is to connect all types of representations of proportions. (4-58) **It may be a good idea to have students complete the proportion web for each problem as they are discussed in the lesson to help solidify the connections. This would ultimately take the place of problem 4-58. I can determine the constant of proportionality (unit rate). I can translate a real world situation into an equation and create a table to demonstrate proportionality. I can explain what the point (1, r) means in context, where r is the unit rate. Calculator: No Literacy/Teaching Strategy: Traveling Salesman (Closure)

Bell Work

In the previous lessons, you studied different ways to represent proportional relationships.  You organized information into tables and graphs.  You also wrote equations modeling the proportional relationships.  Proportional relationship equations are of the form  y = kx, where  k  is the constant of proportionality.  

Today you will find connections between different representations of the same proportional relationship, explore each representation more deeply, and learn shorter ways to go from one representation to another.  As you work today, keep these questions in mind: How can you see growth in the rule? How do you know your rule is correct? What does the representation tell you? What are the connections between the representations?

4-55. Graeme earns $4. 23 for each half hour that he works 4-55. Graeme earns $4.23 for each half hour that he works.  How much money does he earn during a given amount of time? a. Represent this situation using a table b. What is the constant of proportionality (or the unit rate)?  How can you find it from a table?  c. How can you use a table to determine if a relationship is proportional? 

4-56. Jamie ran 9. 3 miles in 1. 5 hours 4-56. Jamie ran 9.3 miles in 1.5 hours. How far can she run in a given amount of time, if she runs at a constant rate? a. Represent this situation with a graph.  b. What is the constant of proportionality? How can you find it on a graph?   c. How can you use a graph to determine if a relationship is proportional? 

4-57. A recipe calls for 2  cups of of flour to make two regular batches of cookies. Shiloh needs to make multiple batches of cookies. Represent this situation with an equation. What is the constant of proportionality? How can you identify it in an equation?  How can you use an equation to determine if a relationship is proportional?

4-58. CONNECTIONS WEB FOR PROPORTIONAL RELATIONSHIPS Your teacher will assign your team a situation from the previous problems. Your team’s task is to create a poster showing every way you can represent the proportional relationship and the connections between each representation. Use the web below to help you get started.

Practice A rice recipe uses 6 cups of rice for 15 people. At the same rate, how much rice is needed for 40 people? A plane travels 3400 miles in 8 hours. How far would it travel in 6 hours at this rate? Arrange these rates from least to greatest: 30 miles in 25 minutes 60 miles in one hour 70 miles in 1 hr Arrange these readers from fastest to slowest: Abel read 50 pages in 45 minutes Brian read 90 pages in 75 minutes Charlie read 175 pages in 2 hours.