Lesson 4.2.3 – Teacher Notes Standard: 7.RP.A.1 - Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. 7.RP.A.2a, b, c, d - Recognize and represent proportional relationships between quantities. Fully mastery can be expected with the exception of problems relating to distance, rate, and time. Lesson Focus: The focus of this lesson is to build meaning and connections of all five standards listed. All problems in the lesson 4-46 through 4-49 tie directly to one or more standards; However, problem 4-47 addresses all listed standards within the problem. (4-47) **Teachers should make sure to bring focus to the use of the equation to represent the proportional relationship. I can determine the constant of proportionality (unit rate). Calculator: No Literacy/Teaching Strategy: Teammates Consult (4-46); Red-Light-Green-Light (4-47); Reciprocal Teaching (All)

Bell Work

Proportional relationships can be identified in both tables and graphs Proportional relationships can be identified in both tables and graphs. Today you will have an opportunity to take a closer look at how graphs and tables for proportional relationships can help you organize your work to find any missing value quickly and easily.

4-47. THE YOGURT SHOP Jell E. Bean owns the local frozen yogurt shop.  At her store, customers serve themselves a bowl of frozen yogurt and top it with chocolate chips, frozen raspberries, and any of the different treats available.  Customers must then weigh their creations and are charged by the weight of their bowls. Jell E. Bean charges $32 for five pounds of dessert, but not many people buy that much frozen yogurt.  She needs you to help her figure out how much to charge her customers.  She has customers that are young children who buy only a small amount of yogurt as well as large groups that come in and pay for everyone’s yogurt together.

4-47. THE YOGURT SHOP Jell E. Bean charges $32 for five pounds of dessert, but not many people buy that much frozen yogurt.  She needs you to help her figure out how much to charge her customers.  She has customers that are young children who buy only a small amount of yogurt as well as large groups that come in and pay for everyone’s yogurt together. a. Is it reasonable to assume that the weight of the yogurt is proportional to its cost?  How can you tell?    b. Assuming it is proportional, make a table that lists the price for at least ten different weights of yogurt.  Be sure to include at least three weights that are not whole numbers. 

4-47. THE YOGURT SHOP Jell E. Bean charges $32 for five pounds of dessert, but not many people buy that much frozen yogurt.  She needs you to help her figure out how much to charge her customers.  She has customers that are young children who buy only a small amount of yogurt as well as large groups that come in and pay for everyone’s yogurt together. What is the unit rate of the yogurt? (Stores often call this the unit price.) Use the unit rate to write an equation that Jell E. Bean can use to calculate the amount any customer will pay. 

4-47. THE YOGURT SHOP Jell E. Bean charges $32 for five pounds of dessert, but not many people buy that much frozen yogurt.  She needs you to help her figure out how much to charge her customers.  She has customers that are young children who buy only a small amount of yogurt as well as large groups that come in and pay for everyone’s yogurt together. d. If Jell E. Bean decided to start charging $0.50 for each cup before her customers started filling it with yogurt and toppings, could you use the same equation to find the new prices? Why or why not?

Practice Sarah’s grape vine grew 15 inches in 6 weeks, write an equation to represent its growth after t weeks. On average Max makes 45 out of 60 shots with the basketball, write an equation to represent the average number of shots made out of x attempts. The tax on a $600 vase is $54. Write and solve and equation to find what the tax on a $1700 vase would be. While baking, Evan discovered a recipe that required ½cups of walnuts for every 2 ¼ cups of flour. Write and solve an equation to find how many cups of walnuts will he need for 4 cups of flour.