1. FOCUS 1: PROPORTIONAL REASONING STANDARDS: 7.RP.1, 7.NS.2D, 7.NS.3, 7.EE.4A, 7.G.1 RESOURCE: CONNECTED MATH PROGRAM 2 COMPARING AND SCALING: INVESTIGATION 3.4

2. COMPARING & SCALING Ratio, Proportion, and Percent Investigation #3- CMP2

3. Mathematical & Problem-Solving Learning Goals for Comparing & Scaling Rates Examine & Connect the idea of unit rate to what you already know about ratios and about linear relationships (3.1) Further develop understanding of unit rates and how to compute and interpret them (3.2) Work with the important application of rates to miles per hour (speed) (3.2) Introduce the concept of “average” or “steady” rate of progress (3.2) Introduce and formalize the meaning of unit rate and computation strategies for computing unit rates (3.3) Relate unit rate to the slope of the line representing the equation of the underlying relationship (3.3) Confront the issue of what it means to divide in rate situations (3.4)

4. Investigation 3.4 Learning Target Confront the issue of what it means to divide in rate situations

5. In this problem, the questions will help you decide which way to divide when you are finding a unit rate. The questions will also help you with the meaning of the quotient after you divide.

6. Getting Ready for Problem 3.4

7. 3.4 Two Different Rates Use division to find unit rates to solve the following questions. Label each unit rate. Part A: SuperFoodz has oranges on sale at 10 for $2. 1. What is the cost per orange? 2. How many oranges can you buy for $1? 3. What division did you perform in each case? How did you decide what each division means? 4. Complete this rate table to show what you know.

9. Part B: Noralie used 22 gallons of gas to go 682 miles. 1. What are the two unit rates that she might compute? 2. Compute each unit rate and tell what it means. 3. Which seems more useful to you? Why?

11. Part C: It takes 100 maple trees to make 25 gallons of maple syrup. 1. How many maple trees does it take for 1 gallon of syrup? 2. How much syrup can you get from one maple tree?

12. Part D: A 5-minute shower requires about 18 gallons of water. 1. How much water per minute does a shower take? 2. How long does a shower last if you use only 1 gallon of water?

13. Part E: At the CornerMarket grocery store, you can buy eight cans of tomatoes for $9. The cans are the same size as those at CannedStuff, which sells six cans for $5. 1. Are the tomatoes at CornerMarket a better buy than the tomatoes at CannedStuff? 2. What comparison strategies did you use to choose between CornerMarket and CannedStuff tomatoes? Why?

15. Explore 3.4 Have you thought about? Why does dividing make sense here? How can you decide what the label for the answer to the division should be? How is labeling the quantities in the division helpful?

16. CLASS DISCUSSION & SHARING Share answers and supporting arguments for each problem Share alternative unit rates and labels for making comparisons Share models of the divisions with the quantity labels carried with the numerator and the denominator Discuss the language “per” and its meaning

17. Pre-Algebra Homework A.C.E Application, Connections, & Extensions #12, 27-31 Copy your answers in your math workbook