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## Focus 1: Proportional Reasoning

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**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 3.3**Comparing and Scaling**Ratio, Proportion, and Percent Investigation #3- CMP2**Mathematical & Problem-SolvingLearning 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**Investigation 3.3Learning Target**• Introduce and formalize the meaning of unit rate and computation strategies for computing unit rates • Relate unit rate to the slope of the line representing the equation of the underlying relationship**Getting Ready for Problem 3.3**The ads below use rates to describe sale prices. To compare prices in sales such as these, it’s often useful to find a unit rate. A unit rate is a rate in which one of the numbers being compared is 1 unit. The comparisons “45 miles per gallon,” “$3.50 per hour,” “8.5 kilometers per hour,” and “two sandwiches for each person” are all unit rates. “Per gallon” means “for one gallon” and “per hour” means “for one hour.”**3.3 Comparing CD Prices**MUSIC CITY CD Sale! 5 for $49.95 CD WORLD Huge Savings! 7 for $65.80**3.3 Unit Rates and Equations**Use unit rates to compare the ad prices and to find the costs of various numbers of CDs at each store. • Which store has the lower price per CD? • For each store, write an equation (a rule) that you can use to calculate the cost c for any purchase of n compact discs. • Use the equations you just wrote for Question B. Write new equations to include 5% sales tax on any purchase.**Suppose a Web site sells CDs for $8.99 per disc. There is no**tax, but there is a shipping charge of $5 for any order. Write an equation to give the cost c of any order for n discs from the Web site. • Use your equation from Question C or make a rate table to answer each question. • How many discs do you have to order from the Web site to get a better deal than buying from Music City? • How many discs do you have to order from the Web site to get a better deal than buying from CD World?**Explore 3.3Have you thought about?**• What are the variables in the situation, and what letters are good representations for the variables? • Which seems to be the independent variable, and which the dependent variable?**Class Discussion & Sharing**• Explain what a rate is and give some examples of different kinds of rates. • What does unit rate mean? What are some examples where a unit rate is useful? • What variables were you dealing with in the various parts of the problem? How did you decide which was the independent and which was the dependent variable?**How do the dependent and the independent variables show up**in an equation? • What are some ways of making comparisons among the options for buying CD? • How did you figure out the answers to Q. E? • If you made a graph for numbers of CDs and prices for each of the three companies, what would each graph look like? Are they straight lines? Do they go through the origin?**Pre-Algebra Homework**A.C.E Application, Connections, & Extensions #9, 11, 24, 25 Copy your answers in your math workbook