549 6.rp rp.a Buy one and get 25% Two for the price of one off the second Buy two and get 50% off the Three for the price of second one two

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1 549 6.rp.2 The grocery store sells beans in bulk. The grocer's sign above the beans says, 5 pounds for $4. At this store, you can buy any number of pounds of beans at this same rate, and all prices include tax. Alberto said, The ratio of the number of dollars to the number of pounds is 4:5. That's $0.80 per pound. Beth said, "The sign says the ratio of the number of pounds to the number of dollars is 5:4. That's 1.25 pounds per dollar." 1. Are Alberto and Beth both correct? Explain. 2. Claude needs two pounds of beans to make soup. Show Claude how much money he will need. 3. Dora has $10 and wants to stock up on beans. Show Dora how many pounds of beans she can buy. 4. Do you prefer to answer parts (b) and (c) using Alberto's rate of $0.80 per pound, using Beth's rate of 1.25 pounds per dollar, or using another strategy? Explain rp.a Four different stores are having a sale. The signs below show the discounts available at each of the four stores. Two for the price of one Buy one and get 25% off the second Buy two and get 50% off the Three for the price of second one two 1. Which of these four different offers gives the biggest percentage price reduction? Explain your reasoning clearly. 2. Which of these four different offers gives the smallest percentage price reduction? Explain your reasoning clearly.

2 135 6.rp.3, 6.g.a Alexis needs to paint the four exterior walls of a large rectangular barn. The length of the barn is 80 feet, the width is 50 feet, and the height is 30 feet. The paint costs $28 per gallon, and each gallon covers 420 square feet. How much will it cost Alexis to paint the barn? Explain your work g.1 Mariko has an 80:1 scale-drawing of the floor plan of her house. On the floor plan, the dimensions of her rectangular living room are 1 7/8 inches by 2 1/2 inches. What is the area of her real living room in square feet? rp.1 Travis was attempting to make muffins to take to a neighbor that had just moved in down the street. The recipe that he was working with required 3/4 cup of sugar and 1/8 cup of butter. Travis accidentally put a whole cup of butter in the mix. a. What is the ratio of sugar to butter in the original recipe? What amount of sugar does Travis need to put into the mix to have the same ratio of sugar to butter that the original recipe calls for? b. If Travis wants to keep the ratios the same as they are in the original recipe, how will the amounts of all the other ingredients for this new mixture compare to the amounts for a single batch of muffins? c. The original recipe called for 3/8 cup of blueberries. What is the ratio of blueberries to butter in the recipe? How many cups of blueberries are needed in the new enlarged mixture?

3 86 8.ee.5 Nia and Trey both had a sore throat so their mom told them to gargle with warm salt water. Nia mixed 1 teaspoon salt with 3 cups water. Trey mixed 1/2 teaspoon salt with 1 1/2 cups of water. Nia tasted Trey s salt water. She said, I added more salt so I expected that mine would be more salty, but they taste the same. 1. Explain why the salt-water mixtures taste the same. 2. Find an equation that relates s, the number of teaspoons of salt, with w, the number of cups of water, for both of these mixtures. 3. Draw the graph of your equation from part b. 4. Your graph in part c should be a line. Interpret the slope as a unit rate f.5 Antonio and Juan are in a 4-mile bike race. The graph below shows the distance of each racer (in miles) as a function of time (in minutes). 1. Who wins the race? How do you know? 2. Imagine you were watching the race and had to announce it over the radio, write a little story describing the race.

4 578 f.if.b (algebra 1, math 1) In order to gain popularity among students, a new pizza place near school plans to offer a special promotion. The cost of a large pizza (in dollars) at the pizza place as a function of time (measured in days since February 10th) may be described as (Assume t only takes whole number values.) 1. If you want to give their pizza a try, on what date(s) should you buy a large pizza in order to get the best price? 2. How much will a large pizza cost on Feb. 18th? 3. On what date, if any, will a large pizza cost 13 dollars? 4. Write an expression that describes the sentence "The cost of a large pizza is at least A dollars B days into the promotion," using function notation and mathematical symbols only. 5. Calculate C(9) C(8) and interpret its meaning in the context of the problem. 629 f.le.1 (math 1, algebra 1) In (a) (e), say whether the quantity is changing in a linear or exponential fashion. 1. A savings account, which earns no interest, receives a deposit of $723 per month. 2. The value of a machine depreciates by 17% per year. 3. Every week, 9/10 of a radioactive substance remains from the beginning of the week. 4. A liter of water evaporates from a swimming pool every day. 5. Every 124 minutes, 1/2 of a drug dosage remains in the body.

5 645 f.le.2, f.le.3, a.rei.11 (algebra 1, math 1) The population of a country is initially 2 million people and is increasing at 4% per year. The country's annual food supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.5 million people per year. 1. Based on these assumptions, in approximately what year will this country first experience shortages of food? 2. If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur? In approximately which year? 3. If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur? 231 f.bf.1c (+ standard, STEM classes or 4 th year course) According to the U.S. Energy Information Administration, a barrel of crude oil produces approximately 20 gallons of gasoline. EPA mileage estimates indicate a 2011 Ford Focus averages 28 miles per gallon of gasoline. 1. Write an expression for G(x), the number of gallons of gasoline produced by x barrels of crude oil. 2. Write an expression for M(g), the number of miles on average that a 2011 Ford Focus can drive on g gallons of gasoline. 3. Write an expression for M(G(x)). What does M(G(x)) represent in terms of the context? 4. One estimate (from claimed that the 2010 Deepwater Horizon disaster in the Gulf of Mexico spilled 4.9 million barrels of crude oil. How many miles of Ford Focus driving would this spilled oil fuel?

6 387 f.if.5 (algebra 1, math 1) John makes DVDs of his friend s shows. He has realized that, because of his fixed costs, his average cost per DVD depends on the number of DVDs he produces. The cost of producing x DVDs is given by C(x)= x. 1. Suppose John made 100 DVDs. What is the cost of producing this many DVDs? How much is this per DVD? 2. Complete the table showing his costs at different levels of production. 3. Explain why the average cost per DVD levels off. 4. Find an equation for the average cost per DVD of producing x DVDs. 5. Find the domain of the average cost function. 6. Using the data points from your table above, sketch the graph of the average cost function. How does the graph reflect that the average cost levels off? rp.3 Joe was planning a business trip to Canada, so he went to the bank to exchange $200 U.S. dollars for Canadian (CDN) dollars (at a rate of $1.02 CDN per $1 US). On the way home from the bank, Joe s boss called to say that the destination of the trip had changed to Mexico City. Joe went back to the bank to exchange his Canadian dollars for Mexican pesos (at a rate of 10.8 pesos per $1 CDN). How many Mexican pesos did Joe get?

7 595 f.if.4, f.tf.5 (algebra 2, math 3) A wheel of radius 0.2 meters begins to move along a flat surface so that the center of the wheel moves forward at a constant speed of 2.4 meters per second. At the moment the wheel begins to turn, a marked point P on the wheel is touching the flat surface. 1. Write an algebraic expression for the function y that gives the height (in meters) of the point P, measured from the flat surface, as a function of t, the number of seconds after the wheel begins moving. 2. Sketch a graph of the function y for t > 0. What do you notice about the graph? Explain your observations in terms of the real-world context given in this problem. 3. Write an algebraic expression for the function x that gives the horizontal position (in meters) of the point P as a function of t, the number of seconds after the wheel begins moving. 4. Sketch a graph of the function x for t > 0. Is there a time when the point P is moving backwards? Use your graph to justify your answer.