Georgia Department of Education Common Core Georgia Performance Standards Framework Student Edition Seventh Grade Mathematics Unit 3
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1 SE Learning Task: Orange Fizz Experiment I. Introductory Problems A useful way to compare numbers is to form ratios. Talk to your classmates about what is the same and what is different about these ratio statements. 1. The ratio of boys to girls in Ms. Dade s class is 12 boys to 18 girls. 2. The ratio of boys to the class in Mr. Hill s class is 14 boys to 30 students. 3. The ratio of cats to dogs in our house is The ratio of cats to animals in Darla s house is 2:6. July 2013 Page 13 of 38
2 II. Orange Fizz Experiment A famous cola company is trying to decide how to change their drink formulas to produce the best tasting soda drinks on the market. The company has three different types of formulas to test with the public. The formula consists of two ingredients: orange juice concentrate and carbonated water. You are a scientist working for this company, and you will get paid a large commission if you can find the right formula that will sell the best. Your job is to find out which of the formulas cost the most based upon their concentration, as well as which one is the best tasting of the flavors. Using the company s new formulas, you must follow the recipe to the strict guidelines: Formula A: Formula B: Formula C: 1 tablespoons of orange concentrate to 2 tablespoons of carbonated water 2 tablespoons of orange concentrate to 5 tablespoons of carbonated water 2 tablespoons of orange concentrate to 3 tablespoons of carbonated water Part A: Using part-to-whole comparison 1. Which formula will make a drink that has the strongest orange taste? Show your work and explain your choice. 2. Which formula has the highest percentage of carbonated water in the mixture? Estimations may be used. Show your work and justify your answer. July 2013 Page 14 of 38
3 Part B: Using part-to-part comparison 1. For researchers to test their product, they will need to produce enough of each of the three drink formulas to take to various locations around the area for taste testing. Researchers would like for at least 100 people to sample each formula. Each sample will contain 1 of a cup of liquid. Formula A: 1 cup of concentrate to 2 cups of carbonated water Formula B: 2 cups of concentrate to 5 cups of carbonated water Formula C: 2 cups of concentrate to 3 cups of carbonated water Fill in the table to determine the least amount of concentrate and carbonated water that you would have to use to serve 1 cup servings to 100 people. Formula A: Orange Concentrate cups (3 servings) cups (6 servings) cups (9 servings) cups (51 servings) cups ( servings) 34 cups ( servings) 70 cups ( servings) I. How much orange concentrate and carbonated water is needed to serve at least 100 people? a. Orange Concentrateb. - July 2013 Page 15 of 38
4 Formula B: Concentrate cups (7 servings) cups (14 servings) 8 28 cups (28 servings) 35 cups (49 servings) 26 cups ( servings) 98 cups (98 servings) cups ( servings) II. How much orange concentrate and carbonated water is needed to serve at least 100 people? c. Orange Concentrated. Formula C: Orange Concentrate cups (5 servings) cups (10 servings) 20 cups ( servings) 36 cups ( servings) 57 cups ( servings) cups ( servings) III. How much orange concentrate and carbonated water is needed to serve at least 100 people? e. Orange Concentrate f. July 2013 Page 16 of 38
5 2. Your lab technicians will be bringing you all of the supplies that you will need in order to make the formulas at the sites Orange Concentrate Formula A Formula B Formula C Total 3. Your lab technician calls you that he only has gallon jugs. (Hint: one gallon=16 cups) a. How many gallons of orange concentrate do you need to make Formula A? Justify your answer. b. How many gallons of carbonated water do you need to make Formula B? Justify your answer. July 2013 Page 17 of 38
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