Yum Yum Cereal. 1. Find the total surface area of the rectangular prism. Show your work, step by step. 11 cm

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1 Yum Yum Cereal Part 1 Congratulations on being hired as the new design engineer for Yum Yum Cereal Company. You are excited to use all of your expertise to make your new boss proud. 1. Find the total surface area of the rectangular prism. Show your work, step by step. 11 cm 14 cm 4 cm SA = 2. Find the volume of the rectangular prism above. Explain your steps. V = 3. If the volume of a rectangular prism is 240 cm 3, what could be the dimensions? Draw and label diagrams showing at least three possible rectangular prisms with this volume. Math Grade 7: Yum Yum Cereal Page 1

2 Part 2 Yum Yum Cereal Company just got a huge contract with Super Size Mart. Since you were just hired at Yum Yum Cereal Company, you get to design the next cereal box. The new cereal box must have a volume of 4000 cm 3. Your task will be to create a flier that contains your proposal for the best cereal box design for the cereal that Yum Yum will sell to Super Size Mart. Answer the following questions to complete this task. 4. Create two different-sized cereal boxes that would hold a volume of 4000 cm 3 of cereal. Draw each box below and label its dimensions. Show your work to verify that the boxes you drew would hold 4000 cm 3 of cereal. 5. Find the surface area of each box you created. Show all your work. 6. It costs $ per cm 2 for the cardboard used to make the boxes. How much will it cost to produce each box you created in question 9? Math Grade 7: Yum Yum Cereal Page 2

3 7. The shelves at Super Size Mart are each 30 cm wide, 40 cm high, and 600 cm long. There are 4 shelves in each unit. Based on this information, would you recommend producing either of the boxes you designed to hold the Yum Yum cereal? Explain your reasoning. Math Grade 7: Yum Yum Cereal Page 3

4 Part 3 8. Based on your work in questions 4 through 7, recommend the best size of cereal box for Yum Yum Ceral Company to sell at Super Size Mart. You can use one of the boxes you already designed or come up with a new one. Make sure the volume is 4000 cm 3, that it is economical, and that it will fit on the shelves. To share your recommendation, create a flier that includes this information: a sketch of the box with the dimensions labeled, calculations showing the volume and surface area, the cost to produce a box of this size, and at least two different reasons why you chose this size box. Organize your work neatly and creatively so that your new boss will be impressed. Math Grade 7: Yum Yum Cereal Page 4

5 T-Shirts Bill and Jose are going to order T-shirts for their school clubs. The T-shirts will have the club logo printed on the front. Bill asks two local T-shirt companies to give him a price. Paula s Printing charges $21.50 for each T-shirt. Shantay s Shirts has a one-time set-up fee of $63 and then charges $18 for each T-shirt. 1. Bill needs to order 30 T-shirts for his club. Which company should Bill choose to spend the least amount of money? Use math to justify your recommendation. 2. Complete the table to explore the cost of buying various numbers of T-shirts from Paula s Printing and Shantay s Shirts Number of T-shirts Cost for Paula s Cost for Shantay s 3. Write a linear equation that represents the cost of buying T-shirts from Paula s Printing. Identify the meaning of each variable in your equation. 4. Write a linear equation that represents the cost of buying T-shirts from Shantay s Shirts. Identify the meaning of each variable in your equation. Math Grade 7: T-Shirts Page 1

6 5. Jose s club had a bake sale to raise money for T-shirts and made $495. Write a note to Jose explaining which company will allow his club to buy the most shirts with the money they raised. Explain how you arrived at your answer. 6. Jose thinks that Paula s Printing will always be cheaper. Defend or refute Jose s thinking using the table, the equations, or any other mathematics you can come up with. 7. Is there a number of shirts that would cost the same at either company? What would that number be? Show and explain all work. Math Grade 7: T-Shirts Page 2

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8 Linflower Seeds Part 1 1. Tim grows linflowers from seeds. But not all of his seeds start to grow. He has found that for every 100 seeds he sows, only about 75 start to grow. a. Tim sows 20 linflower seeds. How many would you expect to grow? Explain your reasoning. b. Tim sows 24 seeds in a box. Each mark on the box below shows the position of a seed. Guess which of the seeds start to grow. Draw circles around the seeds that do not start to grow. (Note: There is more than one correct way to show your answer to this question.) Explain your reasoning. Math Grade 7: Linflower Seeds Page 1

9 Part 2 2. a. Fill in the table showing the number of seeds planted compared to the number of seeds that start to grow. Number of Seeds Planted (x) Number of Seeds That Grow (y) b. Graph your table Math Grade 7: Linflower Seeds Page 2

10 Part 3 Tim has been hired by the city to plant snapdragons in the park. Again, the number of seeds he plants does not yield the same number of flowers. Answer the following questions to help Tim plan for his park job. You get to decide how many of the planted seeds will sprout. 3. Create a table of x- and y-values that represents a proportional relationship for your snapdragons. a. Explain how you know the relationship is proportional. b. What equation models the values in the table? 4. Create a table of x- and y-values that represents a linear, non-proportional relationship. a. Explain how you know the relationship is non-proportional. b. What equation models the values in the table? Math Grade 7: Linflower Seeds Page 3