Lesson PROBLEM SOLVING

Transcription

1 Name Problem Solving Compare Volumes Essential Question: How can you use the strategy make a table to compare different rectangular prisms with the same volume? Unlock the Problem PROBLEM SOLVING Lesson Measurement and Data 5.MD.C.5b MATHEMATICAL PRACTICES MP1, MP7 Adam has 50 one-inch cubes. The cubes measure 1 inch on each edge. Adam wonders how many rectangular prisms, each with a different-size base, that he could make with all of the one-inch cubes. Use the graphic organizer below to help you solve the problem. Read the Problem What do I need to find? I need to find the number of, each with a different-size, that have a volume of. What information do I need to use? I can use the formula and the factors of. How will I use the information? Solve the Problem Complete the table. Base (sq in.) Height (in.) Volume (cu in.) (1 1) 50 (1 1) 50 = 50 (1 2) 25 (1 2) 25 = 50 (1 5) 10 (1 5) 10 = 50 (1 10) 5 (1 10) 5 = 50 (1 25) 2 (1 25) 2 = 50 (1 50) 1 (1 50) 1 = 50 I will use the formula and the factors of 50 in a that shows all of the possible combinations of dimensions with a volume of without repeating the dimensions of the bases. 1. MATHEMATICAL PRACTICE 1 Evaluate What else do you need to do to solve the problem? 2. How many rectangular prisms with different bases can Adam make using 50 one-inch cubes? Chapter

2 Try Another Problem Mrs. Wilton is planning a rectangular flower box for her front window. She wants the flower box to hold exactly 16 cubic feet of soil. How many different flower boxes, all with whole-number dimensions and a different-size base, will hold exactly 16 cubic feet of soil? Use the graphic organizer below to help you solve the problem. Read the Problem Solve the Problem What do I need to find? What information do I need to use? How will I use the information? 3. How many flower boxes with different-size bases will hold exactly 16 cubic feet of soil, using whole-number dimensions? Math Talk MATHEMATICAL PRACTICES 1 Make Sense of Problems Explain how a flower box with dimensions of (1 2) 8 is different from a flower box with dimensions of (2 8)

3 Name Share and Show MATH BOARD 1. A company makes concrete paving stones in different sizes. Each stone has a volume of 360 cubic inches and a height of 3 inches. The stones have different lengths and widths. No stones have a length or width of 1 or 2 inches. How many different paving stones, each with a different-size base, have a volume of 360 cubic inches? Unlock the Problem Use the Problem Solving MathBoard. Underline important facts. Choose a strategy you know. WRITE Math Show Your Work First, think about what the problem is asking you to solve, and the information that you are given. Next, make a table using the information from the problem. Finally, use the table to solve the problem. 2. What if the 360 cubic-inch paving stones are 4 inches thick and any whole number length and width are possible? How many different paving stones could be made? Suppose that the cost of a paving stone is $2.50, plus $0.18 for every 4 cubic inches of concrete. How much would each paving stone cost? 3. One company makes inflatable swimming pools that come in four sizes of rectangular prisms. The length of each pool is twice the width and twice the depth. The depth of the pools are each a whole number from 2 to 5 feet. If the pools are filled all the way to the top, what is the volume of each pool? Chapter 11 Lesson

4 MATHEMATICAL PRACTICES COMMUNICA E CONSTRUCT ARGUMENTS On Your Own 4. DEEPER Ray wants to buy the larger of two aquariums. One aquarium has a base that is 20 inches by 20 inches and a height that is 18 inches. The other aquarium has a base that is 40 inches by 12 inches and a height that is 12 inches. Which aquarium has a greater volume? By how much? Math WRITE Show Your Work 5. SMARTER Mr. Rodriguez works at a store. He wants to arrange 12 toys in a display shaped like a rectangular prism. The toys are in cube-shaped boxes. How many rectangular prisms with a different-size base can he make with the boxes? 6. MATHEMATICAL PRACTICE 6 Marilyn has 4,000 one-inch cubes. She wants to pack them into a carton. The carton is 1 foot high and its base is 1 foot by 2 feet. Will all the cubes fit into the carton? Explain how you know. 7. SMARTER Dakota s wading pool has a volume of 8,640 cubic inches. Which could be the dimensions of the wading pool? Mark all that apply. A B 24 in. by 30 in. by 12 in. 27 in. by 32 in. by 10 in. C D 28 in. by 31 in. by 13 in. 30 in. by 37 in. by 18 in. 696

5 Name Problem Solving Compare Volumes Practice and Homework Lesson COMMON CORE STANDARD 5.MD.C.5b Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Make a table to help you solve each problem. 1. Amita wants to make a mold for a candle. She wants the shape of the candle to be a rectangular prism with a volume of exactly 28 cubic centimeters. She wants the sides to be in whole centimeters. How many different molds can she make? 10 molds 2. Amita decides that she wants the molds to have a square base. How many of the possible molds can she use? 3. Raymond wants to make a box that has a volume of 360 cubic inches. He wants the height to be 10 inches and the other two dimensions to be whole numbers of inches. How many different-sized boxes can he make? 4. Jeff put a small box that is 12 inches long, 8 inches wide, and 4 inches tall inside a box that is 20 inches long, 15 inches wide, and 9 inches high. How much space is left in the larger box? 5. Mrs. Nelson has a rectangular flower box that is 5 feet long and 2 feet tall. She wants the width of the box to be no more than 5 feet. If the width is a whole number, what are the possible volumes for the flower box? 6. WRITE Math Using drawings of rectangular prisms, define in your own words, perimeter, area, and volume. Use color pencils to highlight what each term refers to. Chapter

6 Lesson Check (5.MD.C.5b) 1. Corey bought a container shaped like a rectangular prism to hold his photo collection. If the container s dimensions are 6 in. by 8 in. by 10 in., what is its volume? 2. Aleka has a box for keepsakes that has a volume of 576 cubic inches. The length of the box is 12 inches and the width is 8 inches. What is the height of the box? Spiral Review (5.MD.A.1, 5.MD.C.3, 5.MD.C.5a, 5.MD.C.5b) 3. A movie is 2 hours and 28 minutes long. It starts at 7:50 p.m. At what time will the movie end? 4. How many rectangular faces does a pentagonal pyramid have? 5. An aquarium is in the shape of a rectangular prism. Its length is 24 inches, its width is 12 inches, and its height is 14 inches. How much water can the aquarium hold? 6. What is the volume of the rectangular prism shown? m 3 m 6 m FOR MORE PRACTICE GO TO THE Personal Math Trainer