LESSON 2 SESSION 1 Explore Finding Volume Using Unit Cubes

LESSON 2SESSION 1Explore Finding Volume Using Unit CubesPreviously, you learned that you can fill a solid figure with unitcubes to find its volume. Use what you know to try to solve theproblem below.Carl filled the clear box shown below with unit cubes tofind its volume. The unit cubes Carl used all have sidelengths of 1 foot. What is the volume of the box?1 ft1 ft1 ftLearning Targets   Measure volumes by counting unitcubes, using cubic cm, cubic in,cubic ft, and improvised units.   Find the volume of a rightrectangular prism with wholenumber side lengths by packing itwith unit cubes, and show that thevolume is the same as would befound by multiplying the edgelengths, equivalently by multiplyingthe height by the area of the base.Represent threefold whole-numberproducts as volumes.SMP 1, 2, 3, 4, 5, 6, 7TRY IT Math Toolkitunit cubesgrid paperisometric dot papersquare sticky notesDISCUSS ITAsk your partner: How didyou get started?Tell your partner: I startedby . . . Curriculum Associates, LLC Copying is not permitted.Lesson 2 Find Volume Using Unit Cubes17

LESSON 2SESSION 1EXPLORECONNECT IT1LOOK BACKDescribe the measurement unit Carl should use and explain how he can find thevolume of the box.2 LOOK AHEADVolume is measured in cubic units. Here are some cubic units you might use tomeasure volume.Unit of Volumecubic inchcubic centimetercubic foot1 in. 1 in. 1 in. 1 cm 1 cm 1 cm1 ft 1 ftUnit Cube1 ft1 in. 1 in. 1 in.1 cm 1 cm 1 cm1 ft 1 ft 1 ft1 in. 1 in. 1 in. 1 cm 1 cm 1 cm1 ft 1 ft1 ftCarl has another box as shown below. What is its volume?1 in.1 in.1 in.3 REFLECTWhat is the same and what is different about the volume of Carl’s two boxes?18Lesson 2 Find Volume Using Unit Cubes Curriculum Associates, LLC Copying is not permitted.

Name:LESSON 2SESSION 1Prepare for Finding Volume Using Unit Cubes1Think about what you know about solid figures. Fill in each box.Use words, numbers, and pictures. Show as many ideas as you can.What Is It?What I Know About ItrectangularprismExamples2ExamplesExamplesInstead of using cubic units to measure volume,Paulina wants to measure volume using boxesof pencils. What is the volume of this rectangularprism using boxes of pencils as the unit of measure? Curriculum Associates, LLC Copying is not permitted.Lesson 2 Find Volume Using Unit Cubes19

LESSON 23SESSION 1Solve the problem. Show your work. Jan filled the box shown below with unit cubes to find its volume.The unit cubes Jan used all have side lengths of 1 centimeter. What isthe volume of the box?1 cm1 cm 1 cmSolution420Check your answer. Show your work.Lesson 2 Find Volume Using Unit Cubes Curriculum Associates, LLC Copying is not permitted.

LESSON 2SESSION 2Develop Finding Volume Using Unit CubesRead and try to solve the problem below.Abigail uses cardboard to build a rectangular prism like the one shownbelow. What is the volume of the prism?3 cm1 cm2 cmTRY IT4 cm1 cm1 cmMath Toolkit unit cubes 1-cm grid paper isometric dot paperDISCUSS ITAsk your partner: Why didyou choose that strategy?Tell your partner:I knew . . . so I . . . Curriculum Associates, LLC Copying is not permitted.Lesson 2 Find Volume Using Unit Cubes21

LESSON 2DEVELOPExplore different ways to understand finding the volume of a rectangular prism. Abigail uses cardboard to build a rectangular prism like the one shownbelow. What is the volume of the prism?3 cm1 cm2 cm4 cm1 cm1 cmPicture ItYou can find the volume of the prism by filling it withunit cubes and counting the number of cubes.Use unit cubes that are each 1 cubic centimeter.3 cm2 cm4 cmModel ItYou can also find the volume by counting the numberof cubes in one layer and the number of layers.Use unit cubes that are each 1 cubic centimeter.1 layer22Lesson 2 Find Volume Using Unit Cubes3 layers Curriculum Associates, LLC Copying is not permitted.

SESSION 2Connect ItNow you will use the problem from the previous page to help you understand howto find the volume of a rectangular prism.1Look at the model in Picture It on the previous page. Count the number of cubesin one layer. There arecubes in one layer.2How could you find the number of cubes in one layer without counting the cubes?3Once you know how many cubes are in one layer, what else do you need to knowto find the volume?4There are 8 cubes in each layer and there are 3 layers. What multiplicationexpression can you write to find the volume of the prism?5What is the volume of Abigail’s rectangular prism?6Explain how you can use multiplication to find the volume of a rectangular prism.7 REFLECTLook back at your Try It, strategies by classmates, and Picture It and Model It.Which models or strategies do you like best for finding the volume of a rectangularprism? Explain. Curriculum Associates, LLC Copying is not permitted.Lesson 2 Find Volume Using Unit Cubes23

LESSON 2SESSION 2DEVELOPAPPLY ItUse what you just learned to solve these problems.8What is the volume of the rectangular prism at theright? Show your work.1 in.1 in.1 in.Solution9Mr. Wong finds the volume of a box by filling it with 1-foot unit cubes, as shownbelow. What is the volume of Mr. Wong’s box? Show your work.Solution10Jamila wants to find the volume of the rectangular boxat the right. What is the volume of the box?A 18 cubic unitsB 30 cubic centimeters6 cmC 36 cubic centimetersD 36 cubic inches24Lesson 2 Find Volume Using Unit Cubes1 cm1 cm 1 cm2 cm3 cm Curriculum Associates, LLC Copying is not permitted.

Name:LESSON 2SESSION 2Practice Finding Volume Using Unit CubesStudy the Example showing how to use layers to find the volume of a rectangularprism. Then solve problems 1–7.ExampleKeith uses this box to store his colored markers.What is the volume of the box?4 in.6 in.2 in.Think about filling the box with 1-inch cubes.One layer has 2 rows of 6 cubes, or 12 cubes.There are 4 layers of cubes.12 1 12 1 12 1 12 5 48, or 12 3 4 5 48The volume of the box is 48 cubic inches.1Prism G is filled with unit cubes that have side length 1 centimeter.There arelayers withcubes 1cubes in each layer.cubes 5cubesThe volume is2G.Prism H is filled with unit cubes that have side length 1 foot.There arelayers with3cubes 5The volume is Curriculum Associates, LLC Copying is not permitted.cubes in each layer.Hcubes.Lesson 2 Find Volume Using Unit Cubes25

LESSON 23SESSION 2What is the volume of the rectangular prism at the right?Show your work.2 ft2 ft4 ftSolution4Jenn noticed that she can fit two juice boxes sideby side on the bottom of this box. She can maketwo more layers like the one shown to fill the box.Using a juice box as a measure of volume, what isthe volume of the larger box?Solution5A box is 2 inches long, 1 inch wide, and 6 inches tall. What is the relationshipbetween the volume of this box and the one in problem 4? Tell how you know.6Box D and Box E are made from unit cubes of the same size.Which has a greater volume, Box D or Box E? Explain.7Add a layer to Box D and compare the volume of the newBox D to the volume of Box E.DE26Lesson 2 Find Volume Using Unit Cubes Curriculum Associates, LLC Copying is not permitted.

LESSON 2SESSION 3Refine Finding Volume Using Unit CubesComplete the Example below. Then solve problems 1–9.EXAMPLEThe student started byfinding the number ofcubes in thebottom layer.Pedro has a storage box with a volume of 36 cubic feet.He knows that the box is 4 feet long and 3 feet wide. Howhigh is the box?Look at how you could show your work using a drawing andmultiplication facts.4 3 3 5 1212 33 ft4 ft5 3612 3 3 5 36PAIR/SHARECould you solve thisproblem another way?SolutionappLy it1 A box measures 6 centimeters long, 2 centimeters wide, and4 centimeters high. What is the volume of the box? Show your work.How many layers of cubeswill there be in the box?4 cm2 cm6 cmPAIR/SHARESolution Curriculum Associates, LLC Copying is not permitted.Can you use multiplicationto solve this problem?Lesson 2 Find Volume Using Unit Cubes27

LESSON 22REFINEKamala made the figure below using cubes. What is the volume ofKamala’s figure? Show your work.How many cubes are therein each layer?1 in.1 in.1 in.PAIR/SHAREHow did you decide whichmethod to use to solve theproblem?Solution3What is the volume of the rectangular prism below?There is more than one wayto find the volume of arectangular prism.1 ft1 ft 1 ftA 6 square feetB 6 cubic feetC 8 square feetD 8 cubic feetNam chose D as the correct answer. How did he get that answer?PAIR/SHAREDoes Nam’s answer makesense?28Lesson 2 Find Volume Using Unit Cubes Curriculum Associates, LLC Copying is not permitted.

SESSION 34How many 1-centimeter unit cubes are in the bottomlayer of the rectangular prism at the right?A 31 cmB 61cmC 121 cmD 245Which expressions can be used to find thevolume, in cubic feet, of the rectangularprism at the right?A 30 3 4B (5 1 6) 3 41 ft1 ft 1 ftC 30 1 30 1 30 1 30D 51614E 30 1 46Flora has a rectangular gift box that has a volume of 24 cubic inches. The box is2 inches tall. Determine if the gift box could have the given length and width.YesNoLength: 11 inches; Width: 11 inchesABLength: 4 inches; Width: 3 inches Length: 10 inches; Width: 2 inches Length: 6 inches; Width: 2 inches Length: 12 inches; Width: 1 inch Curriculum Associates, LLC Copying is not permitted.Lesson 2 Find Volume Using Unit Cubes29

LESSON 27SESSION 3REFINEBoth figures are filled with unit cubes ofthe same size. Which rectangular prism hasthe greater volume, Figure A or Figure B?Show your work.ABhas the greater volume.8Part A Mato drew the rectangular prism shown below. Draw and label a differentrectangular prism with the same volume as Mato’s prism.4 cm2 cm5 cmPart B Explain how you know that the volume of your prism is the same as thevolume of Mato’s prism.9 MATH JOURNALJorge uses 1-centimeter cubes to make a rectangular prism. Each layer of his prismis 5 cubes long and 2 cubes wide. His prism has 6 layers. Explain two ways to findthe volume of Jorge’s prism.SELF CHECK30Go back to the Unit 1 Opener and see what you can check off.Lesson 2 Find Volume Using Unit Cubes Curriculum Associates, LLC Copying is not permitted.

LESSON 3SESSION 1Explore Finding Volume Using FormulasPreviously, you learned how to find volume by counting unit cubesand by using addition and multiplication strategies. Now you willlearn how to find volume using a formula. Use what you know to tryto solve the problem below.Becky uses 1-inch cubes to create a model for a smallpaper gift bag she is making. Her model is a rectangularprism. What is the volume of Becky’s model?Learning Targets   Apply the formulas V 5 l 3 w hand V 5 b 3 h for rectangularprisms to find volumes of rightrectangular prisms with wholenumber edge lengths in the contextof solving real world andmathematical problems.   Recognize volume as additive. Findvolumes of solid figures composedof two non-overlapping rightrectangular prisms by adding thevolumes of the non-overlappingparts, applying this technique tosolve real world problems.SMP 1, 2, 3, 4, 5, 6, 7, 81 in.1 in. 1 in.TRY ITMath Toolkit unit cubes grid paper isometric dot paperDISCUSS ITAsk your partner: Do youagree with me? Why or whynot?Tell your partner: I agreewith you about . . .because . . . Curriculum Associates, LLC Copying is not permitted.Lesson 3 Find Volume Using Formulas33