WORDS TO KNOW Lesson 27 CHAPTER 4 - Mastery Education

CHAPTER 4REPRESENT SOLIDS USING NETSWORDS TO KNOWnetfaceVocabulary in ActionLesson 27ƔREPRESENT SOLIDS USING NETS 6.G.4A three-dimensional figure can be represented with a two-dimensionaldrawing called a net.ƔThe net must have the correct number of faces, or flat surfaces, andeach face needs to be the correct shape.ƔEdges are where the faces meet and dashed lines are sometimesused to show edges that will fold. Solid lines show where the orld ConnectionLucy bought a snow globe that measures 4 inches at its widest and is 5 inchestall. She wants to put it in a decorated box as a surprise for her sister. Hermother has a container with many boxes, but all of them are opened up to layflat. In which box will her snow globe fit? Let’s practice the skills in the GuidedInstruction and Independent Practice and see how Lucy solves her problem atthe end of the lesson!2 in.5 in.4 in.2 in.6 in.5 in.5 in.5 in.5 in.5 in.2 in.Lesson 275 in.5 in.2 in. 4 in.5 in.4 in.5 in.ƔA prism is made up of two bases joined by rectangular sides, or faces.ƔThe bases of a prism are two faces of a prism and are both thesame shape.ƔThe bases give the prism its name and it will have as manyrectangular sides as there are sides to the base.A pyramid has a polygonal base and triangular sides that meet at a point.ƔWhenever you see a net whose sides are all triangular, it is apyramid.EXAMPLEA triangular prism has two triangular bases, joined by three rectangularsides. The net for a triangular prism shows the 2 triangular bases and 3rectangular faces.THINK ABOUT ITWhat I Am Going to LearnƔHow three-dimensional figures can be represented with twodimensional drawings called netsƔThe different components of netsƔHow to determine which solids (or three-dimensional figures) arerepresented by different netsWhat examples of triangular prismshave you seen in your everyday life?This cheese is cut in the shape of a triangular prism.What I May Already Know 2.G.1, 4.MD.3Ɣ[ 292 ]I know the parts and characteristics of two- andthree-dimensional figures.ƔI can find the area of two-dimensional figures.ƔI can find the volume of three-dimensional figures.masteryeducation.com Mathematics Level FJust as you can draw a net for a three-dimensional figure, you can use a net todetermine what type of solid it makes.Copying is prohibited.Copying is prohibited.Chapter 4 Geometry masteryeducation.com[ 293 ]

Lesson 27REPRESENT SOLIDS USING NETSEXAMPLEStep Two Start by drawing the bottom base of the figure. Use dashedlines for the edges of the base because these are edges that would befolds if you created the shape by folding a net. Label the edges with theirlengths.The net shows 4 triangles. If all triangles are folded up, they meet atone point, so this is a pyramid. The base is a square, so this is a squarepyramid.TURN AND TALKThink about Lucy’s problem fromthe beginning of the lesson. Do youthink a box in the shape of a squarepyramid might solve her problem?Lesson 27REPRESENT SOLIDS USING NETS2 in.3 in.2 in.1 in.1 in.Step Three Add the faces that attach directly to the base. In this case,those are the front, back, left, and right sides of the prism. Label theirdimensions.The Palace of Peace and Reconciliation in Astana, Kazakhstan is in theshape of a square pyramid.3 in.1 in.1 in.2 in.Step Four Draw the top base. Remember: You can think about this net asa shape you will fold together into the three-dimensional prism. That willhelp you decide where to attach the final face.1 in.1 in. 2 in.3 in.Attach the top base so that it would fold over from one of the sides. Labelthe face’s dimensions.1 in.GUIDED INSTRUCTION2.Which of the following nets would not form a triangular prism whenfolded?1.Draw the net for the rectangular prism.A three-dimensional figure can be represented with a two-dimensionaldrawing called a net. Think of the prism as a box, and you can cut andunfold it to make a net.HINT, HINTThink of the net that does not havetwo triangular bases and threerectangular sides.A cereal box is an example of a rectangular prism. Have you ever opened acereal box at the seams? If you did this, you would see the net of a rectangularprism.1 in.1 in. ׇ 3 in.Step One List all the faces of the figure and their dimensions. All facesmust be included in the net.2 in.TIPS AND TRICKSThis is just one method fordrawing nets. Try starting with oneside to “unroll” the figure.[ 294 ]A rectangular prism is made up of 6 rectangular faces:2 rectangles: 2 cm by 1 cm (sides, long)2 rectangles: 3 cm by 1 cm (bases)2 rectangles: 3 cm by 2 cm (sides, short)masteryeducation.com Mathematics Level FCopying is prohibited.Copying is prohibited.Chapter 4 Geometry masteryeducation.com[ 295 ]

Lesson 27REPRESENT SOLIDS USING NETSREPRESENT SOLIDS USING NETSINDEPENDENT PRACTICESKETCH ITHow Am I Doing?Can you draw a net of an item yousee in the room right now?What questions do you have?Lesson 27WORK SPACEAnswer the questions.1.Which figure could be formed with this net? ׇ What is an example of a pyramid, rectangular prism, or triangularprism you see or use every day? Do you think the designers used a2.What does the net shown below represent?net when coming up with the design?Color in the traffic signalthat shows how you aredoing with the skill. ׇ pentagonal prism square prism triangular prism rectangular prismI am stuck.I almosthave it.3.Iunderstandthe skill.[ 296 ]masteryeducation.com Mathematics Level FCopying is prohibited.Which net represents a triangular pyramid? ׇ Copying is prohibited.Chapter 4 Geometry masteryeducation.com[ 297 ]

Lesson 27REPRESENT SOLIDS USING NETS4.REPRESENT SOLIDS USING NETSLesson 27Part BWhich figure will this net make?Use the grid to draw a net that corrects Travis’s mistake. Make the netfor a square prism with base edges of 2 cm and a height of 4 cm. Leteach box in the grid measure 1 cm on each side. ׇ 6.WORK SPACEDescribe how to construct a net for a triangular prism. Include thenumber of faces you would use and the shape of each face.5. Part AHINT, HINTTravis drew the net of a square prism below. Explain why his net isincorrect.As you draw, make sure you areincluding all faces. Think aboutwhich edges touch for the dashedlines.[ 298 ]masteryeducation.com Mathematics Level FCopying is prohibited.Copying is prohibited.Chapter 4 Geometry masteryeducation.com[ 299 ]

Lesson 27REPRESENT SOLIDS USING NETS7.REPRESENT SOLIDS USING NETSUse the rectangles in the box to make a net for a rectangular prism withdimensions 2 cm by 4 cm by 1 cm. Use the space below to draw and labelthe net.Objects can be used more than once.9.Lesson 27Which of the following nets would represent a square pyramid?WORK SPACE ׇ 4 cm4 cm2 cm2 cm1 cm1 cm 8. How is the number of rectangular faces of a prism related to its base?Explain your answer and give an example. [ 300 ]masteryeducation.com Mathematics Level FCopying is prohibited.Copying is prohibited.Chapter 4 Geometry masteryeducation.com[ 301 ]

Lesson 27REPRESENT SOLIDS USING NETSEXIT TICKET6.G.4Now that you’ve mastered the representing three-dimensional figures with two-dimensionalnets, let’s solve the problem in the Real-World Connection.Lucy made a snow globe that measures 4 inches at its widest and is 5 inches tall. She wants toput it in a decorated box as a surprise for her sister. Her mother has a container with manyboxes, but all of the boxes are opened and lay flat. Lucy needs to pick one box and fold it. Inwhich package will her snow globe fit?2 in.5 in.4 in.2 in.6 in.5 in.5 in.5 in.5 in.5 in.2 in.5 in.5 in.2 in. 4 in.5 in.4 in.5 in.The snow globe is a ball, or sphere, so it will be 4 inches wide in each direction. Which packagewill Lucy use? Explain why you chose this package and why the other two packages will notwork.[ 302 ]masteryeducation.com Mathematics Level FCopying is prohibited.

Lesson 27PRACTICE TESTREPRESENT SOLIDS USING NETSTEACHER NOTESAnswer the questions.1.Which figures have an area of 36 square units? Select the three correct answers.REAL-WORLD GOAL FOR STUDENTS Students will understand how nets of three-dimensional figures can be applied in the realworld by identifying which net(s) satisfy given constraints.TIPS FOR THE STRUGGLING LEARNER 4 ׇ 129Students may struggle with the idea that a net shows all the faces, edges, and vertices of athree-dimensional figure. Have students use grid paper and rulers to construct nets. Havestudents draw, cut out, and fold their nets to show their connection to three-dimensionalfigures.6ACTIVITIES FOR THE ADVANCED LEARNER Students can use rulers and grid paper to construct nets of three-dimensional figures withgiven dimensions. 9 12Students can use rulers and grid paper to construct a more complicated figure, maybe acomposition of a rectangular prism and two square pyramids on each end, or even tworectangular pyramids.8412628 383216[ 304 ]masteryeducation.com Mathematics Level FCopying is prohibited.Copying is prohibited.Chapter 4 Geometry masteryeducation.com[ 305 ]

Chapter 42.PRACTICE TESTPRACTICE TESTChapter 4Part BDescribe how to find the area of the shape. Sketch the figures that you woulduse and explain which measures you need.Explain how to use your drawing in Part A to find the area of the shape, and find its area.4.1How many cubes with edge lengths of 4 inch does it take to fill a 1-inch cube? ׇ 4 16 32 645. Part AA right rectangular prism has side lengths of 11.5 cm, 8.4 cm, and 6.5 cm.What is the volume of the prism?3. Part ADraw line segments to show how to use smaller shapes to find the area of the figure.Write your answer in the box.cubic centimeters[ 306 ]masteryeducation.com Mathematics Level FCopying is prohibited.Copying is prohibited.Chapter 4 Geometry masteryeducation.com[ 307 ]

Chapter 4PRACTICE TESTPRACTICE TESTPart B8.Chapter 4What is the area of the triangle?Describe two different ways to find the volume of the prism in Part A.y54321 5 4 3 2 10 112345x 2 3 4 5 ׇ 10 14 15 209.6.Which of these coordinates have a distance of 6 units between the points?Select the two correct answers. ( ׇ 6, 1) and ( 6, 5) ( 4, 2) and (2, 2) ( 2, 3) and ( 6, 3) ( 0, 1) and (0, 6) ( 3, 4) and (3, 2)7.10. Is each figure one of the faces in a net of a rectangular pyramid? Select Yes or No.A rectangle has vertices at (ⴚ2, 4), (ⴚ2, ⴚ1), (5, ⴚ1), and (5, 4). Find the perimeter of the rectangle.Write your answer in the box.Perimeter [ 308 ]Circle all of the nets that represent a triangular prism.unitsmasteryeducation.com Mathematics Level FCopying is eYesNod.trapezoidYesNoCopying is prohibited.Chapter 4 Geometry masteryeducation.com[ 309 ]

Chapter 4PRACTICE TESTPRACTICE TEST11. Choose the name from the box that matches each net. Write the correct name13. Shakira calculated the surface area of the square pyramid. Her calculations are shown below.under the net. The names cannot be used more than once.triangular prismtriangular pyramid12 m 16 m 192 m2rectangular prismChapter 41rectangular pyramid216 m(12 m 16 m) 96 m2192 m2 4(96 m2) 576 m212 mExplain her error and how to correct it.12. Which of the following figures have a surface area less than 50 cm2? Select the two correct answers.4 cm3 cm ׇ 3 cm 3 cm6 cm14. What is the surface area of the right triangular prism?0.5 cmSurface area 2 cm 5 cm2 cm13 in.5 in.in.212 in. 15. Circle the number that correctly completes the statement.7 cm3 cm15 in.Write your answer in the box.1 cm4m6m 6 cm1 cm1m2 cmThe surface area of the rectangular prism is24square meters.346896[ 310 ]masteryeducation.com Mathematics Level FCopying is prohibited.Copying is prohibited.Chapter 4 Geometry masteryeducation.com[ 311 ]

A triangular prism has two triangular bases, joined by three rectangular sides. The net for a triangular prism shows the 2 triangular bases and 3 rectangular faces. This cheese is cut in the shape of a triangular prism. Just as you can draw a net for a three-dimensional fi gure, you can use a