15.3 PROBLEM SOLVING Figures Classify Plane

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15.3 FiguresPROBLEM SOLVING ?Classify PlaneEssential Question How can you use the strategy draw a diagram toclassify plane figures?Texas EssentialKnowledge and SkillsHow can you use thestrategy draw a diagramto classi fy plane f igures?Geometry and Measurement—3.6.AClassify and sort two- and three-dimensional solids, includingcones, cylinders, spheres, triangular and rectangular prisms,and cubes, based on attributes using formal geometriclanguage Also 3.6.BMATHEMATICAL PROCESSES3.1.B Use a problem-solving model3.1.D Communicate mathematical ideas and reasoningAre You Ready?Access Prior KnowledgeUse the Are You Ready? 15.3 in theAssessment Guide to assess students’understanding of the prerequisite skillsfor this lesson.VocabularyLesson OpenerMaking ConnectionsInvite students to tell you what they know about figures.Venn diagramGo to Multimedia eGlossary atthinkcentral.comWhat figures do you know? (Answers will vary.) What everyday things arequadrilaterals? (Answers will vary.) What everyday things are not quadrilaterals?(Answers will vary.)Using the Digital LessonModel different figures with objects in the room. Have students identify thequadrilaterals.Learning TaskWhat is the problem the students are trying to solve? Connect the story to the problem. What is the problem asking you to find? (the differences between quadrilaterals andother polygons) How many sides does a quadrilateral have? (4) What are other closed figures that do not have four sides called? (polygons)Literacy and MathematicsView the lesson opener with the students. Then, choose one or more of thefollowing activities. Have students write a short story about a road trip that they took or would like totake. Have them mention different figures in their story. Write the word sort on the board. Explain the different meanings of the word andhave students write a sentence for each meaning of the word.ResourcesFor the studentFor the teacherInteractiveStudent Editionprovides studentswith an interactive learningenvironment!Digital ManagementCenter organizes programresources by TEKS!Math on the SpotVideo TutoreTeacherEditionOnline AssessmentSystemiTools VirtualManipulativesSoar to Success MathOnline InterventionLesson 15.3 493A

Name15.3Unlock the Problem?Make sure students understand how to use aVenn diagram. This Venn diagram shows how setsof things, in this case, rectangles and rhombuses,are related. Discuss the attributes of rectangles: fourright angles, two pairs of opposite sides that areparallel, and two pairs of sides of equal length.PROBLEM SOLVINGPlane FiguresEssential QuestionHow can you use the strategy draw a diagram to classify plane figures?A Venn diagram shows how sets of things arerelated. In the Venn diagram at the right, onecircle has figures that are rectangles. Figures thatare rhombuses are in the other circle. The figuresin the section where the circles overlap are bothrectangles and rhombuses.2 pairs of opposite sides that are parallelReadrectangles do not always have 4 sides of equal length. Why do squares fit in both categories? Squares haveall the characteristics of both rhombuses and rectangles:4 sides of equal length, 2 pairs of opposite sides that areparallel, and 4 right angles.what type of quadrilateral is in bothcirclesThey all have 4 sides and 4 angles.Rectangles andthe circles labeledIntermediate: Activity 263.G.1, 4.D, 4.F.2Advanced: Activity 272.I.3, 3.B.3, 4.DAdvanced High: Activity 62.I.5, 3.G.2, 4.G.2thinkcentral.com for the ELL ActivityGuide containing these leveled activities.parallelograms, rectangles, rhombuses, squaresrhombuses, squareslength?What is my plan or strategy? Houghton Mifflin Harcourt Publishing Company4.C.3, 4.F.3, 4.G.3Which quadrilaterals have 2 pairs ofopposite sides that are parallel?Which quadrilaterals have 4 sides of equalPlanDraw a different quadrilateral, such as a trapezoid,on the board. Ask students to discuss whether itfits into either side of the Venn diagram. Responsesshould include that a trapezoid has only 1 pair ofopposite sides that are parallel and sides of differentlengths. So it cannot be a rectangle or a rhombus.SolveWhat is true about all quadrilaterals?What information am I given?Go DeeperBeginning: Activity 39RhombusesWhat do I need to find?RhombusesELPSRectanglesWhat type of quadrilateral is in both circles? What are some characteristics of rhombuses thatdo not apply to all rectangles? Possible answer:Leveled ActivitiesGeometry andMeasurement—3.6.AAlso 3.6.BMATHEMATICAL PROCESSES3.1.B, 3.1.DUnlockUnlock thethe ProblemProblem Which of these characteristics are alsocharacteristics of rhombuses? 4 sides of equal length,English Language Learners ClassifyI will describe the figures in the sectionWhich quadrilaterals have 4 right angles?where the circles overlap by their sidesrectangles, squaresand angles so I can name the figures.The quadrilaterals in the section where theMath Talk: No; possible explanation:a trapezoid has only 1 set of oppositesides that are parallel and sides ofdifferent lengths.Math TalkMathematical ProcessesDoes afit in the Venndiagram? Explain.ELL Language Support2 pairs of oppositecircles overlap have4 sidessides that are parallel,4 right angles.of equal length, andsquares are in both circles.So,Module 15 493VisualSmall GroupELPS 2.C.4, 4.C.3, 4.DStrategy: Model Language Teachers model language to teach pronunciation. Write Venn diagram on the board. Read the words and have studentsrepeat. Draw a Venn diagram and label the circles Quadrilaterals and Polygonswith Parallel Sides. Read the headings aloud and have students repeat. Work together to draw figures in each section. Have students nameeach figure aloud as it is entered. Discuss which figures might go in the section where the circles overlap.Possible answer: rectangle, square, rhombus, parallelogram, trapezoid493 Module 15

TryTry AnotherAnother ProblemProblemThe Venn diagram at the right shows thefigures Abbie used to make a picture. Wherewould the figure shown below be placed in theVenn diagram?QuadrilateralsPolygons withRight AnglesTry Another ProblemMake a table on the board. List the attributes ofquadrilaterals in one column and the attributes ofpolygons with right angles in another column.Read Describe some differences between quadrilateralsand polygons with right angles. Possible answer: notall polygons with right angles will have 4 sides.SolveDiscuss the characteristics of trapezoids that occurin both lists, and explain that they belong in theoverlapping section of the Venn diagram.What do I need to find?where the figure shown would be placed inthe Venn diagramWhat is true about all quadrilaterals?They all have 4 sides and 4 angles.What is true about all polygons? They areclosed figures made up of line segments.What information am I given?the circles labeled Quadrilaterals andPolygons with Right AnglesPlanMath TalkHow can you describe the figures in thesection where the circles overlap? Theyare all quadrilaterals with right angles.Mathematical ProcessesUse Math Talk to focus on students’ understandingof polygon attributes.Does the figure shown have right angles?YesWhat is my plan or strategy?Does the figure have 4 sides? YesGo DeeperI will use what I know about two-dimensionalfigures to find where the figure should beplaced.So, the figure goes in the section wherethe circles overlap.Demonstrate to students that Venn diagrams can beused to compare more than two sets of objects. Askstudents to identify each category, and discuss whyeach figure fits the section it is in.How many figures do not have right angles?3 figures2.polygons; Possible explanation:all the figures are made up ofline segments; all the figuresare closed.How many red figures have right angles but are1 red figurenot quadrilaterals?3.Analyze What is a different way to sort the figures?Possible answer: Polygons with Parallel Sides andMath TalkMathematical ProcessesWhat name can be usedto describe all the figuresin the Venn diagram?Explain how you know.Polygons with Right Angles494EnrichVisual / IndividualPartnersPolygons with Sidesof Equal LengthQuadrilaterals Houghton Mifflin Harcourt Publishing Company1.TrianglesMaterials: paper, markers Draw a large Venn diagram on paper. Label the circles Polygons withEqual Side Lengths and Polygons with Parallel Sides. Each student should use a marker to draw in a shape in one section athis turn. Challenge students to find as many shapes as possible to fit eachsection, and to explain why those in the overlapping section arecorrectly placed. If a student cannot think of a shape that fits any category, it is the nextstudent’s turn. Have students draw a new diagram with new labels and repeat theactivity.Go to Go to thinkcentral.com for additional enrichmentactivities in the Enrich Activity Guide.COMMON ERRORSCEErrorStudents may not look for all the correctattributes.Example Students may forget to exclude thefigures that do not share all the attributes of thelabeled circle.Springboard to Learning Remind students thatthey have to check for each attribute requiredin the problem. Encourage students to cross offfigures as they are excluded and to check off eachrequired attribute when they have met it.Lesson 15.3 494

NameShareShare andand ShowShowShare and ShowUse the Venn diagram for 1–2.The first problem connects to the learning model.Have students use the MathBoard to explain theirthinking.1.Jordan is sorting the figures at the right in a Venn diagram.Where does thego?First, look at the sides and angles of the polygons.Use the checked exercises for Quick Check. Studentsshould show their answers for the Quick Check on theMathBoard.Next, draw the polygons in the Venn diagram below.4 sides of equal lengthThe figure above has0 right angles.andPolygonswithRight AnglesSo, the figure goes in the circle labeled32Quick Check1IFTHENPolygonswith All Sides Equal in Length2.a student misses the checked exercisesProblemProblem SolvingSolving3.ProblemsProblem 3 requires students to apply their knowledgeof the attributes of figures to label the Venn diagram.Multi-Step Use Math LanguageEva drew the Venn diagram at the right. Whatlabels could she have used for the diagram?Where would each label go?Possible answer: Left circle: Quadrilaterals withProblem 4 requires students to draw a Venn diagramand show one way a parallelogram, a rectangle, asquare, a trapezoid, and a rhombus can be sorted.Parallel Sides; Right circle: Polygons with Right Angles4. Houghton Mifflin Harcourt Publishing CompanyThrough the Math on the Spot Video Tutor,students will be guided through an interactivesolving of this type of H.O.T. problem. Use thisvideo to also help students solve the H.O.T.problem in the Interactive Student Edition. Withthese videos and the H.O.T. problems, studentswill build skills needed in the TEXAS assessment.Where in the Venn diagram would youplace a ? only in thecircle labeled Polygons with Right AnglesDifferentiate Instruction withRtI Tier 1 Lesson 73MMath on the SpotVideo TutorVMulti-Step DisplayDraw and label a Venn diagram to showone way you can sort a parallelogram,a rectangle, a square, a trapezoid, anda rhombus. Check students’ drawings.Module 15 Lesson 3 4953Math on the Spot videos are in theInteractive Student Edition and atthinkcentral.com.Polygons withAll Sides Equalin LengthRtI Tier 1 Lesson 7321Enrich 71NameNameLESSON73Problem Solving Classify Plane FiguresOBJECTIVE Solve problems by using the strategy draw a diagram to classify plane figures.A Venn diagram shows how sets of thingsare related. This Venn diagram shows howquadrilaterals and polygons with all sides ofequal length are related. The figures in thesection where the circles overlap showfigures that belong to both groups.QuadrilateralsEnrich 7113.6.APolygons with AllSides of Equal LengthTriple TroubleSome Venn diagrams have three overlapping circles. Lookat the figures in each circle of the Venn diagram below.Write a label for each circle.ABWhat types of polygons are in both circles?ReadWhat do I need to find?what types of polygons arein both circlesWhat information am I given?The circles are labeledQuadrilaterals and Polygonswith All Sides of Equal LengthSolveCWhat is true about all polygons in thecircle labeled Quadrilaterals?They all have 4 sides.1.What is true about all polygons in theother circle?Which polygons are in the section wherethe circles overlap?2. Houghton Mifflin Harcourt Publishing Company495 Module 15What is my plan or strategy?I will describe the figures in thePossible answer: Polygonshave 4 sides that are of equal lengthLabel for circle B:Possible answer: Polygonswith All Sides of Equal Lengthfigures that are quadrilaterals and thatPlanLabel for circle A:with Right AnglesThey all have sides of equal length.3.a rhombusSo, a square andarein the section where the circles overlap.Label for circle C:Possible answer: Polygonswith More Than 3 Sidessection where the circles overlap1. Brad drew the Venn diagram at theright. What type of figures are in thesection where the circles overlap?Triangles4.Polygons withRight AnglesNo; a figure that belongs in that sectionwould have to have 3 sides of the samelength AND a right angle. No triangle canhave both a right angle and all sides equal.triangles that have1 right angleGeometry and MeasurementIs there a plane figure that belongs in the sectionwhere circles A and B overlap, but not circle C? Explain.145Enrich Houghton Mifflin Harcourt Publishing CompanyE71

Mathematical ProcessesModel Reason CommunicateDailyDaily AssessmentAssessment TaskTask3Daily Assessment TaskFill in the bubble for the correct answer choice.5.Max classifies the street signs he sees by shape, and then sortsthem in a Venn diagram. The circles are labeled “Polygons withRight Angles” and “Polygons with All Sides Equal in Length.”Which sign is in the section where the two circles overlap?1Can students use the strategy draw a diagram toclassify plane figures?THENIFA2CNO Soar to Success MathWarm-Up 38.31BDYES 6.Multi-Step Jenna makes a design using patternblocks. Which pattern block is placed incorrectlyin the Venn diagram?ACBDPolygons withAll Sides Equalin LengthPolygons withOpposite SidesParallelTEXAS Test Prep7.What label could describe Circle A?APolygons with 4 Right AnglesBPolygons with 2 Pairs of Opposite SidesThat Are ParallelCPolygons with 2 Pairs of Sides of Equal LengthDPolygons with All Sides of Equal Length496AQuadrilateralswith Right Angles Houghton Mifflin Harcourt Publishing Company Image Credits: (tl) Corbis; (bl) pm/Alamy; (tr) David Frazier/Corbis; (br) Phil Degginger/Alamy Images Enrich 71Homework and PracticeLesson 15.3TEXAS Test Prep CoachTest Prep Coach helps teachers to identify commonerrors that students can make.In the Test Prep exercise, if students selected:A They overlooked the polygons with no rightangles in Circle A.B and C They overlooked the triangle and pentagonin Circle A.?Essential QuestionWriteMathHow can you use the strategy draw a diagram toclassify plane figures? Possible answer: I can draw a Venndiagram to sort figures based on their side lengths, typesof angles, and number of pairs of parallel sides. If a figurefits both categories, it goes in the section where the circlesoverlap.Differentiated Centers KitActivitiesClassification ActStudents complete orangeActivity Card 18 by classifyingtwo-dimensional figures basedon their attributes.ActivitiesWhat Figure?Students complete purple ActivityCard 18 by identifying anddefining two-dimensional figuresby playing a game.Lesson 15.3 496

515.3Geometry and Measurement—3.6.AAlso 3.6.BMATHEMATICAL PROCESSES 3.1.B, 3.1.DNamePROBLEM SOLVINGPlane FiguresFill in the bubble completely to show your answer. Classify4.Use the Venn diagram for 1 and 2.1.Draw the polygons in the Venn diagram.Polygons withParallel Sides6.Where in the Venn diagram would you place a?only in the circle labeled Polygons with Right Angles Houghton Mifflin Harcourt Publishing CompanyMulti-Step Jessica draws this Venndiagram. Which of the following twofigures can she place only in circle A?CDPossible answer: Quadrilaterals with Parallel SidesModule 15 Lesson 3Homework and PracticeUse the Homework and Practice pages to providestudents with more practice on the concepts andskills of this lesson.Module 15ACBDACBDPolygons withRight AnglesPolygons with2 Pairs of Equal SidesABBTia wants to include the figures at theright in one circle of a Venn diagram.What label can she use?497-498Sean draws a Venn diagram withtwo circles and labels the circles“Polygons with 4 Equal Sides” and“Polygons with Parallel Sides.” Whichfigure can he draw where the circlesoverlap?AProblemProblem SolvingSolving3.Fran draws a Venn diagram withtwo circles and labels the circles“Polygons with Parallel Sides”and “Quadrilaterals with ParallelSides.” Which figure belongs onlyin the circle labeled “Polygons withParallel Sides?”Polygons withRight Angles5.2.TEXAS Test PrepLessonLesson CheckCheck497498 Houghton Mifflin Harcourt Publishing CompanyHo mewo r kand Practice

Next, draw the polygons in the Venn diagram below. The figure above has _ sides of equal length and _ right angles. So, the figure goes in the circle labeled _ 2. Where in the Venn diagram would you place a ? Use the Venn diagram for 1–2. 3. Multi-Step Use Math Language Eva drew the Venn diagram at the right. What labels could she have .

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