WIXLIB

17.2Find Perimeter?Essential Question How can you measure perimeter?Texas EssentialKnowledge and SkillsGeometry and Measurement—3.7.BDetermine the perimeter of a polygon or a missing lengthwhen given perimeter and remaining side lengths inproblemsMATHEMATICAL PROCESSES3.1.C Select tools, technology, and techniques3.1.E Create and use representationsHow can you measureperimeter ?Are You Ready?Access Prior KnowledgeUse the Are You Ready? 17.2 in theAssessment Guide to assess students’understanding of the prerequisite skillsfor this lesson.MaterialsLesson OpenerMaking ConnectionsInvite students to tell you what they know about triangles.What is a triangle? (A triangle is a plane figure with three straight sides and threeangles.) Where do you see triangles in everyday life? (Possible Answer: In art work,on your math textbook.)Inch rulerVocabularyGo to Multimedia eGlossary atthinkcentral.comUsing the Digital LessonYou may wish to remind students about the properties of triangles. Draw a fewtriangles and indicate the sides and angles in the triangle.Learning TaskWhat is the problem the students are trying to solve? Connect the story to the problem. What is the problem you are trying to solve? (Find the perimeter of the triangle.) What tool are you going to use? (A ruler.) What are you going to measure with the ruler? (The perimeter of the triangle.) Have students think about how they found the perimeter using grid paper inthe past.Literacy and MathematicsChoose one or more of the following activities. Have students explain how they might find the perimeter without using gridpaper. Have students explain their reasoning to a partner. Have students discuss how they have used rulers in the past. Have students explainhow they used rulers to measure various objects.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 17.2 551A

NameUnlock the Problem17.2?HandsOnReview with students that perimeter is the distancearound a figure.Find PerimeterEssential QuestionHow can you measure perimeter?You can estimate and measure perimeter in standard units,such as inches and centimeters.ActivityHandsOnUnlockUnlock thethe ProblemProblemIntroduce the activity by having students use acustomary benchmark for length.Find the perimeter of the cover of a notebook.answersActivity Materials inch ruler Possibleare given. What part of your hand is about 1 inch long?STEP 1 Estimate the perimeter of a notebookPossible answer: the distance from the tip of my thumb tothe first knuckle is about 1 inch.in inches. Record your estimate.side of the notebook to the nearest inch.The length is about 12 inches, or about 1 foot long.STEP 3 Record and add the lengths of the sides measuredto the nearest inch.In Step 1, have students estimate the perimeterwithout using their rulers.42 inches.to the nearest inch isExplain how your estimatecompares with yourmeasurement.Try This! Find the perimeter.Answers will vary. Possible answer: the estimate,40 inches, is close to but less than the actual measurement, 42 inches. Houghton Mifflin Harcourt Publishing CompanyIn Step 3, remind students they need to add thelengths of the sides to find the perimeter.Try This!Mathematical ProcessesSo, the perimeter of the notebook cover measuredStudents will measure to the nearest inch instead ofthe nearest half inch so that they do not have to addfractional parts.Use Math Talk to check students’ understanding ofusing an estimate to check for reasonableness.Math Talk429 12 12 9 In Step 2, students measure each side of thenotebook to the nearest inch.Mathematical Processes40 inchesSTEP 2 Use an inch ruler to measure the length of each What is the length of a sheet of notebook paper?Math TalkGeometry andMeasurement—3.7.BMATHEMATICAL PROCESSES3.1.C, 3.1.EUse an inch ruler to find the lengthof each side.Use a centimeter ruler to find the lengthof each side.Add the lengths of the sides:Add the lengths of the sides:1 2 1 2 63 3 3 3 126 inches.The perimeter is12 centimeters.The perimeter isModule 17 551If the sides of the figures are measured correctly,each length will be a whole number of inches orcentimeters.English Language LearnersELL Language SupportLeveled ActivitiesELPSBeginning: Activity 201.A.1, 3.G.2, 4.C.3Intermediate: Activity 543.B.3, 3.D.2, 4.F.2Strategy: Creative GroupingAdvanced: Activity 572.C.4, 3.D.2, 3.EMaterials: inch rulerAdvanced High: Activity 184.C.4, 4.E, 4.F.7Go to thinkcentral.com for the ELL ActivityGuide containing these leveled activities.Interpersonal / SocialPartners / Small GroupELPS 3.G.2, 4.F.1, 4.F.7 Partner advanced English learners or studentswho are fluent in English with beginning andintermediate English learners. Have them measure perimeter. Have students describe how to measureperimeter with an inch ruler.3 in.3 in.3 in.3 in. 3 in. 3 in. 9 in.551 Module 17

HandsOnShareShare andand ShowShow1.Use an inch ruler to find the perimeter of the triangle.Share and ShowMath Talk1in.11in.Explain how manynumbers you add togetherto find the perimeter ofa figure.in.3 inchesPossible explanation: the numberof addends is equal to thenumber of sides a figure has.Use a centimeter ruler to find the perimeter.2. 3.cm cm cmcm Math Talk cmBefore the figures on this page are measured,you might choose to have students estimate eachperimeter. After the figures have been measured,discuss how the estimates can be used to help decidethe reasonableness of the exact answers.cmcm 14 centimetersMathematical ProcessesUse Math Talk to focus on students’ understandingof the relationship between the number of sides ofa figure and the number of addends needed to findthe perimeter of a figure.cm cm 4.The first problem connects to the learning model.Have students use the MathBoard to explain theirthinking.Mathematical ProcessesThink: How long iseach side?HandsOn13 centimetersUse the grid paper to draw a figure that has a perimeterof 24 centimeters. Label the length of each side. Check students’ drawings.Use the checked exercises for Quick Check. Studentsshould show their answers for the Quick Check on theMathBoard.1 cm32Quick Check1a student misses the checked exercises Houghton Mifflin Harcourt Publishing CompanyIF552THENDifferentiate Instruction withRtI Tier 1 Lesson 84COMMON ERRORSCEErrorWhen a length is not given, the length isassumed.Example Students assume all sides of a triangle arethe same length and measure only one side.EnrichVisualIndividualSpringboard to Learning Point out that unlessstudents are told a triangle has three sides of equallength, they must measure each side to check thatthey are the same.Materials: crayons, 1-Inch Grid Paper (see eTeacher Resources) Write the following perimeters on the board:perimeter 12 inchesperimeter 15 inchesperimeter 8 inches Have students begin by drawing a rectangle with a perimeter of 12inches. Then, have students draw other rectangles and figures with aperimeter of 12 inches. Challenge students to draw at least 3 different figures for eachperimeter.Go to Go to thinkcentral.com for additional enrichmentactivities in the Enrich Activity Guide.Lesson 17.2 552

NameProblemProblem SolvingSolvingProblem Solving5.For Problem 7, students need to analyze and solve amultistep problem. First, they find the perimeter ofthe square garden. Then, they multiply the perimeterby 5 to find the cost of the fence.6.7.Ask students to explain how multiplication andaddition can be used to find the perimeter of arectangle. Double the length and double the width (orMath on the Spot videos are in theInteractive Student Edition and atthinkcentral.com.8 in.4 in.8 in.4 in.7 in.Multi-Step Analyze How much greateris the perimeter of the bird photo than theperimeter of the cat photo?5 in.Write MathShow Your WorkMulti-Step Erin is putting a fencearound her square garden. Each side of hergarden is 3 meters long. The fence costs 5 for each meter. How much will the fence cost? 608. Houghton Mifflin Harcourt Publishing Company Image Credits: (tl) Comstock Images/Getty Images; (tr) Alan Carey/CorbisThrough 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.7 in.4 inchesGo DeeperMMathon the SpotVideo TutorVWhich of the animal photos has a perimeterof 26 inches?bird photoFor Problem 8, some students may find it helpful tofirst sketch the rectangle and label one of its sides as10 feet.multiply each measure by 2), and then find the sum of theproducts.5 in.Use the photos for 5–6.ProblemsWrite MathGary’s garden is shaped likea rectangle with two pairs of sides of equal length, andit has a perimeter of 28 feet. Explain how to find thelengths of the other sides if one side measures 10 feet.Possible explanation: I know that his garden has four sideswith two pairs of sides of equal length; 10 10 20;28 20 8; 8 2 4; so, each of the other two sides is4 feet; 10 4 10 4 28.9.Evaluate Jill says that finding the perimeter of a figurewith all sides of equal length is easier than finding theperimeter of other figures. Do you agree? Explain.Yes; possible explanation: because all of the sides haveequal length, I can multiply the length of one side by thenumber of sides the figure has.Module 17 Lesson 2 5533RtI Tier 1 Lesson 8421Enrich 80NameNameLESSON84Enrich 801Find Perimeter3.7.BOBJECTIVE Measure perimeter of polygons using inch and centimeter rulers.Measure each side to the nearest 1 2 inch.Kelsey wants to know the perimeter of the figure below.She can use an inch ruler to find the perimeter.Then find the perimeter of each figure.(Hint: 1 2 1 1 2 5 1).1 in.Step 1 Choose one side of the figure tomeasure. Place the zero mark ofthe ruler on the end of the side.Measure to the nearest inch. Writethe length.Find My Perimeter1.1 in.1 in.2 in.12 in.12 in.2 in.Step 2 Use the ruler to measure theother three sides. Write the lengths.2 in.Step 3 Add the lengths of all the sides.21 1 2 1 5So, the perimeter of the figure is 5 inches.in. 12in. 12.12in. 112in. 55inches8inches12 2 in.Use an inch ruler to find the perimeter.1 in.1.112 2 in.2 1 2inches2 in.71 2 in.2 in.3 in.1 in.611 2 in.2 in.2 in. Houghton Mifflin Harcourt Publishing Company2.in. 11 1 2in. 12 1 2in. 11 1 2in. 5Explain how you added the measurements inExercise 2 to find the perimeter.3.Possible explanation: I first added 2 1 1 12 1 1, which is 6. Then I added 12 1 12 1 12 1 12 ,incheswhich is 2. Then I added 6 1 2 to get8 inches.553 Module 17Geometry and Measurement167Enrich Houghton Mifflin Harcourt Publishing CompanyE80