Chapter 4 Lesson1-0 Points, Line Segments, Lines, And Rays

Chapter 4Lesson1-0Points, Line Segments,Lines, and RaysNCTM Standards 1, 2, 3, 6, 7, 8, 9, 10Common Core State Standards 4.G 1Lesson PlannerSTUDENT OBJECTIVES n To recognize, draw, and name points, rays, line segments, and lines n To identify points, rays, line segments, and lines in two dimensionalfigures(CCRG p. CC 7)Open Ended Problem Solving / Headline StorySkills Practice and Review—Recognizing Multiples(CCRG pp. CC 8–CC 10)Introducing Points, Line Segments, Lines,and Rays (CCRG p. CC 8) CCRG: Activity Masters, Connect the Dots,Memory Game Cards Points,Line Segments, Lines, and Rays(CCRG p. CC 9) ruler or straightedge LAB Masters, CCRG pp. CC 12–CC 13Playing a Game: Memory (CCRG p. CC 10)(CCRG p. CC 11)Leveled Problem Solving (CCRG p. CC 11)Practice Master, CCRG p. CC 14Intervention Activity (CCRG p. CC 11)Extension Master, CCRG p. CC 15Extension Activity (CCRG p. CC 11)Lesson NotesLesson 4.1-0 has been added. Use this lesson before Lesson 4.1.About the LessonAbout the MathematicsThis lesson introduces students to points, linesegments, lines, and rays. These are the figures thatthey will encounter in the remaining lessons aboutangles, triangles, quadrilaterals, and parallel andperpendicular lines. Students are familiar with linesfrom their work with number lines. A line is a straightpath of points that has no beginning or end. A linesegment is a portion of a line that has two endpoints.A ray has one endpoint and extends forever in onedirection.A point is an undefined term in mathematics. It hasno size or shape, just position. Each of the figuresthat students will study in this lesson are made up ofpoints. You may want to bring up the fact that, forexample, even though a line segment generally onlyhas its two endpoints labeled, it is made up of aninfinite number of points between those endpoints.Students will name these figures according to thepoints they contain. It is not important right now forstudents to master this fact, but you may want topoint out that AB is different from BA since the firstletter in the name of a ray designates the endpoint. Inthe next lesson, students are introduced to angles. Inthis lesson, students are shown pictures of an angleand you may want to point out that an angle is madeup of two rays that share an endpoint.CC 6 Common Core Resource GuideChapter 4 Lesson 1-0

DevelopingMathematicalLanguageVocabulary: point, endpoint,line, line segment, rayA point is undefined. It is just adot on the page with no size orshape, just position. A line is astraight path of points that has nobeginning or end. A line segmentis a portion of a line that has twoendpoints. A ray is a portion of aline which has one endpoint andextends forever in one direction.Open-Ended Problem SolvingRead the Headline Story to the class. Encourage students to solve theproblem by drawing a picture and using information from the story.A.J. and Paulo each thoughtof a number. A.J.’s numberis less than 10. Paulo’snumber is greater than 10but less than 50. When theirnumbers are multiplied theproduct is a multiple of 5.Beginning Draw a line segment,line, and ray on the board. Point toeach and have students name them.Intermediate Draw a linesegment, line, and ray. Pointto each part of the figures andhave students tell you what itrepresents. For example: theendpoints of the line segment, theendpoint of the ray, the arrows onthe line.Advanced Name each figure andhave students draw them on theboard or on paper.Possible responses:The ones digit of the product must be 0 or 5. If AJ’s number is 5 thenPaulo’s number could be any number between 10 and 50. If A.J.’snumber is not 5 then Paulo’s number must be a multiple of 5. Thelargest product could be 9 3 45 or 405.Skills Practice and ReviewRecognizing MultiplesRemind students that a multiple of 5 must end in either 0 or 5(5, 10, 15, and so on.) Ask students what the possible ones digitcould be for a multiple of 2. 0, 2, 4, 6, 8 Then ask what the possibleones digit could be for a multiple of 3. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Whatabout a multiple of 4? 0, 2, 4, 6, 8Common Core Resource Guide CC 7TMG4CCRG CH04 L1-0 TG p06-p11.indd 712/28/10 11:04:43 AM

Introducing Points, Line Segments,Lines, and Rays20MINMaterials For the students: AM:Connect the Dots,ruler or straightedge For the teacher:transparency of AM:Connect the Dots(optional)NCTM Standards 1, 2, 3, 6, 7, 8, 9, 10CCSS 4.G 1Concept AlertUp to this point studentshave probably referred toall straight paths as lines.Encourage them to usecorrect terminology whenreferring to line segments andrays. Rays will form the sidesof angles and line segmentswill form the sides of twodimensional figures that theywill study later in this chapter.Purpose To introduce students to the terms point, line, line segment, and ray andhave them draw, identify, and name each of these figuresIntroduce Give students Activity Master: Connect the Dots. Display Activity Master:Connect the Dots or draw the points on the board. Tell students that the dot on the firstline is called a point. Its name is A. Two points can be connected to form different figures.Use a ruler or straightedge to connect the second set of points and ask students to dothe same. Tell them that this is a line segment. It has two endpoints. Write the name ofthis line segment, BC , next to the figure. Draw a line through the third set of points andput arrows at each end. Ask students to do the same. Tell them that this is a line. A linepasses through the two points and extend in both directions forever. Write the nameof this line, DE , next to the figure. Draw a ray through the last set of points and put anarrow at one end. Ask students to do the same. Tell them that this is a ray. A ray hasone endpoint and extends forever in one direction. Write theConnect the Dotsname of this ray, FG , next to this figure. Mention that points areusually named with capital letters.NameDateActivity MasterUse a ruler to draw each figure.pointATask Ask students to find points, line segments, lines,and rays in the letters on the bottom of Activity Master:Connect the Dots. All of the letters in MATH are formed byconnecting points with either lines, line segments, rays, or acombination of these figures. Help students to label the M withthe names of the figures. You might also list the names of eachfigure that makes up the M: BC , DC , BA, and DE. Do students demonstratean ability to identify eachof the figures? Do students demonstrate anunderstanding of the labelsattached to each figure? Do students demonstratean understanding that bothsegments and rays areportions of a line?BCline segmentDElineFGrayName the figures that each letter in the word MATH is made from.HDBACGEFKIL MNORPQSTJM M is formed with two rays and two line segmentsA A is formed with three line segmentsT T is formed with a line and a rayH H is formed with three lines School Specialtywhole classline segmentsBDCC 16Activity Master: Connect the DotsCommon Core Resource GuideTMG4CCRG CH04 L1-0 AM2 p16.indd 1812/23/10 5:47 PMCEAraysShare Once students have had time to label the remaining letters askthem to share their findings with the class. Students can draw the figureson the board or label them on your transparency of Activity Master:Connect the Dots.Talk MathWhat makes a line segment different from a line? A lineextends on forever in both directions. A line segment ispart of a line and has two endpoints.Do you think a line named AB is the same figure as a linenamed BA? Possible answer: If A and B are the same pointsthen the line that goes through them is the same line andyou can name it both ways.CC 8 Common Core Resource GuideTMG4CCRG CH04 L1-0 TG p06-p11.indd 8Chapter 4 Lesson 1-012/28/10 11:04:45 AM

Points, Line Segments, Lines, and RaysindividualsLAB Masters, CCRG pp. CC 12–CC 13Purpose To identify, name, and draw points, line segments, lines, and raysLesson Activity Book Master, CCRG p. CC 12Chapter 4Lesson 1-020MINNCTM Standards 1, 2, 3, 6, 7, 8, 9, 10CCSS 4.G 1Lesson Activity Book Master, CCRG p. CC 13Drawings will vary.Draw the following figures.Introducing Points, LineSegments, Lines, and RaysA. CDC. GHB. EFNCTM Standards 1, 2, 3, 4, 6, 7, 8, 9, 10Common Core State Standards 4.G 1I dentify each figure that contains points X and Yas a line segment, line, or a ray.GDEFHCA.YB.C. YXD.YUse letters and symbols to name each figure shown.XXrayA.XYlineline segmentB.QF.C. TSUPrayPQE. XRRSTUG.YXYChallenge XY and XZ can meet at point X to make a straight line.ray School Specialityline segmentYline segment School SpecialityXYZXWhat other figure could XY and XZ make? Draw that figure.Possible Answer: They could make an angle.YXDrawings will vary.Common Core Resource GuideCC 12 Common Core Resource GuideTMG4CCRG CH04 L1-0 LAB p12-p13.indd 2ZTMG4CCRG CH04 L1-0 LAB p12-p13.indd 312/23/10 6:17:17 PMCC 1312/23/10 6:17:18 PMTeaching Notes for LAB Master,CCRG page CC 12Teaching Notes for LAB Master,CCRG page CC 13Students identify objects as line segments, lines, or rays. Allfigures have two named points X and Y.Students interpret the symbols given for figures and drawthe corresponding figures. Students use the symbols for linesegments, lines, and rays to name each figure. When drawingEF make sure students draw E as the endpoint of the ray.Differentiated InstructionAbove Level For students who finish early, have themdraw some real world objects and label line segments, lines,and rays in their drawings.Chapter 4 Lesson 1-0TMG4CCRG CH04 L1-0 TG p06-p11.indd 9Challenge ProblemThis problem previews angles, which students will explore inthe next lesson.Common Core Resource Guide CC 912/28/10 11:04:47 AM

15MINMaterials For each pair ofstudents: Cards cut fromAM: Memory GameCardsNCTM Standards 1, 2, 3, 6, 7, 8, 9, 10CCSS 4.G 1Concept AlertCheck to be sure thatstudents recognize thatsegments can make up sometwo-dimensional figures.For example, one card has asquare on it that is made upof four segments. Anothercard pictures a circle with itsdiameter, which is a segment.DifferentiatedInstructionBasic Level If studentsare having a difficult timerecognizing the figures on thecards have them lay out all ofthe cards face up and practicenaming the figures with theirpartners. Once they haveagreed which figures are on allof the cards they can flip themover and try the Memory game.Playing a Game: MemoryPurpose To practice identifying line segments, lines, and raysGoal To find the most pairs of cards that match.Prepare materials. For each pair: Cut the cards out along the dotted lineson Activity Master: Memory Game Cards.How to PlayEach pair of students should mix up the cards andplace them in an array face down in front of them.NameDateActivity Master XMemory Game CardsStudents take turns flipping over pairs of cards fromthe array to see if they can make a match. Whenstudents flip over each card they should state whichfigures are pictured. A match consists of any twocards that contain a matching figure. For example,a card might have a segment and another card mighthave a square—made up of four segments. This is amatch.If the student finds a match they take that pair andtake another turn. If not, the cards are flipped overagain and the next student takes a turn. School SpecialtypairsActivity Master: Memory Game CardsCC 18Common Core Resource GuideTMG4CCRG CH04 L1-0 AM2 p17.indd 1812/23/10 6:31:40 PMSince there are multiple ways of making matches with each card theremay be two cards left in the array at the end of the game that do notmatch. The player with the most matching pairs once all of the possiblematches have been made is the winner.Reflect and Summarize the LessonTrue or false: A segment is contained in every line.True. A line is made up of an infinite number of points so you can identify two points as endpointsof a segment.CC 10 Common Core Resource GuideTMG4CCRG CH04 L1-0 TG p06-p11.indd 10Chapter 4 Lesson 1-012/28/10 11:04:49 AM