Teaching the Lesson materials

Key ActivitiesStudents review points, line segments, lines, and rays.

Key Concepts and Skills• Identify and draw line segments, lines, and rays. [Geometry Goal 1]• Describe characteristics of line segments, lines, and rays. [Geometry Goal 1]• Use letter and symbol notation to name line segments, lines, and rays. [Geometry Goal 1]

Key Vocabularypoint • line segment • endpoint • line • ray

Ongoing Assessment: Informing Instruction See page 26.

Ongoing Assessment: Recognizing Student Achievement Use a Math Log or Exit Slip.[Geometry Goal 1]

Ongoing Learning & Practice materials

Students play Addition Top-It to practice addition facts.

Students practice and maintain skills through Math Boxes and Study Link activities.

Differentiation Options materials

Students model line segments with rubber bands on a geoboard.

Students solve a collinear-points puzzle.

Students playSprouts.

Students discuss the meaning of tools in a mathematical context.

� Student Reference Book, p. 313� Teaching Masters (Math Masters,

pp. 9 and 10)� geoboard; rubber bands; index cards

ELL SUPPORTENRICHMENTENRICHMENTREADINESS

3

� Math Journal 1, p. 5� Student Reference Book, p. 263� Study Link Master (Math Masters, p. 8)� Game Master (Math Masters, p. 506)� per partnership: 4 each of number

cards 1–10 (from the EverythingMath Deck, if available)

� 3 six-sided or 2 polyhedral dice perpartnership (optional)

2

� Math Journal 1, p. 4� Student Reference Book, pp. 88–91� Teaching Aid Master (Math Masters,

p. 388 or 389; optional)� slate or marker board; chalk or

dry-erase marker� socks brought by students� yardstick or ruler for demonstration

purposes; Geometry Template; compass; calculator

See Advance Preparation

1

Lesson 1�2 23

Objectives To introduce tools for geometry; and to reviewpoints, line segments, lines, and rays.

Technology Assessment Management SystemMath Log or Exit SlipSee the iTLG.

Additional InformationAdvance Preparation For Part 1, assign and record an ID number for each student.Label students’ math tools with their ID numbers. Have extra socks for students to useas slate erasers.

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24 Unit 1 Naming and Constructing Geometric Figures

� Math Message Follow-Up(Student Reference Book, pp. 88 and 89)

Have students share their answers in small groups. Then askthem to look around the classroom for other geometric shapes and patterns. Point out the line segments found in objects such as windows, doors, and bulletin boards.

� Discussing the Care of Students’ Math ToolsIn Lesson 1-1, students were introduced to the Student ReferenceBook as a resource tool. Tell them that in this lesson they will begiven additional tools. Students will use one of these tools to drawline segments, lines, and rays.

Pass out the rulers, Geometry Templates, compasses, and calculators to students.

Remind students of the following:

� The numbers on the tools identify each student’s tools andother materials borrowed during the school year. Other fourthgraders will use them next year, so they should take good careof them.

� They should put misplaced tools in a lost-and-found box.

� A straightedge and a ruler are different. A straightedge is anytool used for drawing straight lines. A ruler is a measuring toolas well as a straightedge. A straightedge may not be used as aruler unless it is divided into unit intervals.

WHOLE-CLASS ACTIVITY

WHOLE-CLASS ACTIVITY

1 Teaching the Lesson

Getting Started

Math MessageRead Student ReferenceBook, pages 88 and 89 with a partner. List three placeswhere geometry can be foundin our world.

Mental Math and Reflexes Pass out a slate and piece of chalk (or a marker board and dry-erase marker)to each student and explain how they are to be used:

1. You pose a problem. (How much is 12 � 7?)2. Students write the answer on their slates.3. When you give the signal, they show their answers.4. Students then erase their answers with the socks they brought from home.5. At the end of the session, they store their chalk (or markers) in the socks.Suggestions:

NOTE Some students may benefit fromdoing the Readiness activity before you begin Part 1 of the lesson. See theReadiness activity in Part 3 for details.

9 � 0 � 97 � 2 � 511 � 1 � 1012 � 6 � 6

14 � 6 � 816 � 9 � 712 � 7 � 517 � 8 � 9

90 � 40 � 5070 � 30 � 4060 � 20 � 40140 � 70 � 70

Geometry and Constructions

Geometry in Our World

The world is filled with geometry. There are angles, segments,lines, and curves everywhere you look. There are 2-dimensionaland 3-dimensional shapes of every type.

Many wonderful geometric patterns can be seen in nature. You can find patterns in flowers, spider webs, leaves, seashells,even your own face and body.

The ideas of geometry are also found in the things people create.Think of the games you play. Checkers is played with roundpieces. The gameboard is covered with squares. Basketball andtennis are played with spheres. They are played on rectangularcourts that are painted with straight and curved lines. The next time you play or watch a game, notice how geometry isimportant to the way the game is played.

The places we live in are built from plans that use geometry.Buildings almost always have rectangular rooms. Outside wallsand roofs often include sections that have triangular shapes.Archways are curved and are often shaped like semicircles (half circles). Staircases may be straight or spiral. Buildingsand rooms are often decorated with beautiful patterns. You seethese decorations on doors and windows; on walls, floors, andceilings; and on railings of staircases.

Student Reference Book, p. 88

Student Page

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� Reviewing Points, Line Segments, Lines, and Rays1. Draw two dots on the board and label them A and B. Tell

students that the dots represent points. Use a straightedge to connect the dots. Remind the class that this figure is called a line segment and that letters are often used to nameline segments.

Point out the following:

� One name for this line segment is “line segment AB.” WriteA�B� on the board and say that this is a short way to write“line segment AB.”

� Another name for this line segment is “line segment BA.”Write B�A� on the board. Explain that points A and B arecalled the endpoints of the line segment.

Line segment AB, line segment BA, A�B�, or B�A�

� Although there are two ways of naming a line segment by itsendpoints, both names refer to the same segment.

● How would you describe a line segment to someone who has never seen one before? Sample answers: It is straightand thin. It has a beginning and an end. Its length can be measured.

2. Review how a line can be represented by extending line segment AB in both directions and drawing an arrowhead ateach end.

� Explain that this line is called “line AB” or “line BA.”

� Write AB��� and BA��� on the board, and say that these are shortfor “line AB” and “line BA.”

Line AB, line BA, A��B��, or B��A��

● How is a line different from a line segment? Sampleanswers: It is like a line segment except that it has nobeginning and no end. One way to think of a line is to imagine a line segment that goes on without end in bothdirections. A line segment is part of a line.

3. Finally, ask students to imagine a line segment that goes onwithout end in only one direction. This is called a ray.

To support English language learners, ask: Have you ever heardthe word ray? What are some different ways you have heard itused? Sample answers: A ray of sunshine, my neighbor Ray

AB

BA

endpointendpoint

WHOLE-CLASS ACTIVITY

Lesson 1�2 25

Adjusting the Activity

As the class participates in this activity, labelthe drawings on the board as line segment,line, and ray. Display these drawingsthroughout the unit as a visual reference for students.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

ELL

Geometry and Constructions

The clothes people wear are often decorated with geometricshapes. So are the things they use every day. Everywhere inthe world, people create things using geometric patterns.Examples include quilts, pottery, baskets, and tiles. Somepatterns are shown here. Which are your favorites?

Make a practice of noticing geometric shapes around you. Payattention to bridges, buildings, and other structures. Look at the ways in which simple shapes such as triangles, rectangles,and circles are combined. Notice interesting designs. Sharethese with your classmates and your teacher.

In this section, you will study geometric shapes and learn how to construct them. As you learn, try to create your ownbeautiful designs.

Student Reference Book, p. 89

Student Page

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26 Unit 1 Naming and Constructing Geometric Figures

4

Points, Line Segments, Lines, and RaysLESSON

1�2

Date Time

Use a straightedge to draw the following:

1. a. Draw and label line segment RT ( �RT ).

b. What is another name for �RT ?

2. a. Draw and label line BN (BN ). Draw and label point T on it.

b. What are 2 other names for BN ?

3. a. Draw and label ray SL (SL��). Draw and label point R on it.

b. What is another name for SL��?

4. a. Draw a line segment from each point to each of the other points.

b. How many line segments did you draw?

c. Write a name for each line segment you drew.

(Or letters may be in reverse order.)OM, ON, OP, MP, MN, NP

6

M

O P

N

SRS R L

BT, NT, TN, TB, NBB T N

TRR T

90 91

Math Journal 1, p. 4

Student Page

� Draw a picture of ray CD on the board, and write its name CD���.

Ray CD or C�D��

� Tell students that point C is the endpoint of ray CD.

� Remind students that the letter that names the endpoint of aray is always written first. Ask someone to draw a picture ofray BA.

Ray BA or B�A��

● Is it ever possible to draw all of a line? no All of a line segment?yes All of a ray? no

To summarize, draw the line shown below on the board.

● How many line segments can you name using the pointsmarked on this line? Give alternative names. 3 line segments:X�Y�, Y�Z�, and X�Z�; alternative names: Y�X�, Z�Y�, and Z�X�

● How many rays can you name? 4 rays: XY��� (or XZ���), ZX��� (or ZY���),YZ���, and YX���

Be sure students understand the following:

� XY��� and XZ��� name the same ray.

� Point X is the endpoint of the ray.

� The endpoint is always the first letter in the name of a ray. The second letter can be any other point on the ray.

� Points Y and Z are both on the ray. The same is true for ZX���and ZY���.

� Drawing Line Segments,Lines, and Rays(Math Journal 1, p. 4; Student Reference Book, pp. 90 and 91)

Students practice drawing and labeling line segments, lines, and rays. Model how students can refer to pages 90 and 91 of the Student Reference Book to review points, line segments, lines, and rays.

Ongoing Assessment: Informing InstructionWatch for students who draw only four line segments for Problem 4 on journalpage 4. Encourage them to focus on connecting each point to each of the otherpoints rather than making a shape.

INDEPENDENTACTIVITY

ZYX

AB

DC

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Adjusting the Activity

Ongoing Assessment:Recognizing Student Achievement

Use a Math Log or an Exit Slip (Math Masters, page 388 or 389) to assess students’ ability to describe a line segment and a line. Have students explain thedifference between a line segment and a line. Students are making adequateprogress if they are able to explain that a line segment has a beginning and anend, and a line continues in both directions without end. Some students mayinclude drawings and symbols as part of their explanations.

[Geometry Goal 1]

� Playing Addition Top-It(Student Reference Book, p. 263; Math Masters, p. 506)

Students play Addition Top-It to develop automaticity with addition facts. Consider having students record several rounds of play on Math Masters, page 506.

Use these game variations as appropriate:� Extend the range of addends. Use all the cards in the Everything Math Deck,

or use two polyhedral dice with numbers 1 through 20.� Practice addition with three addends using three cards or three dice, including

one or more polyhedral dice.� Practice adding 2-digit numbers. Use only the number cards 1 through 9.

Each player turns over four cards, forms two 2-digit numbers, and finds the sum.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

� Math Boxes 1�2(Math Journal 1, p. 5)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 1-4. The skill in Problem 5previews Unit 2 content.

� Study Link 1�2(Math Masters, p. 8)

Home Connection Students list at least five things thatremind them of line segments. They draw and label lines,line segments, and rays, and write about the differences.

INDEPENDENTACTIVITY

INDEPENDENTACTIVITY

PARTNER ACTIVITY

2 Ongoing Learning & Practice

Math Log or Exit Slip

5

Math Boxes LESSON

1�2

Date Time

1225 � 13

20 � 7

6 � 2

4 � 3

40 � 23

7 � 3

1. Subtract mentally.

a. 6 � 3 �

b. 7 � 4 �

c. 14 � 7 �

d. 16 � 9 �

e. � 9 � 4

f. � 17 � 985

7733

2. Draw and label line QR.Draw point S on it.

What are two other names for line QR?

Sample answers:Q S R

SR, QS, QR,RS, SQ, RQ

91

3. Complete.

Max read books.

Sue read books.

Ira read books.

Pat read books.

4573

4. Cross out thenames that donot belong in thename-collectionbox. Label thebox with thecorrect number.

14976

5. Subtract mentally or with apaper-and-pencil algorithm.

a. 86 � 21 �

b. 93 � 24 � 6965

12–15

0

1

2

3

4

5

6

7Reading Team Totals

Num

ber o

f Boo

ks

Max Sue Ira Pat

Students

Math Journal 1, p. 5

Student Page

STUDY LINK

1�2 Line Segments, Lines, and Rays

90 91

Name Date Time

1. List at least 5 things in your home that remind you of line segments.

Use a straightedge to complete Problems 2 and 3. Sample answers:2. a. Draw and label line AB.

b. Draw and label line segment AB.

c. Explain how your drawings of AB and AB are different.

3. a. Draw and label ray CD.

b. Anita says CD can also be called DC. Do you agree? Explain.

4. Explain how a ruler is different from a straightedge.

Answers vary.

A BA B

D C

5. 13 � 7 � 6. 15 � 8 � 7. � 90 � 50

8. 140 � 60 � 9. � 57 � 39 10. 115 � 86 � 2918804076

The line has arrows on both ends,but the line segment does not.

No. A ray’s endpoint must be listed firstwhen naming a ray.

A ruler has markings on it, so it canbe used to measure.Practice

Math Masters, p. 8

Study Link Master

Lesson 1�2 27

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28 Unit 1 Naming and Constructing Geometric Figures

LESSON

1� 2

Name Date Time

Collinear-Points Puzzle

Three or more points on the same line are called collinear points.

Example: Points A, B, and C are collinear points on the line below. ABC means that A, B, and C are collinear points, and point B is between points A and C.

1. The following are true statements about EH:EFH and FGH The following are false statements about EH:FEH and FHG

a. Name two more true statements about line EH.

b. Name two more false statements about line EH.

2. Place collinear points J, K, L, M, N, and O on the line belowusing these clues:

� J and O are not betweenany points.

� MKL

� NLJ

� MKN

3. Show a different solution to the puzzle in Problem 2.

4. Create a collinear-points puzzle on the back of this page. Be sure to giveenough clues. Record your solution on the line below. Ask someone to solve your puzzle. Can the problem solver find more than one solution to your puzzle?

O N L K M J

HFG, EGF, GFH, GEH, GHEGEF, HEF,

HGE, GFE, EGH, EFGHGF, HFE,

A B C

Sample answers:

O M K N L J

Answers ar

E F G H

Math Masters, p. 10

Teaching Master

LESSON

1� 2

Name Date Time

Geoboard Line Segments

A line segment is made up of 2 points andthe straight path between them. Rubberbands can be used to represent linesegments on a geoboard.

Example:

This line segment touches 5 pins.

Practice making line segments, and then follow the directions below.Record your work.

1. Make a line segment that touches4 pins.

3. Make the shortest line segment possible.

2. Make a line segment that touches4 different pins.

4. Make the longest line segment possible.

5. Cami says she cannot make a line on her geoboard. Do you agree? Explain why or why not. (Hint: Look up line in the glossary of your Student Reference Book.)

directions, so it has no end points.Yes. A line extends forever in both

90

Sample answers:

Math Masters, p. 9

Teaching Master

� Modeling Line Segments(Math Masters, p. 9)

To explore the characteristics of line segments using a concretemodel, have students make line segments on a geoboard. Thelimited size of the geoboard reinforces the notion that a linesegment is part of a line, while a line goes on without end in both directions.

� Solving a Collinear-Points Puzzle(Math Masters, p. 10)

To further explore characteristics of lines, have students solvepuzzles involving collinear points.

� Playing Sprouts(Student Reference Book, p. 313)

To further explore line segments and points, have students playSprouts. Although the rules of Sprouts are quite simple, the gameinvolves subtle strategies and gives students experience withsimple vertex-edge graphs. The dots are the vertices, and the linesare the edges.

� Building Background for Mathematics WordsTo provide language support for mathematical tools, ask studentsto generate a list of mathematical tools they know. Write thename of each tool on the board. When you introduce a compass,explain the distinction between a compass that tells direction anda compass used to draw geometric figures. Have students discusshow they use each tool.

Planning Ahead

Note that Part 1 of Lesson 1-3 requires straws and twist-ties.

5–15 Min

SMALL-GROUP ACTIVITY

ELL SUPPORT

15–30 Min

PARTNER ACTIVITY

ENRICHMENT

15–30 Min

PARTNER ACTIVITY

ENRICHMENT

5–15 Min

PARTNER ACTIVITY

READINESS

3 Differentiation Options

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