Chapter 4 Lesson1-0 Points, Line Segments, Lines, … Core Resource Guide Points, Line Segments,...

Lesson1-01-0

Chapter 4 • Lesson 1-0CC 6 Common Core Resource Guide

Lesson 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 dimensional

figures

(CCRG p. CC 7)

Open Ended Problem Solving / Headline Story Skills Practice and Review— Recognizing Multiples

(CCRG pp. CC 8–CC 10)

Introducing Points, Line Segments, Lines, and Rays (CCRG p. CC 8)

Points, Line Segments, Lines, and Rays (CCRG p. CC 9)

Playing a Game: Memory (CCRG p. CC 10)

• CCRG: Activity Masters, Connect the Dots, Memory Game Cards

• ruler or straightedge

• LAB Masters, CCRG pp. CC 12–CC 13

(CCRG p. CC 11)

Leveled Problem Solving (CCRG p. CC 11)

Intervention Activity (CCRG p. CC 11)

Extension Activity (CCRG p. CC 11)

Practice Master, CCRG p. CC 14

Extension Master, CCRG p. CC 15

Lesson Notes

About the LessonThis lesson introduces students to points, line segments, lines, and rays. These are the figures that they will encounter in the remaining lessons about angles, triangles, quadrilaterals, and parallel and perpendicular lines. Students are familiar with lines from their work with number lines. A line is a straight path of points that has no beginning or end. A line segment is a portion of a line that has two endpoints. A ray has one endpoint and extends forever in one direction.

About the MathematicsA point is an undefined term in mathematics. It has no size or shape, just position. Each of the figures that students will study in this lesson are made up of points. You may want to bring up the fact that, for example, even though a line segment generally only has its two endpoints labeled, it is made up of an infinite number of points between those endpoints. Students will name these figures according to the points they contain. It is not important right now for students to master this fact, but you may want to point out that AB is different from BA since the first letter in the name of a ray designates the endpoint. In the next lesson, students are introduced to angles. In this lesson, students are shown pictures of an angle and you may want to point out that an angle is made up of two rays that share an endpoint.

Points, Line Segments, Lines, and Rays

Lesson 4.1-0 has been added. Use this lesson before Lesson 4.1.

Chapter 4

NCTM Standards 1, 2, 3, 6, 7, 8, 9, 10Common Core State Standards 4.G 1

Common Core Resource Guide CC 7

Developing Mathematical Language Vocabulary: point, endpoint, line, line segment, ray

A point is undefined. It is just a dot on the page with no size or shape, just position. A line is a straight path of points that has no beginning or end. A line segment is a portion of a line that has two endpoints. A ray is a portion of a line which has one endpoint and extends forever in one direction.

Beginning Draw a line segment, line, and ray on the board. Point to each and have students name them.

Intermediate Draw a line segment, line, and ray. Point to each part of the figures and have students tell you what it represents. For example: the endpoints of the line segment, the endpoint of the ray, the arrows on the line.

Advanced Name each figure and have students draw them on the board or on paper.

Open-Ended Problem SolvingRead the Headline Story to the class. Encourage students to solve the problem by drawing a picture and using information from the story.

A.J. and Paulo each thought

of a number. A.J.’s number

is less than 10. Paulo’s

number is greater than 10

but less than 50. When their

numbers are multiplied the

product is a multiple of 5.

Possible responses:

The ones digit of the product must be 0 or 5. If AJ’s number is 5 then Paulo’s number could be any number between 10 and 50. If A.J.’s number is not 5 then Paulo’s number must be a multiple of 5. The largest product could be 9 3 45 or 405.

Skills Practice and ReviewRecognizing Multiples

Remind 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 digit could be for a multiple of 2. 0, 2, 4, 6, 8 Then ask what the possible ones digit could be for a multiple of 3. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 What about a multiple of 4? 0, 2, 4, 6, 8

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Concept AlertUp to this point students have probably referred to all straight paths as lines. Encourage them to use correct terminology when referring to line segments and rays. Rays will form the sides of angles and line segments will form the sides of two-dimensional figures that they will study later in this chapter.

20MIN

whole class

Materials• For the students: AM:

Connect the Dots, ruler or straightedge

• For the teacher: transparency of AM: Connect the Dots (optional)

Introducing Points, Line Segments, Lines, and Rays

Purpose To introduce students to the terms point, line, line segment, and ray and have them draw, identify, and name each of these figures

Introduce 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 first line 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 do the same. Tell them that this is a line segment. It has two endpoints. Write the name of this line segment, BC , next to the figure. Draw a line through the third set of points and put arrows at each end. Ask students to do the same. Tell them that this is a line. A line passes through the two points and extend in both directions forever. Write the name of this line, DE , next to the figure. Draw a ray through the last set of points and put an arrow at one end. Ask students to do the same. Tell them that this is a ray. A ray has one endpoint and extends forever in one direction. Write the name of this ray, FG , next to this figure. Mention that points are usually named with capital letters.

Task 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 by connecting points with either lines, line segments, rays, or a combination of these figures. Help students to label the M with the names of the figures. You might also list the names of each figure that makes up the M: BC , DC , BA, and DE .

CA

B D

E

rays

line segments• Do students demonstrate

an ability to identify each of the figures?

• Do students demonstrate an understanding of the labels attached to each figure?

• Do students demonstrate an understanding that both segments and rays are portions of a line? Share Once students have had time to label the remaining letters ask

them to share their findings with the class. Students can draw the figures on the board or label them on your transparency of Activity Master: Connect the Dots.

Talk Math What makes a line segment different from a line? A line

extends on forever in both directions. A line segment is part of a line and has two endpoints.

Do you think a line named AB is the same figure as a line named BA? Possible answer: If A and B are the same points then the line that goes through them is the same line and you can name it both ways.

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CC 16 Common Core Resource Guide

Connect the DotsUse a ruler to draw each figure.

Name the figures that each letter in the word MATH is made from.

M

A

T

H

pointA

B C

D E

F G

line segment

line

ray

B

CA

D

E

F J

IG

H K L M

N P

O R

Q TS

Activity Master

M is formed with two rays and two line segments

A is formed with three line segments

T is formed with a line and a ray

H is formed with three lines

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Activity Master: Connect the Dots

NCTM Standards 1, 2, 3, 6, 7, 8, 9, 10CCSS 4.G 1


Chapter 4 • Lesson 1-0 Common Core Resource Guide CC 9

20MIN

individuals

Points, Line Segments, Lines, and Rays LAB Masters, CCRG pp. CC 12–CC 13

Purpose To identify, name, and draw points, line segments, lines, and rays

Teaching Notes for LAB Master, CCRG page CC 12Students identify objects as line segments, lines, or rays. All figures have two named points X and Y.

Differentiated InstructionAbove Level For students who finish early, have them draw some real world objects and label line segments, lines, and rays in their drawings.

Teaching Notes for LAB Master, CCRG page CC 13Students interpret the symbols given for figures and draw the corresponding figures. Students use the symbols for line segments, lines, and rays to name each figure. When drawing

EF make sure students draw E as the endpoint of the ray.

Challenge ProblemThis problem previews angles, which students will explore in the next lesson.


X

YX

Y X

YXY

X

YX

Y

X Y


�Identify each figure that contains points X and Y as a line segment, line, or a ray.

A. B. C. D.

E. F. G.

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Lesson1-01-0Chapter 4

NCTM Standards 1, 2, 3, 4, 6, 7, 8, 9, 10Common Core State Standards 4.G 1

ray line line segment ray

line segment ray line segment

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Q

P

SR

U

T

XY Z

Draw the following figures.

Use letters and symbols to name each figure shown.

A. CD B. EF C. GH

A. B. C.

Challenge XY and XZ can meet at point X to make a straight line.

What other figure could XY and XZ make? Draw that figure.

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Possible Answer: They could make an angle.

Drawings will vary.

Drawings will vary.

PQ TURS

D

C

FEH

G

XZ

Y


Lesson Activity Book Master, CCRG p. CC 12 Lesson Activity Book Master, CCRG p. CC 13



Reflect and Summarize the Lesson

True 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 endpoints of a segment.


15MIN

pairs

Materials• For each pair of

students: Cards cut from AM: Memory Game Cards


Playing a Game: Memory

Purpose To practice identifying line segments, lines, and rays

Goal To find the most pairs of cards that match.

Prepare materials. For each pair: Cut the cards out along the dotted lines on Activity Master: Memory Game Cards.

How to Play Each pair of students should mix up the cards and

place them in an array face down in front of them.

Students take turns flipping over pairs of cards from the array to see if they can make a match. When students flip over each card they should state which figures are pictured. A match consists of any two cards that contain a matching figure. For example, a card might have a segment and another card might have a square—made up of four segments. This is a match.

If the student finds a match they take that pair and take another turn. If not, the cards are flipped over again and the next student takes a turn.

Since there are multiple ways of making matches with each card there may be two cards left in the array at the end of the game that do not match. The player with the most matching pairs once all of the possible matches have been made is the winner.

Concept AlertCheck to be sure that students recognize that segments can make up some two-dimensional figures. For example, one card has a square on it that is made up of four segments. Another card pictures a circle with its diameter, which is a segment.

Differentiated InstructionBasic Level If students are having a difficult time recognizing the figures on the cards have them lay out all of the cards face up and practice naming the figures with their partners. Once they have agreed which figures are on all of the cards they can flip them over and try the Memory game.


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Name Date Activity Master X

Memory Game Cards

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Activity Master: Memory Game Cards


Chapter 4 • Lesson 1-0 Common Core Resource Guide CC 11

Leveled Problem Solving

Monica connected points P and Q with a straightedge.

Basic LevelShe began at P and drew a line that ended at Q. What kind of figure did Monica draw? Explain. A segment. Monica made P and Q the endpoints of the segment.

On LevelShe began at Q and drew a line that passed through P and did not stop at P. What kind of figure did Monica draw? Explain. A ray. The endpoint of the ray is Q. It passes through P and keeps going on forever.

Above LevelMonica added a point, R, above P. She connected these points with segments. What kind of figure did she draw? A triangle.

Intervention Activity Extension Activity

Drawing Geometric Figures

Write the name of several line segments, lines, and rays on the board. Have students draw each figure. You might use symbol notation, for example, AB , GH , DC , XY , ST , or you might write out the word, for example, ray AB.

What’s My Angle?

Draw three different angles with A as the vertex.

A CB

A C

B

A

C

B

Ask students to use their own words to describe each figure.

Possible answers: The straight angle can be described as a line. The right angle can be compared to the corner of a piece of paper. The acute angle looks like a piece of pie.

Practice Master, CCRG p. CC14 Extension Master, CCRG p. CC15


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PracticeLesson 1-0

Identify each figure that contains points X and Y as a line segment, a line, or a ray.

Use a ruler or straightedge to draw each figure.

lineCD rayAB linesegmentMN

X Y X Y

X Y

Z X Y

B D

X

Y

BA

N

EW

E F

D

X Y

Test Prep AngleDEFismadeupofwhichtworays? A. rayEDandrayEF B. rayEDandrayEF C. rayDEandrayFR D. rayDEandrayFE

ray

line segment

line segment line

ray

C D A B M N

line

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ExtensionLesson 1-0

Points, Line Segments, Lines, and RaysWhen line segments, lines, or rays share one point they intersect.

1. AB and CD

A

B

DC

3. AB and CD

A B

C D

2. AB and CD

D

C

BA

4. AB and CD

A

B

D

C

Decide whether or not each pair of figures will intersect. Write yes or no and explain your reasoning.

A

BD

C

No. Line segments do not extend Yes. The ray will extend straight

No. Line segments do not extend No. These lines will not share any

past their endpoints. through segment AB.

past their endpoints.points no matter how far you extend

them.

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X

YX

Y X

YXY

X

YX

Y

X Y


�Identify�each�figure�that�contains�points�X�and�Y as�a�line�segment,�line,�or�a�ray.

A. B. C. D.

E. F. G.

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Lesson1-01-0Chapter 4

NCTM Standards 1, 2, 3, 4, 6, 7, 8, 9, 10Common Core State Standards 4.G 1



Q

P

SR

U

T

XY Z

Draw�the�following�figures.

Use�letters�and�symbols�to�name�each�figure�shown.

A.�CD B.�EF C.�GH

A. B. C.

Challenge XY �and�XZ �can�meet�at�point�X�to�make�a�straight�line.

What�other�figure�could�XY �and�XZ �make?�Draw�that�figure.

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PracticeLesson 1-0

Identify each figure that contains points X and Y as a line segment, a line, or a ray.

Use a ruler or straightedge to draw each figure.

lineCD rayAB linesegmentMN

X Y X Y

X Y

Z X Y

B D

X

Y

BA

N

EW

E F

D

X Y

Test Prep AngleDEFismadeupofwhichtworays? A. rayEDandrayEF B. rayEDandrayEF C. rayDEandrayFR D. rayDEandrayFE

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ExtensionLesson 1-0

Points, Line Segments, Lines, and RaysWhen line segments, lines, or rays share one point they intersect.

AB and CD

A

B

DC

AB and CD

A B

C D

AB and CD

D

C

BA

AB and CD

A

B

D

C

Decide whether or not each pair of figures will intersect. Write yes or no and explain your reasoning.

A

BD

C

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Connect the DotsUse a ruler to draw each figure.

Name the figures that each letter in the word MATH is made from.

M

A

T

H

pointA

B C

D E

F G

line segment

line

ray

B

CA

D

E

F J

IG

H K L M

N P

O R

Q TS

Activity Master

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Name Date Activity Master

Memory Game Cards

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Chapter 4 Lesson1-0 Points, Line Segments, Lines, … Core Resource Guide Points, Line Segments,...

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