Chapter 4
Lesson
1-0
Points, Line Segments,
Lines, and Rays
NCTM Standards 1, 2, 3, 6, 7, 8, 9, 10
Common Core State Standards 4.G 1
Lesson Planner
STUDENT 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)
• 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 13
Playing a Game: Memory (CCRG p. CC 10)
(CCRG p. CC 11)
Leveled Problem Solving (CCRG p. CC 11)
Practice Master, CCRG p. CC 14
Intervention Activity (CCRG p. CC 11)
Extension Master, CCRG p. CC 15
Extension Activity (CCRG p. CC 11)
Lesson Notes
Lesson 4.1-0 has been added. Use this lesson before Lesson 4.1.
About the Lesson
About the Mathematics
This 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.
A 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.
CC 6 Common Core Resource Guide
Chapter 4 • Lesson 1-0
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.
Open-Ended Problem Solving
Read 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.
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.
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 Review
Recognizing 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
Common Core Resource Guide CC 7
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Introducing Points, Line Segments,
Lines, and Rays
20
MIN
Materials
• 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, 10
CCSS 4.G 1
Concept Alert
Up 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 twodimensional figures that they
will study later in this chapter.
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
Connect the Dots
name of this ray, FG , next to this figure. Mention that points are
usually named with capital letters.
Name
Date
Activity Master
Use a ruler to draw each figure.
point
A
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.
• 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?
B
C
line segment
D
E
line
F
G
ray
Name the figures that each letter in the word MATH is made from.
H
D
B
A
C
G
E
F
K
I
L M
N
O
R
P
Q
S
T
J
M M is formed with two rays and two line segments
A A is formed with three line segments
T T is formed with a line and a ray
H H is formed with three lines
© School Specialty
whole class
line segments
B
D
CC 16
Activity Master: Connect the Dots
Common Core Resource Guide
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C
E
A
rays
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.
CC 8 Common Core Resource Guide
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Chapter 4 • Lesson 1-0
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Points, Line Segments, Lines, and Rays
individuals
LAB Masters, CCRG pp. CC 12–CC 13
Purpose To identify, name, and draw points, line segments, lines, and rays
Lesson Activity Book Master, CCRG p. CC 12
Chapter 4
Lesson 1-0
20
MIN
NCTM Standards 1, 2, 3, 6, 7, 8, 9, 10
CCSS 4.G 1
Lesson Activity Book Master, CCRG p. CC 13
Drawings will vary.
Draw the following figures.
Introducing Points, Line
Segments, Lines, and Rays
A. CD
C. GH
B. EF
NCTM Standards 1, 2, 3, 4, 6, 7, 8, 9, 10
Common Core State Standards 4.G 1
IdentifyeachfigurethatcontainspointsXandY
asalinesegment,line,oraray.
G
D
E
F
H
C
A.
Y
B.
C. Y
X
D.
Y
Use letters and symbols to name each figure shown.
X
X
ray
A.
X
Y
line
linesegment
B.
Q
F.
C. T
S
U
P
ray
PQ
E. X
R
RS
TU
G.
Y
X
Y
Challenge XY and XZ can meet at point X to make a straight line.
ray
© School Speciality
linesegment
Y
linesegment
© School Speciality
X
Y
Z
X
What other figure could XY and XZ make? Draw that figure.
Possible Answer: They could make an angle.
Y
X
Drawings will vary.
Common Core Resource Guide
CC 12 Common Core Resource Guide
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CC 13
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Teaching Notes for LAB Master,
CCRG page CC 12
Teaching Notes for LAB Master,
CCRG page CC 13
Students identify objects as line segments, lines, or rays. All
figures have two named points X and Y.
Students 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.
Differentiated Instruction
Above Level For students who finish early, have them
draw some real world objects and label line segments, lines,
and rays in their drawings.
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Challenge Problem
This problem previews angles, which students will explore in
the next lesson.
Common Core Resource Guide CC 9
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15
MIN
Materials
• For each pair of
students: Cards cut from
AM: Memory Game
Cards
NCTM Standards 1, 2, 3, 6, 7, 8, 9, 10
CCSS 4.G 1
Concept Alert
Check 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
Instruction
Basic 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.
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.
Name
Date
Activity Master X
Memory Game Cards
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.
© School Specialty
pairs
Activity Master: Memory Game Cards
CC 18
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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.
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.
CC 10 Common Core Resource Guide
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Chapter 4 • Lesson 1-0
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Leveled Problem Solving
Monica connected points P and Q with a straightedge.
Basic Level
She 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 Level
She 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.
Practice
Date
Practice Master,
CCRG p. CC14
Lesson 1-0
Name
Points, Line Segments, Lines, and Rays
Identify each figure that contains points X and Y
as a line segment, a line, or a ray.
X
X
Y
ray
line segment
Z
X
1. AB and CD
N
D
A
X
C
E
D
A
B
D
Yes. The ray will extend straight
past their endpoints.
through segment AB.
3. AB and CD
4. AB and CD
line segment MN
M
N
© School Specialty
Test Prep
Angle DEF is made up of which two rays?
A. ray ED and ray EF
B. ray ED and ray EF
C. ray DE and ray FR
D. ray DE and ray FE
B
No. Line segments do not extend
D
E
© School Specialty
C
D
C
Use a ruler or straightedge to draw each figure.
ray AB
B
D
ray
line
line CD
A
A
B
C
2. AB and CD
B
Y
W
line segment
Decide whether or not each pair of figures will intersect.
Write yes or no and explain your reasoning.
line
Y
A
Y
Y
B
X
When line segments, lines, or rays share one point
they intersect.
X
Y
Extension
Date
Extension Master,
CCRG p. CC15
Lesson 1-0
Name
Points, Line Segments, Lines, and Rays
Above Level
Monica added a point, R, above P.
She connected these points with
segments. What kind of figure did
she draw? A triangle.
A
B
C
D
A
D
B
C
No. Line segments do not extend
No. These lines will not share any
points no matter how far you extend past their endpoints.
F
them.
CC 14
Common Core Resource Guide
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Intervention Activity
Extension Activity
Drawing Geometric Figures
What’s My Angle?
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.
Draw three different angles with A as the vertex.
B
A
B
C
B
C
A
C
A
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.
Chapter 4 • Lesson 1-0
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Common Core Resource Guide CC 11
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Chapter 4
Lesson 1-0
Introducing Points, Line
Segments, Lines, and Rays
NCTM Standards 1, 2, 3, 4, 6, 7, 8, 9, 10
Common Core State Standards 4.G 1
Identify each figure that contains points X and Y
as a line segment, line, or a ray.
A.
Y
B.
C. Y
X
D.
Y
X
X
X
Y
E. X
F.
G.
Y
X
Y
X
Y
© School Speciality
CC 12 Common Core Resource Guide
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Draw the following figures.
A. CD
C. GH
B. EF
Use letters and symbols to name each figure shown.
A.
B.
Q
R
S
C. T
U
P
© School Speciality
Challenge XY and XZ can meet at point X to make a straight line.
Y
X
Z
What other figure could XY and XZ make? Draw that figure.
Common Core Resource Guide
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Name
Practice
Lesson 1-0
Date
Points, Line Segments, Lines, and Rays
Identify each figure that contains points X and Y
as a line segment, a line, or a ray.
X
X
Y
Z
X
X
Y
X
Y
B
D
Y
N
Y
Y
W
A
X
B
E
Use a ruler or straightedge to draw each figure.
line CD
ray AB
line segment MN
Angle DEF is made up of which two rays?
A. ray ED and ray EF
B. ray ED and ray EF
C. ray DE and ray FR
D. ray DE and ray FE
CC 14
© School Specialty
Test Prep
D
E
F
Common Core Resource Guide
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Name
Extension
Lesson 1-0
Date
Points, Line Segments, Lines, and Rays
When line segments, lines, or rays share one point
they intersect.
A
Decide whether or not each pair of figures will intersect.
Write yes or no and explain your reasoning.
AB and CD
C
B
D
AB and CD
B
A
B
A
D
C
D
C
© School Specialty
AB and CD
AB and CD
A
B
C
D
A
D
B
C
Common Core Resource Guide
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Name
Activity Master
Date
Connect the Dots
Use a ruler to draw each figure.
point
A
B
C
line segment
D
E
line
F
G
ray
Name the figures that each letter in the word MATH is made from.
A
H
D
B
C
G
E
F
K
I
L M
N
O
R
P
Q
S
T
J
M
A
T
CC 16
© School Specialty
H
Common Core Resource Guide
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Name
Date
Activity Master
© School Specialty
Memory Game Cards
CC 17
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