Unit 9
Geometry: Points, Lines and Angels
Fourth Grade
Grade Level: 4th
Subject Area: Mathematics
Lesson Title: Geometry: Points, Lines, and
Unit Number: 9
Lesson Length: 11 days
Angles
Lesson Overview
This unit bundles student expectations that address identifying basic elements of geometry,
lines of symmetry, and the classification of two-dimensional figures based on properties and
attributes. According to the Texas Education Agency, mathematical process standards
including application, tools, communication, representations, relationships, and justifications
should be integrated (when applicable) with content knowledge and skills so that students are
prepared to use mathematics in everyday life, society, and the workplace.
During this unit, students examine the foundations of geometry by identifying points, lines, line
segments, rays, angles, and perpendicular and parallel lines. These concepts are essential for
the ability to classify two-dimensional figures based on the presence or absence of parallel or
perpendicular lines or the presence or absence of angles of a specified size. Although
students have recognized examples of quadrilaterals in previous grade levels, students are
expected to use formal geometric language such as parallel, perpendicular, acute, obtuse,
and right angle to classify two-dimensional figures. Additionally, students apply knowledge of
right angles to identify acute, right, and obtuse triangles. Symmetry is explored within twodimensional figures as students identify and draw one or more lines of symmetry, if they exist,
for two-dimensional figures.
After this unit, in Unit 10, students will closely examine angles as they measure angles in
degrees using a protractor and draw angles of a given measure. They will also determine the
measure of an unknown angle formed by two non-overlapping adjacent angles given one or
both angle measures. In Grade 5, students will classify two-dimensional figures based on their
attributes and properties in a hierarchy of sets and subsets using graphic organizers.
Unit Objectives:
Students will
 identify points, lines, line segments, rays, angles, and perpendicular and parallel lines.
 apply knowledge of right angles to identify acute, right, and obtuse triangles.
 identify and draw one or more lines of symmetry, if they exist, for two-dimensional
figures.
 classify two-dimensional figures based on the presence or absence of parallel or
perpendicular lines or the presence or absence of angles of a specified size
Standards addressed:
TEKS:
4.1 Mathematical process standards. The student uses mathematical processes to acquire
and demonstrate mathematical understanding. The student is expected to:
4.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
4.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems.
4.1D Communicate mathematical ideas, reasoning, and their implications using multiple
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Unit 9
Geometry: Points, Lines and Angels
Fourth Grade
representations, including symbols, diagrams, graphs, and language as appropriate.
4.1E Create and use representations to organize, record, and communicate mathematical
ideas.
4.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
4.1G Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
4.6 Geometry and measurement. The student applies mathematical process standards to
analyze geometric attributes in order to develop generalizations about their properties. The
student is expected to:
4.6A Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines.
4.6B Identify and draw one or more lines of symmetry, if they exist, for a two-dimensional
figure.
4.6 C Apply knowledge of right angles to identify acute, right, and obtuse triangles.
4.6 D Classify two-dimensional figures based on the presence or absence of parallel or
perpendicular lines or the presence or absence of angles of a specified size.
ELPS
1A use prior knowledge and experiences to understand meanings in English
1C use strategic learning techniques such as concept mapping, drawing, memorizing,
comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary
2A distinguish sounds and intonation patterns of English with increasing ease
2C learn new language structures, expressions, and basic and academic vocabulary heard
during classroom instruction and interactions
2D monitor understanding of spoken language during classroom instruction and interactions
and seek clarification as needed
3A practice producing sounds of newly acquired vocabulary such as long and short vowels,
silent letters, and consonant clusters to pronounce English words in a manner that is
increasingly comprehensible
3B expand and internalize initial English vocabulary by learning and using high-frequency
English words necessary for identifying and describing people, places, and objects, by retelling
simple stories and basic information represented or supported by pictures, and by learning and
using routine language needed for classroom communication
3D speak using grade-level content area vocabulary in context to internalize new English
words and build academic language proficiency
4C develop basic sight vocabulary, derive meaning of environmental print, and comprehend
English vocabulary and language structures used routinely in written classroom materials
4D use prereading supports such as graphic organizers, illustrations, and pretaught topicrelated vocabulary and other prereading activities to enhance comprehension of written text
4H read silently with increasing ease and comprehension for longer periods
5B write using newly acquired basic vocabulary and content-based grade-level vocabulary
5F write using a variety of grade-appropriate sentence lengths, patterns, and connecting
words to combine phrases, clauses, and sentences in increasingly accurate ways as more
English is acquired
5G narrate, describe, and explain with increasing specificity and detail to fulfill content area
writing needs as more English is acquired.
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Unit 9
Misconceptions:



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
Geometry: Points, Lines and Angels
Fourth Grade
Students may confuse the notation for lines, line segments, and rays.
Students might use the terms parallel and perpendicular interchangeably, rather than
making a connection between the terms and the attributes they represent.
Students may misunderstand that notations for points, lines, and rays are only
representations of abstract ideas and are not actual objects.
Students may refer to a square or rhombus as a diamond.
Some students may not associate the line of symmetry as the line of reflection.
Underdeveloped Concepts:
 Students may understand that many shapes fall under the classification of
quadrilaterals, but may not know how the name of each quadrilateral depends on its
attributes.
 Some students may think that two-dimensional figures are only polygons.
Vocabulary:
Acute – an angle that measures less than 90°
Acute triangle – a triangle in which each of the three angles is acute (less than 90 degrees)
Angle – two rays with a common endpoint (the vertex)
Angle congruency marks – angle marks indicating angles of the same measure
Classify – applying an attribute to categorize a sorted group
Congruent – of equal measure, having exactly the same size and same shape
Degree – the measure of an angle where each degree represents
of a circle
Intersecting lines – lines that meet or cross at a point
Line – a set of points that form a straight path that goes in opposite directions without ending
Line of symmetry – line dividing an image into two congruent parts that are mirror images of
each other
Line segment – part of a line between two points on the line, called endpoints of the segment
Obtuse – an angle that measures greater than 90° but less than 180°
Obtuse triangle – a triangle that has one obtuse angle (greater than 90 degrees) and two
acute angles
Parallel lines – lines that lie in the same plane, never intersect, and are always the same
distance apart
Perpendicular lines – lines that intersect at right angles to each other to form square corners
Point – a specific location in space
Polygon – a closed figure with at least 3 sides, where all sides are straight (no curves)
Ray – part of a line that has one endpoint and continues without end in one direction
Right – an angle (formed by perpendicular lines) that measures exactly 90°
Right triangle – a triangle with one right angle (exactly 90 degrees) and two acute angles
Side congruency marks – side marks indicating side lengths of the same measure
Straight – an angle that measures 180° (a straight line)
Triangle – a polygon with three sides and three vertices
Two-dimensional figure – a figure with two basic units of measure, usually length and width
Related Vocabulary:
 Circle
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Unit 9
Geometry: Points, Lines and Angels
 Decagon
 Diagonal
 Dodecagon
 Equilateral triangle
 Heptagon or septagon
 Hexagon
 Horizontal
 Isosceles triangle
 Label
 Line of reflection
 Nonagon or enneagon
 Octagon
 Parallelogram
 Pentagon
 Quadrilateral
 Rectangle
 Rhombus
 Scalene triangle
 Side
 Square
 Trapezoid
 Undecagon or hendecagon
 Unit
 Vertex
 Vertical
List of Materials:

Fourth Grade
See each individual day for materials needed.
INSTRUCTIONAL SEQUENCE
Phase Engage/Explain
Materials:
 1 sheet of white paper per student
 1 ruler per student
 Vocabulary Day 1 Worksheet
 Math Journal
 Note Cards
Day 1
Objective:
We will play “Simon Says” as a class to discover points, line segments, lines and rays. Please
see script in “What’s the teacher doing?”
Activity:
Students and teachers will work together to identify points, line segments, lines and rays by
following specific directions given by the teacher. Finally, students will use their new
information to complete the Vocabulary Day 1 Worksheet to be added to their math journal.
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Unit 9
Geometry: Points, Lines and Angels
Fourth Grade
This will help students create a beginning understanding of vocabulary needed to be
successful in the start of this unit.
After the vocabulary lesson is complete, have students write the definition and an example on
a note card and the word on another card.
Have students partner up and play memory with the vocabulary words and definition/example.
What’s the teacher doing?
What are the students doing?
I’d like to use my pencil to mark a specific
location on my paper. How do you think I
could do that?
Students’ response may be: You could put an
X.
(Draw an X.) Ok, so is this the location I’ve
marked? (Point to the upper right corner of
the X.)
Students should point out that point should be
in the center of the X
Explain to students that we just need a
small dot on the page to identify our specific
location on the page.
Have students draw a small dot on their
paper and label it with an A. Then have
students choose a different location, draw
and label a dot as B.
Ask: How many points could you draw on Answer will vary, but should get across the idea
this paper?
that students can cover their page with points.
Have students connect point A and point B
with their ruler.
Compare what you drew to what your
partner drew. Are your drawings the
same? What is different about them?
Explain that we will call this line segment
AB. (Write AB) Line segments have two
endpoints. Continue to explain that we can
call this line segment BA
Have student draw and label a point C.
Then, have them connect A and C to create
AC
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One is longer than the other. This one is
horizontal, and this one looks more diagonal.
They are both straight. They both begin at point
A and end with point B.
Unit 9
Geometry: Points, Lines and Angels
Ask: Could you extend AC to make it
longer? If you had a really big piece of
paper, could you continue to extend the
segment in both directions? What if your Answers will vary
paper extended forever? Could the
segment go on forever?
Fourth Grade
Have students extend AC and add an arrow
on both ends to indicate that the line goes
on forever. We call this AC.
What is different about AC and AB?
Possible answers: This one is longer/This one
doesn’t have points on the ends/ This one has
arrows/ The line goes past point A and point C
Have students draw another point on the
page and label it point D. Then use their
ruler to connect point B and point D. The
line should extend past point D. Explain to
students that this is called a ray. We call this
BD.
The final product may look similar to this:
Have students glue this page into their math
journals.
Finally, have students work to complete the
Vocabulary Day 1 Worksheet with the
knowledge learned from today’s lesson.
Have students glue this page into their math
journals.
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Unit 9
Geometry: Points, Lines and Angels
Phase Explain/Explore
Day 2
Materials:
Math Journal
Foldable Example
Day 2 Finding Lines worksheet
Toothpicks
Construction paper
Scissors
Markers
Glue or tape
Fourth Grade
Objective:
We will learn to identify different types of lines.
Activity:
Begin by watching a video about different types of lines. This can be found on brainpopjr.com
or there are several different options on youtube.
http://www.brainpopjr.com/math/geometry/pointslinessegmentsrays/
https://www.youtube.com/watch?v=NytgqC81iCo
Have students add notes about perpendicular, parallel, and intersecting lines to their journal in
the form of a foldable. Students will write vocabulary word and definition. Then, they will build
the different types of lines with toothpicks on the inside left flap of the foldable. Have students
glue the foldable into their math journal.
Then have students work in partners to complete the Finding Lines worksheet
If time allows, have students review with the game linked below.
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/line_shoot.htm
What’s the teacher doing?
What are the student’s doing?
After the video, the teacher will model how
to create the foldable.
Students will create a foldable with line type and
definition included.
The teacher will pass out toothpicks and
monitor as students build line examples with
them.
Students will use toothpicks to construct the
different line types.
The teacher will facilitate a discussion about
the different types of lines.
Possible questions include:
How are the lines different?
How are they similar?
Parallel lines do not intersect
Intersecting and perpendicular lines intersect.
Answers will vary
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Unit 9
Geometry: Points, Lines and Angels
In what ways will this knowledge help you in
real life?
While students are working on the
worksheet the teacher will walk around and
monitor while conferring with students.
Fourth Grade
Then students will be given Finding Lines
worksheet to complete with a partner.
Possible questions include:
How did you know what type of line that is?
What type of line did you find most often?
How would you have designed this house?
Phase: Explain
Day 3
Materials:
Construction paper
Scissors
Markers
Rulers
Foldable Example
Glow stick bracelets (thin flexible glow sticks)
Objective:
We will learn about different types of angles by creating a foldable. Then we will go on a
scavenger hunt to find examples of the angles.
Activity:
Students will work with the teacher to create a foldable that provides examples and definitions
of each type of angle.
Students will work with a partner to build/ quiz each other on different angle types with glow
stick bracelets.
Then students will go on a scavenger hunt around the classroom, school, or playground
(whichever the teacher prefers) and look for examples of the different types of angles.
What’s the teacher doing?
What are the students doing?
The teacher will model for students how to
create the foldable. As the foldable is being
created the teacher will instruct students to
share with their partner ideas on how the
angles got their name.
Possible Questions:
Where might you see this type of angle in
the real world?
How do you think this angle got its name?
What is a memory trick that we can use to
help us remember this angle?
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Students will follow teacher’s example to create
the foldable.
They will complete a pair share with their
partner to brainstorm a list of ideas about how
the angles got their names.
Unit 9
Geometry: Points, Lines and Angels
Fourth Grade
Next, the teacher will turn give each student
2 glow stick bracelets and turn off the lights.
Have students work with a partner to create
different types of angles and quiz each
other on what types of angle it is.
Students will work with a partner quizzing them
on different angles with glow sticks.
Then the teacher will take the class on a
walk around the building while they try to
find examples of each of the type of angles.
Students will walk around different areas of their
school looking for examples of different types of
angles
Phase: Explore
Students record answers on Angle Scavenger
Hunt.
Day 4
Materials:
Class set of Judy Clocks
Day 4 Angles Around the Clock Worksheet
Labeling Clocks Worksheet
Day 4 Exit Ticket
Note: if you do not have Judy Clocks the Angles Around the Clock worksheet has a blank
clock at the top that can be used as a paper template
Objective:
We will identify the different types of angles on a clock.
Activity:
As a class, students and teacher will work together to find different types of angles on a clock.
Then students will answer questions about different angles with their clocks.
What’s the teacher doing?
What are the students doing?
The teachers will call out times for students
to create on their clocks.
Students will display the time called out by the
teacher on their Judy Clock.
Once students have displayed the times
have them turn to a partner and describe
what type of angle it is.
Students will describe to their partner the type
of angle that is described
Possible Questions:
What type of angle is created by this time?
How do you know?
What many minutes would have to pass
turn it into a ________ angle?
Repeat this process several times for a
guided practice.
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Answers will vary
Unit 9
Geometry: Points, Lines and Angels
Then, have students work to fill out the
Rock Around the Clock worksheet with a
partner.
Fourth Grade
Students will complete the Rock Around the
Clock worksheet with a partner
Then independently, students will complete
the Labeling Clocks Worksheet.
Students can complete Day 4 Exit Ticket
before they leave class/transition to next
subject. This is a STAAR level multiple
choice question.
Phase: Elaborate
Day 5
Materials:
Shape Task Cards
Triple Venn-Diagram Page
Objective:
We will work to identify different types of angles in two-dimensional shapes.
Activity:
Students will work in small groups to sort shapes onto a triple Venn-Diagram. They will look for
different types of angles within the shapes. They will cut out the shapes and glue them onto
the Venn-Diagram.
When they are finished students will create their own shape that has at least one of each
angle.
Example:
What’s the teacher doing?
What are the students doing?
Teacher will provide groups with instructions
and then break class into groups based on
level preferences.
It is important to note to students that we
aren’t classifying the figures this way. We
are just examining them. Point out the
circle, also. It doesn’t have a home.
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Unit 9
Geometry: Points, Lines and Angels
Fourth Grade
Students will work in small groups and will
identify the angles within the shapes. They will
Teacher will walk around conferring with
add these shapes to the triple Venn-diagram.
groups.
Then students will create their own shape using
at least one of each type of angle.
Possible Questions:
What section of the Venn-diagram does this
shape belong in?
How do you know?
Can you point out the different angles in this
shape?
How will you create your own shape?
Phase: Explain/Explore
Day 6
Materials:
Construction paper
Crayons
Scissors
Foldable example
Objective:
We will create a foldable that explains the different types of triangles.
Activity:
Students and teachers will work together to create a foldable that explains scalene, isosceles,
equilateral, acute, right and obtuse triangles.
Then students will play a game on the computer to help identify the different types of angles
and triangles. Depending on technology options in the classroom, this could be a whole
group, small group or independent activity.
What’s the teacher doing?
What are the students doing?
The teacher will model for students how to
create the foldable. As the foldable is being
created the teacher will guide discussion
about the triangle types and how they got
their name.
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Students will follow teacher’s example to create
the foldable.
Unit 9
Geometry: Points, Lines and Angels
Fourth Grade
Possible Questions:
Where might you see this type of triangle in
the real world?
How do you think this triangle got its name?
What is a memory trick that we can use to
help us remember this triangle?
Students will play the game located at the
website on the following page.
http://www.sheppardsoftware.com/mathgames/
geometry/shapeshoot/triangles_shoot.htm
Day 7
Phase: Explain/Explore
Materials:
Plain white paper
White paper with shapes pre-traced or cut for students (teacher created)
Scissors
Objective: We will identify lines of symmetry in common shapes.
Activity:
Have students fold a sheet of white paper in half and cut out a shape. Discuss how this line
acts as a line of symmetry.
Then in pairs have students fold similar shapes at the same time. For example, partner 1
would fold a square and partner 2 will fold a rectangle. Also, partner 1 will fold a circle and
partner will an oval. Then, partner 1 will fold the parallelogram and partner 2 will fold a
rhombus.
What’s the teacher doing?
What are the students doing?
Going shape pair at a time give the students Students will work with a partner to determine
instructions that follow a similar pattern to
the different lines of symmetry in similar
the following:
shapes.
“In your pair, one person fold the rectangle
and the other the square as many ways as
you can so that when it is folded, the
shapes match. If you find a fold that creates
two shapes that match, use a straightedge
to record the line created by the fold.”
Possible Questions:
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Unit 9
Geometry: Points, Lines and Angels
What did you notice about the figure you cut Answers will vary.
out?
What did you notice when you folded these?
Why do you think the square had more folds
with sides that matched than the rectangle?
Fourth Grade
It is important to note on the circle fold that
a circle has an infinite amount of folds
because there are no straight edges and is
all equidistant from the center.
Phase: Explore
Day 8
Materials:
Shape Riddle Cards
Shape Task Cards
Construction Paper
Objective:
We will solve riddles that describe different 2D shapes.
Activity:
Students will read a set of riddle cards and find the matching shape. There are several
different options that can be used with this activity. Students can play a memory or it can be
adapted into I have, Who has. Students can cut and paste onto construction paper. The end
result is up to the teacher and their particular classes learning style.
What’s the teacher doing?
What are the students doing?
While students are playing whatever version
of the game the teacher decides, the
teacher will walk around monitoring and
conferring with students.
Students will match the riddle with the shape
that it matches.
Possible Questions:
What clues lead you to know it was this
shape?
What other clue could be added to this list?
Phase: Elaborate
Day 9
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Unit 9
Geometry: Points, Lines and Angels
Materials:
Poster board or chart paper
Build a Map Worksheet
Colored Pencils
Fourth Grade
Objective:
We will create a city map following specific directions about shapes and lines included.
Activity:
Whole group, the class will create a map of the school on a sheet of chart paper. We will pay
attention to what types of lines we create with the hallways. Discuss specific shapes that are
used to create each room. Include the playground as that should incorporate different shapes
and angles. Create a t-chart to the side of the map that explains the shapes, angles and lines
discovered during the drawing of the map.
Then, independently students will complete the Build a Map worksheet where they will follow
the directions to create a city.
If time permits, give students extra graph paper to create their own city.
What’s the teacher doing?
What are the students doing?
The teacher will model the drawing of a
map, by creating one of the school with
student guidance.
Students will direct the teacher in what shapes,
angles and lines that should be included in the map
of the school
The teacher will monitor the classroom
conferring with students during this
activity.
If needed, this is an ideal time to pull
back small groups that are in need of
extra instruction.
Students will show mastery of the skill by
completing the Build a Map worksheet.
Small groups will work with the teacher in order to
master any weak skills.
Possible Questions:
How did you make the decision to place
your street there?
Where are your parallel/perpendicular
lines located?
What aspects do you need to include in
________?
Phase: Elaborate
Day 10
14
Unit 9
Geometry: Points, Lines and Angels
Materials:
Shape Museum Worksheet
Colored Pencils
Day 10-Exit Ticket
Fourth Grade
Objective:
We will create a geometric museum by creating abstract art with different geometrical features.
Activity:
Whole group, we will look at the first page of Shape Museum Worksheet together. Students
will label and identify shapes, angles and lines in the given artwork. Then, students will use all
the different aspects of geometry that they have learned in the past week in order create a
piece of abstract art. When students are finished they will write a summary of the different
shapes, lines and angles that they used in their art. Art will be displayed in the classroom. At
the end of the activity, students will go on a gallery walk. They will make comments about each
piece on a post-it and place it around the artwork.
What’s the teacher doing?
What are the students doing?
The teacher will monitor the classroom
conferring with students during this
activity.
Students will show mastery of the skill by
completing the Shape Museum worksheet.
If needed, this is an ideal time to pull
back small groups that are in need of
extra instruction.
Small groups will work with the teacher in order to
master any weak skills.
Possible Questions:
What types of lines did you include in
your art?
What shapes are in your artwork?
Did you include any symmetry in your
artwork?
Before students transition to the next
class or subject, have them complete
the Day 10 Exit Ticket. This is a
STAAR level question that requires
justification.
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Unit 9
Phase: Evaluate
Geometry: Points, Lines and Angels
Day 11
Fourth Grade
Materials:
Performance Assessment
Objective:
We will complete the Performance assessment portion of this unit
Activity:
Analyze the situation(s) described below. Organize and record your work for each of the
following tasks. Using precise mathematical language, justify and explain each mathematical
process.
1) Consider the following geometric drawing.
a) Using the drawing identify and record an example of each of the following using appropriate
mathematical labels:
 Point
 Line
 Line segment
 Ray
 Acute angle
 Obtuse angle
 Right angle
 Lines that appear to be parallel
 Lines that appear to be perpendicular
2) Mandy created a stained glass design for her front door.
a) Identify which of the figures in the design can be classified as a(n):
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Unit 9
Geometry: Points, Lines and Angels
Fourth Grade
If a figure is not present in the design, explain its characteristics, create a sketch of it, and
label it appropriately.
b) Sketch or trace each of the figures from Mandy’s design separately. Identify and
draw one or more lines of symmetry, if they exist for each figure in the design.
What’s the teacher doing?
What are the students doing?
Teacher will monitor students on the
performance indicator to assess
whether more re-teaching is needed
before the unit test.
Display understanding of the skills taught in this unit
by completing the performance indicator.
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