4th
Unit 9
Six Weeks
Grade Level: 4th Grade
Subject Area: Math
Lesson Title: Geometry – Points, Lines, and
Unit Number: 9
Lesson Length: 11
Angles
Days
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.
Unit Objectives:
Students will…
 the foundations of geometry by identifying points, lines, line segments, rays, angles,
and perpendicular and parallel lines
 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
 use formal geometric language such as parallel, perpendicular, acute, obtuse, and right
angle to classify two-dimensional figures
 apply knowledge of right angles to identify acute, right, and obtuse triangles
 explore symmetry within two-dimensional figures as students identify and draw one or
more lines of symmetry, if they exist, for two-dimensional figures
Standards addressed:
TEKS:
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
representations, including symbols, diagrams, graphs, and language as appropriate.
4.1E Create and use representations to organize, record, and communicate mathematical
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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.
4.6A Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines.
Supporting Standard
4.6B Identify and draw one or more lines of symmetry, if they exist, for a two-dimensional
figure. Supporting Standard
4.6C Apply knowledge of right angles to identify acute, right, and obtuse triangles.
Supporting Standard
4.6D 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.
Readiness Standard
ELPS:
ELPS.c.1A - use prior knowledge and experiences to understand meanings in English
ELPS.c.1C - use strategic learning techniques such as concept mapping, drawing,
memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level
vocabulary
ELPS.c.2A - distinguish sounds and intonation patterns of English with increasing ease
ELPS.c.2C - learn new language structures, expressions, and basic and academic vocabulary
heard during classroom instruction and interactions
ELPS.c.2D - monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
ELPS.c.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
ELPS.c.3B - expand and internalize initial English vocabulary by learning and using highfrequency 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
ELPS.c.3D - speak using grade-level content area vocabulary in context to internalize new
English words and build academic language proficiency
ELPS.c.4C - develop basic sight vocabulary, derive meaning of environmental print, and
comprehend English vocabulary and language structures used routinely in written classroom
materials
ELPS.c.4D - use pre-reading supports such as graphic organizers, illustrations, and pretaught
topic-related vocabulary and other pre-reading activities to enhance comprehension of written
text
ELPS.c.4H - read silently with increasing ease and comprehension for longer periods
ELPS.c.5B - write using newly acquired basic vocabulary and content-based grade-level
vocabulary
ELPS.c.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
ELPS.c.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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Misconceptions:
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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.
Vocabulary:
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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
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width
Related Vocabulary:
 Circle
 Decagon
 Diagonal
 Dodecagon
 Equilateral triangle
 Heptagon or septagon
 Hexagon
 Horizontal
 Isosceles triangle
 Scalene triangle
 Side
 Square
 Trapezoid
 Undecagon or hendecagon
 Unit
 Vertex
 Vertical
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Label
Line of reflection
Nonagon or enneagon
Octagon
Parallelogram
Pentagon
Quadrilateral
Rectangle
Rhombus
INSTRUCTIONAL SEQUENCE
Phase: 1 Engage
Day 1
Materials: paper, tape, What’s My Name handout, Points, Lines, and Rays Defined
handout
Activity: Points, Lines, Line segments, and Rays. Students investigate and define
points, lines, line segments, and rays kinesthetically and record the appropriate name
for each representation.
1. Invite 4 or 5 student volunteers to come up to the front of the classroom. Assign each student volunteer a
letter. Record each letter on a sheet of paper and tape it to the front of each student volunteer’s shirt. Instruct
Points
the student volunteers to stand in a straight row in the
front of the classroom.
A
B
C
D
2. Display only the definition for “point” on teacher resource: Points, Lines, and Rays Defined. Explain to
students that each student volunteer, and the letter on their shirt, represents a point, and that a point is an
exact location in space represented by a dot. Explain to students that to name a point, only one letter is used
such as “point A” or “point B.”
3. Instruct the student volunteers to hold hands and extend their arms so they are level and parallel with the
floor.
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A
B
C
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D
4. Explain to students that these student volunteers are standing in a line, and that they represent a line where
each student (and the letter on his/her shirt) represents a point on the line. Explain that the arms of the
students at the ends represent a line that goes on forever in both directions.
5. Using the displayed teacher resource: Points, Lines, and Rays Defined, uncover the definition for “line.”
Explain to students that any 2 points on the line can name the entire line, and that the order of the letters
does not matter. However, it is important to say the word line prior to the two letters. The line can also be
recorded according to any 2 points on the line, such as “line AC” or AC (with arrows on both ends). A line
can be named with one lower case cursive letter, line a, such as the following:
A
B
C
a
D
6. Instruct each student volunteer to use their letter and another letter to name their line. (e.g., if the student
represents point A, and he chooses point D, then he should say, “line AD” or “line DA.” If the student chooses
point B, then he should say, “line AB” or “line BA.”). As each name is listed, record the verbal description with
various line labels for the class to see (e.g., line AC, DB , line d , etc.)
7. Instruct the student volunteers at the ends of the line to drop their free hands down to their sides.
A
8.
9.
10.
11.
B
C
D
Ask:
 How does this change the line? Answers may vary. The line no longer continues in both directions; the
line now stops on both ends; etc.
Explain to students that the student volunteers are now representing a line segment.
Using the displayed teacher resource: Points, Lines, and Rays Defined, uncover the definition for “line
segment.” Explain to students that a line segment is part of a line between 2 endpoints and line segments
are named using just the endpoints of the line. However, it is important to say the word line segment prior to
the two letters. Line segments can be recorded as “line segment AC” or AC (with no arrows on either end).
Instruct a student volunteer to name their line segment. Record the verbal description with various line
segment labels for the class to see (e.g., line segment AD, DA , etc.)
Prompt the student volunteer representing point D to hold their free hand back up and out to the side so that
it is parallel with the ground.
A
B
C
D
Ask:
 How does this change the line segment? Answers may vary. There is a line with only one endpoint;
the line only continues in one direction; etc.
12. Explain to students that the student volunteers are now representing a ray.
13. Using the displayed teacher resource: Points, Lines, and Rays Defined, uncover the definition for “ray.”
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Explain to students that a ray is part of the line that has an endpoint, and the other part continues in one
direction without end. Explain that rays are named with the endpoint of the ray as the “first name” for the ray
and another point on the ray as the “last name” for the ray. Facilitate a class discussion about naming rays.
Ask:
 What is the name of our ray if “A” is our endpoint? (ray AD)
 Could this model be named ray AB? Ray AC? Explain. (yes) Answers may vary. Since the ray begins
with A and the line extends through points B & C, the ray could be referred to as ray AD, ray AB, or ray
AC; etc.
 Could the model be named ray DA? DC? CA? BA? Explain. (no) Answers may vary. When naming a
ray, you must begin with the endpoint. The model represents the endpoint as A and none of the above
rays begin with A; etc.
14. Explain to students that rays can be recorded as ray AD or AD (with an arrow on the right side).
15. Instruct the student volunteers to return to their desks.
Place students in pairs. Distribute handout: What’s My Name? to each student. Instruct student pairs to name
each line or part of the line using appropriate labels. Continue to display teacher resource: Points, Lines, and
Rays Defined so that students may refer to it while working on the new handout. Allow time for students to
complete the activity. Monitor and assess student pairs to check for understanding. Facilitate a class discussion
to debrief student solutions.
What’s the teacher doing?


Using Points Line Ray printout to
introduce new vocabulary
Asking open ended questions
What are the students doing?
 4-5 students are in front demonstrating
 Discussing vocabulary
Phase: 2 Explore/Explain 1
Day 2
Materials: yard sale stickers, box of toothpicks, Special Lines – Part 1 handout
Activity: Points, Lines, Line Segments, and Rays. Students create graphic organizers to
formally define point, line, line segment, and ray.
Distribute 3 toothpicks to each student. Then distribute 1 page of yard sale stickers to each
table. Here is an example of yard sale stickers.
Distribute Special Lines – Part 1 to each student. Have students work in table groups to
complete the graphic organizer.
This is an example of what it could look like.
As a class, discuss the vocabulary seen in the graphic organizer and have students give
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examples of how these words are used in real-life situations.
What’s the teacher doing

Walking around assessing
students understanding
Phase: 3 Explore/Explain 2
What are the student’s doing?
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
Students complete the graphic organizer
Discussing new vocabulary
Day 3
Materials: Points, Lines and Rays Graphic Organizer, bag of pattern blocks for pairs of
students
Activity: Parallel lines, perpendicular lines, and intersecting lines. Students define and
identify parallel, perpendicular, and intersecting lines using pattern blocks.
1. Facilitate a class discussion to debrief the previously assigned graphic organizers from teacher resource:
Points, Lines, and Rays Graphic Organizers.
2. Explain to students that they will be investigating different types of lines, including intersecting lines. Facilitate
a class discussion about types of lines.
Ask:
 What do you think the words “cross street” or “intersection” mean? Answers may vary. The place
where two (or more) streets meet or cross; etc.
3. Place students in pairs. Distribute a ruler to each student and a Bag of Pattern Blocks to each pair. Instruct
students to each select a trapezoid pattern block from their Bag of Pattern Blocks.
4. Display a trapezoid pattern block for the class to see. Instruct students to examine the corners of the
trapezoid.
Ask:
 A trapezoid has how many vertices? (4 vertices)
Explain to students that each vertex on the figure represents a point of intersection, where two lines cross.
5. Instruct students to trace their figure in their math journal and use a ruler to carefully extend the lines around
the trapezoid. Allow time for students to complete the activity. Monitor and assess students to check for
understanding.
6. Using the displayed trapezoid, model the process of extending the lines around the figure.
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7.
8.
9.
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Unit 9
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Ask:
 What happens to the lines that extend above the trapezoid? (They cross; they intersect.)
 Are there any other intersecting lines in this drawing? Explain. (Yes, the lines at each vertex
intersect.)
Instruct students to label at least one intersection around the trapezoid as “intersecting lines” in their math
journal.
Ask:
 How could you describe the top and bottom horizontal lines on the trapezoid? Answers may vary.
They are the same distance apart; the lines do not touch each other; the lines appear to be parallel; etc.
 What could you do to determine if these lines are indeed parallel? Answers may vary.
Instruct students to use their rulers to measure the distance between the top and bottom horizontal lines in
several places. Explain to students that if the distance is the same, then the lines are parallel.
Instruct students to label the set of lines around the trapezoid as “parallel” in their math journal.
Display a square pattern block for the class to see. Instruct students to each select a square pattern block
from their Bag of Pattern Blocks.
Instruct students to examine the vertices of the square.
Ask:
 A square has how many vertices? (4 vertices)
Remind students that each vertex represents a point of intersection, where two lines cross.
Instruct students to trace their figure in their math journal and to use a ruler to carefully extend the lines
around the square. Allow time for students to complete the activity. Monitor and assess students to check for
understanding.
Using the displayed square, model the process of extending the lines around the figure.
Ask:
 Are there any intersecting lines in this drawing? Explain. (Yes, the lines at each vertex intersect.)
 How are these intersecting lines different from the intersecting lines of the trapezoid? (They form
right angles (square corners) to each other.)
14. Explain to students that intersecting lines that form square corners are called perpendicular lines. Instruct
students to label at least one intersection around the square as “perpendicular” in their math journal.
Ask:
 What happens to the vertical lines that extend above the square? (They continue without touching
and appear to be parallel.)
 How could you describe the horizontal top and bottom lines on the square? Answers may vary.
These lines appear to be parallel; etc.
 What could you do to determine if these lines are indeed parallel? Answers may vary. Measure the
distance between the lines at several points; etc.
15. Instruct students to use their rulers to measure the distance between the lines in several places to determine
if the lines are parallel, then label at least one set of lines around the square as “parallel” in their math
journal.
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16. Display the following sets of lines for the class to see.
Set A
Set B
Ask:
 How would you describe each set of lines? (Set A: When the lines are extended, the lines are
intersecting. Set B: When the lines are extended, the lines are parallel.)
For independent work/assessment, have students complete the worksheet Special Lines – Part 2 using
toothpicks and yard sale stickers to create intersecting, parallel, and perpendicular lines.
What’s the teacher doing?
 Facilitate class and group
discussions
 Walking around assessing
student learning
What are the students doing?
Phase:3 Explore/Explain 3
Day 4
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
using pattern blocks to help represent new
vocabulary
Group discussions
Materials: Geoboards, rubber bands, Dot Paper handout
Activity: Right angles, acute angles, and obtuse angles. Students identify, describe, and
create right, acute, and obtuse angles using dot paper.
1. Remind students that they already know the names of different pairs of lines, and now they will be learning
the names for different types of angles. Facilitate a class discussion about angles.
Ask:
 The hands on a clock meet at a point in the center of the clock. When the hands move, the size of
the opening, or angle, they make also changes. What are some words you could use to describe
the different openings formed by the hands of a clock? Answers may vary. Big; small; narrow; wide;
etc.
2. Distribute a geoboard, 6 rubber bands, and handout: Dot Paper to each student.
3. Display teacher resource: Dot Paper and a geoboard for the class to see. Demonstrate using 2 rubber bands
on the geoboard to stretch outward from the same pin forming 2 line segments. Instruct students to replicate
the model using 2 rubber bands and their geoboard.
Ask:
 These two rubber bands share the same pin. What is the geometric name for this pin? (endpoint or
vertex)
4. Instruct students to adjust their rubber bands to make a square corner with the shared endpoint on their
geoboard. Allow time for students to complete the activity. Monitor and assess students to check for
understanding.
5. Instruct students to use 2 more rubber bands sharing one endpoint to create an opening smaller than a
square corner. Allow time for students to complete the activity. Monitor and assess students to check for
understanding.
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6. Instruct students to use 2 more rubber bands sharing one endpoint to create an opening larger than a square
corner. Allow time for students to complete the activity. Monitor and assess students to check for
understanding.
7. Instruct students to record their work on their handout: Dot Paper and write a description of each pair of
rubber bands. Allow time for students to complete the activity. Monitor and assess students to check for
understanding.

Square corner
Smaller than a square
corner
Larger than a square
corner
8. Remind students that a ray is part of a line that has one endpoint and goes on forever in one direction.
Instruct students to pretend that each rubber band on their geoboard continues forever in one direction away
from the endpoint it shares with the other rubber band. Remind students to draw an arrow at the end of each
line on the dot paper drawings.
Ask:
 How many rays does each of your rubber band pairs have? (2 rays)
9. Explain to students that when two rays or line segments share a common endpoint, they form an angle, and
that they now have 3 angles created on their geoboard. These angles can be classified by the measure of the
opening between the two rays or line segments.
10. Display the following for the class to see:
An angle with a square corner represents a right angle.
An angle smaller than a square corner represents an acute angle.
An angle larger than a square corner represents an obtuse angle.
Ask:
 What type of angle is a square corner? (right angle)
 What type of angle is smaller than a square corner? (acute angle)
 What type of angle is larger than a square corner? (obtuse angle)
 How could you compare a right angle with an acute angle? (The measure of a right angle is greater
than the measure of an acute angle.)
 How could you compare a right angle with an obtuse angle? (The measure of a right angle is less
than the measure of an obtuse angle.)
 Can a right angle have shorter rays than an acute angle? Explain. (yes) Answers may vary. The
length of the rays does not determine the measure of the angle; etc.
11. Display the following angle for the class to see. Instruct students to replicate the angle in their math journal.
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A
B
C
12. Explain to students that angles can be named in at least 2 different ways. Demonstrate recording the “angle”
symbol to name the displayed angle as “angle B” and B . Instruct students to replicate these recordings in
their math journal.
Ask:
 What do you notice about the vertex when naming the angle? (It is always the single letter that
names the angle.)
 What do you know about an angle if you are only told that its name is S? (Point S is its vertex.)
Provide more examples if time allows.
13. Display the following angle for the class to see. Instruct students to replicate the angle in their math journal.
2
Explain to students that angles can also be named with a number. Demonstrate recording the “angle” symbol
to name the displayed angle as “angle 2” and 2 . Instruct students to replicate these recordings in their math
journal.
14. Distribute handout: Angle Notes and Practice to each student as independent practice and/or homework.
What’s the teacher doing?


What are the students doing?

Facilitate open ended
questions
Walking around assessing
Phase: 4 Elaborate

Using geoboards and rubber bands to
represent new vocabulary
Group and whole class discussion
Day 5
Materials: City Map handout, City Maps Recording Sheet - Types of Lines and Types of
Angles handout, yellow-red-blue crayons
Activity: Parallel lines, perpendicular lines, and intersecting lines. Right angles, acute
angles, and obtuse angles. Students locate and identify parallel, perpendicular, and
intersecting lines and right, acute, and obtuse angles on a city map.
Place students in pairs and distribute the worksheet City Map to each student. Use three
different colors to label three different types of streets: (1) yellow – streets that represent
intersecting lines; (2) red – streets that represent parallel lines; and (3) blue – streets that
represent perpendicular lines.
Then, have students use green to label three new pairs of intersecting streets on a map that
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form a right angle, an acute angle, and an obtuse angle.
Record in the worksheet City Maps Recording Sheet – Types of Lines and City Maps
Recording Sheet – Types of Angles, the streets identified according to the types of angles
and the types of lines they represent using the vocabulary.
What’s the teacher doing?
 Assessing students as they
complete worksheet
 Asking open ended questions to
check for understanding
What are the students doing?
 Students work in pairs to highlight new
vocabulary
 Group discussions using new vocabulary
Phase: 5 Evaluate
Day 6
Materials: Lines and Angles Assessment handout
Activity: Types of lines and angles. Students label each figure as a line, ray, line
segment, or angle.
Distribute Lines and Angles Assessment to each student. Monitor the students as they work
independently on the assessment.
What’s the teacher doing?

Monitor students while they
complete assessment
What are the student’s doing?

work independently on assessment
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Phase:1 Engage
Day 6
Materials: Classifying Triangles handout for pairs of students, zip lock bags, Triangle
Template Directions, patty papers, protractor
Activity: Triangle classification. Triangle properties. Students use logic and reasoning
skills to sort a group of triangles by their attributes. Students discover the sum of the
angles of any triangle is 180°. Students explore classifications of triangles using angle
classifications and the relationship between the angles of a triangle.
1. Prior to instruction create a card set: Classifying Triangles for every 2 students by copying on cardstock,
cutting apart, and placing in a plastic zip bag.
2. Place students in pairs and distribute a card set: Classifying Triangles to each pair. Instruct students to sort
the triangles by their attributes and to discuss the characteristics of each of their categories. Allow time for
students to complete the activity. Monitor and assess student pairs to check for understanding. Facilitate a
class discussion about the characteristics used to classify the triangles.
Ask:
 Is there more than one way to classify triangles? (yes, by their sides or by their angles)
 What are the different angle classifications? (acute, obtuse, right, and straight)
1. Display teacher resource: Triangle Template Directions.
2. Place students in pairs. Distribute handout: Triangle Template Directions, 3 sheets of patty paper, and
a protractor to each student. Instruct students to use their patty paper to create each triangle. Allow time
for students to complete the activity. Monitor and assess student pairs to check for understanding.
Facilitate a class discussion to debrief student solutions.
Ask:
 In Triangle 1: What kind of angles are these? (acute)
 How do you know? (they look less than 90)
 How can you be sure? (use a protractor to measure them)
 If you put 3 angles together and they form a straight line, what do you know about the measure of
the straight angle that forms the straight line? (180)
 What is the sum of the angles’ measures? (180)
 How do you know? (A straight line is formed when the angles are put together and a straight line forms
a straight angle with a degree measure of 180.)
 How does the sum compare to your estimate? (they are both 180)
 For Triangle 2: What kind of angles are these? (Angles 1 and 3 are acute and angle 2 is obtuse.)
 How do you know? (angles 1 and 3 look less than 90 and angle 2 looks greater than 90)
 How can you be sure? (use a protractor to measure them)
 If you put 3 angles together and they form a straight line, what do you know about the measure of
the straight angle that forms the straight line? (180)
 What is the sum of the angles’ measures? (180)
 How do you know? (A straight line is formed when the angles are put together and a straight line forms
a straight angle with a degree measure of 180.)
 For Triangle 2: What kind of angles are these? (Angles 1 and 2 are acute and angle 3 is right)
 How do you know? (angles 1 and 2 look less than 90 and angle 3 looks equal to 90)
 How can you be sure? (use a protractor to measure them)
 If you put 3 angles together and they form a straight line, what do you know about the measure of
the straight angle that forms the straight line? (180)
 What is the sum of the angles’ measures? (180)
 How do you know? (A straight line is formed when the angles are put together and a straight line forms
a straight angle with a degree measure of 180.)
3. Using the displayed teacher resource: Triangle Template Directions, facilitate a class discussion about
angles relationships found in triangles.
Ask:
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4th
Unit 9
Six Weeks


What types of angles have you studied so far? (acute, right, straight, and obtuse)
How do you think you can use what you know about angles to classify triangles? (I can classify
them according to their angles.)
 What types of angles did you find in Triangle 1? (all acute)
 What do you think would be a good name for a triangle with all acute angles? (an acute triangle)
 What types of angles did you find in Triangle 2? (one obtuse and two acute)
 Can you have more than one obtuse angle in a triangle? Why or why not? (No, I can only have one
obtuse and two acute.)
 What do you think would be a good name for a triangle with one obtuse angle? (an obtuse
triangle)
 What types of angles did you find in Triangle 3? (one right and two acute)
 Can you have more than one right angle in a triangle? Why or why not? (No, you can only have
one right and two acute.)
 What do you think would be a good name for a triangle with one right angle? (a right triangle)
 Would it be possible to have a “straight” triangle? (No, it is impossible to draw a triangle with a
straight angle.)
 How could you find the measure of angle 2 if you only knew the measures of the other two
angles? (Add the known angles together and subtract the sum from 180.)
4. Distribute a previously created card set: Classifying Triangles to each pair. Instruct student pairs to sort
the triangles using angle relationships. Allow time for student pairs to complete the activity. Monitor and
assess student groups to check for understanding. Facilitate a class discussion about the triangle sorts.
What’s the teacher doing?


Facilitate open ended questions
Walk around and assess student
performance
What are the student’s doing?


Students work in pairs to classify triangles
Use protractors to explore angle degrees
Phase: 2 Explore/Explain 1
Day 7
Materials: Angle Relationships in Triangles handout, protractor, ruler
Activity: Triangle classifications. Triangle properties. Students use triangle properties,
classifications, and side measurements to discover side congruency marks (tick
marks). Students are introduced to the formal language of congruence, isosceles,
scalene, and equilateral.
1. Place students in pairs. Distribute handout: Angle Relationships in Triangles, a protractor, and a ruler to
each student. Instruct student to complete handout with their group. Allow time for students to complete the
activity. Monitor and assess student groups to check for understanding.
Ask:
 How can you measure the lengths of the sides of the triangle? (with a ruler)
 How can you measure the angles of the triangle? (with a protractor)
 Why do you think there are marks on the sides of the triangle? (the sides are congruent)
 What is the relationship between the angle measures and the congruency marks on the
triangles? (if the sides are congruent, then the angle opposite those sides are congruent)
 If one of the angles measure was missing, could you find the angle measure without using a
protractor? (Yes, since each triangle has a total of 180, I can subtract the sum of the two known
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Unit 9
Six Weeks
angles from 180.)
2. Display teacher resource: Angle Relationships in Triangles to facilitate a class discussion about the
relationships found between the congruency marks and the measure of the angles.
Ask:
 What is a triangle called with no equal sides? (scalene)
 What do you know about the angles in a scalene triangle? (there are no congruent angles)
 What is a triangle called with two or more equal sides? (isosceles)
 What do you know about the angles in an isosceles triangle? (the angles opposite the congruent
sides are also congruent)
 What is a triangle called with all sides congruent? (equilateral)
 What do you know about the angles in an equilateral triangle? (all three angles are also congruent)
 What is another name for an equilateral triangle? (equiangular)
 What markings show that sides are congruent? (tick marks or side congruency marks)
 What is the relationship between the angles and congruency marks on the sides of a triangle?
(the angles opposite the congruency marks are also congruent)
 How many degrees are in a triangle? (180 degrees)
 What is the of the angles for problem 1? (60 degrees) Why? (There are 180 degrees in a triangle,
and all angles are congruent, so 180 divided by 3 is 60.)
 What is the measure of the missing angles on problem 4? (45 degrees) Why? (There are 180
degrees in a triangle; this triangle has a right angle which is 90 degrees. 180 – 90 = 90. The other two
angles are congruent and equal 90 degrees together; 90 degrees divided by 2 is 45.)
What’s teacher doing?


Walking around assessing
student progress
Asking open ended questions
What are the student’s doing?

Students explore angles using protractor and
rulers
Phase: 3 Explore/Explain 2
Day 8
Materials: whiteboards, erasers, dry erase markers for each student, Polygon Cards
handout, zip lock bags, Polygon Name Chart, Figure Search handout
Activity: One dimensional. Two dimensional. Students discuss the difference between
one-dimensional and two-dimensional figures. Attributes of polygons. Students define
a polygon as a closed figure with straight sides. Students examine and name polygons
by identifying the number of sides and types of angles within each figure.
1. Distribute a whiteboard and dry erase marker to each student. Remind students that they have learned the
special names for different types of lines and angles. Instruct students to record their responses to each of
the following questions on their whiteboard using pictures and/or words.
Ask:
 What are some examples of lines in the classroom? Answers may vary. The line created by the tiles
on the floor; a pencil; the line along one side of a desk top; the line created where two cabinet doors
meet; etc.
 What are some flat objects in the classroom? Answers may vary. A desk top; book cover; chalkboard;
the face of the clock; etc.
2. Explain to students that the lines they just named are all examples of one-dimensional figures, and the flat
surfaces they just named are all examples of two-dimensional figures.
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Unit 9
Six Weeks
3. Facilitate a class discussion about the differences between one- and two-dimensional figures:
Ask:
 Using the examples on your whiteboard, how could you describe the difference between a onedimensional figure and a two-dimensional figure? Answers may vary. A one-dimensional figure can
be a straight or curved line that does not form a closed figure. A two-dimensional figure is formed by
straight or curved lines that form a closed figure; etc.
4. Explain to students that a dimension is a measure in one direction. A one-dimensional figure has only one
dimension, length. Straight and curved lines are examples of one-dimensional figures.
5. Explain to students that a plane is a flat surface that goes on forever in all directions. A plane figure is a twodimensional figure with two basic units of measure, usually length and width. Two-dimensional figures are
comprised of one-dimensional figures, which can have straight or curved lines.
1. Prior to instruction, create a card set: Polygon Cards for every 2 students by copying on cardstock, cutting
apart, laminating, and placing in a plastic zip bag.
2. Facilitate a class discussion about attributes.
Ask:
 What is an attribute? Can you give examples? Answers may vary. A characteristic that helps define a
figure; etc.
3. Explain to students that they will be investigating the attributes of geometric figures, beginning with twodimensional figures.
2. Place students in pairs. Distribute a card set: Polygon Cards to each group. Instruct student pairs to sort the
figures into 2 or more groups and be ready to explain how they sorted the figures. Allow time for students to
complete the activity. Monitor and assess student pairs to check for understanding. Facilitate a class
discussion to debrief the possible groupings.
Ask:
 What are the groups you created from the sort? Answers may vary. Groups of polygons with right
angles and those without; groups of polygons by the number sides (3, 4, or more than 4, etc.); etc.
3. Explain to students that each figure from their card set: Polygon Cards is a polygon.
Ask:
 How do you know that each figure is a polygon? Answers may vary. Each figure is a closed figure;
each figure has straight sides; etc.
4. Explain to students that one way to sort polygons is by number of sides.
5. Distribute handout: Polygon Names Chart to each student.
6. Display teacher resource: Polygon Names Chart.
Ask:
 How many sides does each of these polygons have? (3, 4, 5, 6, and 8 sides)
7. Demonstrate recording the number of sides on the displayed teacher resource: Polygon Names Chart.
Instruct students to replicate these numbers on their handout: Polygon Names Chart.
8. Explain to students that polygons are named by their sides.
Ask:
 What are polygons with 3 sides called? 4 sides? 5 sides? 6 sides? 8 sides? (triangles;
quadrilaterals; pentagons; hexagons; and octagons)
9. Instruct students to examine the figures on their handout: Polygon Names Chart, determine the number of
angles in each, and record the number of angles and polygon name for each figure. Allow time for students to
complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to
debrief student solutions.
10. Collect handout: Polygon Names Chart to be redistributed in Explore/Explain 2.
11. Distribute handout: Figure Search to each student as independent practice and/or homework.
What’s the teacher doing?


Facilitating group/whole group
discussions
Assessing student achievement
What are the student’s doing?
 Students are using whiteboards to review
lines/ one dimension and two dimensional
figures
 Sorting polygons
Page 16 of 21
Unit 9
Six Weeks
Completing Polygon Name chart worksheet
Completing Figure Search
4th


Phase: 3 Explore/Explain 3
Day 9
Materials: Quadrilateral Cards handout, zip lock bags, dot paper, straws, masking tape,
Quadrilateral Descriptions handout, Quadrilateral Graphic Organizer handout, Polygon
Names Chart handout, Triangle and Quadrilateral Practice handout.
Activity: Triangles and Quadrilaterals. Students identify, describe, and build triangles
and quadrilaterals using straws.
1. Prior to instruction, create a card set: Quadrilateral Cards for every 2 students by copying on cardstock,
cutting apart, laminating, and placing in a plastic zip bag.
2. Facilitate a class discussion to debrief the previously assigned handout: Figure Search.
3. Place students in pairs. Distribute 9 flexible drinking straws, a pair of scissors, and handout: Dot Paper to
each student. Remind students of the terms acute, right, and obtuse angles. Facilitate a class discussion
about how the straws can be used to create triangles.
Ask:
 How many triangles can you make with 9 straws? How do you know? (3; because each triangle has
three sides and 3 x 3 = 9.)
4. Instruct students to use their flexible drinking straws to create triangles with different types of angles, record
the triangles they made on their handout: Dot Paper, and list the different combinations of acute, obtuse, and
right angles that can make a triangle. Allow time for students to complete the activity. Monitor and assess
students to check for understanding. Facilitate a class discussion to debrief student solutions and for students
to share their findings.
Ask:
 Can a triangle have more than one right angle? Explain. (No, there can only be one right angle in a
triangle because the other two have to be less than a right angle to close the figure.)
 Can a triangle have more than one obtuse angle? Explain. (No, there can only be one obtuse angle in
a triangle because the other two have to be less than a right angle to close the figure.)
 Can a triangle have more than one acute angle? Explain. (Yes, a triangle can have all three acute
angles or two acute angles and the third angle either obtuse or right.)
5. Instruct student pairs to create an example of each type of triangle: one with a right angle, one with an obtuse
angle, and one with all acute angles on their handout: Dot Paper. Allow time for students to complete the
activity. Monitor and assess student pairs to check for understanding.
6. Facilitate a class discussion about classifying triangles by their sides.
Ask:
 Can a triangle have three sides of the same length? Explain. (Yes and no because a triangle can
have three sides of equal measure, at least two sides of equal measure, or no sides of equal measure.)
 Could you describe a triangle based on its sides? Explain. (yes) Answers may vary. If a triangle has
3 sides that are equal in length, then it is an equilateral triangle; if a triangle has at least 2 sides equal in
length then it is an isosceles triangle; if a triangle does not have any sides that are equal in length, then it
is a scalene triangle; etc.
7. Explain to students that they have learned how to identify and classify triangles based on their sides and that
now they will be looking at the attributes of quadrilaterals to identify and classify them as well.
Ask:
 What is the same about all polygons that are quadrilaterals? (They all have 4 sides and 4 angles.)
8. Display teacher resource: Quadrilateral Descriptions.
9. Distribute a card set: Quadrilateral Cards to each pair. Instruct student pairs to find a quadrilateral to match
each description from the displayed teacher resource: Quadrilateral Descriptions and record the
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4th
10.
11.
12.
13.
14.
Unit 9
Six Weeks
quadrilateral and description in their math journal. Allow time for students to complete the activity. Monitor
and assess student pairs to check for understanding.
Invite a student volunteer to draw an example of the figure that matches the first description from the
displayed teacher resource: Quadrilateral Descriptions for the class to see. Facilitate a class discussion
about how the figure drawn has only one pair of parallel sides. Explain to students that the special name for
this quadrilateral is “trapezoid.”
Repeat the activity for the next 4 descriptions on the displayed teacher resource: Quadrilateral
Descriptions. Explain the special name for each quadrilateral as a “parallelogram,” “rectangle,”
“rhombus,” and “square.”
Facilitate a class discussion about the characteristics of the quadrilaterals.
Ask:
 What characteristics do you look at when comparing quadrilaterals? Answers may vary. The
lengths of the sides, angles, and if the sides are parallel or not; etc.
 Is it possible for a quadrilateral to have a right angle and an obtuse angle? How do you know?
(Yes; a trapezoid can have both a right angle and an obtuse angle.)
 Is a trapezoid a parallelogram? Explain. (No; because a trapezoid has only 1 set of parallel lines and a
parallelogram has 2 sets of parallel lines.)
 Is it possible for a quadrilateral to have no pairs of parallel sides? Explain. (yes) Answers may vary.
Instruct student pairs to hold up the card from their card set: Quadrilateral Cards that they think represents a
quadrilateral with no parallel sides.
Ask:
 What do you think this quadrilateral is called? Answers may vary.
Explain to students that because this it is a four-sided figure with no pairs of parallel sides, it is called an
“irregular quadrilateral.”
15. Display teacher resource: Quadrilateral Graphic Organizer. Redistribute previously completed handout:
Polygon Names Chart to each student. Facilitate a class discussion about the relationship that exists among
different types of quadrilaterals, as well as the different names for each type of quadrilateral. Instruct students
to add additional names that describe the quadrilaterals on their handout: Polygon Names Chart.
16. Distribute handout: Triangle and Quadrilateral Practice to each student as independent practice and/or
homework.
What’s the teacher doing?


Walking around asking open
ended questions
Assessing student progress
What are the student’s doing?


Students are using straws to build polygons
Comparing quadrilaterals
Page 18 of 21
4th
Unit 9
Six Weeks
Phase: 1 Engage
Day 10
Materials: Symmetry Cards handout, Symmetry Design Cards handout, Alphabet
Symmetry handout
Activity: Symmetry. Students categorize figure cards according to symmetry.
1. Create a card set: Symmetry Cards for every 2 students by copying on cardstock, cutting apart, laminating,
and placing in a plastic zip bag.
2. Remind students they have learned that when figures are translated, rotated, or reflected, they remain
congruent. Explain to students that today they will learn to use the relationship between reflections and
congruency to identify lines of symmetry and vice versa.
3. Place students in pairs. Distribute a pair of scissors to each student and a set of crayons and card set:
Symmetry Design Cards to each pair. Instruct student pairs to cut out their design cards.
4. Instruct student pairs to locate Figure 9 (the rectangle) from their card set: Symmetry Design Cards and fold
the rectangle in half down the middle, horizontally.
Ask:
 What do you notice about your fold? (the sides match exactly)
 What does the crease represent on your design card? (the line of symmetry)
5. Explain to students that when a figure is folded along a line and the sides match exactly, the figure has a line
of symmetry. Instruct students to use a crayon to trace the fold or line of symmetry on the rectangle from their
card set: Symmetry Design Cards.
Ask:
 Does this rectangle have another line of symmetry? How do you know? (yes) Answers may vary.
6. Instruct students to fold the rectangle from their card set: Symmetry Design Cards in half on a vertical fold.
Ask:
 Do the sides match exactly? (yes)
7. Instruct students to use a crayon to trace this fold, or line of symmetry, on the rectangle from their card set:
Symmetry Design Cards.
 Can a figure have more than one line of symmetry? Explain. (yes) Answers may vary. By making
other folds on a figure where the sides match exactly, you may be able to find other lines of symmetry;
etc.
8. Instruct students to fold the rectangle from their card set: Symmetry Design Cards again on a diagonal line.
Facilitate a class discussion for students to describe what they see. Explain to students that the diagonal is
not a line of symmetry for the rectangle because the sides on either side of the fold do not match when
folded. Therefore, this fold will not be traced because it is not a line of symmetry for the rectangle.
9. Distribute handout: Symmetry Design Card Recording Sheet to each student. Instruct students to record
their findings about the rectangle (Figure 9) from their card set: Symmetry Design Cards on the recording
sheet.
Ask:
 Under which column the rectangle (Figure 9) should be placed? How do you know? (“More than
one line of symmetry” column) Answers may vary. It had two folds, both horizontal and vertical, and it had
sides that matched; etc.
 Look at the first column titled “No Line of Symmetry.” Is it possible for a figure to have no line of
symmetry? How do you know? (yes) Answers may vary. You may not be able to fold a figure so that
one half would fit exactly on the other half; etc.
10. Instruct student pairs to complete the remainder of handout: Symmetry Design Card Recording Sheet by
folding the remaining designs from their card set: Symmetry Design Cards. Allow time for students to
complete the activity. Monitor and assess student pairs to check for understanding. Facilitate a class
discussion about the circle (Figure 8) as many students may be unsure of how many lines of symmetry a
circle has.
Ask:
 How many ways could you fold the circle in half so that both halves overlap exactly? (an infinite
number)
 So, how many lines of symmetry does a circle have? (an infinite number)
11. Distribute handout: Alphabet Symmetry to each students as independent practice and/or homework.
Page 19 of 21
4th
What’s the teacher doing?


Asking open ended questions
Checking for understanding
Unit 9
Six Weeks
What are the student’s doing?
1. Working in pairs to explore symmetry
Phase: 5 Evaluate
Day 11
Materials: Performance Assessment 01 handout
Activity: Performance Assessment 01
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
Page 20 of 21
4th
Unit 9
Six Weeks
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):
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?

Walking around
monitoring students
What are the student’s doing?

Working independently to
complete assessment
Page 21 of 21