Running head: GEOMETRY UNIT
Third Grade Geometry Unit:
Lines, Rays, & Angles; Quadrilaterals; and Triangles
Catherine L. DeWitt
The University of Montevallo
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Running head: GEOMETRY UNIT
Table of Contents
Unit Summary……………………………………………………….…….…...Page 4
Focus Questions……………………………………………….………....……Page 5
Background Research & References…………….………………….Pages 6-9
Unit Introduction Letter…………………………………………….……..Page 10
Electronic Resources…………………………………………..……………Page 11
Websites for Students……………………………………………….…Pages 12-13
Children’s Books...……………………………………………………..Pages 14-17
Professional Resources…………………………………..………………...Page 18
Possible Field Trips………………………………….……….………….….Page 19
Possible Guest Speakers…………………………………………………...Page 20
Daily Instructional Activity Grids
 Day 1 Grid: Lines, Rays, and Angles……………….……Pages 21-22
 Day 2 Grid: Quadrilaterals…………………………………...Pages 23-24
 Day 3 Grid: Triangles ……………………………………........Pages 25-26
Pre-Post Assessment…………………………………...…………………...Page 27
Pre-Assessment (High, Medium, Low)…………………………...…Pages 28-37
Post-Assessment (High, Medium, Low)……………………….……Pages 38-47
Culminating Performance
 Pre-Post Assessment Student Score Chart…………..………Page 48
 Pre-Post Assessment Graph………………………………………Page 49
 Unit Analysis…………………………………………………...…Pages 50-53
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Running head: GEOMETRY UNIT
Appendix I: Day 1—Lines, Rays, and Angles
 Participation Checklists…………………………………….………Pages 54-55
 Parallel, Intersecting, and Perpendicular Sheet/Rubric……….Pages 56-57
 Student Examples (High, Medium, Low)………………………...…Pages 58-63
Appendix II: Day 2—Quadrilaterals




Participation Checklists………………………………………….…Pages 64-65
Shape Search Activity Sheet…………………………………….…..…Page 66
Graphic Organizer…………………………………………………..……Page 67
Student Examples (High, Medium, Low) ……………………..……Pages 68-72
Appendix III: Day 3—Triangles
 Types of Triangles Game……………………………………..……Pages 73-74
 Triangle Drawings Activity…………………………………….………Page 75
 Student Examples (High, Medium, Low)…………………...………Pages 76-85
References………………………………………………………..………....Pages 86-87
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Unit Summary:
While the basic concepts of shapes are present in the K-2 curriculum, third
grade students begin to delve into more complex geometric principles. In order for
students to be successful in their future math courses, they must have a solid
foundation of basic geometry. The first part of this unit focuses on developing an
understanding that points, lines, and angles work together to define specific shapes,
and that shapes are categorized by these features. Once students can articulate this
first stepping-stone of geometry, they will be able to categorize and define
polygonal properties. The remaining two parts of the unit—quadrilaterals and
triangles, respectively—guide the students’ understanding in applying what they
previously learned about points, lines, and angles. The concepts presented in this
unit are not only relevant to other math subjects. Students who understand basic
geometric principles can make meaningful connections to the real world through
spatial reasoning and refining the skill of categorization.
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Focus Questions:
1. How do different relationships between lines change angles and twodimensional shapes?
2. How are quadrilaterals categorized and defined?
3. What properties make equilateral, isosceles, and scalene triangles different
from one another?
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Background Research:
How do different relationships between lines change angles and twodimensional shapes?
Geometry primarily focuses on the categorization and manipulation of two-dimensional
(has area, but no volume) and three-dimensional (has both area and volume) shapes (Bright
Horizons). Two-dimensional shapes are commonly described as being flat, while the element of
width in three-dimensional shapes allows for the existence of volume. One of the most basic
geometric elements is a point, which can be defined as “a location in space” (Bailey). In order
to understand how shapes are formed, the concept of defining lines must be understood. A line
is “a collection of points along a straight path that does on and on in opposite directions”
(Bailey). Lines are represented by the existence of arrows on both ends of a straight mark. A
“part of a line having two endpoints” is called a line segment which, instead of arrows, is shown
by the existence of two points (or dots) on both ends of a straight mark (Bailey).
When “two lines [that] meet at an endpoint”, an angle is formed (Bailey). Shapes are
categorized by the different ways in which sets of lines meet, or intersect, to form angles of
different sizes, which are measured in degrees. When lines do not intersect, they are considered
to be parallel. While one pair of parallel lines cannot form an angle, some shapes contain
multiple intersecting pairs which define those shapes’ properties. Perpendicular lines “intersect
at a right angle” (Bailey). A right angle, also known as a 90◦ angle, is referenced to define other
angles. Angles less than 90◦ are acute, while angles greater than 90◦ are obtuse (TERC).
Shapes are defined by the measurements of their angles, and angle measurements are determined
by the relationships between lines. Even a seemingly miniscule alteration of 1◦ can change the
defining properties of a given shape.
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How are quadrilaterals categorized and defined?
When items are categorized, it simply means that they are sorted according to shared,
common properties—or defining characteristics (TERC). Having the ability to sort different
items according to specific properties is an important skill to foster, since learning is most likely
to occur when students are able to make as many connections as possible. Appropriate and
meaningful links between concepts could not be established if a learner lacks the ability to
recognize how different properties relate to one another. The process of categorization is
especially important when unfamiliar terms are presented—such as the overwhelming
vocabulary of mathematics.
In a geometric context, line interactions and angle measurements are the properties
which are considered when categorizing a shape. Two-dimensional shapes that have four sides
and four angles are called quadrilaterals. Specific types of quadrilaterals exist within this
category and each is defined by the dependent relationship between lines and angle
measurements. Quadrilaterals that have two pairs of parallel lines are called parallelograms.
The angle measurements are not as pertinent when categorizing parallelograms. Though
rectangles (four 90◦ angles), squares (four 90◦ angles), and rhombuses (two angles <90◦; two
angles >90◦) may have differing angle measurements, they are all considered to be
parallelograms because each shape is formed by two pairs of parallel lines. The rhombus itself
creates a more specific category, because each of its four sides are parallel and equal in length.
Since squares are parallelograms with equal side-lengths, they are considered to be rhombuses
as well. The last basic type of quadrilateral is a trapezoid, which unlike parallelograms and
rhombuses, has only one pair of parallel lines. The other pair of lines will eventually intersect if
they continue in space (TERC).
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What properties make equilateral, isosceles, and scalene triangles different
from one another?
Having an understanding of angle measurements—right (90◦), acute (<90◦), and obtuse
(>90◦)—is imperative when categorizing types of triangles. When all interior angle
measurements within a triangle are added together, the sum is 180◦. This constant sum dictates
which combinations of angles are possible. For instance, a triangle can never have more than
one right angle or one obtuse angle. Since a right angle is 90◦, two right angles totaling 180◦
would not allow for the third angle to exist. If a shape does not have exactly three angles and
three sides, it is not a triangle (TERC).
Right triangles have exactly one right (90◦) angle. While the side lengths of right triangles
are not vital to its classification, the other two angles must be acute in order for the triangle to
maintain its properties. Similarly, obtuse triangles have exactly one angle greater than 90◦ and
two acute angles, all of which when added together equal exactly 180◦. When each angle of a
triangle measures less than 90◦, it is called an acute triangle. Right, obtuse, and acute triangles
do not have specific side-lengths by which to identify them.
The three other major classifications of triangles, however, are defined by both their
interior angles and the lengths of each side. When a triangle’s sides are all “exactly the same
length” and “each interior angle measures exactly 60◦” (60◦ x 3 = 180◦), it is classified as an
equilateral triangle (TERC). When only two of a triangle’s side lengths are equal, it is
categorized as an isosceles triangle. Finally, scalene triangles contain absolutely no equal angle
measurements and no even side lengths (TERC).
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Background Research References:
Bright Horizons Family Solutions (2013). Beginning geometry at home. Retrieved April 13,
2013 from the Bright Horizons website: http://www.brighthorizons.com/family
resources/prepare-your-child-forschool/teaching-geometry-at-home/
Bailey, B. Lines, rays, and angles. [Original Content].
TERC (2008). Third grade investigations in number, data, and space: Unit 4, investigation 3: 2-D
geometry measurement- Perimeter, angles, and area (pp. 104-123). Glenview, IL: Pearson.
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Dear Family,
We will begin learning about geometry on
Monday. This unit will consist of three main
topics: lines, rays, and angles; classifying
quadrilaterals; and classifying triangles. Your
child’s attendance is especially important
during this unit, as each new lesson will build
upon the material from the preceding day. The
students will also be participating in several fun
activities which require them to move around
the classroom, so please ensure that they are
dressed appropriately each day.  Please
contact me if you have any further questions.
Thank you,
Catherine DeWitt
Monday:
*Lines, Rays, & Angles
Tuesday:
*Parallel &
Perpendicular lines
activity
Wednesday:
*Quadrilaterals
Thursday:
*Shape scavenger hunt
Friday:
*Triangles
Weekend Work:
Be sure to review all inclass assignments to
prepare for the
geometry test on
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Electronic Resources:
YouTube / SchoolTube videos:
Meadville Area Senior High. (2009). [moshea]. (2009, December 15). Triangle Rap [Video file].
Retrieved from http://www.schooltube.com/video/85f53d5c55c24da6aea4/
Sesame Workshop. (1987). [tiradorfranco2]. (2007, May 1). Square one TV: Triangle song [Video
file]. Retrieved from:
http://www.youtube.com/watch?feature=player_embedded&v=st6rHVc76d4
Computer Games:
IXL Learning. (2013). Third grade- Classify quadrilaterals. [Web game]. Retrieved March 16,
2013, from the IXL website: http://www.ixl.com/math/grade-3/classify-quadrilaterals
Pierce, R. (2012). Classifying quadrilaterals. [Web game]. Retrieved March 17, 2013, from the
Math is Fun website: http://www.mathsisfun.com/geometry/quadrilaterals-interactive.html
Popovici, D. (2007-2013). Classifying triangles. [Web game]. Retrieved March 17, 2013 from:
http://www.ixl.com/math/grade-3/classify-quadrilaterals
Sheppard, B. Jr. (2012). Line shoot - Geometry: Math games. [Web game]. Retrieved March 16
2013, from:
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/line_shoot.htm
Smith, R. (2013). Shapes game for kids. [Web game]. Retrieved March 16, 2013, from the
Science Kids website: http://www.sciencekids.co.nz/gamesactivities/math/shapes.html
Devices & Software:




Projector
ELMO
Smart Pad
PowerPoint software
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Websites for Student Use:
 Classifying Quadrilaterals: This simple game is intended for third grade
students and focuses predominately on quadrilaterals, though prior
knowledge of basic geometric principles is required. After a student selects
an answer, immediate feedback from the website is provided. While the
game is not incredibly complex or creative, it is useful for students who do
not respond well when faced with excessive visual and auditory stimulation.
IXL Learning. (2013). Third grade- Classify quadrilaterals. [Web game]. Retrieved March 16,
2013, from the IXL website: http://www.ixl.com/math/grade-3/classify-quadrilaterals
 Interactive Quadrilaterals: Students who learn best through exploration can
benefit greatly from this website. The presented shapes can be easily
manipulated so the player can alter it as specific, defining properties remain
constant. The display of angles and diagonals can be turned on or off
depending on the individual students’ needs, and each of the vertices are
clearly labeled.
Pierce, R. (2012). Classifying quadrilaterals. [Web game]. Retrieved March 17, 2013, from the
Math is Fun website: http://www.mathsisfun.com/geometry/quadrilaterals-interactive.html
 Classifying Triangles: This timed game requires players to categorize
triangles as either acute, right, or obtuse. For students who are having
trouble with the basic concepts of angles, this activity can serve as useful
reinforcement before adding more complicated triangle classifications such
as isosceles, equilateral, and scalene. Once students have more practice
understanding the types of angles within the shape of a triangle, proper
terminology and definitions should come more naturally.
Popovici, D. (2007-2013). Classifying triangles. [Web game]. Retrieved March 17, 2013 from:
http://www.math-play.com/classifying-triangles/classifying-triangles.html
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 Line Shoot Geometry: For students who retain material best when they may
not notice they are learning, this first-person-shooter style of game is a
promising option. Before beginning, different types of lines are defined in
simple, straightforward terms. The player can decide to play in “relaxed” or
“timed” mode, which can help teachers regulate computer use. While the
game does have minimal sound-effects, it is not nearly as distracting as
many other computer games tend to be.
Sheppard, B. Jr. (2012). Line shoot - Geometry: Math games. [Web game]. Retrieved March 16
2013, from:
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/line_shoot.htm
 Shapes Game for Kids: This interactive game is a great way to assess how
well students can categorize a wide range of shapes. Rather than classify
types of quadrilaterals or types of triangles alone, the game presents both
types of polygons along with categories based on properties. It is not
unnecessarily complicated and struggling students should be able to use the
website successfully.
Smith, R. (2013). Shapes game for kids. [Web game]. Retrieved March 16, 2013, from the
Science Kids website: http://www.sciencekids.co.nz/gamesactivities/math/shapes.html
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Children’s Books:
1. Shape Up! : Fun with Triangles and Other Polygons
Shape Up! helps students better understand geometric concepts by incorporating common
objects such as bread, toothpicks, pretzels, and paper foldables when explaining a term. The
illustrations are dynamic and attractive, so the information may be more engaging to those who
struggle to find mathematics interesting. The book also contains a student-friendly glossary of
terminology which can serve as a valuable classroom reference.
Adler, D. A. (1998). Shape up!: Fun with triangles and other polygons. New York: Holiday
House.
2. The Very Greedy Triangle
This whimsically quirky story surrounds the life of a personified triangle who finds himself
constantly unsatisfied with the number of sides he has. Numerical prefixes (tri, quad, hexa, octa,
deca, etc.) and their defining characteristics are incorporated as the triangle becomes a
quadrilateral, a hexagon, an octagon, etc. as he wishes for more and more sides. The story also
addresses where these geometric forms can be identified in the real world. Eventually, the
triangle wishes for so many sides that they smooth over, and the greedy shape becomes a circle.
Burns, M. (1994). The very greedy triangle. New York: Scholastic.
3. What’s Your Angle, Pythagoras?
While this work of historical fiction may be too lengthy for struggling readers to
comprehend independently, it provides a historical context about the study of geometry. Once
students can make connections between different subject areas, they are more likely to absorb the
new information. The narrative nature of What’s Your Angle, Pythagoras? allows for abstract
mathematical concepts to become more relatable and less intimidating. Some students may also
be able to relate to the adolescent portrayal of Pythagoras, as he is depicted as a smart,
mischievous young man. He uses his curiosity to critically analyze the world around him—a
quality that learners of all ages should aim to possess.
Ellis, J. (1961). What’s your angle, Pythagoras?: A math adventure. Watertown, MA:
Charlesbridge.
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4. The Great Polygon Caper (Adventures in Mathopolis)
For students who are more enthusiastic about reading than they are math, parts of this
book may seem more like a comic strip and less like a story about geometry. While some parts
of the book explicitly define geometric concepts, the stylized cartoon illustrations and goofy
puns provide some balance. Students may be able to relate to the skateboarding protagonist who
uses his knowledge of geometry to defeat villains and save “Mathopolis”.
Ferrel, K. (2008). The great polygon caper: Adventures in mathopolis.
5. The Usborne Illustrated Dictionary of Math
This simple dictionary is easy to read and is filled with colorful illustrations which can
help students better understand a huge range of mathematical terms. It is organized according to
broad math subjects, so it is easier for students to quickly make connections among different
definitions. The dictionary also provides links to suggested websites to accompany each topicmany of which are student-friendly. Both the book and the recommended websites can serve as
useful tools for math students on virtually any skill level.
Large, T. (2003). The Useborne illustrated dictionary of math. London: Useborne
6. Groovy Geometry
This book is packed with creative and diverse activities which can benefit students at any
skill level. Many of the activities could serve as useful resources for students to use in math
centers or for the purposes of enrichment. Many of the activities are simple enough for students
to complete independently without the need for explicit instruction from the teacher.
Long, L. (2003). Groovy geometry: Games and activities that make math easy and fun. Hoboken,
NJ: John Wiley & Sons.
7. Mummy Math: An Adventure in Geometry
This child-friendly tale takes place in the historically mysterious country of Egypt.
Members of the Zills family must use geometry to find an infamous burial chamber. Mummy
Math incorporates geometric elements into the plot without overwhelming readers with
Running head: GEOMETRY UNIT
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intimidating mathematical jargon. The book can be easily comprehended by students on varying
reading levels and would make a valuable addition to any classroom library.
Neuschwander, C. (2005). Mummy math: An adventure in geometry. New York: Square Fish
8. Las formas en el Deporte (Shapes in Sports)
This short book is predominately picture-oriented and focuses on ways in which
geometric shapes appear in sports. Students in any classroom are incredibly diverse; whether
referring to their interests, the languages they speak, or their reading abilities. Las formas en el
Deporte can serve as a useful math tool for Spanish-speaking students who need to make
connections to real-world experiences or interests.
Rissman, R. (2009). Las formas en el deporte. Chicago: Heinemann Library.
9. Math Curse
John Scieszka’s Math Curse is filled with quirky illustrations and humorously
complicated and overwhelming math problems. While the text may not directly improve the
students’ math skills, the book itself might provide students who tend to have math-anxiety some
comic relief. The “problems” presented involve relatable subjects, such as riding the school bus
and dealing with a typical day at school. Even though the story is more humorous than
informative, it does demonstrate ways in which people can approach seemingly impossible word
problems.
Scieszka, J. (1995). Math curse. New York: Viking.
10. Geometry (Real Life Math Series)
This book series is directly correlated with the NCTM standards. Its contents are
organized according to several different contexts of geometry, such as art, architecture, design,
and geometric forms found in nature. Most of the activities presented encourage higher-order
thinking skills and a critical approach to identifying geometric elements in the real world.
Sherwood, W. (2001). Real life math: Geometry. Portland, ME: Walch.
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Running head: GEOMETRY UNIT
Professional Resources:
 Alabama Learning Exchange; Alabama Course of Study
Alabama Department of Education (2007). Alabama learning exchange 3rd grade courses of study
for mathematics. Retrieved March 11, 2013, from the ALEX website:
http://alex.state.al.us/standardAll.php?grade=3&subject=MA2010&summary=2
Alabama Department of Education (2007). Alabama learning exchange 4th grade courses of study
for Mathematics. Retrieved March 13, 2013, from the ALEX website:
http://alex.state.al.us/standardAll.php?grade=4&subject=MA2010&summary=2
 National Council of Teachers of Mathematics
National Council of Teachers of Mathematics. (2009). Principles and standards for school
mathematics grades K-5. Retrieved March 12, 2013 from:
http://investigations.terc.edu/library/components/principles_standards.pdf
 TERC (Technical Education Research Centers)
TERC (2008). Third grade investigations in number, data, and space: Unit 4, investigation 3: 2-D
geometry measurement- Perimeter, angles, and area (pp. 104-123). Glenview, IL: Pearson.
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Possible Field Trips:
 Students can explore local trails and parks to hunt for shapes found in
nature.
 Classes can visit the Birmingham Museum of Art (or another art museum
nearby) to discover the ways in which artists incorporate geometric
principles into their body of work.
 Using a map of the school, students can navigate through hallways and
identify how they relate to one another in the context of parallel and
perpendicular lines.
 Students can visit a variety of architecturally unique buildings and document
the variety of angles and lines used in their design.
Running head: GEOMETRY UNIT
Possible Guest Speakers:
 Cartographer: explain how important knowledge of lines and angles are
when working with maps
 Architect: describe how being accurate when working with angles is
imperative to ensure that buildings are safe
 Engineer: discuss how geometry is used every day
 Artist: provide an aesthetic perspective on shapes and their significance in
culture
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Day One: Lines, Rays, and Angles
Focus Question: How do different relationships between lines change angles and
two-dimensional shapes?
National
Standard
NCTM
Geometry
Standard: In
grades 3-5, all
students should
analyze
characteristics
and properties
of two- and
threedimensional
geometric
shapes and
develop
mathematical
arguments
about
geometric
relationships.
ALCOS
Standard
4th Grade
23.) Recognize
angles as
geometric
shapes that are
formed
wherever two
rays share a
common
endpoint, and
understand
concepts of
angle
measurement.
[4-MD5]
26.) Draw
points, lines,
line segments,
rays, angles
(right, acute,
obtuse), and
perpendicular
and parallel
lines. Identify
these in twodimensional
figures. [4-G1]
Objective
The students
will create
their own lines,
points, and
rays in order to
demonstrate
their
understanding
of relationships
between
lines/line
segments
(parallel,
perpendicular,
intersecting)
and angles
(acute, right,
obtuse).
Activity
Assessment
Description
First, the
teacher will
define and
explain the
following
geometric
elements: line,
point,
segment, ray,
intersection,
parallel,
perpendicular,
and angle
(including
acute, right,
and obtuse).
After the
students have
an opportunity
to ask
questions and
discuss the
information,
they will use
pretzel sticks
and
marshmallows
to construct
models of each
of the
mentioned
elements.
Examples:
•Participation
checklist (see
copy of
checklist in
Appendix)
• “Parallel,
Intersecting,
and
Perpendicular”
worksheet (see
copy of
worksheet in
Appendix)
Materials
•Slideshow
presentation
•2 bags of
pretzel sticks
(4/student)
•2 bags of
small
marshmallows
(8/student)
• 25 napkins
(1/student)
•25 copies of
the “Parallel,
Intersecting,
and
Perpendicular”
worksheet
•Participation
checklist
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• To construct
a ray, the
students will
stick one
marshmallow
to one end of a
pretzel stick to
represent a
point.
•To construct
intersecting
lines, the
students will
make an ‘X’
with the pretzel
sticks.
The students
will then be
able to use
their models
when
completing a
brief
assessment.
•Line Shoot
Game
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Day Two: Quadrilaterals
Focus Question: How are quadrilaterals categorized and defined?
National
ALCOS
Standard
Objective
Activity
Description
The students
will search the
classroom for
quadrilaterals
(each student
must document
at least four)
and categorize
each item based
on its
properties. The
students may
use their
graphic
organizers to
determine
whether their
items are
rectangles,
squares,
rhombuses,
parallelograms,
and/or
trapezoids.
The teacher will
begin by having
the students
compare and
contrast squares
and rectangles,
since these
shapes should
already be
familiar. After
a short
discussion, the
teacher will
define and
explain the
following twodimensional
geometric
figures:
quadrilateral,
rectangle,
square,
parallelogram,
rhombus, and
trapezoid.
Each student
will then be
given a blank
graphic
organizer (to be
completed by
the students as
they refer to the
displayed
example) and a
Shape Search
Assessment
Materials
Standard
NCTM
Geometry
Standard: In
grades 3-5, all
students
should
analyze
characteristics
and properties
of two- and
threedimensional
geometric
shapes and
develop
mathematical
arguments
about
geometric
relationships-
• identify,
compare, and
analyze
attributes of
two- and
threedimensional
shapes and
develop
vocabulary to
describe the
attributes;
3rd Grade
24.)
Understand
that shapes in
different
categories
(e.g.,
rhombuses,
rectangles, and
others) may
share attributes
(e.g., having
four sides), and
that the shared
attributes can
define a larger
category (e.g.,
quadrilaterals).
Recognize
rhombuses,
rectangles, and
squares as
examples of
quadrilaterals,
and draw
examples of
quadrilaterals
that do not
belong to any
of these
subcategories.
[3-G1]
•Participation •Slideshow
checklist (see Presentation
copy of
checklist in
Appendix)
•25 copies of a
blank graphic
organizer
•Shape
(1/student; see
Search
copy of graphic
activity (see
organizer in
copy of
Appendix)
“What
shapes do
you see?”
•25 copies of
sheet in
the “What
Appendix)
shapes do you
see?” sheet
(1/student)
•Participation
checklist
•Interactive
Quadrilaterals
•Quadrilateral
Classification
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• classify twoand threedimensional
shapes
according to
their
properties and
develop
definitions of
classes of
shapes such as
triangles and
pyramids
24
activity sheet.
The students
will search the
classroom for at
least four
examples of
quadrilaterals
and identify
how to
categorize each
one based on
specific
properties.
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25
Day Three: Triangles
Focus Question: What properties make equilateral, isosceles, and scalene triangles
different from one another?
National
ALCOS
Standard
Objective
Activity
Description
The students
will
demonstrate
their
understanding
of the distinct
properties of
equilateral,
isosceles, and
scalene
triangles by
playing the
“Types of
Triangles”
dice game.
Once
completed,
they will be
able to draw
an examples
of each
triangle
discussed.
(equilateral,
isosceles,
scalene, right,
obtuse, and
acute)
The teacher
will open the
lesson by
playing a short
video which
defines
equilateral,
isosceles, and
scalene,
triangles.
Further
explanation
will follow, as
well as a short
review of
right, obtuse,
and acute
angles (as
related to
triangles).
The students
will meet with
their three
o’clock
appointment
to complete
the “Types of
Triangles”
game. To
complete this
activity, each
student in their
groups will
take turns
rolling a die
Assessment
Materials
Standard
NCTM
Geometry
Standard: In
grades 3-5, all
students
should
analyze
characteristics
and properties
of two- and
threedimensional
geometric
shapes and
develop
mathematical
arguments
about
geometric
relationships-
• identify,
compare, and
analyze
attributes of
two- and
threedimensional
shapes and
develop
vocabulary to
3rd Grade
24.)
Understand
that shapes in
different
categories
(e.g.,
rhombuses,
rectangles, and
others) may
share attributes
(e.g., having
four sides),
and that the
shared
attributes can
define a larger
category (e.g.,
quadrilaterals).
Recognize
rhombuses,
rectangles, and
squares as
examples of
quadrilaterals,
and draw
examples of
quadrilaterals
that do not
belong to any
of these
subcategories.
[3-G1
•“Types of
Triangles”
sheet
•Student
drawings of
each triangle
•25 copies
of “Types
of
Triangles”
sheet
•25 dice
(1/group)
•25 copies
of
“Triangle
Drawings”
sheet
•25 rulers
•Right,
Obtuse,
Acute
•Grouping
Triangles
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describe the
attributes;
• classify
two- and
threedimensional
shapes
according to
their
properties and
develop
definitions of
classes of
shapes such
as triangles
and pyramids
26
three times;
recording each
number on the
sheet. Once
each partner
has three
numbers
(representing
each side
length of a
triangle), they
will determine
what type of
triangle they
have. Three
different
measurements/
numbers =
scalene (2
points), three
of the same
numbers =
equilateral (6
points), and
two of the
same numbers
= isosceles (4
points). After
14 turns, the
students will
determine who
has the most
points. Timepermitting, the
students will
return to their
desks and
draw each
type of
triangle.
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Pre-Post Assessment Scores
Student
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Pre-Assessment Post-Assessment
Score
Score
30%
80%
30%
80%
45%
40%
55%
15%
95%
35%
35%
45%
75%
50%
50%
95%
25%
65%
55%
80%
15%
90%
75%
35%
105%
25%
75%
40%
25%
105%
20%
35%
75%
35%
105%
30%
55%
5%
50%
40%
75%
48
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Pre-Post Assessment Scores
Geometry Summative Assessment
120%
Percentage Correct
100%
80%
60%
40%
20%
0%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Student
Series1
Pre-assessment
Series2
Post-assessment
16
17
18
19
20
21
22
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Unit Analysis:
Day 1: Lines, Rays, and Angles
To introduce the lesson, I provided the students with marshmallows (to represent points)
and pretzel sticks (to represent lines). Overall, the students were able to use this activity to
demonstrate their understanding of the difference between parallel and non-parallel lines. When
asked to identify specific types of non-parallel lines (ie: intersecting and perpendicular) much of
the class, with the exception of high-performing students, expressed some confusion. The
aforementioned “high-performers” caught on to these concepts and were able to demonstrate
their understanding rather quickly, as they have already been introduced to geometry in their
gifted resource class (GRC).
The thorough prior knowledge within that tier of students served as a helpful addition in the
beginning of the lesson, since they were better able to articulate material in third grade-friendly
terms. Conversely, those students’ eagerness to progress directly conflicted with the lowerperforming students’ need for reinforcement and explicit instruction. Out of either boredom or
frustration, both extremes became more concerned with their pretzels than responded to the
activity. The majority of students (those in the “medium” or “average” tier of performance)
continued to participate and ask meaningful questions.
If I were to teach this lesson again, I would spend more time emphasizing how angle
measurements determine the interaction between these lines. While I briefly explained this
relationship, I feel that all students, though especially the lower tier, would have benefitted from
more reinforcement—predominately regarding 90ͦ /right angles and how to define perpendicular
lines. The assessment results from this lesson ranged from 0% - 100% with the average falling
between 67% and 78%. While many of the errors from the lower-performing students were due
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to their failure to follow directions, I still felt unsatisfied with the students’ comprehension of the
material.
Day 2: Quadrilaterals
Most of the class seemed engaged and confident during the beginning of the lesson when
they were able to share and discuss their prior experiences with quadrilaterals. However, as soon
as new material was presented, some students expressed significant frustration. I noticed a
distinct divide between the students once the challenge of distinguishing among quadrilaterals
beyond rectangles and squares was presented. While I tried to elaborate on the properties of
each type of quadrilateral, it was evident to me that a handful of students were still struggling;
this was understandable based on their prior knowledge. On the other end of the spectrum,
students in GRC were eager to begin learning new material, while the lower-performers and
some of the average students were still struggling to recall material from the previous lesson.
Even though the instructional aspect of the lesson required significant improvement, the
“Shape Search” activity went better than expected. Students of every performance-level were
able to find shapes around the room and the whole class benefitted from the opportunity to move
around the classroom. Since they all wanted to participate, managing their noise-level and
guiding their focus came naturally. Each student was responsible for his or her own individual
work, so every person had an opportunity to work at a pace which was appropriate. Higher
performers were branching out to more complicated shapes while the lower-performers were
making significant, meaningful connections for the first time. Average performers fell
somewhere in between, but progress was evident for each individual child.
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If I were to reteach this subject, I would be sure to spend more time reinforcing the material
from the previous lesson on lines and angles. I’d prefer for the students to take more time
becoming proficient in the foundational content of the previous lesson than push them forward
because it is in conjunction with the plan. The “Shape Search” worked surprisingly well as a
way to get the students excited about geometry and to help them make real-world connections to
the material.
Day 3: Triangles
Based on my observations and assessment results, the lesson on triangles was the most
successful part of the geometry unit. After receiving helpful feedback from my CT and
reflecting on the lesson on quadrilaterals, I made sure to dedicate more time to reviewing lines
and angles. While I was initially concerned that this modification would prevent me from
completing the lesson, it quickly became evident that the amount of time spent reviewing was
vital to the majority of the students’ learning. Even though the higher-performing students were
antsy during the review, most every student was able to contribute meaningful ideas when
learning the new material—not just the GRC group. The rapport and attitude of the class as a
whole improved significantly once student performance gaps were minimized.
Rather than me spending the majority of instruction time explaining the properties of each
type of triangle, the students discussed ways in which they were able to differentiate among the
triangles. Even though some explanations required extensive revising, the students benefitted
much more from actively providing input than they do from spending more time passively
listening. I also benefitted greatly from listening to their explanations. Not only did this provide
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me with more perspective on their unique thought processes, but I also realized that it can be just
as important for the teacher to listen attentively to the students just as I would expect for them to
listen attentively to me. By demonstrating that I genuinely value their input, students tended
interact more respectfully within the whole group.
Unlike the previous two lessons from this unit, it seems that this lesson worked well with
this particular group of students. If I were to reteach it, I would spend more time developing
mnemonic devices to help guide the students’ thinking. The triangle drawing activity, though
not incredibly dynamic, served as an effective way to bring individual ideas from the discussion
together and neatly conclude the lesson.
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Appendix i-1
Participation Checklist
Lesson: Lines, Rays, and Angles
Student
Giselle
Mirella
Irvin
Ivetthmaria
Lilla
Aiden
Pedro
Antony
Cole
Nicholas
Coleman
Hope
Jordan
Ashley
Cristian
Donniesha
Liliana
Vidhi
Chloe
Trey
Lorenzo
Bryce
Adia
S: Satisfactory
P: Progressing
U:Unsatisfactory
Date: 3/29/13
Observations / Notes
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Appendix i-2
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Appendix i-3
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Appendix i-4
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Appendix i-5
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Appendix i-6
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Appendix i-7
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Appendix i-8
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Appendix i-9
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Appendix i-10
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Appendix ii-1
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Participation Checklist
Lesson: Quadrilaterals
Student
Giselle
Mirella
Irvin
Ivetthmaria
Lilla
Aiden
Pedro
Antony
Cole
Nicholas
Coleman
Hope
Jordan
Ashley
Cristian
Donniesha
Liliana
Vidhi
Chloe
Trey
Lorenzo
Bryce
Adia
S: Satisfactory
P: Progressing
U:Unsatisfactory
Date: 4/1/13
Observations / Notes
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Draw four quadrilaterals you found!
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Appendix ii-4
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Appendix ii-5
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Appendix ii-6
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Appendix ii-7
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Appendix ii-8
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Appendix ii-9
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Appendix iii-1
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Name: _________________________
Triangle Drawings
Right Triangle
Equilateral Triangle
Obtuse Triangle
Isosceles Triangle
Acute Triangle
Scalene Triangle
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