Grade 02
Unit 04: Two-and Three-Dimensional Figures
5E Lesson Plan Math
Grade Level: Second Grade
Lesson Title: Two-and Three-Dimensional Figures
Subject Area: Math
Lesson Length: 10
days
THE TEACHING PROCESS
Lesson Overview
This unit bundles student expectations that address creating, sorting, and classifying
two- and three-dimensional figures, as well as composing and decomposing geometric
figures based on geometric attributes. According to the Texas Education Agency,
mathematical process standards including application, tools and techniques,
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.
Prior to this unit, in Grade 1, students used both formal and informal geometric
language to identify two- and three-dimensional figures based on attributes. Students
also created, composed, and partitioned two-dimensional figures.
During this unit, students analyze attributes of two-dimensional shapes and threedimensional solids in order to develop generalizations about their properties. Using
formal geometric language, students classify and sort polygons with 12 or fewer sides
by identifying the number of sides and number of vertices. While mastery of the names
of polygons with seven or more sides is not expected according to the standards,
students should be aware that all two-dimensional polygons have a specific name
based on the number of sides and vertices in the figure. It is also important that
students are exposed to both regular figures where sides are the same length and
irregular figures where sides are not the same length. While exploring two-dimensional
figures, students not only determine the number of vertices and sides, but also
examine if the sides are equal in length, and if the corners are square. Although
students at this grade level are expected to use formal geometric language, the term
“right angle” when referring to corners is not an expectation until Grade 4. However,
teachers may begin to associate the words “square” and “right” when describing
corners of two-dimensional figures. Students use attributes based on formal geometric
language to classify and sort three-dimensional solids, including spheres, cones,
cylinders, rectangular prism (including cubes as special rectangular prisms), and
triangular prisms. Students develop spatial visualization skills, meaning the creation
and manipulation of mental representations of shapes, as they investigate creating
two-dimensional shapes based on given attributes of the figures. Spatial visualization
is also reinforced as students compose two-dimensional shapes and threedimensional solids with given properties or attributes. Students also decompose twodimensional shapes into equal or unequal parts and use geometric attributes to
identify and name the resulting parts.
After this unit, in Grade 3, students will continue to use geometric attributes and formal
language as they classify and sort two- and three-dimensional figures, including
further investigation of two-dimensional shapes classified as quadrilaterals. Students
will apply their knowledge of geometric figures as they investigate area of rectangles.
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
In Grade 2, creating, sorting, and classifying two- and three-dimensional figures, as
well as composing and decomposing geometric figures based on geometric attributes
are included within the Grade 2 Texas Response to Curriculum Focal
Points (TxRCFP): Applying knowledge of two-dimensional shapes and threedimensional solids, including exploration of early fraction concepts. This unit is
supporting the development of the Texas College and Career Readiness Standards
(TxCCRS): III.A. Geometric Reasoning – Figures and their properties and IX.
Communication and Representation.
In the primary grades, the instruction of geometry concepts relies heavily on hands-on
manipulation of concrete objects. While early experiences with naming shapes is
critical to geometry, research by the National Research Council (2001) concludes that
rather than limiting geometrical investigations to simply identifying shapes, students
who are “encouraged to reflect on and articulate their developing
knowledge…subsequently [demonstrate] levels of reasoning well beyond their earlier
performance, both in their precision of language and in their use of arguments based
on the properties of shapes” (p. 285). Van de Walle (2005) explains that the teaching
of geometry involves the gradual attainment of concept levels based on the accurate
application of formal geometric vocabulary focused more on properties of figures than
on simple identification. He states, “As students begin to be able to think about
properties of geometric objects without the constraints of a particular object, they are
able to develop relationships between and among these properties” (p. 207). The
advent of virtual three-dimensional manipulation using technology has increased the
need for a well-developed spatial sense and understanding of geometric attributes and
properties in order for students to be prepared for the future.
National Research Council. (2001). Adding it up: Helping children learn
mathematics. Kilpatrick, J., Swafford, J., and Findell, B. (Eds.) Mathematics Learning
Study Committee, Center for Education Division of Behavioral and Social Sciences
and Education. Washington, DC: National Academy Press.
Texas Education Agency & Texas Higher Education Coordinating Board.
(2009). Texas college and career readiness standards. Retrieved
fromhttp://www.thecb.state.tx.us/collegereadiness/crs.pdf
Texas Education Agency. (2013). Texas response to curriculum focal points for
kindergarten through grade 8 mathematics. Retrieved
fromhttp://projectsharetexas.org/resource/txrcfp-texas-response-curriculum-focalpoints-k-8-mathematics-revised-2013
Van de Walle, J., & Lovin, L. (2005). Teaching student-centered mathematics grades 3
– 5. Boston, MA: Pearson Education, Inc.
Unit Objectives:
Students will…
 Create, sort, and classify two- and three-dimensional figures, as well as
composing and decomposing geometric figures based on geometric attributes.
 Use formal language to classify and sort polygons with 12 or fewer sides by
identifying the number of sides and number of vertices.
 Be aware of figures where sides are the same length and irregular figures
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
where sides are not the same length.
Develop spatial visualization skills in creating a mental representation of twoand three-dimensional shapes based on given attributes of the figures.
Standards addressed:
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TEKS:
2.1A- Apply mathematics to problems arising in everyday life, society, and the
workplace.
2.1C- 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.
2.1E- Create and use representations to organize, record, and communicate
mathematical ideas.
2.1F- Analyze mathematical relationships to connect and communicate mathematical
ideas.
2.1G- Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
2.8A- Create two-dimensional shapes based on given attributes, including number of
sides and vertices.
2.8B- Classify and sort three-dimensional solids, including spheres, cones, cylinders,
rectangular prisms (including cubes as special rectangular prisms), and triangular
prisms, based on attributes using formal geometric language.
2.8C- Classify and sort polygons with 12 or fewer sides according to attributes,
including identifying the number of sides and number of vertices.
2.8D- Compose two-dimensional shapes and three-dimensional solids with given
properties or attributes.
2.8E- Decompose two-dimensional shapes such as cutting out a square from a
rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles
and identify the resulting geometric parts.
ELPS:
ELPS.c.1A- use prior knowledge and experiences to understand meanings in English
ELPS.c.2A- distinguish sounds and intonation patterns of English with increasing ease
ELPS.c.2D- monitor understanding of spoken language during classroom instruction
and interactions and seek clarification as needed
ELPS.c.3D- speak using grade-level content area vocabulary in context to internalize
new English words and build academic language proficiency
ELPS.c.3I- adapt spoken language appropriately for formal and informal purposes
Misconceptions:
Underdeveloped Concepts:
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Although some students may be able to identify regular figures, they may not
be able to identify irregular figures due to limited exposure to a variety of
images and lack of understanding regarding the attributes of a given figure
(e.g., a student may be able to identify a regular hexagon from exposure to
pattern blocks, but fail to recognize any closed six-sided figure as a hexagon).
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
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Although some students may sort or classify a set of figures by size, orientation,
texture, or color, they may have difficulty sorting and classifying figures based
on geometric attributes.
Some students may categorize two-dimensional figures incorrectly based on
only a few attributes of the figure rather than considering all of the figure’s
defining attributes (e.g., a student may say, “If the shape has four sides, it is a
square,” although this may not be true because a four-sided figure could also
be a rectangle or rhombus).
Students may have difficulty remembering formal geometric terms or
distinguishing formal vocabulary from informal vocabulary (e.g., students may
confuse the informal edge and the formal side of a two-dimensional figure with
the formal edge of a three-dimensional figure).
Some students may call a three-dimensional figure by the name of one of its
two-dimensional faces (e.g., a student may refer to a cube as a square, etc.).
Vocabulary:
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Attributes of three-dimensional figures – characteristics that define a
geometric figure (e.g., faces, curved surfaces, edges, vertices, etc.)
Attributes of two-dimensional figures – characteristics that define a
geometric figure (e.g., sides, vertices, etc.)
Classify – applying an attribute to categorize a sorted group
Compose figures – to combine smaller geometric figures to form a larger
geometric figure
Decompose figures – to break a geometric figure into two or more smaller
geometric figures
Edge – where the sides of two faces meet on a three-dimensional figure
Face of a prism – a polygon that forms a surface of a prism
Irregular figure – a polygon with side lengths and/or corners that are not all
equal
Polygon – a closed figure with at least 3 sides, where all sides are straight (no
curves)
Properties of three-dimensional figures – relationship of attributes within a
geometric figure (e.g., a rectangular prism has 6 faces and each pair of
opposite faces are the same size and shape, etc.) and between a group of
geometric figures (e.g., a cube and a rectangular prism both have 6 faces with
opposite faces equal in size and shape; however, a cube has only square faces
but a rectangular prism can have square or rectangular faces; etc.)
Properties of two-dimensional figures – relationship of attributes within a
geometric figure (e.g., a square has 4 sides equal in length and 4 square
corners, etc.) and between a group of geometric figures (e.g., a square and a
rectangle both have 4 sides and 4 square corners; however, a square has 4
sides equal in length but a rectangle has only opposite sides equal in length;
etc.)
Regular figure – a polygon with all side lengths and corners equal
Side – a straight outer boundary between two vertices (line segment) of a two4
Grade 02
Unit 04: Two-and Three-Dimensional Figures
dimensional figure
Sort – grouping objects or figures by a shared characteristic or attribute
Three-dimensional figure – a figure that has measurements including length,
width (depth), and height
Two-dimensional figure – a figure with two basic units of measure, usually
length and width
Vertex (vertices) in a three-dimensional figure – the point (corner) where
three or more edges of a three-dimensional figure meet
Vertex (vertices) in a two-dimensional figure – the point (corner) where two
sides of a two-dimensional figure meet
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Related Vocabulary:
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Circle
Cone
Cube
Curved surface
Cylinder
Decagon
Dodecagon
Flat surface
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Heptagon or
septagon
Hexagon
Nonagon or
enneagon
Octagon
Orientation
Pentagon
Rectangle
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Rectangular Prism
Rhombus
Sphere
Square
Triangle
Triangular Prism
Undecagon or
hendecagon
INSTRUCTIONAL SEQUENCE
Phase One: Engage
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Materials:
Literature-The Greedy Triangle-if
the book is not available a reading
of it can be found on YouTube.
chart paper (2 sheets per teacher)
tape (1 roll per teacher)
sticky notes (2 notes per 2
students)
cardstock (1 sheet per 2 students,
2 sheets per teacher)
plastic zip bags (sandwich size) (1
per 2 students, 1 per teacher)
scissors (1 per teacher)
marker (1 per teacher, 1 per
student)
geoboard (commercial) (1 per
teacher)
rubber bands (3 per teacher)
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Handouts:
Teacher Resource: Open or Closed?
KEY (1 per teacher)
Card Set: Open or Closed? (1 per
teacher)
Card Set: It Figures (1 per 2 students)
Class Resource: Geoboards (1 per
student)
Teacher Resource: Polygons and Not
Polygons KEY (1 per teacher)
Handout: Polygons and Not Polygons
(1 per student)
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
Day 1 Activity:
Prior to instruction, create a class T-Chart on a piece of chart paper with partial labels
as shown below. Do not title—open or closed that will be done as the lesson
progresses.
Figures that are
Figures that are
___________________
__________________
Prior to instruction, create a card set Open or Closed? For the teacher, cutting apart
and placing in a plastic bag.
Prior to instruction, create a card set: It Figures for every 2 students, cutting apart,
and placing in a plastic bag.
Prior to instruction, run copies of paper geoboards (1 per students)
Prior to instruction create a class (anchor chart) Polygon Chart by writing the word
“Polygon” at the top of a sheet of chart paper. Display for the class to see.
Activity 1:
Introduce the lesson by reading The Greedy Triangle or another two-dimensional
figure book.
Show the students the Polygon chart.
Say:
 Today we will define the term “Polygon” by discovering the three attributes of a
polygon.
Show the students the Open or Closed T-Chart. Choose two open figures and tape
them on the right side and two closed figures and tape them on the left side of the
chart.
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
Figures that are
Figures that are
__________________
__________________
Say:
Look at the chart and notice the figures that have been placed on it. I will pass out a
few more figure cards to some students and their job will be to decide which side of
the T-Chart to place their card. We will do this activity in silence. Allow time for each
student to place their figure card on the chart.
Turn and Talk: Have the students talk to a neighbor about the chart and where the
students have placed the cards. They should ask their neighbor if they agree with
where they cards were placed, if they don’t then they should tell where they think they
should go and why. If they agree then they should tell their neighbor why they agree
with the placements.
Have a class discussion about what they talked with their neighbors about, the
placement of the cards.
Ask:
*Have all of the cards been placed on the chart correctly? (answers may
vary)
*If you don’t agree where would you have placed the cards? (answers
may vary) Allow students to come up to the chart and move a card they don’t
agree with its placement.
Ask:
*What could be the title of the first column?
*What could be the title of the second column?
Explain to the students that the first column of the Open or Closed? T-Chart contains
figures that are polygons and the second column contains figures that are not
polygons. Complete the titles of each column by adding Open and Closed to the
correct columns.
*Based on what we have learned from the Open or Closed? T-Chart, what is
one attribute of a polygon? (Answers may vary. Polygons must be closed
figures; polygons cannot be open figures)
Refer students to the Polygon Chart. Record the first part of the definition of a polygon
as discovered in Activity 1.
Draw the following figure on the board.
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
Ask:
*Is this figure a polygon? (no) Explain. (It is not a closed figure. It is an open
figure.)
*What would we need to do to make this “open” figure a “closed” figure?
Demonstrate how to change the “open” figure to a closed figure.
Open
Closed
*Does this figure now match what we know to be true about polygons? (yes)
Explain. (It is a polygon because all sides are closed)
Phase: Explore/Explain
Activity 2:
Place the students in pairs. Give each pair a card set: It Figures and two sticky notes
to each student pair.
Instruct students to observe the figures on the cards. Instruct students to sort the
cards into two groups, and record their sorting rule on the two sticky notes, labeling
each group of cards. Explain to students that the rule they use to group their figures is
called an “attribute”. An attribute describes the figure or the group of figures. Instruct
students to be prepared to explain what attribute describes their sort. Allow time for
students to complete the activity.
Have a class discussion examining the different ways the figures could be sorted.
Ask:
*What attributes did you use to group your figures? Answers may vary.
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
Straight sides; curved sides; no corners; with sides; no sides; etc.
Explain to the students that the attribute that they will use to further define a polygon is
straight sides (no curves)
Ask:
*If you now know that a polygon has to be closed, and has only straight
sides, who can demonstrate which cards would represent a polygon?
Answers may vary.
Invite a student to display the polygons from their card set: It Figures. Have a
discussion about the cards presented as polygons, whether the class agrees with the
selection, and if all the polygons in the set were displayed.
Refer students to the displayed Polygon Chart. Record the second part of the
definition of a polygon as discovered in Activity 2.
Instruct students to place the figures back into the plastic bag for collection.
Activity 3:
Display a geoboard for the class to see. Explain to the students that geoboards can
be used to create polygons. Place one rubber band on the geoboard.
Distribute a paper geoboard to each student.
Ask:
*How could you draw this figure on a geoboard handout? (Draw a straight
line.)
Using your finger, model how to draw a straight line touching each peg
encompassed by the rubber band. Instruct students to draw the line on their
paper geoboard.
Ask:
*Is this a polygon? (no) Explain. Answers may vary. It is just a straight line;
it is not open or closed; etc.
Explain that the model on the displayed geoboard represents on line that could
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
become one
side of a polygon.
Using the
previous
displayed geoboard, add one more rubber band to the
figure.
Using your finger, model how to draw another straight line touching each peg
encompassed by the second rubber band. Instruct the students to draw the line
on their paper geoboard.
Ask:
*Is this a polygon? (no) Explain. Answers may vary. It is just two straight lines
and is open; it is not a closed figure; etc.
Explain that the model on the geoboard represents an open figure which is not a
polygon.
*How could this figure be changed to become a polygon? (Add one more
rubber band connecting the open ends.)
Using the displayed geoboard, add one more rubber band to the previous figure.
Using your finger; model how to draw another straight line touching each peg
encompassed by the third rubber band. Instruct students to draw the line on their
paper.
Ask:
*Is this a polygon? (yes) Explain. Answers may vary. It is closed, it has no
curved sides; etc.
*What is the least number of sides that will create a polygon? (3 sides)
Refer students to the displayed Polygon Chart. Record the third part of the definition
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
of a polygon as discovered in Activity 3.
Summarize all 3 activities:
Distribute handout: Polygons and Not Polygons to each student. Explain the
handouts instructions, clarifying any questions. Instruct students to complete the
handouts independently. Allow time for students to complete the handout. Monitor
and assess students to check for understanding.
Have a class discussion to go back over the handout and clarify any misconceptions.
What’s the teacher doing?
What are the students doing?
*Setting expectations for manipulatives
Used.
*Leading class discussion.
*Monitoring students.
*Checking for understanding.
*Using manipulatives correctly.
*Participating in discussions.
Phase Two: Explore/Explain
Materials:
 string (1 piece approximately 2 yards
in length)(1 per teacher)
 chart paper (2 – 3 sheets per teacher)
 geoboard (commercial) (1 per
student, 1 per teacher)
 rubber bands (2 per student, 2 per
teacher)
 marker (1 per teacher)
 Polygon Chart (1 per teacher)
(previously created)
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Handouts:
Teacher Resource: Shape Detectives
KEY (1 per teacher)
Teacher Resource: Shape Detectives (1
per teacher)
Handout: Shape Detectives (1 per
student)
Teacher Resource: Notes & Practice –
Polygons KEY (1 per teacher)
Teacher Resource: Notes & Practice –
Polygons (1 per teacher)
Handout: Notes & Practice – Polygons
(1 per student)
Teacher Resource: All About Figures
KEY (1 per teacher)
Handout: All About Figures (1 per
student)
Day 2 Activity:
Students explore a variety of two-dimensional shapes and identify their attributes.
Activity:
1. Prior to instruction. Create a Not Polygon Chart by writing the word “Not a
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
Polygon” at the top of a sheet of chart paper. Display the Not a Polygon Chart
next to the displayed Polygon Chart for the class to see.
2. Invite all Students to a large, open part of the room. Instruct students to form a
circle holding hands. When the circle is formed, they are to drop hands and not
move from their “spot”.
3. Instruct one student to hold one end of the string (not moving their location)
while the teacher moves to the center of the circle holding the other end of the
string as the student end of the string is passed from one student to the next
around the circle until all student held the string.
Ask:
*As the string moved from student to student, what figure was created?
(a circle)
*What did you notice about the string? Answers may vary. It was long
enough for each of us to hold it; none of us had to change our positions; etc.
*What do I (the teacher) represent in the circle? (the center of the circle)
*Which student is the farthest from the center? (None, we are all the
Same distance from the center.)
*Which student is the closest to the center? (None, we are all the same
distance from the center.)
*If I represent the center of the circle, would you say that each person is
the same distance from the center of the circle? (yes)
*How could you define a circle? (A circle is a closed, curved figure where all
points are the same distance from the center.)
4. Still standing in the center of the circle, instruct students to the left and right of you
to take two steps backward while students in the front and back of you do not move at
all. Students should have now formed an oval. Instruct one students to hold one end
of the string while the teacher holds the other end of the string. Ask students to
observe the string as it is passed from student to student, reminding them not to move
their location.
Ask:
*Were all students able to hold the end of the string without moving from
their location? (no)
Explain. (I am too far, and the string is to short.)
*Is the figure a circle? (no) Explain. (The figure is not a circle because some
students are closer to the center, and others are farther away.)
*What figure have you created? (an oval) If students do not know the name
of the figure, the teacher may explain that the figure is called an oval.
*How is the circle different from the oval? Answers may vary. In a circle, all
the points on the curve are the same distance from the center; in an oval, not
all of the points on the curve are the same distance from the center.
5. Using the displayed Polygon Chart, review the definition of a polygon.
Ask:
*Is a circle a polygon? (no) Explain. (It is curved; it does not have straight
sides.)
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
*Is an oval a polygon? (no) Explain. (It is curved; it does not have straight
sides.)
*Is an oval a circle? (no) Explain. (In an oval, not all points are the same
distance from the center.)
6. Using the displayed Not a Polygon Chart, write the word “Circle” and draw a picture
of a circle next to the word.
Ask:
*How could you define circle? (A circle is a closed, curved figure where all
points are the same distance from the center.)
7. Using the displayed Not a Polygon Chart, write the word “Oval” and draw a picture
next to the word.
Ask:
*How could you define oval? (An oval is a closed, curved figure where all
points are not the same distance from the center.)
8. Instruct students to return to their seats and distribute handout: Shape Detective to
each student. Instruct students to determine if each figure is a circle or an oval. Allow
time for students to complete the activity. Monitor and assess students to check for
understanding.
9. Display teacher resource: Shape Detectives. Facilitate a class discussion
regarding student responses.
Ask:
*What strategy did you use to prove whether the figure was a circle or an
oval? Answers may vary. I drew several lines from the center of the circle to
the side in different places, then compared the lines to see if they are the
same; I used a piece of string that is the length of the distance from the center
to the curved line, then used it to measure all the different points on the circle;
etc.
10. Using the displayed Polygon Chart, write “Types of Polygons” under the
polygons definition.
11. Display a geoboard for the class to see. Distribute a geoboard and a rubber
band to each student. Instruct students to use the rubber band and the
geoboard to create a three-sided polygon. Allow time for students to create
their figure. Using the displayed geoboard, model one three-sided polygon
figure for the class to see.
12. Reference the polygon definition on the Polygon Chart.
Ask:
*Is your figure a polygon? (yes) Explain. Answers may vary. It is closed, it
has at least 3 sides, the sides are straight; it is not open and does not have
any curved parts; etc.
*The polygon you created has how many sides? (3 sides)
Instruct the class to chorally count the vertices as they touch each side of
their figure on their geoboard.
*The polygon you created has how many vertices? (3 vertices)
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
Instruct the class to chorally count the vertices as they touch each vertex of
their figure on their geoboard.
*What is the name of the polygon you created? (triangle)
*How could you define a triangle? (A triangle is a polygon with 3 sides and
3 vertices.)
13. Write “Triangle” on the Polygon Chart and record its definition. Invite student
volunteers to display their created triangle on their geoboard for the class to
see. Each time a different type of triangle is presented, draw it on the Polygon
Chart next to the word Triangle”. On one triangle, write side for each line
segment of the figure and the “vertex” where each side or line segment
touched another side or line segment.
14. Distribute handout: Notes & Practice-Polygons to each student. Instruct
students to find the examples of triangles on their handout: Notes & PracticePolygons. Using the displayed teacher resource: Notes & PracticePolygons, model for the students how to record “Triangle” under the column
“Type of Polygon” and how to record the number of sides and the number of
vertices for a triangle.
15. Instruct students to remove the triangle from their geoboard. Distribute a
second rubber band to students. Instruct the students to use their geoboard
and their two rubber bands to create two different four-sided polygons (one
rubber band per polygon). Allow time for students to create their figures.
Using the displayed geoboard, model one four-sided figure for the class to
see.
16. Reference the polygon definition on the Polygon Chart.
Ask:
*Are your figures polygons? (yes) Explain. Answers may vary. They are
closed, they have straight sides, and they have at least three sides; etc.
*Each polygon you created has how many sides? (4 sides)
Instruct the class to chorally count the sides as they touch each side of their
quadrilateral.
*Each polygon you created has how many vertices? (4 vertices)
Instruct the class to chorally count the vertices as they touch each vertex of
their quadrilaterals.
*How are the two figures you created alike? (They 4 sides and 4 vertices.)
*How are the two figures you created different? Answers may vary. The
sides on one figure are all the same length, and the sides on the other figure
are not all equal; one figure has a side that slants, and the other figure has
straight up and down sides; etc.
*What type of polygons are these? Answers may vary. Square; rectangle;
rhombus; etc.
Ask:
*How could we define a square, rectangle or rhombus? (A square, a
rectangle or rhombus is a polygon with 4 sides and 4 vertices.)
Tell the students that there are differences in these four-sided polygons. In
tomorrow’s lesson we will look at and define the differences in each of these
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Grade 02
Unit 04: Two-and Three-Dimensional Figures
polygons attributes.
17. Write “square”, “rectangle” and “rhombus” on the Polygon Chart and record its
definition. Invite student volunteers to display their created 4-sided polygon
on their geoboard for the class to see. On one of the four-sided polygons,
write “side” for each line segment of the figure and “vertex” where each side
or line segment touches another side or line segment.
18. Instruct students to find the examples of a square, rectangle and rhombus on
their handout: Notes & Practice-Polygons. Using the displayed teacher
resource: Notes & Practice-Polygons, model for students how to record
square, rectangle, rhombus under the column “Type of Polygon” and how to
record the number of sides and number of vertices for a four-sided polygon.
19. Instruct students to remove the four-sided polygon from their geoboard.
Instruct students to use one rubber band and their geoboard. Instruct
students to use on rubber band and the geoboard to create a five-sided
polygon. Allow time for students to create their figure. Using the displayed
geoboard, model one five-sided figure for the class to see.
20. Reference the polygon definition on the Polygon Chart.
Ask:
*Is your figure a polygon? (yes) Explain. Answers may vary. It is closed, it
has at least 3 sides, the sides are straight; it is not open and does not have
any curved parts; etc.
*The polygon you created has how many sides? (5 sides)
Instruct the class to chorally count the sides as they touch each side of their
figure on their geoboard.
*The polygon you created has how many vertices? (5 vertices)
Instruct the class to chorally count the vertices as they touch each vertex of
their figure on their geoboard.
*What is the name of the polygon you created? (pentagon)
*How could you define pentagon? (A pentagon is a polygon with 5 sides
and 5 vertices.)
21. Write “Pentagon” on the Polygon chart and record its definition. Invite student
volunteers to display their created pentagon on their geoboard for the class to
see. Each time a different type of pentagon is presented, draw it on the
Polygon Chart next to the word “Pentagon”. On one pentagon, write “side” for
each line segment of the figure and “vertex” where each side or line segment
touches another side or line segment.
22. Instruct students to find the examples of pentagons on their handout: Notes
& Practice-Polygons. Using the displayed teacher resource: Notes &
Practice-Polygons, model for the students how to record “Pentagon” under
the column “Type of Polygon” and how to record the number of sides and
number of vertices for a pentagon.
23. Instruct students to remove the pentagon from their geoboard. Instruct
15
Grade 02
Unit 04: Two-and Three-Dimensional Figures
students to use one rubber band and the geoboard to create a six-sided
polygon. Allow time for students to create their figure. Using the displayed
geoboard, model one six-sided figure for the class to see.
24. Reference the polygon definition on the Polygon Chart.
Ask:
*Is your figure a polygon? (yes) Explain. Answers may vary. It is closed, it
has at least 3 sides, the sides are straight; it is not open and does not have
any curved parts; etc.
*The polygon you created has how many sides? (6 sides)
Instruct the class to chorally count the sides as they touch each side of their
figure on their geoboard.
*The polygon you created has how many vertices? (6 vertices)
*What is the name of the polygon you created? (hexagon)
*How could you define hexagon? (A hexagon is a polygon with 6 sides and
6 vertices.)
25. Write “Hexagon” on the Polygon chart and record its definition. Invite student
volunteers to display their created hexagon on their geoboard for the class to
see. Each time a different type of hexagon is presented, draw it on the
Polygon Chart next to the word “Hexagon”. On one hexagon, write “side” for
each line segment of the figure and “vertex” where each side or line segment
touches another side or line segment.
26. Instruct students to find the examples of hexagons on their handout: Notes &
Practice-Polygons. Using the displayed teacher resource: Notes &
Practice-Polygons, model for the students how to record “Hexagon” under
the column “Type of Polygon” and how to record the number of sides and
number of vertices for a hexagon.
27. Instruct students to remove the hexagon from their geoboard. Instruct
students to use one rubber band and the geoboard to create a seven-sided
polygon. Allow time for students to create their figure. Using the displayed
geoboard, model one seven-sided figure for the class to see.
28. Reference the polygon definition on the Polygon Chart.
Ask:
*Is your figure a polygon? (yes) Explain. Answers may vary. It is closed, it
has at least 3 sides, the sides are straight; it is not open and does not have
any curved parts; etc.
*The polygon you created has how many sides? (7 sides)
Instruct the class to chorally count the sides as they touch each side of their
figure on their geoboard.
*The polygon you created has how many vertices? (7 vertices)
Instruct the class to chorally count the vertices as they touch each vertex of
their figure on their geoboard.
*What is the name of the polygon you created? (heptagon)
*How could you define heptagon? (A heptagon is a polygon with 7 sides
and 7 vertices.)
16
Grade 02
Unit 04: Two-and Three-Dimensional Figures
29. Instruct students to find the examples of heptagons on their handout: Notes
& Practice-Polygons. Using the displayed teacher resource: Notes &
Practice-Polygons, model for the students how to record “heptagon” under
the column “Type of Polygon” and how to record the number of sides and
number of vertices for an heptagon.
30. Instruct students to remove the heptagon from their geoboard. Instruct
students to use one rubber band and the geoboard to create an eight-sided
polygon. Allow time for students to create their figure. Using the displayed
geoboard, model one eight-sided figure for the class to see.
31. Reference the polygon definition on the Polygon Chart.
Ask:
*Is your figure a polygon? (yes) Explain. Answers may vary. It is closed, it
has at least 3 sides, the sides are straight; it is not open and does not have
any curved parts; etc.
*The polygon you created has how many sides? (8 sides)
Instruct the class to chorally count the sides as they touch each side of their
figure on their geoboard.
*The polygon you created has how many vertices? (8 vertices)
Instruct the class to chorally count the vertices as they touch each vertex of
their figure on their geoboard.
*What is the name of the polygon you created? (octagon)
*How could you define octagon? (A octagon is a polygon with 8 sides and 8
vertices.)
Write “Octagon” on the Polygon chart and record its definition. Invite
student volunteers to display their created octagon on their geoboard for the
class to see. Each time a different type of octagon is presented, draw it on
the Polygon Chart next to the word “octagon”. On one octagon, write “side”
for each line segment of the figure and “vertex” where each side or line
segment touches another side or line segment.
32. Instruct students to find the examples of octagons on their handout: Notes &
Practice-Polygons. Using the displayed teacher resource: Notes &
Practice-Polygons, model for the students how to record “Octagon” under
the column “Type of Polygon” and how to record the number of sides and
number of vertices for an octagon.
33. Instruct students to remove the octagon from their geoboard. Instruct
students to use one rubber band and the geoboard to create a nine-sided
polygon. Allow time for students to create their figure. Using the displayed
geoboard, model one nine-sided figure for the class to see.
34. Reference the polygon definition on the Polygon Chart.
Ask:
*Is your figure a polygon? (yes) Explain. Answers may vary. It is closed, it
has at least 3 sides, the sides are straight; it is not open and does not have
17
Grade 02
Unit 04: Two-and Three-Dimensional Figures
any curved parts; etc.
*The polygon you created has how many sides? (9 sides)
Instruct the class to chorally count the sides as they touch each side of their
figure on their geoboard.
*The polygon you created has how many vertices? (9 vertices)
Instruct the class to chorally count the vertices as they touch each vertex of
their figure on their geoboard.
*What is the name of the polygon you created? (nonagon)
*How could you define nonagon? (A nonagon is a polygon with 9 sides and
9 vertices.)
35. Write “Nonagon” on the polygon chart and record its definition. Invite student
volunteers to display their created nonagon on their geoboard for the class
to see. Each time a different type of nonagon is presented, draw it on
the Polygon Chart next to the word “nonagon”. On one nonagon, write “side”
for each line segment of the figure and “vertex” where each side or line
segment touches another side or line segment.
36. Instruct students to find the examples of nonagons on their handout: Notes &
Practice-Polygons. Using the displayed teacher resource: Notes &
Practice-Polygons, model for the students how to record “nonagon” under
the column “Type of Polygon” and how to record the number of sides and
number of vertices for a nonagon.
37. Instruct students to remove the nonagon from their geoboard. Instruct
students to use one rubber band and the geoboard to create a ten-sided
polygon. Allow time for students to create their figure. Using the displayed
geoboard, model one ten-sided figure for the class to see.
38. Reference the polygon definition on the Polygon Chart.
Ask:
*Is your figure a polygon? (yes) Explain. Answers may vary. It is closed, it
has at least 3 sides, the sides are straight; it is not open and does not have
any curved parts; etc.
*The polygon you created has how many sides? (10 sides)
Instruct the class to chorally count the sides as they touch each side of their
figure on their geoboard.
*The polygon you created has how many vertices? (10 vertices)
Instruct the class to chorally count the vertices as they touch each vertex of
their figure on their geoboard.
*What is the name of the polygon you created? (decagon)
*How could you define decagon? (A decagon is a polygon with 10 sides
and 10 vertices.).
39. Write “Decagon” on the polygon chart and record its definition. Invite student
volunteers to display their created decagon on their geoboard for the class
to see. Each time a different type of decagon is presented, draw it on
18
Grade 02
Unit 04: Two-and Three-Dimensional Figures
the Polygon Chart next to the word “decagon”. On one decagon, write “side”
for each line segment of the figure and “vertex” where each side or line
segment touches another side or line segment.
40. Instruct students to find the examples of nonagons on their handout: Notes &
Practice-Polygons. Using the displayed teacher resource: Notes &
Practice-Polygons, model for the students how to record “decagon” under
the column “Type of Polygon” and how to record the number of sides and
number of vertices for an decagon.
41. Instruct students to remove the decagon from their geoboard. Instruct
students to use one rubber band and the geoboard to create an eleven-sided
polygon. Allow time for students to create their figure. Using the displayed
geoboard, model one eleven-sided figure for the class to see.
42. Reference the polygon definition on the Polygon Chart.
Ask:
*Is your figure a polygon? (yes) Explain. Answers may vary. It is closed, it
has at least 3 sides, the sides are straight; it is not open and does not have
any curved parts; etc.
*The polygon you created has how many sides? (11 sides)
Instruct the class to chorally count the sides as they touch each side of their
figure on their geoboard.
*The polygon you created has how many vertices? (11 vertices)
Instruct the class to chorally count the vertices as they touch each vertex of
their figure on their geoboard.
*What is the name of the polygon you created? (undecagon)
*How could you define undecagon? (A undecagon is a polygon with 11
sides and 11 vertices.).
43. Write “undecagon” on the polygon chart and record its definition. Invite
student volunteers to display their created undecagon on their geoboard for
the class to see. Each time a different type of undecagon is presented, draw it
on the Polygon Chart next to the word “undecagon”. On one undecagon,
write “side” for each line segment of the figure and “vertex” where each side or
line segment touches another side or line segment.
44. Instruct students to find the examples of undecagons on their handout: Notes
& Practice-Polygons. Using the displayed teacher resource: Notes &
Practice-Polygons, model for the students how to record “undecagon” under
the column “Type of Polygon” and how to record the number of sides and
number of vertices for an undecagon.
45. Instruct students to remove the undecagon from their geoboard. Instruct
students to use one rubber band and the geoboard to create an twelve-sided
polygon. Allow time for students to create their figure. Using the displayed
geoboard, model one twelve-sided figure for the class to see.
19
Grade 02
Unit 04: Two-and Three-Dimensional Figures
46. Reference the polygon definition on the Polygon Chart.
Ask:
*Is your figure a polygon? (yes) Explain. Answers may vary. It is closed, it
has at least 3 sides, the sides are straight; it is not open and does not have
any curved parts; etc.
*The polygon you created has how many sides? (12 sides)
Instruct the class to chorally count the sides as they touch each side of their
figure on their geoboard.
*The polygon you created has how many vertices? (12 vertices)
Instruct the class to chorally count the vertices as they touch each vertex of
their figure on their geoboard.
*What is the name of the polygon you created? (dodecagon)
*How could you define dodecagon? (A dodecagon is a polygon with 12
sides and 12 vertices.).
47. Write “dodecagon” on the polygon chart and record its definition. Invite
student volunteers to display their created dodecagon on their geoboard for
the class to see. Each time a different type of dodecagon is presented, draw it
on the Polygon Chart next to the word “dodecagon”. On one undecagon,
write “side” for each line segment of the figure and “vertex” where each side or
line segment touches another side or line segment.
48. Instruct students to find the examples of dodecagons on their handout: Notes
& Practice-Polygons. Using the displayed teacher resource: Notes &
Practice-Polygons, model for the students how to record “dodecagon” under
the column “Type of Polygon” and how to record the number of sides and
number of vertices for an dodecagon.
49. Distribute handout: All About Figures to each students. Explain to students
that they are to determine if each shape is a polygon by answering the
questions. Allow time for students to complete the activity. Facilitate a class
discussion to debrief handout: All About Figures.
What’s the teacher doing?
What are the student’s doing?
*Leading class discussion.
*Using manipulatives correctly.
*Setting expectations for the
*Verbally participating and recording on
manipulatives that are being used
their information sheets.
*Monitor and assess students checking
for understanding.
Phase Explore/Explain
Materials:
 chart paper (1 sheet per teacher)
 scissors (1 per teacher)
 index card (1 per student, 1 per
teacher)
 markers (2 different colors) (1 set per
Handouts:
Handout: Corner Checkers (1 per class)
Teacher Resource: Four-Sided Figures
(1 per teacher)
 Handout: Four-Sided Figures (1 per
student)


20
Grade 02
Unit 04: Two-and Three-Dimensional Figures
student, 1 set per teacher)
 Polygon Chart (1 per teacher)
(previously created)





Teacher Resource: Opposite Box (1 per
teacher)
Teacher Resource: Four-Sided Figures
KEY (1 per teacher)
Teacher Resource: Four-Sided Figures
(1 per teacher)
Handout: Four-Sided Figures (1 per
student)
Teacher Resource: Rooms for Rent
KEY (1 per teacher)
Handout: Rooms for Rent (1 per
student)
Day 3 Activity:
Students explore squared corners and other attributes of four-sided polygons.
Prior to instruction, create a corner checker for each student and each teacher by
copying handout Corner Checkers, and cutting each square with precision. Also
create a chart labeled Four-Sided Figures
Activity:
1. Distribute handout: Special Four-Sided Figures and one index card to each
student.
Display teacher resource: Special Four-Sided Figures.
Ask:
*Are all these figures polygons? (yes) Explain. (They all have straight sides,
no curves, at least three sides, and are all closed.)
*What do all of these polygons have in common? (They all have 4 sides
and 4 vertices.)
*What is the name of each four-sided presented? (rectangle, rhombus, and
square)
Turn and Talk- Tell the students they are going to turn and talk to their shoulder
neighbor about this question:
*How are these four-sided figures different? Answers may vary. The length
of their sides is different; some sides are slanted and some sides are straight;
etc.
Allow time for students to observe the differences among the figures. Listen carefully
to the descriptive language used by the students.
On the Four-Sided Figures chart, write the name of each figure along with a drawing
of each figure. Leave space for the definitions to be added after the students have
explored each figure. Instruct the students to record the name of each figure on their
handout: Special Four-Sided Figures, in the center of each figure.
Say:
Today you will explore how these figures are different. One of the
differences is the length of the sides. The “length of the sides” is an additional
attribute for identifying special four-sided figures. In order to discuss the
lengths of the sides, the definition of opposite will need to be discussed.
2. Display teacher resource: Opposite Box.
21
Grade 02
Unit 04: Two-and Three-Dimensional Figures
Ask:
*What object is on the opposite side of the cat? (the hat)
*What object is on the opposite side of the rat? (the bat)
*What does it mean to be on the opposite side? Answers may vary. To be
directly across from each other; etc.
Demonstrate how opposite sides do not share a common vertex.
3. Instruct the students to observe the square on handout: Special Four-Sided
Figures. Model placing and index card beside the square on handout: Special
Four-Sided Figures and marking the position of the two vertices of the square
to indicate the length of the side as each student models the same.
Example:
4. Instruct students to compare the length of the opposite side to the measured
side of the first figure by moving the index card to the opposite side of the figure
and comparing lengths.
Ask:
*Is the opposite side of the figure the same length? (yes)
Model outlining the opposite sides that are the same length with a marker as each
student models the same.
Ask:
*Do you think the other sides of the figure are the same length as the
outlined sides? (yes)
Model comparing the other lengths of the figure with the marked on the index card to
confirm that all sides are equal in length. Allow time for students to measure and
verify the lengths. Once students have confirmed that all sides are equal in length,
instruct them to outline the square on their handout: Special Four-Sided Figures.
5. Instruct students to determine which sides of each four-sided figures on their
handout: Special Four-Sided Figures are equal in length. Remind students
to use their index card to first check on set of opposite sides of a four-sided
figure by placing their index card next to one of the sides and marking the
length, the comparing it to the length of the opposite side. If opposite sides are
equal, students are to outline the two opposite sides with the same color
marker.
22
Grade 02
Unit 04: Two-and Three-Dimensional Figures
Instruct students
to repeat this process for the other set of
opposite sides on
the figure. If the
other set of sides are equal in length but not
the same length
as the first set of sides, students are to mark those sides using a different color
marker.
Example:
6. Allow time for students to compare their handout. Monitor and assess students
to check for understanding. Facilitate a class discussion to debrief students
findings. As each figure is discussed, record the defining attribute of sides for
each four-sided figure on Four-Sided Figures chart.
Ask:
*What did you discover about the lengths of the sides on the rectangle?
(opposite sides are always equal in length)
*What did you discover about the lengths of the sides on the rhombus?
(all sides are always equal in length)
*What did you discover about the lengths of the sides on the square? (all
sides are always equal in length)
Explain that the length of the sides is an attribute that helps to identify the differences
between four-sided figures.
*Are there any figures that are defined exactly the same based on their
sides?
Which ones? (yes; rhombus and square)
7. Distribute a Corner Checker to each student. Explain to the students that all
corners of this figure represent a “square corner”. Model for students how to
place a small mark or star using a marker in one of the square corners of the
Corner Checker as each student models the same. Explain to students that to
help distinguish between a rhombus and a square, another attribute regarding
corners is needed.
8. Divide the class into four equal groups. Assign each group a corner of the
room in which to stand. Explain that the corner, where two sides of the floor
meet in the room, is similar to a vertex, where two sides meet on a figure.
Instruct students to take turns using their Corner Checker to determine if the
corner of the room where they are standing in is a square corner.
Ask:
*Does the Corner Checker “fit” in your corner of the room? (yes) How do
you know? Answers may vary. When I slid the marker corner of my Corner
of the wall, the sides of my Corner Checker also lined up against the wall; the
Corner Checker fit perfectly into the corner like a puzzle piece; etc.
Explain that although some walls or sides may be angled or slanted, most rooms have
“square corner.”
9. Instruct students to return to their seats. Refer students to handout: FourSided Figures. Instruct students to use their Corner Checker to
23
Grade 02
Unit 04: Two-and Three-Dimensional Figures
determine which figures have “square corner”. Explain to students that when
they find a square corner on the figure, they are to place a small mark or star
(like the one on their Corner Checker) in the corner of the figure. Allow
students time to complete the activity. Monitor and assess students to check
for understanding.
Ask:
*Which figure did you determine have square corners? (the rectangle and
the square)
*How many square corners does a rectangle and a square have? (4)
Explain to the students that a rectangle and a square will “always” have 4
square corners. Add the attribute “all square corners” under the definition of
rectangle and square on the displayed Four-Sided Figures Chart.
10. Place students in pairs. Distribute handout: Four-Sided Figures to
each student. Display teacher resource: Four-Sided Figures
Explain to the students how to complete the handout by reviewing the
completed row. Instruct students to work with their partner to
complete the handout. Allow time for students to complete the activity.
Monitor and assess students to check for understanding. Facilitate a
class discussion to debrief the handout.
11. Reference the displayed Four-Sided Figures chart.
Ask:
*What is the definition of a rectangle? (A rectangle is a polygon with 4 sides,
4 vertices, and opposite sides that are always equal in length)
*Are all of the attributes of a rectangles also attributes of a square? (yes)
*Why do you think the square is referred to as “a special types of
rectangle”? (Because a square is a polygon with 4 sides and 4 vertices, and
opposite sides are always equal in length just like the rectangle.)
*What makes the square different from the rectangle? (A square has a
special attribute—all 4 sides are always equal in length)
*Do all of the attributes of a square hold true for a rectangle? (no) Explain.
(The rectangle does not have all four sides equal in length. Only opposite
sides are always equal in length.)
*Can we say a rectangle is a special square? (no) Why? (All 4 sides of the
rectangle are not equal in length.)
*What is the special relationship between a rectangle and a square? (A
square is a special type of rectangle.)
12. Distribute handout: Room for Rent. Explain to students that the figures
represent different shaped rooms. Instruct students to answer all questions
regarding each figure. They may use their index cards to check side lengths
and their Corner Checker when asked about square corners. Allow students
time to complete the handout. Monitor and assess students to check for
understanding. Debrief and discuss the handout at the end of class or the
following day.
24
Grade 02
Unit 04: Two-and Three-Dimensional Figures
What’s the teacher doing?
What are the students doing?
*Leading class discussion
*Modeling and explaining what the
students should be doing.
*Monitoring and assessing students
work.
*Participating in the class discussion.
*Using manipulatives correctly.
Phase Explore/Explain





Materials:
chart paper
construction paper cut in 9 inch
strips, each strip a half inch wide
tape
scissors
glue stick



Handouts:
Teacher Resource: Regular and
Irregular Triangles (1 copy per
teacher) (cut out the shapes)
Handout: Regular and Irregular
Figures each student (1 copy per
student)
Handout:: Sorting Regular and
Irregular Figures(1 copy per student)
Day 4 Activity:
T-Chart using chart paper and write Regular Figures and Irregular Figures at the top of
chart drawing or leaving lines define each. Display the T-Chart next to the displayed
Polygon Chart for the class to see.
Regular Figures
______________
_____________
Irregular Figures
_____________
_____________
25
Grade 02
Unit 04: Two-and Three-Dimensional Figures
Activity:
1. Tell the students that we have learned the names of polygons with 3-12 sides
(refer the Polygon Chart).
Tell the students they are going to Turn and Talk with their shoulder neighbor
about the polygons we have learned. They should name a polygon and tell
how many sides it has.
2. Tell them that now we are going to define how figures with the same amount of
sides can be sorted into Regular Figures or Irregular Figures (refer to the TChart).
Display the two triangle figures from teacher resources (separate from the TChart): Regular and Irregular Triangles.
Ask:
*Do the triangles look alike? (Yes)
*How do the triangles look alike? (They both have three sides)
*How do the triangles look different? (They are shaped different, there sides
are different lengths)
Have a student come up and use strips of construction paper to hold on each
line of the first triangle and make a fold with each strip where the line of each
side ends then snip each fold line. Hold the strips together and ask if the lines
look the same length.
Ask:
*Are the strips of construction paper the same length? (yes)
Complete the same procedure with the second triangle.
Ask:
* Are the strips of construction paper the same length? (no)
Tell the students that this information we have just gathered will help us define
Regular and Irregular Figures.
Ask:
*Does anyone know how we could define Regular and Irregular Figures
with the information we just gathered about the triangles? (The sides of
Regular Figures all have the same length and the sides of Irregular Figures do
not have the same length.)
3. Distribute Handout: Regular and Irregular Figures
Write the definitions on the Regular and Irregular Figures Chart. The
students should also copy the definitions on their handout.
Then have a student come up and tape the regular triangle on the Regular side
of the T-Chart and the regular triangle on the Irregular side of the T-Chart.
4. Distribute the handout: Sorting Regular and Irregular Figures
Have the students work with a partner to first count the sides of each figure and
record the number on the each of the figures then they should compare the
figures that have the same amount of sides to decide which one is regular and
irregular.
Then they should glue down each shape on the correct side of the T-Chart.
Remind the students that they should be referring to the definition they wrote
26
Grade 02
Unit 04: Two-and Three-Dimensional Figures
on the T-Chart page.
5. When most of the students are finished sorting the figures on their T-Chart, bring
them back together and go over which figures were regular and which figures
were irregular. Students should make corrections as needed.
What’s the teacher doing?
What are the students doing?
*Leading the discussion
*Participating in the class discussion.
*Counting and labeling the sides of
figures.
*Communicating with their partner when
sorting the figures.
*Rotating to each paired group to check
for understanding.
Phase Explore/Explain











Materials:
geoboard (commercial) (1 per
student)
rubber bands (1 per student)
glue (1 per student)
notebook paper (1 sheet per student)
Polygon Chart (1 per teacher)
(previously created)
Four-Sided Figures Chart (1 per
teacher) (previously created)
cardstock (3 sheets per 8 students)
scissors (1 per student, 1 per teacher)
ruler or straight edge (1 per student)
pencil (1 per teacher)
paper (plain) (1 sheet per student)
Handouts:
Teacher Resource: Parallelograms (1
sheet per 8 students)
 Teacher Resource: Grandma’s Problem
KEY (1 per teacher)
 Handout: Grandma’s Problem (1 per
student)
 Teacher Resource: Grandma’s Scraps
(1 sheet per 4 students)

Day 5 Activity:
Prior to instruction, create 1 rectangle for each student and teacher by copying teacher
resource: Rectangles on cardstock and cutting apart. Also, create 2 triangles for each
student by copying teacher resource: Grandma’s Scraps on cardstock and cutting
apart.
Students will be:
Decomposing and composing two-dimensional figures.
27
Grade 02
Unit 04: Two-and Three-Dimensional Figures
Activity:
1. Distribute a geoboard and a rubber band to each student. Instruct students to
create a rectangle using the rubber band and geoboard. Allow time for
students to complete their rectangle. Invite student volunteers to display
their created rectangle on their geoboard for the class to see.
Turn and Talk: Have the students turn and talk to their shoulder neighbor about their
rectangle. Have them each tell how they know that their figure is a rectangle
Ask:
*Is your rectangle a polygon? (yes) Explain. Answers may vary. The
figure is closed, it has at least 3 sides, and does not have any curved figures;
etc.
*How can you verify that you created a rectangle? (There are 4 vertices
and all corners are square. There are 4 sides and opposite sides are equal in
length. I could measure the sides to make sure that opposite sides are equal in
length. I could use our Corner Checker to make sure all four corners are
squares.)
Instruct students to re-position the rubber band from their rectangle to
form a square.
*How did you reposition the rubber band to create a square from a
rectangle? (I had to make sure that all four sides were of equal length.)
*How can you verify that you created a square? (There are 4 vertices and all
corners are square. There are 4 equal sides. I could measure the sides to
make sure that all sides are equal in length. I could use our Corner Checker to
make sure all four corners are squares.)
Instruct students to re-position the rubber band from their square to
form a rhombus.
*How did you reposition the rubber band to create a rhombus from a
square? (I had to make sure that all four sides were of equal length.)
*How can you verify that you created a rhombus? (There are 4 vertices, 4
sides, and all sides are equal in length. I could measure the sides to make sure
that all sides are equal in length.)
2. Instruct students to create a square on the geoboard. Instruct students to lay their
pencil on the geoboard to divide the four-sided polygon into two different twodimensional figures. Model a square with the pencil dividing the figure on the board for
the students to see.
Example:
28
Grade 02
Unit 04: Two-and Three-Dimensional Figures
pencil
Ask:
*What figures did you create? (I created 2 triangles.) Explain. Answers may
vary. I know they are triangles because they are three sided polygons; etc.
Referencing the displayed Polygon Chart, verify the newly created figure
according to the recorded attributes.
*Can you divide the square another way to create two different figures?
Answers may vary. Referencing the displayed Polygon Chart, verify the name
of the newly created figure according to the recorded attributes.
3. Distribute a pair of scissors, 1 rectangle, and 1 sheet of paper to each
student. Instruct students to cut the rectangle in any direction; however,
the cut must be straight. Allow time for students to decide how to cut their
parallelogram. When students have completed the task, instruct them to glue
the two newly created figure on a sheet of paper and identify each newly
created figure according to its attribute. If necessary, students may reference
the displayed Polygon Chart or Four-Sided Figures Chart for polygon
name and attributes.
Example:
Ask:
* What two figures did you create? Answers may vary. I made 2 rectangles;
1 triangle and 1 four-sided figure; etc.
* Are the newly created figures polygons? (yes)
* When cutting a polygon with a straight line, will the new figure always
be polygons? (yes) Explain. (You will never get a curved surface with a
straight cut; the new figures will still be closed; they will have three or more
sides.)
* If you took a curved surface and cut it with a straight line, will the new
figures be polygons? (no) Explain. (The other side where the cut was not
made will still be curved.)
4. Distribute handout: Grandma’s Problem, 2 triangles, and a ruler or straight
29
Grade 02
Unit 04: Two-and Three-Dimensional Figures
edge to each student. As a class, chorally read the problem on the handout.
Instruct students to use their scissors and ruler or straight edge to make
straight cuts on the triangles to create new polygons. Instruct students to glue
and identify the name of the newly created figures on the handout: Grandma’s
Problem, in the space provided. Instruct students to verify the newly created
figures according to their attributes. If necessary, students may reference the
displayed Polygon Chart or Four-Sided Figures Chart for polygon
name and attributes.
What’s the teacher doing?



Modeling expectations.
Leading class discussion.
Monitoring students.
What are the students doing?



Using manipulatives correctly.
Following instructions.
Cutting, gluing and naming new
figures.
Phase One: Engage

Materials:
Captain Invincible and the
Space Shapes by Stuart J.
Murphy (story can also be found
on YouTube)

Handouts:
Three-Dimensional Figures (1 per 4
students) *optional if geometric
solids are not available.
http://www.youtube.com/watch?v=r6x4VLjYyBk





Teacher Tipster: 3D Shapes
Song (for teacher to watch)
3D Shapes Song Lyrics
3D Shapes: sphere, cone,
cylinder, rectangular prism, cube,
and triangular prism
Cardstock, tape, scissors
(*optional if assembling ThreeDimensional Figures)
Riddle Cards
Day 6 Activity:
Prior to Instruction:
If geometric solids are not available, assemble Three-Dimensional Figures (1 per 4
students). Watch Teacher Tipster on 3D Shapes Song.
Instructional Procedures:
1. Bring students together on the carpet and introduce three-dimensional figures with
the book, Captain Invincible and the Space Shapes by Stuart J. Murphy. If book is
not available, the story can be found on YouTube. When reading the story, stop and
30
Grade 02
Unit 04: Two-and Three-Dimensional Figures
point at the different geometrical solids on the pages. Name each one and ask if
students can see other shapes in the pictures.
2. Divide students into groups of 3 – 4. Distribute, Three-Dimensional Figures to
each group and allow them about a minute to discuss and explore each shape.
3. Bring class back together and hold up models of solid figures, one at a time, and
ask students to name each figure. Ask students:
 What descriptive words would help you identify the objects? Possible
answers: round, flat, edges, points, sides
 How could you identify each object without seeing? Possible answers:
feeling or hearing a description of its shape.
 Which shape has the most faces? Cube, rectangular prism
 What two solids are most alike? Cube, rectangular prism
 How are cylinders and cones alike and different? Possible answers: alikeone curved surface, at least 1 flat surface shaped like a circle. Difference– a
cone has 1 vertex and a cylinder has none. A cone has 1-flat surface and a
cylinder has 2.
 Which shapes have six vertices? triangular prism
4. Display and discuss real-world objects shaped like solid figures such as a tissue
box is a rectangular prism and a thermos is a cylinder.
5. Display the 3-D Shapes Song lyrics and teach the students the song with the
geometric figures and hand movements.
6. Close the activity by using riddles cards with vocabulary words from the unit to see
if students can identify the 3-D shape.
What’s the teacher doing?
 Introducing 3-D Shapes through a
story, song, and models.
 Uses vocabulary words to
describe and identify the objects.
 Uses real-world objects shaped
like solid figures to connect
students to learning.
What are the students doing?
 Participating in class discussions
and answering questions.
 Learning the 3-D shapes song and
hand movements.
Phase Two: Explore/Explain



Materials:
Riddle Cards, 3-D shape cards,
and real-world object shaped like
the solid figures cards
Poster board and Velcro (optional)
“The Number Crew: Shape
Handouts:
31
Grade 02
Unit 04: Two-and Three-Dimensional Figures
Sorting” Video on discovery
education
https://app.discoveryeducation.com/sear
ch?Ntt=3D+shapes
Day 7 Activity:
Students will be playing a game with the riddle cards from the previous day to
determine the unknown solid figure and its real-world objects shaped like the solid
figures.
Optional: You may put Velcro behind each card and have students match it under the
correct category on a poster board.
Instructional Procedures:
1. Prior to instruction, copy and laminate 5 or 6 sets of cards for the game.
2. Watch a short 3D video, “The Number Crew: Shape Sorting” on discovery
education. After the video, review shapes with models and questions.
Show students the square and the cube shapes and ask the following question:
 Why do you think the cube is called a solid figure and the square is not?
Answers may vary. Because you can pick up the cube and feel all the sides or
faces, and the square is flat; the cube has an extra dimension that can be
measured; etc.
Show students a model of a rectangular prism and ask:
 How many faces does a rectangular prism have? Physically point to the
faces and count aloud. (6 faces)
 What shape do the faces make? (a rectangle or a square)
 Who can describe the number of faces and the type of each face for a
rectangular prism? (6 faces, 2 squares and 4 rectangles or 6 rectangles)
Show students a model of a cube and ask:
 Who can describe the number of faces and the type of each face for a
cube? (6 faces, 6 squares)
Show students a model of a triangular prism and ask:
 Who can describe the number of faces and the type of each face for a
triangular prism? (5 faces, 2 triangles and 3 rectangles)
Show students a model of a cylinder and ask:
 How could you describe the surfaces of a cylinder? (1 curved surface and 2
flat surfaces shaped like circles)
 What other shapes have curved surfaces? (cone and sphere)
Show students a model of a cone and ask:
 How could you describe the surfaces of a cone? (1 curved surface and 1
flat surface shaped like a circle)
 Is a circle a polygon? (no) Explain. (A circle is not a polygon because it does
not have three or more straight sides).
Show students a model of a sphere and ask:
 How could you describe the surfaces of a sphere? (1 curved surface)
32
Grade 02
Unit 04: Two-and Three-Dimensional Figures
3. After the review, students are placed in groups of 3 or 4 for the game. Distribute a
set of Riddle Card Game Activity to each student group. Allow time for students to
match the cards in the correct category.
4. Once students have finished arranging the cards, have them transfer the
information into their math journals. When students draw the shapes into their
journals, have them indicate the vertices with circles, edges with a highlighter and
faces with numbers.
5. At the end of the lesson, go over the activity with the students.
What’s the teacher doing?


Facilitate discussion and review
three-dimensional shapes using
media, models, questions and
hands-on activity.
Monitor and assist students as
they build their riddle card game
activity.
What are the students doing?




Participate in discussion and answer
questions from the three-dimensional
review.
Build and match the cards from the
Riddle Card Game Activity.
Write results from Riddle Card Game
Activity in math journal.
Work in teams of 3-4.
Phase Two: Explore/Explain
Materials:
Handouts:
Geometric solids (cube,
 3-D Shapes Table (1 per student)
triangular prism, rectangular
 3-D Shapes Table Key (1 per
prism)
teacher)
 Toothpicks
 Marshmallows or dots candy
 Straws or coffee stirrers
 Three-Dimensional Figures
Anchor Chart (previously
created)
Day 8 Activity:
Students will construct models of three-dimensional shapes using marshmallows or
dots candy and toothpicks. Using formal geometric language, students will identify
each solid and its attributes.

Instructional Procedures:
1. Place students in pairs. Distribute only one of the following three-dimensional solids
to each pair: a cube, triangular prism or a rectangular prism.
2. Say: Today you are architects. Your job is to create a model of the threedimensional figure at your table using toothpicks, straws, coffee stirrers, and
marshmallows/dots candy.
3. Explain to students that they are not to cut the toothpicks, straws, coffee stirrers,
marshmallows/dot candy, and they must use all the items they predict they will need.
33
Grade 02
Unit 04: Two-and Three-Dimensional Figures
Allow students time to discuss with their partner how many toothpicks, straws, coffee
stirrers, marshmallow/dots candy they predict they will need to build their threedimensional figure. When each pair decides, distribute the requested number to the
pair. Allow time for students to complete the construction of their model.
4. When all students have completed building their model, ask students to display their
three-dimensional figure and model.
Ask:
 How did you determine exactly how many items you needed to create
your figure? Answers may vary. We counted the number of sides and that is
how many toothpicks we needed, and we needed a marshmallow to connect
two toothpicks together. We counted the number of vertices to determine the
number of marshmallows, and counted the number of sides to guess the
number of toothpicks, etc.
Instruct students to place their finger on a toothpick, straw or coffee stirrer.
Ask:
 What part of the figure does the toothpick, straw or coffee stirrer
represent? (an edge)
Explain to students that this part of the shape represents the edges. Demonstrate how
the faces meet to create an edge.
Instruct students to place their finger on a marshmallow or dots candy:
Ask:
 What part of the figure does the marshmallow or dots candy represent?
(a vertex)
Explain to students that the marshmallows represent the vertices. Demonstrate how
two ends of the edges come together at the vertex (corner).
Ask:
 What part of the figure is not represented? Answers may vary. The sides of
the shape; the faces; etc.
5. Using the Three-Dimensional Anchor Chart, record the number of edges and
vertices of each figure. Invite a student pair that created a cube to display their model
and geometric solid.
34
Grade 02
Unit 04: Two-and Three-Dimensional Figures
Ask:

How many toothpicks, straws, or coffee stirrers did you need to make the
edges on a cube? (12 toothpicks, straws, coffee stirrers or edges)
 How many marshmallows or dots candy did you need to make the
vertices on this figure? (8 marshmallows, dots candy or vertices)
 The cube has how many faces? (6 faces)
 What are the shapes of the faces and how many of each type of face
create this figure? (6 squares)
 Does this figure have faces in any other shapes? (no)
 What is the name of this figure? (a cube)
 If this figure had a face that was not a square, would it still be a cube?
(no) Explain. Answers may vary. It could not be a cube because a cube has all
square faces; it could not be a cube because all square faces are an attribute
of a cube; etc.
6. Invite a student pair that created a triangular prism to display their model and
geometric solid.
Ask:
 How many toothpicks, straws, or coffee stirrers did you need to make the
edges on a cube? (9 toothpicks, straws, coffee stirrers or edges)
 How many marshmallows or dots candy did you need to make the
vertices on this figure? (6 marshmallows, dots candy or vertices)
 The cube has how many faces? (5 faces)
 What are the shapes of the faces and how many of each type of face
create this figure? (2 triangles and 3 rectangles)
 What is the name of this figure? (a triangular prism)
 If this figure had only triangular faces, would it still be a triangular prism?
(no) Explain. Answers may vary. It could not be a triangular prism because it
35
Grade 02
Unit 04: Two-and Three-Dimensional Figures
would not have rectangular faces; etc.
7. Invite a student pair that created a rectangular prism to display their model and
geometric solid.
Ask:
 How many toothpicks, straws, or coffee stirrers did you need to make the
edges on a rectangular prism? (8 toothpicks, 4 straws or coffee stirrers or 12
edges)
 How many marshmallows or dots candy did you need to make the
vertices on this figure? (8 marshmallows, dots candy or vertices)
 The rectangular prism has how many faces? (6 faces)
 What are the shapes of the faces and how many of each type of face
create this figure? (2 squares and 4 rectangles)
 What is the name of this figure? (a rectangular prism)
 If this figure had only square faces, would it still be a rectangular prism?
(no) Explain. Answers may vary. It could not be a rectangular prism because it
would not have rectangular faces; etc.
 How is a rectangular prism like a cube? (It has the same number of vertices
and edges.)
 How is a rectangular prism different from a cube? (The lengths of the
edges are not all the same on the rectangular prism; the cube has all edges the
same length.)
 What are the attributes of a rectangle? (Four square corners, 4 sides, and
opposite sides the same length.)
 What are the attributes of a square? (Four square corners, and all 4 sides
the same length)
8. Display a cone, cylinder, and a sphere.
Ask:
 Could you use toothpicks and marshmallows to create any of these
figures? (no) Explain. Answers may vary. These figures are circular; these
figures have curved surfaces; etc.
 How could you describe the surfaces of these figures? (A cone is made up
of 1 curved surface and 1 flat surface shaped like a circle; a cylinder is made up
of 1 curved surface and 2 flat surfaces shaped like a circle. A sphere made up
of 1 curved surface.)
9. Distribute handout: 3-D Shapes Table to each student. Explain to students that
they are to complete the table by listing the number of edges, vertices, and faces for
each figure. Instruct students to practice drawing three-dimensional figures by tracing
each three-dimensional figure on their handout several times. Then, instruct students
to draw each three-dimensional figure at the bottom of their handout.
What’s the teacher doing?
What are the students doing?
 Establishing norms and
 Predict the number and type of
expectations for constructing
material needed to build their solid
three-dimensional figures.
model.
 Facilitating discussions through
 Create solid model with a partner.
questioning strategy.
 Participate in classroom discussions.
36
Grade 02
Unit 04: Two-and Three-Dimensional Figures

Create a 3-D Shape Anchor
Chart with the students.
 Monitor and assist students as
they build their solid model and
complete their 3-D Shapes
Table.
Phase Three: Elaborate

Complete the 3-D Shapes Table
independently.
Materials:
Handouts:
 Tape (clear) (1 strip per student)
 Clue Sheet (1 per student)
 Scissors (1 per teacher)
 Card Set: What Am I? (1 set per
teacher)
 Plastic zip bag (1 per teacher)
 Clue Sheet KEY (1 per teacher)
 Pencil (1 per student)
Day 9 Activity:
Students observe two- and three-dimensional figures found in the real world and
identify the shapes by determining their attributes.
Instructional Procedures:
1. Prior to instruction, create a class card set: What Am I? by copying, laminating,
cutting apart, and placing in a plastic zip bag.
2. Display teacher resource: 3-D Shapes Table. Facilitate a class discussion to
debrief student responses on handout: 3-D Shapes Table by discussing similarities
and differences among the figures.
3. Explain to students that both two- and three-dimensional figures form our whole
world.
Ask:
 What three-dimensional figures do you think you would find least often in
the world? Explain. Answers may vary. I think cones, because not very many
things are in the shape of a cone; I think prisms because I never see them; etc.
 What two-dimensional figures do you think you would find most often in
the world? Explain. Answers may vary. Squares, rectangles and triangles
because they are used most in construction; etc.
Say:
 Today we will be playing a game in which each of you will have a picture
card taped to your back. You must guess the name of the threedimensional figure that the real-life object is representing by gathering
clues from other students. You may ask questions about the attributes of
their figure. You may not ask, “Is my object a rectangular prism?” You are
to record their clues on the handout: Clue Sheet, gathering at least 6
attribute clues before guessing your figure. When you guess correctly,
you may remove the picture from your back to see the real-life object.
4. Tape one card from the card set: What am I? on the back of each student.
Distribute handout: Clue Sheet to each student. Once every student has a card taped
on their back, instruct students to bring a pencil and begin asking clues regarding their
real-life object. Allow time for students to complete the activity. Monitor and assess
students to check for understanding. Once all students have determined their figure,
ask students to return to their seat.
37
Grade 02
Unit 04: Two-and Three-Dimensional Figures
Ask:

What questions were most helpful in determining your figure? Answers will
vary. The number vertices; the number of faces; does my figure have square
faces; etc.
 If attributes were not used to describe figures, how could you describe
the figure to your classmates? Explain. Answers may vary. It would be hard
because I might use a description that my classmate would not understand; I
would not know how to tell them what I saw; etc.
5. Place students in groups of 4. Explain to students that for the next game each group
will compete for points. The teacher will display a three-dimensional figure. Each
group will have approximately one minute to quietly discuss all of the attributes of the
figure. Select one student from each group to name one attribute for the displayed
figure. If the student is correct, the table group receives one point. Continue to ask
each table group to name one other attribute for the figure. If a student repeats a given
attribute or identifies an incorrect attribute, the table group does not receive a point.
When all table groups have had an opportunity to name an attribute of the figure, ask
the class to name the geometric figure. Continue playing the game by introducing a
different three-dimensional figure.
What’s the teacher doing?
 Setting clear expectations on
how to play the game, What am
I?
 Monitor and assess students to
check for understanding.
Phase Five: Evaluation





Materials:
A variety of commercial and realworld polygons
A variety of commercial and realworld three-dimensional figures
A variety of arts and crafts
supplies
Paper, pencil, scissors, glue, and
a sheet of poster-sized or manila
paper
A collection of uniform-sized
triangles, squares, and
rectangles and a set of unit
cubes
What are the students doing?
 Practice using attributes to describe
solid shapes.
 Participate in classroom discussions
and activities.

Handouts:
Performance Assessment #1 (1 per
student)
38
Grade 02
Unit 04: Two-and Three-Dimensional Figures
Day 10 Activity:
Prior to assessment, the teacher will provide the following for each of the following
tasks:
1. A variety of commercial and real-world polygons
2. A variety of commercial and real-world three-dimensional figures
3. A variety of arts and crafts supplies
4. Paper, pencil, scissors, glue, and a sheet of poster-sized or manila paper
5. A collection of uniform-sized triangles, squares, and rectangles and a set of
unit cubes
Students will be completing the Peformance Assessment #1
What’s the teacher doing?
 Setting clear expectations for
testing environment
 Walking around and monitoring
to check for understanding
 Answering any questions
students may have
What are the students doing?
 Completing Performance
Assessment #1
 Working quietly and independently
39