Lauren Coogle
Initial Planning Reflection
The lessons preceding my own dealt with SOL 2.15 – identifying a line of symmetry, and SOL 2.16 – identify plane and solid
geometric figures. Using geometric blocks, the students created shapes with the blocks, selected a line of symmetry, and then proceeded to
create the shape's mirror image. From observing the students, I noticed that many continued to struggle with the differences between 2D and
3D shapes. Some students were still referring to the sphere as a 'circle' or 'ball.' Cubes/squares were also being mixed up or referred to as
'boxes.'
I planned my lesson weeks before actually teaching it. My original ideas involved identifying shapes by known properties. My lesson
ideas asked questions like: “Given a shape with a given number of vertices, create as many different 2D shapes as you can using scissors and
paper,” or; “Given a shape with a certain number of edges, create as many 2D shapes as you can. For each different shape you create, note
how many vertices you have.”
After discussing my lesson ideas with the classroom teacher, she decided to target application of vocabulary when assessing
geometric figures. We agreed on a lesson where students named and described solid geometric figures using the terms: edges, faces, and
vertices. She let me create and deliver the lesson the way I wished as long as it fit that description. A few days before giving the lesson, I
decided to add an additional element. Could students determine the shapes and their properties using different models?
LESSON MAP
Topic: Exploring
Time Frame: (30-40 mins)
Grade Level: 2
Date: 3/25/2016
Solid Geometric
Figures
Purposes & Objectives:
Primary VA SOL Geometry
2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures
(circle/sphere, square/cube, and rectangle/rectangular prism).
(adapted from: http://www.doe.virginia.gov/testing/)
[3:53 PM, 4/28]
As per the classroom teacher's
suggestion, I tried to create the
lesson using to Bloom's Taxonomy (
http://images.google.com). While I did
not reach the 'creation' stage with
this lesson, I did incorporate
justification of ideas in the
discussion component.
Prerequisite Knowledge:
VA SOL:
1.12 The student will identify and trace, describe, and sort plane geometric figures (triangle, square,
rectangle, and circle) according to number of sides, vertices, and right angles.
1.13 The student will construct, model, and describe objects in the environment as geometric shapes
(triangle, rectangle, square, and circle) and explain the reasonableness of each choice.
Where to next?:
VA SOL:
3.14 The student will identify, describe, compare, and contrast characteristics of plane and solid geometric
figures (circle, square, rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and
cylinder) by identifying relevant characteristics, including the number of angles, vertices, and edges, and
Lauren Coogle
the number and shape of faces, using concrete models.
3.15 The student will identify and draw representations of points, line segments, rays, angles, and lines.
Launch
Materials:
2D and 3D geometric
figures, soft cube
[4:02 PM, 4/28]
I
used
the
pedagogy
of
mathematical reasoning to write my
launch. However, I overloaded this
section with too much information
(http://images.google.com). I should
have focused more on the content of
the lesson, and less about what the
class covered yesterday. That part of
the discussion muddled the lesson a
little.
The day before, the class covered
identification of 2D and 3D shapes.
I should have just stuck to the
faces/edges/vertices
talk.
The
students were confused when I only
used 3D shapes for my lesson. It
related, but not enough for the
amount of time I spent having the
students
demonstrate
their
knowledge to me. It ended up
cutting into the rest of the lesson. I
actually ran out of time, which was
very disappointing.
Activities
 We will begin the activity by tossing a
squishy cube around the circle and having
the students apply their knowledge of solid
geometric figures.
 The students will recall previously learned
vocabulary words: figure, edge, face,
vetrices/vertex as those terms apply to a
cube.
 Students will explain and describe their
understanding of these terms.
 Students should know that a face any
individual surface of a figure. A common
misconception is that a figure only has one
face, or that a face is the front of the figure.
 Ensure that students see shapes from
multiple orientations to clear up the
misconceptions about faces.
 Students should know that a vertex is a
corner. The edge joins vertices. A common
misconception is that an edge is the corner.
 Some students may know that an edge is also
a line segment.
 Students will do a think-pair-share to
determine the differences between 2D and
3D figures.
 I will be listening for descriptive terms such
as: depth, length, and height.
 This will lead into the exploratory phase of
the lesson which aims to solidify student
understanding of the terms: sphere, cube,
rectangular prism, cylinder, and triangular
prism.
Teacher Questions
 What is an edge?
 What is a vertex?
 What if we have more
than one vertex? What is
the word for that?
 What is the difference
between a face and an
edge?
 What is the difference
between an edge and a
vertex?
 Is it possible for a shape
to have zero edges, faces,
or vertices?
 What is a dimension?
 What are the three
dimensions?
 What is the difference
between a 2D and 3D
figure?
 Can anyone show me a
2D shape in this room?
 Can anyone show me a
3D shape in this room?
 Why is this shape not 2D?
 Why is this shape not 3D?
Lauren Coogle

[4:16 PM, 4/28]
Students struggled with the different
representations of the same shape more
than anything. I expected students to
have difficulty with remembering the
shape names. That was not a problem
until I switched some of the
manipulatives. They had been working
with the same models for too long.
I struggled pacing the activity. I was
engrossed in student analysis of the
materials. I did not have the time to
change groups for the second part of the
activity. Although, I still have the type Astudents leading the way; I ultimately
decided that I should give equal time to
both sections. Also, I wanted plenty of
time to hear student reasoning for their
compare and contrast.
Explore
Materials:
Multiple examples of
circles, squares,
rectangles, triangles,
cubes, rectangular
prisms, square
pyramids, spheres,
cones, cylinders, and
triangular pyramids
Shape Recording
Sheet
Venn Diagram
In the next phase of the lesson, students will
classify, describe, and analyze shapes
according to a list of the properties: faces,
edges, and vertices.
 Following a guided exploration with tangible
models, the students will be able to compare
and contract two given shapes. During the
discussion, the students will explain and
defend their findings using the three
properties from the first part of the
exploration.
 During the students' independent guided
exploratory, students will use the solid
geometric shapes to identify and record the
number of faces, edges, and vertices.
 I will be listening out for vocabulary and the
appropriateness of student analysis and assist
as needed.
 Students will work in small groups of 4-6
students. Together, students will complete the
front side of the sheet involving classification
of shapes according to properties.
 Students may continue to be confused by edges
and vertices.
 Facilitate understanding by asking students to
show you the location of faces, edges, and
vertices on the shapes.
 We will return to the carpet and interpret our
findings. I will be listening for students to draw
connections between shapes.
 Students will be asked to justify, critique, and
support their opinions using knowledge of the
materials.
 The students will break into new groups of 4-6.
Together, students will analyze two shapes.
The students will evaluate what is similar and

What distinguishes – or,
sets apart - a sphere from
the other shapes?
 What evidence to we have
to support that
conclusion?
 Which shapes have the
same number of faces?
 Do those shapes have any
other characteristics in
common?
 What connections can we
make between these
shapes?
 What is the difference
between a triangular
prism and a pyramid?
 What is the difference
between a square
pyramid and a triangular
pyramid?
 For example, a student may
say that a triangular pyramid
has a base of triangles;
whereas, a square pyramid
Lauren Coogle
[4:32 PM, 4/28]
From the discussion, students could
accurately describe the terms edges,
faces, and vertices. Students could also
give me examples from the initial set of
wooden 3D shapes provided. Students
justified their comparisons between the
wooden 3D shapes using the vocabulary
as I hoped they would. The only
difficulty came from understanding that
the different models of the same shapes
still retain the same properties. Students
were checking and re-checking to see if
this was indeed, true.
I did not to do the informal assessment
that the instructor does at the end of
every math lesson. I know the students
are used to this, but we ran out of time.
different between the two shapes.
 Given two shapes, the students will be able to
distinguish between the number of faces,
edges, and vertices. The students will use this
knowledge to determine what is similar and
different about the two shapes.
Discuss
• Students will present their analysis to the
Materials:
class. Using the 3D shapes, students will point
Completed Shape
out what characteristics distinguish the two
Recording Sheet and
shapes they were given. Students will identify
Venn Diagram
contrasts between the two shapes.
different models of 3D • I will listen for the inclusion of the vocabulary,
geometric shapes to be which is the focus of the lesson: edges, faces,
used as a reference
vertices.
• Additionally, I will listen for appropriate
application of the vocabulary.
• Use the discussion to clarify the expectations
of the assignment. Make sure students
understand
• I will check in with the 1-4 informal
assessment of student understanding. Students
will hold up fingers corresponding to their
comfort level with the material. (1= Novice, 2 =
Apprentice, 3 = Practitioner, 4 = Expert)
has a base that is a square. If
the vocabulary is not used,
model it for students. Support
interpretations by connecting
2D representations to 3D
models.
 Where else do we see these
shapes out in the world?
 How about in the
classroom?
 How many faces does this
shape have?
 Does a shape have to have
a face? Why or why not?
Explain your reasoning.
 Students may say yes.
However, spheres have zero
faces. While faces, edges,
and vertices are criteria
that we are using to classify
shapes, they do not
determine whether or not a
3D solid is a shape.
 Who feels confident that
they could teach someone
about edges, faces, and
vertices?
Formative Assessment:
 This exploration should be drawing students toward the realization that a sphere has no faces, edges, or
vertices. Students will demonstrate their understanding through a Venn Diagram comparing two
different shapes.
 As suggested on page 407 of the text, I will listen to student analysis to determine level of
understanding (Van de Walle, 2013). If students are beginning to group shapes by like characteristics,
using appropriate vocabulary, and conducting critical analysis of the differences between shapes; then,
I can determine whether individual students are moving toward the learning target.
 I will differentiate between students needs by having lines on some Venn Diagrams. This will make it
Lauren Coogle
easier for students to write their answers. Different learning styles could sketch or write answers.
Complete sentences or bullet points could be used if sentences are cumbersome.
Pair struggling students with students that can explain their understanding of the terms and shape
properties.
Reflection:
My lesson was inspired by Table 20 – Categories of Three-Dimensional Shapes on page 413 in
Elementary and Middle School Mathematics (Van de Walle, 2013). According to the van Hiele levels of
geometric thought, “At level 1, classifying and sorting focus more deeply on the properties that make the
shape what it is (not just that it looks like the others in its group)” (Van de Walle, 2013, pp. 404). One of
the goals of my lesson was for students to apply attributes to an entire category of shapes, versus looking
at each shape individually.
The strength of this lesson was the scaffolding. I went from highly organized and structured with
the shape analysis, to structured with more variables (ie. the shapes themselves). I also went from known
shapes to less familiar versions of shapes. For the initial phase of the explore, I used the wooden shapes
that the students were accustomed to working with.
Then, when it came time for the Venn Diagram, I added in shapes like a water bottle lid with a
paper bottom for a cylinder. Some students recognized that the water bottle lid was hollow. It was not a 3D
solid, but it was still a cylinder. I wanted students to refer to the front of their charts and realize that I was
giving them the same shapes to analyze.
The weakness of this lesson was I underestimated the difficulty of applying properties across
representations of the same model. I should have created more teacher questions around this idea. I was
hoping to bring students toward the level 2 van Hiele logical reasoning as to what defines a shape (Van de
Walle, 2013, pp. 406). Some students were getting there. Others, I had to ask more questions about what
they were thinking. From a developmental perspective, it was interesting to see some students reach for
the understanding that it is the same shape no matter how it is represented. Just like with counting by ones,
some students had to check and re-check that a new rectangular prism had not 'tricked' them by having
extra edges or vertices.
While I was walking around the room, I did hear some excellent analysis of the shapes. I heard a
girl say, “Well, this one has the same number of faces as the cube, but it's a rectangle; so, it's a rectangular
prism.” Another group of students used whether or not the shape could roll as a defining characteristic. I
asked students to tell me why they were testing that property. The students told me that if it rolled, it did
not have any edges. I had not expected students to think that way. Giving this lesson was a learning
experience for me, too.
I did not change the groups for the second part of the analysis as planned. The first part of the
exploratory took more time than I had expected. In order to fit in the entire lesson in my time slot, I elected
to keep the students in their same groups. I had planned to change group dynamics for many reasons.
Lauren Coogle
When the students work in groups, certain students consistently dominate the analysis. If even for a brief
time, I wanted to pair the strong personalities together for socialization reasons.
Following my lesson, the teacher taught a lesson on origami. The students made a square pyramid
and identified the faces, edges, and vertices. Her lesson was similar to my original idea: “Given a shape
with a certain number of edges, create as many 2D shapes as you can. For each different shape you create,
note how many vertices you have.” After watching her lesson, I would teach something with less rules to
follow. Too many students got bogged down by the technical aspect of the origami. There was a lot of
anxiety about making the shape 'correctly' that took away from the lesson.
I like the idea of making the shape 3D. It was something I had not considered during my initial
planning session. However, I would rather have students create their own origami shape without strict
guidelines as to the outcome. Meeting the needs of multiple levels, students could choose whether to
analyze a 2D or 3D representation. If students did not want to cut and glue, they could draw a shape. I
think it would be more meaningful for students to create a shape. Then, using what they know, students
could come to their own conclusions.
Resources
Van de Walle, J., Karp, K., Bay-Williams, J. (2013). Elementary and Middle School Mathematics:
Teaching Developmentally (8th Ed.). Boston: Pearson.
Additional Reflections on the Teaching Experience
My classroom teacher gave me feedback that I agreed with. I went in knowing what I wanted to teach and what I was looking for out
of the students. However, teaching the lesson completely revised my opinion of where to go next. Almost all of the students understood the
terms edges, faces, and vertices. The compare and contrast of different shapes needed work. I would also need supporting lessons to help
them build connections beyond the classroom.
The section I needed to improve was the Formative Assessment. Listening to twenty-four different students discussing shapes was
overwhelming. Some of the students were beginning to group shapes, while others were struggling with the mathematical language. After
my lesson, I re-read the chapter to see what I could improve. On page 407, I realized that I was trying to move level 1 thinkers to level 2. In
reality, I should have focused on moving everyone from level 0 to level 1 (Van de Walle, 2013). Asking for counterexamples was a little
beyond the scope of the lesson.
Lauren Coogle
LESSON MAP - REVISED
Topic: Exploring Solid Geometric Figures
Time Frame: (30-40 mins)
Grade Level: 2
Date: N/A
Purposes & Objectives:
Primary VA SOL Geometry
2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and
rectangle/rectangular prism).
(adapted from: http://www.doe.virginia.gov/testing/)
Prerequisite Knowledge:
VA SOL:
1.12 The student will identify and trace, describe, and sort plane geometric figures (triangle, square, rectangle, and circle) according to
number of sides, vertices, and right angles.
1.13 The student will construct, model, and describe objects in the environment as geometric shapes (triangle, rectangle, square, and
circle) and explain the reasonableness of each choice.
Where to next?:
VA SOL:
3.14 The student will identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square,
rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics,
including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models.
3.15 The student will identify and draw representations of points, line segments, rays, angles, and lines.
Activities
Teacher Questions
Launch
 We will begin the activity by selecting a shape in the room.
 Can anyone show me a 2D shape
Materials:
in this room?
 The students will name and identify the shape.
2D and 3D geometric
 Can anyone show me a 3D shape
 They will recall previously learned vocabulary words:
figures within the
in this room?
figure, edge, face, vetrices/vertex as those terms apply to a
classroom
 Why is this shape not 2D?
that shape.
 Students will determine whether the shape is 2D or 3D and
 Why is this shape not 3D?
provide justification for their reasoning.
 What is an edge?
 Students will explain and describe their understanding of
 What is a vertex?
these terms.
 What if we have more than one
 Students should know that a vertex is a corner. The edge
vertex? What is the word for that?
joins vertices. A common misconception is that an edge is
 What is the difference between a
the corner.
face and an edge?
 I will be listening for descriptive terms such as: depth,
 What is the difference between an
length, and height.
edge and a vertex?
Lauren Coogle


Explore
Materials:
paper
scissors
pens
pencils
Discuss
Materials:
Different models of
geometric shapes from
around the classroom to be
This will lead into the exploratory phase of the lesson.
In the next phase of the plan, students will answer the
following prompt, “Given a shape with a given number of
vertices, create as many different 2D shapes as you can using
scissors and paper.”
 Using their understanding of geometry, the students will be
able to create shapes and determine the number of vertices,
faces, and edges of that shape.
 During the students' independent guided exploratory, students
will use scissors, paper, pens, and pencils to create shapes.
 I will be listening out for vocabulary and the appropriateness
of student analysis and assist as needed.
 Students will work independently for 3-5 minutes.
 Together, students will partner up and try to compare what is
similar and different between their created shapes.
 Students may continue to be confused by edges and vertices.
 Facilitate understanding by asking students to show you the
location of faces, edges, and vertices on the shapes.
 We will return to the carpet and interpret our findings. I will be
listening for students to draw connections between shapes.
 Students will be asked to justify, critique, and support their
opinions using knowledge of the materials.
 The students will break into new groups. Together, students
will analyze two shapes. The students will evaluate what is
similar and different between the two shapes.
 Given two shapes, the students will be able to distinguish
between the number of faces, edges, and vertices. The students
will use this knowledge to determine what is similar and
different about the two shapes.
• Students will describe and classify their shape to the best of
their ability.
• I will listen for the inclusion of the vocabulary, which is the
focus of the lesson: edges, faces, vertices.
• Additionally, I will listen for appropriate application of the





Is it possible for a shape to have
zero edges, faces, or vertices?
What is a dimension?
What are the three dimensions?
What is the difference between a
2D and 3D figure?
What distinguishes – or, sets apart
- a sphere from the other shapes?
 What evidence to we have to
support that conclusion?
 Which shapes have the same
number of faces?
 Do those shapes have any other
characteristics in common?
 What connections can we make
between these shapes?
 What is the difference between a
triangular prism and a pyramid?
 What is the difference between a
square pyramid and a triangular
pyramid?
 For example, a student may say that
a triangular pyramid has a base of
triangles; whereas, a square pyramid
has a base that is a square. If the
vocabulary is not used, model it for
students. Support interpretations by
connecting 2D representations to 3D
models.
 Where else do we see these shapes
out in the world?
 How about in the classroom?
 How many edges does this shape
have?
Lauren Coogle
used as a reference
vocabulary.
 Does a shape have to have a face?
• I will guide students toward clarifying misconceptions that
Why or why not? Explain your
occur.
reasoning.
• We will discuss how in the real world, shapes may be tricky to  Students may say yes. However,
classify by their proper names. Shapes we see may even be made
spheres have zero faces. While faces,
up of more than one shape. However, we can make valid
edges, and vertices are criteria that
inferences by knowledge of properties of shapes to draw
we are using to classify shapes, they
conclusions about what we see.
do not determine whether or not a
• I will check in with students using an exit ticket. Students will
3D solid is a shape.
write or draw one shape with a number of edges that I determine.  What is the difference between a
vertex and an edge?
 In your own words, rephrase what I
am asking you to do.
Formative Assessment:
 As suggested on page 407 of the text, I will listen to student analysis to determine level of understanding (Van de Walle, 2013). If
students are beginning to group shapes by like characteristics, using appropriate vocabulary, and conducting critical analysis of the
differences between shapes; then, I can determine whether individual students are moving toward the learning target.
 I will differentiate between students needs by having pre-cut shapes, suggesting number of vertices to use, or helping the student
keep track of their results with a chart in their notebook. This will make it easier for students to record their findings. Different
learning styles could draw shapes instead of cutting them out. Complete sentences or bullet points could be used if sentences are
cumbersome.
Pair struggling students with students that can explain their understanding of the terms and shape properties.
Reflection:
Post-Planning Reflection
I realized that with a few minor changes, I could have a completely different lesson with a better outcome. After teaching the lesson, I
believe students would benefit from creating their own understanding of shape properties. Student thinking was a little rigid. I wish I had
advocated for my idea; but, at the same time, it is not my classroom.
In this lesson – although maybe not explicitly – I tried to created a real-world context. We see shapes every day, even if we are not
calling them by their technical terminology. What was missing from my first attempt was the connection to the bigger picture. I realized that
when working the students. The students performed amazingly with what they were familiar. If I had not included the alternative models, I
would have thought they were experts on the topic. I finally saw a gigantic pitfall of direct instruction. These students understood geometry
in the context of the wooden 3D shapes and the confines of that classroom. There was not a great deal of flexibility or connections within
their understanding.
Lauren Coogle
Overall Reflection
This experience taught me to be flexible with my expectations. Students do not always respond in the way which I think they will. I
can read all the material in the world and still be surprised by their understandings.
Another essential part of this lesson plan for me was collaboration. I went to the team math meeting, discussed at length with my
classroom teacher, and read the related chapter to help prepare me for my lesson. However, what surprised me about my lesson was the
rigidity of it. I had one outcome from the beginning. Students would understand the terms. Period. While this created predictability in the
outcome, it did not allow for different directions led by the students. It would have been better to see what students knew through application
of their knowledge. I could have been a better facilitator that way. I would have been less surprised by the fact that students depended on
familiar models and could not generalize the material.
The feedback I received from students was overwhelmingly positive. I worried that students would be frustrated because there was
some difficulty moving back and forth between representations of 3D shapes. Instead, students took it as an opportunity of wonder. They
were excited by the realization that other shapes fit into the categories they already knew about. For my part, I enjoyed the compare and
contrast more than the straightforward fill in the chart. It provided me more insight into student thinking than regurgitation of the vocabulary.
Lauren Coogle
An example of the worksheet I created for the shape
exploration.
A student example of one of the Venn Diagrams used for the
compare and contrast activity. I also printed copies with lines
as a form of differentiation. (http://images.google.com).