3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
5E Lesson Plan Math
Grade Level: 3
Subject Area: Math
Lesson Title: Two- and Three-Dimensional
Unit Number: 10
Lesson Length: 10
Figures
Days
Lesson Overview:
This unit bundles student expectations that address sorting and classifying two- and threedimensional figures, identifying examples and non-examples of quadrilaterals, and
decomposing two congruent two-dimensional figures into parts with equal areas and
expressing the area of each part as a unit fraction of the whole. 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 2, students analyzed attributes of two-dimensional shapes and
three-dimensional solids in order to develop generalizations about their properties. Using
formal geometric language, students classified and sorted polygons with 12 or fewer sides by
identifying the number of sides and number of vertices.
During this unit, students continue to develop their understanding of geometric figures by
sorting and classifying two- and three-dimensional figures that may vary in size, shape, and
orientation based on attributes using formal geometric language. Students focus their
exploration of two-dimensional figures as they explore subcategories of quadrilaterals,
including rhombuses, parallelograms, trapezoids, rectangles, and squares. Students use
formal language to describe the attributes and properties of each subcategory of quadrilaterals
as well as recognizing and drawing quadrilaterals that do not fit into any of the subcategories.
Students also apply previous understanding of area and fractions to their exploration of twodimensional figures. Students decompose two congruent two-dimensional figures into parts
with equal areas and express the area of each part as a unit fraction of the whole. Students
discover that equal shares of the same whole do not always have the same shape but are
equal if the areas of each part are equal. A solid understanding of the properties and attributes
of geometric figures is critical to students’ future success in the study of geometry.
Unit Objectives:
The students will… continue to develop their understanding of geometric figures by sorting and
classifying two- and three-dimensional figures that may vary in size, shape, and orientation
based on attributes using formal geometric language.
The students will… focus their exploration of two-dimensional figures as they explore
subcategories of quadrilaterals, including rhombuses, parallelograms, trapezoids, rectangles,
and squares.
The students will… use formal language to describe the attributes and properties of each
subcategory of quadrilaterals as well as recognizing and drawing quadrilaterals that do not fit
into any of the subcategories.
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
The students will…also apply previous understanding of area and fractions to their exploration
of two-dimensional figures.
The students will…decompose two congruent two-dimensional figures into parts with equal
areas and express the area of each part as a unit fraction of the whole.
The students will…discover that equal shares of the same whole do not always have the same
shape but are equal if the areas of each part are equal. A solid understanding of the properties
and attributes of geometric figures is critical to students’ future success in the study of
geometry.
Standards addressed:
TEKS:
3.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
3.1C 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.
3.1D Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate.
3.1E Create and use representations to organize, record, and communicate mathematical
ideas.
3.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
3.1G Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
3.6 Classify and sort two- and three-dimensional figures, including cones, cylinders,
A spheres, triangular and rectangular prisms, and cubes, based on attributes using
formal geometric language.
Readiness Standard
3.6 Use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and
B squares as examples of quadrilaterals and draw examples of quadrilaterals that do
not belong to any of these subcategories.
Supporting Standard
3.6 Decompose two congruent two-dimensional figures into parts with equal areas and
E express the area of each part as a unit fraction of the whole and recognize that
equal shares of identical wholes need not have the same shape.
Supporting Standard
ELPS:
ELPS.c.1A use prior knowledge and experiences to understand meanings in English
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
ELPS.c.2D monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
ELPS.c.3C speak using a variety of grammatical structures, sentence lengths, sentence types,
and connecting words with increasing accuracy and ease as more English is acquired
ELPS.c.3D speak using grade-level content area vocabulary in context to internalize new
English words and build academic language proficiency
ELPS.c.4D use prereading supports such as graphic organizers, illustrations, and pretaught
topic-related vocabulary and other prereading activities to enhance comprehension of written
text
ELPS.c.4H read silently with increasing ease and comprehension for longer periods
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level
vocabulary
ELPS.c.5 spell familiar English words with increasing accuracy, and employ English
C
spelling patterns and rules with increasing accuracy as more English is
acquired
ELPS.c.5F write using a variety of grade-appropriate sentence lengths, patterns, and
connecting words to combine phrases, clauses, and sentences in increasingly accurate ways
as more English is acquired
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to fulfill content
area writing needs as more English is acquired.
Misconceptions:
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Some students may think a quadrilateral must fall into one of the subcategories of
trapezoids, rectangles, rhombuses, or squares rather that recognizing any four-sided
figure as a quadrilateral.
Some students may think figures with equal area must look the same rather than
recognizing various combinations of length and width that equal the same area.
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 sixsided figure as a hexagon).
Some students may have difficulty recognizing geometric figures if the figures have
been transformed by orientation or size.
Some students may list attributes of a figure separately, but not see the
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
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interrelationships between figures (e.g., a square and rectangle as the only examples of
quadrilaterals).
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).
Some students may call a three-dimensional figure by the name of one of its twodimensional faces (e.g., a student may refer to a cube as a square, etc.).
Vocabulary:
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Area – the measurement attribute that describes the number of unit squares (or square
units) a figure or region covers
Attributes of three-dimensional figures – characteristics that define a geometric
figure (e.g., edges, vertices, faces [bases], etc.)
Attributes of two-dimensional figures – characteristics that define a geometric figure
(e.g., faces [bases], curved surfaces, edges, vertices, etc. )
Base of a cone – the flat surface shaped like a circle
Bases of a cylinder – the two congruent, opposite flat surfaces shaped like circles
Bases of a prism – the two unique, equal faces that are opposite each other
Classify – applying an attribute to categorize a sorted group
Congruent – of equal measure
Congruent figures – figures that are the same size and same shape
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 congruent
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 [bases] are
congruent, etc.) and between a group of geometric figures (e.g., a cube and a
rectangular prism both have 6 faces with opposite faces [bases] congruent; 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 congruent sides 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 congruent sides but a rectangle has only
opposite sides congruent; etc.)
Quadrilateral – a polygon with 4 sides and 4 vertices
Regular figure – a polygon with all side lengths and corners congruent
Side – a straight outer boundary between two vertices (line segment) of a twodimensional 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
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
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Two-dimensional figure – a figure with two basic units of measure, usually length and
width
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Unit fraction – a fraction in the form representing the quantity formed by one part of
a whole that has been partitioned into b equal parts where b is a non-zero whole
number
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
Closed figure
Cone
Cube
Cylinder
Decagon
Denominator
Dodecagon
Equilateral triangle
Heptagon or septagon
Hexagon
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Isosceles triangle
Length
Nonagon or enneagon
Numerator
Octagon
Open figure
Parallelogram
Partition
Pentagon
Rectangle
Rectangular prism
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Rhombus
Scalene triangle
Sphere
Square
Square corner
Square unit
Surface of a threedimensional figure
Trapezoid
Triangular prism
Undecagon or
hendecagon
Width
List of Materials:
Math Journal
Construction Paper
Attribute Shapes or Blocks (teacher-made using the worksheet or real blocks for the students
to trace)
Blank paper for Triangle Foldable
Identifying Shapes Worksheet and Key
Polygon Names Handout
Flat Toothpicks
Polygon-Types A Worksheet and Key
Polygon-Types B Worksheet and Key
Coloring Shapes Worksheet and Key
Painters Tape
Index Cards
Dry-Erase Boards
Clipboards for each student (or pairs)
Solid Figures (3-D) Worksheet (Key is anchor chart included in the lesson)
Solid Figures (3-D) Worksheet Solid Figures (for cutting)
Faces, Edges, and Vertices Worksheet and Key
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
3-D Solid Figure Sort and Classify Worksheet and Key
Rules for Sorting Solid Figures Worksheet and Key
2D and 3D Shapes Venn Diagram Worksheet and Key
INSTRUCTIONAL SEQUENCE
Phase – Engage and Explore
Day 1 Activity:
The students will define vocabulary related to polygons, and draw examples on a flip chart.
The students will sort quadrilaterals and non-quadrilaterals according to attributes on a TChart.
Materials:
Math Journal
Construction Paper
Attribute Shapes or Blocks (tracers the teacher has previously cut out for the students to trace,
or real blocks for the students to trace)
Lesson:
The teacher will put the following words on the Smartboard or white board, one at a time:
parallel, not parallel, square corner, and polygon.
The class will discuss the words and what they each mean and look like. Can anyone tell me
what the word, parallel, means? Students may answer that parallel means even or straight.
The teacher will draw a picture of a rectangle on the board, and highlight two opposite sides.
The teacher will ask again if anyone can tell the class what parallel means? Students
may say that they are two lines that are opposite of each other.
The teacher will draw a picture of a rectangle on the board, and highlight two sides that
intersect. The teacher will tell the students that these lines are NOT parallel.
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
The teacher will ask again if anyone can tell the class what parallel means? The
students will say they are lines that don’t cross or meet EVER. If lines meet or cross, then
the lines would be what? Not parallel
The teacher will ask a volunteer to come to the board to draw a large rectangle. (They have
previously been taught the attributes of a rectangle.) The teacher will then use attribute
blocks, to show the students how to tell if a shape has a square corner. (The teacher will take
their square-tile, and place it in the corner of the rectangle to show the square corner.) What
are some shapes that you think would have a square corner? Square and rectangle (or a
triangle with a square corner)
The teacher will ask several volunteers to come up to the board to draw different shapes. The
teacher will also draw some shapes that are open and some irregular polygons. The teacher
will circle the shapes that are polygons. Why do you think I have circled some of these
shapes? Because they have straight sides. What is different about the shapes that I have
circled, versus the shapes that are not circled? The shapes that are not closed are not
circled. The shapes that are curved are not circled.
Examples of irregular polygons: polygons that do not have equal sides
The teacher will explain that the shapes that are circled are polygons. Polygons must follow
three rules: Based on the shapes on the board, can anyone tell me a rule for being a
polygon? Closed shape, straight lines, and three or more lines
The teacher will model how to make a flip chart of the words. This flip chart will be glued in the
student’s Math Journals for future reference.
The students will complete the flip chart. (orange flip chart picture example located below)
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
After the class has completed their flip charts and have them glued into their Math Journals,
the teacher will begin discussing the attributes of quadrilaterals.
There are many types of polygons. One group of polygons is quadrilaterals. The teacher will
write the word, quadrilateral, on the board. Can anyone tell me what the prefix, quad,
means…think quadruplets, quad-cab, quadruple? Four If “quad” means four, what do
you think quadrilateral means? Four sides Are there any shapes you can think of that
would be quadrilaterals? Square, rectangle, rhombus, parallelogram, trapezoid
The teacher will give each student attribute shapes to trace onto colored construction paper.
Include quadrilaterals and non-quadrilaterals. (If a teacher does not have attribute blocks,
they can easily make attribute block tracers out of file folders for the students to trace.) The
students will trace the blocks onto construction paper, and cut out the shapes. The students
will sort the shapes by quadrilateral and not-quadrilateral on their desks. The students will
make a T-chart in their Math Journal. The first side of the T-chart will be labeled,
quadrilaterals, and the second side will be labeled, not-quadrilaterals.
quadrilaterals (4 sided)
not quadrilaterals
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
The teacher will ask a student to hold up a shape and wait for all students to find the same
shape. The class will decide whether the shape is a quadrilateral, or not a quadrilateral, and
glue it down on the appropriate side of the t-chart. If the shape is a quadrilateral, the students
will label the quadrilateral with the correct name. Continue until all the shapes have been
sorted. Which shapes has all the sides the same length? Square and rhombus What
shapes have square corners? Square and rectangle Which shapes have parallel lines?
All of them How is a rectangle different from a square? Rectangle has opposite sides are
the same length, and a square has all sides the same length.
**Use the following example as a guide for definitions.
What’s the teacher doing?
What are the students doing?
The teacher is helping students define
vocabulary.
The students are defining vocabulary with the
teacher’s guidance.
The teacher is modeling how to make a
flip chart.
The students are making a flip chart.
The teacher is defining and discussing
attributes of quadrilaterals.
The students are answering questions about
polygons and quadrilaterals.
The students are sorting quadrilaterals in
accordance to their attributes.
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
Phase: Explore and Engage
Day 2 Activity:
The students will sort and classify triangles according to their attributes.
The students will make a triangle anchor chart for their Math Journals.
Materials:
Math Journals
Blank paper for Triangle Foldable
Lesson:
The teacher will draw an equilateral triangle on the Smartboard or whiteboard. What shape is
this? Triangle How can you tell it is a triangle? There are three sides, three angles, and
three vertices.
The teacher will draw a scalene triangle on the board. How are these two shapes alike?
They are both triangles and both have three sides How are these two shapes different?
The first triangle has equal sides and the second triangle has no equal sides
The teacher will draw a isosceles triangle on the board. How is this triangle similar to the
other two? They all have three sides How are these shapes different? Equilateral triangle
has three equal sides, scalene triangle has two equal sides, and isosceles triangle has no
equal sides.
The students will each place a copy of the following triangle pictorial models into their Math
Journal for future reference.
The teacher will make the following anchor chart to post in their classroom, if wanted. (Do not
need to include acute, obtuse, and right triangles, but it is an option.)
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
The teacher will give each student a blank piece of paper. The students will fold the paper into
three sections. The students will label each section as Equilateral, Isosceles, or Scalene. The
students will use the information and pictorial models they have placed in their Math Journals
to draw examples of each type of triangle in the correct folded section of the paper. This can
be counted for a grade.
What’s the teacher doing?
What are the students doing?
The teacher is reviewing triangles.
The students are reviewing triangles.
The teacher is helping students classify
triangles as Equilateral, Isosceles or
Scalene based on the number of equal
sides.
The students are classifying triangles.
The students are completing the triangle folded
paper activity.
The teacher is making an anchor chart
to identify different types of triangles.
The teacher is modeling the triangle
folded paper activity.
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
Phase – Explore and Engage
Day 3 Activity:
The students will continue studying regular and irregular polygons, up to and including 12
sided shapes.
The students will classify polygons based on the number of sides.
Materials:
Math Journal
Identifying Shapes Worksheet and Key
Polygon Names Handout
Flat Toothpicks
Polygon-Types A Worksheet and Key
Polygon-Types B Worksheet and Key
Coloring Shapes Worksheet and Key
Lesson:
The teacher will introduce the lesson by defining the difference between regular and irregular
polygons.
Regular Polygon: All the sides are the same length
Irregular Polygon: The sides are different lengths
If needed, the teacher can use the Identifying Shapes Worksheet to show examples of
regular and irregular polygons.
The teacher will then pass out the Polygon Names Handout. The students will trim the
handout and glue it into their Math Journals.
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
The teacher will explain to the students that each polygon has a name based on the number of
sides it has. The teacher will review with the students that polygons are two-dimensional (2D)
shapes. 2D shapes have length and width, but do not have height.
The teacher will pass out a handful of flat toothpicks to each student. The teacher will orally
instruct the students to construct polygons of various sides, using their correct name. (The
students will do this on their desks…they are not gluing on paper.)
The teacher will ask the students to make a hexagon using their toothpicks. The teacher will
ask multiple students to go up to the board to draw a picture of their hexagon. (The teacher
needs to choose students to go to the board who have built their hexagon in different ways.)
Is the first shape drawn on the board a regular or irregular hexagon? Regular
Why is this shape regular? Because the sides and angles are all equal Since all of the
hexagons on the board do not look the same, how can they all be hexagons? Because
they all have six sides and six angles
Continue this activity several times with different polygons. Once the students feel
comfortable with this activity, have each student build the polygon two different ways at their
desks.
The students may use their Polygon Names Handout for reference.
After the hands-on activity, the class will complete Polygon-Types A Worksheet together, to
check for understanding.
Once the class completes the Polygon-Types A Worksheet together, the students may work
on the Polygon-Types B or the Coloring Shapes Worksheet individually, or with a partner.
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
What’s the teacher doing?
What are the students doing?
The teacher is discussing regular
polygons, irregular polygons, and
polygon names.
The students are discussing regular polygons,
irregular polygons, and polygon names.
The students are completing a toothpick activity.
The teacher is observing and monitoring
students while they complete the
The students are completing polygon worksheets.
toothpick polygon activity.
The teacher I monitoring students
working on polygon worksheets.
Phase – Explain and Engage
Day 4 Activity:
The students will review all polygons and discuss their individual attributes.
Materials:
Polygon Sort Game can be downloaded for free from the following website:
http://www.teachersnotebook.com/product/frogsandcupcakes/polygon-sort#
Painters Tape
Index Cards (numbered)
Lesson:
The teacher will pass out marker boards to each student. The class will review polygons by
drawing different shapes on their dry-erase boards.
The teacher will use painters tape to construct different polygons around the room or in the
hallway. The teacher will number each polygon with an index card. The students will be given
a clipboard with a sheet of notebook paper. They will need to number 1. to however many
polygons the teacher has made out of tape. The students will rotate around the room/hallway
and have to write the name of the polygon for each shape.
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
What is the teacher doing?
What are the students doing?
The teacher is reviewing polygon
names with the classroom.
The students are reviewing polygons using dryerase boards.
The teacher instructs the students on
how to complete the polygon painters
tape activity.
The students are reviewing polygons with the
polygon painters tape activity.
The teacher monitors the students for
understanding.
Phase - Explain
Day 5 Activity:
The students will review three-dimensional figures and their attributes.
The students will be able to identify a face, edge and vertex on a three-dimensional shape.
Materials:
Solid Figures 3D Worksheet (key is the anchor chart below)
Lesson:
The teacher will introduce three-dimensional shapes to the class by passing out threedimensional solid figures (or real-life three-dimensional objects). **If there is not enough solid
figures to pass out to each student, have the students work in pairs, or in groups.
The teacher will have the students hold up one solid figure at a time, and discuss the name,
attributes, and real-life objects that are also shaped like that. Group 1, please hold up a
solid figure and tell us what you think the name is? Sphere Can you describe to
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
everyone a sphere? No edges and it rolls What are some real-life objects that are
shaped like a sphere? A basketball, a globe, a soccer ball Is the classroom clock shaped
like a sphere? No, because it is not round, it is flat on the front and the back
**Repeat the questioning with the different three-dimensional shapes until you have covered
them all. This includes, cylinder, triangular prism, rectangular prism, cone, sphere, and cube.
**Instead of a pyramid, students need to do a
triangular prism.
The teacher will make a large anchor chart similar to the one above to post in their classroom.
The students will make a similar chart in their journals, to look at for reference, using the Solid
Figures (3D) Worksheet.
As the students are completing the Solid Figures (3D) Worksheet, the teacher will review
and emphasize edge, vertex, and face. This will also be written on their Solid Figures (3D)
Worksheet.
What’s the teacher doing?
What are the students doing?
The teacher is reviewing solid figure
names with the classroom.
The students are reviewing 3D solid figures using
solid figure manipulatives or real-life solid figures.
The teacher questions the students
The students are reviewing 3D solid figures as the
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
about different attributes and real-life
examples of different 3D solid figures.
teacher questions the class about 3D attributes and
real-life examples.
The teacher monitors the students for
understanding as they complete their
3D anchor chart for their journals.
Phase – Elaborate and Explain
Day 6 Activity:
The students complete a 3D anchor chart in their
Math Journals, for reference.
The students will elaborate their understanding of faces, edges, and vertices.
The students will be able to identify faces, edges, and vertices on three-dimensional models
and real-life three-dimensional objects.
Materials:
Faces, Edges and Vertices Worksheet
Lesson:
The teacher will begin the lesson by asking the students what faces, edges, and vertices are.
The students may use solid three-dimensional figures the teacher has set out, to help them
explain in their own words what faces, edges, and vertices are.
After the students have explained in their own words, and modeled faces, edges and vertices
with solid figures, the teacher will generate a formal definition the students will copy into their
Math Journals.
The teacher will begin the lesson by reviewing three-dimensional shapes around the
classroom. I see a globe, what three dimensional shape is a globe? Sphere What
makes a sphere 3D? Length, width and height I see a filing cabinet, what three
dimensional shape is a filing cabinet? Rectangular prism What makes the rectangular
prism 3D? It has length, width and height. It has faces, vertices, and edges.
The teacher will use the filing cabinet as a model to demonstrate the counting of the faces,
edges and vertices of a rectangular prism. Can I have a volunteer come over to this filing
cabinet and point to a vertex? Student will go to the filing cabinet and point to a corner. Are
there any other vertices on this rectangular prism? Yes, student will point out the 7 other
vertices. What makes a vertex? It is a corner where three or more edges meet. Can I have
a volunteer come over to the filing cabinet and point to an edge? Student will go to the
filing cabinet and point to an edge. Are there any other edges on this rectangular prism?
Yes, there are a total of 12. Now I need a volunteer to point to the faces of the filing
cabinet. Student will go to the filing cabinet and point to the faces of the filing cabinet. I can
see 4 faces, is this correct? No, there are actually 6 faces, we have to count the backside
and part underneath.
The teacher can continue to point out 3D figures in the classroom and question the students
on faces, edges, and vertices.
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
Once the teacher feels the class has a good understanding of faces, edges, and vertices, the
teacher will pair up the students and give them solid figures to work with. The students will
discuss the edges, vertices, and faces of each shape together.
After, the students have worked in pairs discussing the faces, edges, and vertices. The
teacher will give the students the Faces, Edges and Vertices Worksheet. This worksheet
has three-dimensional solid figures and real-life objects. The students will need to draw the
dots on the vertices, pencil or highlight over each edge, and number the faces, to show work.
What’s the teacher doing?
What are the student’s doing?
The teacher is reviewing solid figures
and faces, edges and vertices with the
students.
The students are reviewing 3D solid figures and
discussing the faces, edges, and vertices of the
figures.
The teacher gives formal definitions of
faces, edges and vertices to the
students.
The students are writing the formal definition of
face, edge, and vertex in their Math Journal.
The teacher uses three-dimensional
objects around the classroom to discuss
faces, edges, and vertices..
The students work in pairs to discuss faces, edges,
and vertices using three-dimensional solid figures,
and then on their own to complete the Faces,
Edges, and Vertices Worksheet.
The teacher monitors the students for
understanding as they work in pairs to
point out the faces, edges and vertices
of the solid figure models, and then
individually work on the Faces, Edges,
and Vertices Worksheet.
Phase - Elaborate
Day 7 and 8 Activity:
The students will use formal math vocabulary to describe 3-D figures: cone, cylinder, sphere,
triangular and rectangular prism and cube.
The students will identify, classify and sort 3-D figures according to attributes.
The students will generate a Venn Diagram (graphic organizer) of 2D and 3D Figures.
Materials:
Solid figures
3-D Solid Figure Sort and Classify Worksheet and Key
Rules for Sorting Solid Figures Worksheet and Key
2D and 3D Shapes Venn Diagram
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
Lesson:
The teacher will choose one solid figure at a time and review its attributes (faces, edges,
vertices). The teacher will begin by choosing a cone and a cylinder. “How are these two
solid figures alike?” They both roll. “Can anyone think of another way these two 3-D
shapes are the same?” They both have a circle face. The teacher will choose a cube and a
triangular prism. “How are these two solid figures alike?” They do not roll. “Can anyone
think of another way these two 3-D shapes are alike?” They both have faces. They both
have edges. They both have vertices. The teacher will then choose a sphere and a cylinder.
“How are these two solid figures alike?” They both roll. They both have a curved surface.
“If we want to tell how 3-D shapes are alike, we can classify and sort them in many
ways. The teacher will show a collection of solid figures (cone, cylinder, sphere, triangular
and rectangular prism and cube). Tell the students that they are going to sort the solid figures
based on their attributes. Students may use their Solid Figures (3D) Worksheet from day
five that is in their Math Folder as reference for spelling the names of each solid figure.
The teacher will pass out solid figures or a handout of 3-D figures to each student (or pairs or
groups).
The teacher will write the word, face, on the board. “Who can tell the class what this word
means?” The flat side of a solid figure. “We are going to sort the solid figures into two
groups, the ones that have a face and the ones that do not have a face.” The students
may actually sort the solid figures into groups or they can write the name of the solid figures
into groups. “Who can name the solid figures they sorted into the group that has faces?”
Cone, cylinder, triangular and rectangular prism and cube. “Are there any solid figures that
do not have faces?” Sphere. The teacher will then write the word, edge, on the board. “Can
someone tell the class what this word means?” Where two faces meet. “We are going to
use the same solid figures and sort them into two groups, the ones that have edges and
the ones that do not have edges. Again, students may use real solid figures to sort or they
can write the names of the solid figures. “Who can name the solid figures they sorted into
the group that has an edge?” Triangular and rectangular prism and cube. “Why would you
not include the cylinder in this group?” The faces of the cylinder do not meet. “Are there
any solid figures that do not have edges?” Sphere, cone and cylinder.
The teacher will continue sorting the solid figures using the following attributes: Vertices,
curved surfaces, circular faces, triangular faces, square faces and rectangular faces. The
teacher will monitor for understanding throughout the classifying and sorting activity.
After the class has completed the activity, the teacher will pass out the 3-D Solid Figure Sort
and Classify Worksheet. The students will complete the worksheet by themselves or with a
partner, using their Math Journal for reference. As an enrichment or follow-up to the lesson,
the teacher can have the students complete the Rules for Sorting Solid Figures Worksheet.
Once the students have completed the above two solid figure worksheets, the teacher begin
the Venn Diagram project with the class.
The teacher will review Venn Diagrams with the class, which has been taught in 2 nd grade and
19
3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
in Reading this year.
The students will be making a Venn Diagram of 2D and 3D words. Each student will be given
a blank Venn Diagram Worksheet. The teacher will model on the whiteboard, while the
students work at their desks.
The students will label the first circle, 2D,the second circle, 3D, and they will write the title, Two
Dimensional and 3 Dimensional, at the top of the graphic organizer. How are 2D shapes and
3D shapes different? 2D shapes are flat and have no height. 3D shapes have height and
are solid figures. How are 2D shapes and 3D shapes alike? They are both shapes that
have length and width.
The students will write in the 2D circle, “has no height” and “flat figure”. The students will write
in the 3D circle, “has height” and “solid figure”. The students will write in the center, “shapes”,
“have length” and “have width”.
The teacher will ask the students to help generate a random list of 2D and 3D shapes on the
whiteboard. (Make sure the students include the shapes in the above Venn Diagram
example.)
The teacher will then model how to fill in the Venn Diagram using the words generated by the
students on the whiteboard. They teacher will model filling in the Venn Diagram by doing one
2D shape and one 3D shape. The students will then complete the rest of the Venn Diagram
by themselves. The teacher will give the students time to work, and then go over Venn
Diagram, to check for understanding.
What’s the teacher doing?
The teacher is reviewing solid figures
and faces, edges and vertices with the
students.
What are the students doing?
The students are reviewing 3D solid figures and
discussing the faces, edges, and vertices of the
figures.
20
3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
The teacher reviews formal definitions
of faces, edges and vertices to the
students.
The teacher leads the students in
discussions about classifying solid or
3D figures.
The teacher helps the students
generate a Venn Diagram comparing
2D and 3D shapes.
The students are reviewing the formal definition of
face, edge, and vertex.
The students work individually or in pairs to classify
3D figures by their attributes.
The students complete 3D Solid Figure Sort and
Classify Worksheet and Rules for Sorting Solid
Figures Worksheet.
The students will complete a Venn Diagram
comparing 2D and 3D shapes.
Phase – Explore and Elaborate
Day 9 Activity:
The students will explore equal area by using paper square and rectangles.
The students will decompose two congruent 2D figures into parts with equal areas using graph
paper.
The students will review 2D and 3D figures and formal geometric vocabulary covered in this
unit as preparation of the Performance Indicator Test tomorrow.
Materials:
Four paper squares per student (hand cut or die cut)
Lesson:
The teacher will begin by reviewing the definition for congruent…same size and same shape.
The teacher will distribute two paper squares to each student. The teacher will ask the
students to fold the square in half, flat edge to flat edge. (The teacher will model this for the
students, as they are folding.) Do both sides of the square have the same area? Yes,
because they are congruent…same size and same shape. The teacher will have the students
fold their second square in half from corner to corner, like a triangle. (The teacher will model
this for the students, as they are folding.) Do both sides of the square have the same
area? Yes, because they are congruent…same size and same shape. The teacher will have
the students draw a line on the fold of the two squares. How can we label each side of the
square as a fraction? ½ and ½ . What shapes were created when you divided the
square in half? Triangle and rectangle. The teacher will have the students put the two
squares side-by-side. Are the two squares congruent? Yes, they are the same size and
same shape. The teacher will tell the students that if two shapes are congruent, then when
the shape is divided in half, each half has the same area.
21
3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
The teacher will distribute two more paper squares to each student. The teacher will ask the
students to fold the square into four equal parts. (The teacher will model this for the students,
as they are folding.) Do all four parts of the square have the same area? Yes, because
they are congruent…same size and same shape. The teacher will have the students fold their
second square in four equal parts. (The teacher will model this for the students, as they are
folding.) Do all four parts of the square have the same area? Yes, because they are
congruent…same size and same shape. The teacher will have the students draw a line on the
fold of the two squares. How can we label the four parts of each square as a fraction? ¼
on each part. What shapes were created when you divided the square into four parts?
Squares and rectangles. The teacher will have the students put the two squares side-by-side.
Are the two squares congruent? Yes, they are the same size and same shape. The
teacher will tell the students that if two shapes are congruent, then when the shape is divided
into fourths, each fourth has the same area.
The teacher will now pass out the graph paper with the squares and rectangles drawn on the
paper. (There will be four squares and two rectangles already drawn on the graph paper.)
Are all four squares congruent? Yes, because they are the same size and same shape.
The teacher will model how to decompose the four squares in half, four different ways.
(Horizontally, vertically, and diagonally each way).
The students will divide their squares in half according to the teacher’s model. The students
will then shade ½ of each square. Do all the halves that are shaded have the same area?
Yes, because if two shapes are congruent, then when the shape is divided in half, each half
has the same area.
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3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
The students will divide the first two rectangles in half, according to the teacher’s model.
The students will shade ½ of the rectangles. The teacher will instruct the students to count the
shaded squares in the rectangle. How many squares are in the shaded part of the first
rectangle? 24 How many squares are in the shaded part of the second rectangle? 24
What does this tell us about the area of the shaded part of each rectangle? The area is
equal.
The teacher will orally review 2D and 3D figures with the class. The teacher will also review
formal geometric vocabulary with the students. The teacher will draw on the whiteboard a 2D
shape, and the students will name the shape and identify how many sides and vertices there
are. Include all shapes from Day 1, 2 and 3 activities. The teacher will hold up a solid figure,
and have the students identify the figure and tell how many edges, faces and vertices each
one has. Include all figures from Day 5, 6, 7 and 8 activities.
What’s the teacher doing?
What are the students doing?
The teacher is reviewing the definition
of congruent.
The students are reviewing the definition of
congruent.
The teacher is modeling equal parts of a The students are modeling equal parts of a square
square and rectangle using paper
and rectangle using paper models.
models.
The teacher will review 2D and 3D
figures with the students.
The students will review 2D and 3D figures.
Phase - Evaluate
23
3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
Day 10 Activity:
The students will work on the Performance Indicator from the IFD.
Materials:
Performance Assessment 1and 2.
Performance Assessment 1:
Provide the following for task 1: a collection of at least 20 commercial and real-world twodimensional figures that include regular and irregular figures of various shape, size, and
orientation. Assess students using the following task:
1) Sort a collection of two-dimensional figures into categories based on attributes. Create a
graphic organizer to represent and justify your sort that includes:
a) A title for each category.
b) The name of each figure in the category.
c) Formal geometric language to describe the geometric attribute(s) common to each figure in
the category.
Provide the following for task 2: a collection of at least 20 commercial and real-world threedimensional figures that include cones, cylinders, spheres, triangular and rectangular prisms,
and cubes of various shape, size, and orientation. Assess students using the following task:
2) Sort a collection of three-dimensional figures into categories based on attributes. Create a
graphic organizer to represent and justify your sort that includes:
a) A title for each category.
b) The name of each figure in the category.
c) Formal geometric language to describe the geometric attribute(s) common to each figure in
the category.
Provide the following for task 3: a collection of pre-cut pictorial representations of
quadrilaterals that include 2 – 3 rhombuses, 2 – 3 parallelograms, 2 – 3 trapezoids, 2 – 3
rectangles, and 2 – 3 squares of various size and orientation; a large sheet of manila paper;
and glue. Assess students using the following task:
3) Create a graphic organizer to represent subcategories of quadrilaterals.
a) Fold a large sheet of manila paper to create six sections and label the sections as shown.
24
3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
b) Glue each quadrilateral picture into the appropriate subcategory on the manila paper.
c) In each section, use formal geometric language to describe the geometric attribute(s) that
define the subcategory.
d) In the “Other Quadrilaterals” section of the manila paper, draw 2 – 3 quadrilaterals that
could not be included in any of the other subcategories.
Standard(s): 3.1C , 3.1D , 3.1E , 3.1F , 3.1G , 3.6A , 3.6B ELPS.c.1A , ELPS.c.2D
, ELPS.c.3C , ELPS.c.3D , ELPS.c.4D , ELPS.c.4H , ELPS.c.5B , ELPS.c.5F , ELPS.c.5G
Performance Assessment 2:
Provide 2 congruent paper squares cut from plain paper and 2 congruent paper rectangles cut
from paper with centimeter grid lines. Assess students using the following tasks:
1) Nicole and Jarid each have square vegetable gardens that are the same size. Nicole
divided her vegetable garden into two equal parts using a diagonal line. She planted green
beans on one side and tomatoes on the other. Jarid divided his vegetable garden into two
equal parts using a horizontal line. He also planted green beans on one side and tomatoes on
the other. After comparing their vegetable gardens, Nicole said the area of her garden planted
with green beans is larger than the area of Jarid’s garden planted with green beans. Jarid said
the area of both gardens planted with green beans is equal. Complete the following tasks to
determine who is correct.
a) Select one of the congruent paper squares. Draw a diagonal line to divide the square into
two parts of equal area. Label each part with the name of the shape created and use fraction
notation to label each part as a unit fraction of the whole square. In writing, describe the
strategy used to determine that the two parts are equal in area.
b) Select the other congruent paper square. Draw a horizontal line to divide the square into
two parts of equal area. Label each part with the name of the shape created and use fraction
notation to label each part as a unit fraction of the whole square. In writing, describe the
strategy used to determine that the two parts are equal in area.
c) Use the models created and precise mathematical language to explain and justify why
25
3rd Grade – Unit 10 – Two- and Three-Dimensional Figures
Nicole is correct or why Jarid is correct.
2) Select the 2 congruent paper rectangles. Complete the following tasks:
a) Using one of the paper rectangles, draw lines to divide the rectangle into 4 equal parts. For
each resulting part:
o
o
o
Label the name of the shape created.
Use fraction notation to label each part as a unit fraction of the whole.
Determine and record the area of the part.
b) Using the other paper rectangle, draw lines to divide the rectangle into 4 equal parts in a
different way than the first rectangle was divided. For each resulting part:
o
o
o
Label the name of the shape created.
Use fraction notation to label each part as a unit fraction of the whole.
Determine and record the area of the part.
c) Use the models created and precise mathematical language to explain and justify why a
part of the first rectangle is or is not equal to a part of the second rectangle.
Standard(s): 3.1A , 3.1C , 3.1D , 3.1E , 3.1F , 3.1G , 3.6E ELPS.c.1A , ELPS.c.2D
, ELPS.c.3C , ELPS.c.3D , ELPS.c.4D , ELPS.c.4H , ELPS.c.5B , ELPS.c.5C , ELPS.c.5F
, ELPS.c.5G
What’s the teacher doing?
 Monitor students as they work on
Performance Indicator to
determine if any reteaching is
necessary.
What are the student’s doing?
 The students are completing the
Performance Indicator.
26