Download Geometry Lesson Idea 1

Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Unit 10:
Geometry (7 days)
Possible Lesson 01 (4 days)
Possible Lesson 02 (3 days)
POSSIBLE LESSON 01 (4 days)
This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing
with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and
districts may modify the time frame to meet students’ needs. To better understand how your district is implementing CSCOPE lessons, please contact your
child’s teacher. (For your convenience, please find linked the TEA Commissioner’s List of State Board of Education Approved Instructional Resources and
Midcycle State Adopted Instructional Materials.)
Lesson Synopsis:
Students use various materials to create and describe the attributes of two-dimensional figures. Students use geometric solids to investigate and describe the attributes of
three-dimensional figures.
TEKS:
The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas law.
Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit.
The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148
5.7
Geometry and spatial reasoning.. The student generates geometric definitions using critical attributes. The student is expected to:
5.7
Identify essential attributes including parallel, perpendicular, and congruent parts of two- and three-dimensional geometric figures.
Supporting Standard
Underlying Processes and Mathematical Tools TEKS:
5.14
Underlying processes and mathematical tools.. The student applies Grade 5 mathematics to solve problems connected to everyday
experiences and activities in and outside of school. The student is expected to:
5.14A
Identify the mathematics in everyday situations.
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
5.14D
Use tools such as real objects, manipulatives, and technology to solve problems.
5.15
Underlying processes and mathematical tools.. The student communicates about Grade 5 mathematics using informal language. The
student is expected to:
5.15A
Explain and record observations using objects, words, pictures, numbers, and technology.
5.15B
Relate informal language to mathematical language and symbols.
5.16
Underlying processes and mathematical tools.. The student uses logical reasoning. The student is expected to:
5.16A
Make generalizations from patterns or sets of examples and nonexamples.
5.16B
Justify why an answer is reasonable and explain the solution process.
Performance Indicator(s):
Grade 05 Mathematics Unit 10 PI 01
Create a mobile (e.g., a decorative structure that is suspended so as to turn freely in the air) that displays models of 4 different three-dimensional figures. The mobile should
include 1 prism, 1 pyramid, and 2 curved surfaced figures.
Use the provided die-cuts or nets (cube, rectangular prism, triangular prism, cone, cylinder, triangular pyramid, and square pyramid) to represent the three-dimensional figures
selected. On each net, if applicable, use different map pencil colors to highlight parallel lines and perpendicular and to shade the congruent faces of each figure.
Construct each selected net to create a three-dimensional model. Using geometric attributes, create a description card for each model that includes the following: (1) the formal
geometric name; (2) a description of each of the two-dimensional faces or curved surfaces; (3) the number of faces/curved surfaces; (4) the number of vertices, if applicable; and
(5) the number of edges, if applicable.
Complete the mobile by using yarn or string to attach each description card to the appropriate three-dimensional model and then to a clothes hanger. The completed mobile
should be similar to the sample below:
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Observe the created mobile, and write a journal entry for each of the following: (1) describe the difference between the number of faces, edges, and vertices of the prism and the
pyramid; (2) determine examples of real-world situations/objects in which each three-dimensional model created could be found; and (3) justify how the two-dimensional
attributes define each three-dimensional model.
Standard(s): 5.7 , 5.14A , 5.14D , 5.15A , 5.15B , 5.16A , 5.16B ELPS ELPS.c.1C , ELPS.c.5F
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Grade 05 Mathematics Unit 10 PI 02
Answer each of the following questions regarding the playhouse, using appropriate geometric language and labels:
1. identify the geometric figure that represents the roof, column, house, and top of the column;
2. identify the number of vertices, edges, and faces or curved surfaces on each of the figures identified in step (1); and
3. name all vertices, edges, and faces for the roof and house.
Write a paragraph comparing and contrasting the attributes of the roof, column, house, and top of the column using formal geometric language.
Standard(s): 5.7 , 5.14A , 5.15A , 5.15B ELPS ELPS.c.5B
Key Understanding(s):
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Two- and three-dimensional figures occur in architecture, fabric, art, street maps, and many other real world settings.
Polygons are two-dimensional figures with specific attributes.
Formal geometric vocabulary is used to identify and describe the position and attributes of two- and three- dimensional geometric figures.
The orientation of a two- or three- dimensional figure does not affect its congruency or its symmetry.
Three-dimensional figures consist of two-dimensional figures and are defined and distinguished by their attributes, which include faces, edges, and vertices, which
can be generalized to find examples and non-examples.
Two- and three-dimensional figures consist of essential attributes including parallel, perpendicular, and congruent parts.
Underdeveloped Concept(s):
Some students have difficulty understanding that more than one description may be needed to describe intersecting lines (such as perpendicular lines).
Some students confuse the size of an angle with the length of its sides.
Some students may struggle with naming all possible figures with the given characteristics or struggle with identifying a distinguishing attribute between two figures,
such as the square is a special rhombus with four right angles or a cube is a special rectangular prism with all square faces.
Some students may have difficulty visualizing where right angles are on three-dimensional figures.
Vocabulary of Instruction:
adjacent
attribute
intersecting lines
one-dimensional figure
parallel lines
perpendicular lines
three-dimensional figure
two-dimensional figure
Materials List:
cardstock (2 sheets per 2 students)
cardstock (2 sheets per 2 students)
cardstock (4 sheets per 2 students)
cardstock (4 sheets per 2 students)
cardstock (optional) (9 sheets per 4 students)
clothes hanger (wire) (1 per student)
geometric figures or solids (1 set per 4 students, 1 set per teacher)
index card (4” x 6”) (4 per student)
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
math journal (1 per student)
plastic zip bag (sandwich sized) (1 per 2 students)
plastic zip bag (sandwich sized) (1 per 2 students)
plastic zip bag (sandwich sized) (1 per 2 students)
plastic zip bag (sandwich sized) (1 per 2 students)
scissors (1 per student,1 per teacher)
tape (clear) (1 roll per student)
tape (clear) (optional) (1 roll per teacher)
yarn (6 inch strip) (4 per student)
Attachments:
All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments
that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website.
Lines, Angles, and Congruency Cards
Two-Dimensional Geometric Definitions Notes
Two-Dimensional Attribute Cards
Two-Dimensional Figures Graphic Organizer
Polygon Attributes KEY
Polygon Attributes
Two-Dimensional Figures Visual Graphic Organizer
Polygon Table
Faces, Edges, Vertices, Bases, and Curved Surfaces Cards
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Unit 10:
Suggested Duration: 4 days
Three-Dimensional Geometric Definitions Notes
Three-Dimensional Geometric Patterns
Three Dimensional Attribute Cards
Three-Dimensional Figures Graphic Organizer
Attributes of Three-Dimensional Figures KEY
Attributes of Three-Dimensional Figures
Naming Geometric Figures KEY
Naming Geometric Figures
Geometric Logic
Two- and Three-Dimensional Figure Practice KEY
Two- and Three-Dimensional Figure Practice
GETTING READY FOR INSTRUCTION
Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to
teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using
the Content Creator in the Tools Tab. All originally authored lessons can be saved in the “My CSCOPE” Tab within the “My Content” area. Suggested
Day
1
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Lines, angles, and congruency
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Suggested
Day
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
ATTACHMENTS
Engage 1
Card Set: Lines, Angles, and
Students use logic and reasoning skills to review examples and definitions of lines, angles, and congruency in order
Congruency Cards (1 set per 2
to recognize them as attributes of two-dimensional figures.
students)
Teacher Resource: Lines,
Instructional Procedures:
1. Prior to instruction, create a card set: Lines, Angles, and Congruency Cards for every 2 students by copying
on cardstock, laminating, cutting apart, and placing in a plastic zip bag.
2. Place students in pairs and a distribute card set: Lines, Angles, and Congruency Cards to each pair.
3. Instruct student pairs to match each card with its appropriate definition. Allow time for students to complete their
Angles, and Congruency
Cards (1 set per teacher)
Teacher Resource: TwoDimensional Geometric
Definitions – Notes (1 per
teacher)
matches. Monitor and assess student pairs to check for understanding. Facilitate a class discussion about the
terms and the figures that model them. Verify student matches are correct.
MATERIALS
Ask:
cardstock (2 sheets per 2
What is the difference between parallel lines and perpendicular lines? Answers may vary. Parallel
students)
lines never intersect, and perpendicular lines intersect at a right angle; etc.
scissors (1 per teacher)
Are there examples that could represent perpendicular lines in the alphabet? Explain. (yes)
plastic zip bag (sandwich sized)
Answers may vary. A “T” or “L” could represent perpendicular lines because the letters demonstrate right
(1 per 2 students)
angles (90º); etc.
Are all intersecting lines perpendicular? Explain. (no) Answers may vary. Not all lines that intersect
have to intersect at a right angle; etc.
TEACHER NOTE
If you create two lines and have them intersect like a cross, what kind of lines are these?
A line is the set of all points that form a
(perpendicular lines)
straight path that goes in opposite
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Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
If two lines are perpendicular, what angle measure is created by the intersecting lines? (90º)
directions without ending. If the arrows
Is an acute angle greater than or less than a right angle? (less than a right angle)
on the end of the line were to be
What do you call an angle larger than a right angle (90º) but less than a straight line (180º)? (obtuse
replaced with dots or two endpoints
angle)
indicating a definite beginning and
What are parallel, perpendicular, right, acute, and obtuse attributes that could be used to describe
ending to the line, then that part of a
two-dimensional figures? Explain. (yes) Answers may vary. The sides of two-dimensional figures can be
described as parallel and/or perpendicular; whereas, right, acute, and obtuse are attributes that could be
used to describe angles of two-dimensional figures; etc.
line is called a line segment. If only one
of the arrows on a line were to be
replaced with an endpoint and the other
end of the line continues without end in
4. Display the “Congruent” card from teacher resource: Lines, Angles, and Congruency Cards. Instruct student
pairs to discuss what they think the hash marks on each side of the rectangle and the small boxes at each
angle of the rectangle represent. Invite student volunteers to share their findings.
Ask:
the opposite direction, then that part of
the line is called a ray. A vertex is the
common endpoint of two rays that form
an angle. A vertex of a two-dimensional
What do the hash marks represent on the rectangle? Answers may vary. The hash marks represent
figure is the point (corner) of intersection
congruency, sides that are equal; etc.
of two sides in a two-dimensional figure.
Why do some sides have one hash mark and other sides have two hash marks? Answers may vary.
The sides with one hash mark indicate one set of congruent sides, while the sides with two hash marks
TEACHER NOTE
indicate different set of congruent sides; etc.
Grade 4 introduces formal and symbolic
What do the small boxes at each angle of the rectangle represent? Answers may vary. The small
geometric language for lines, line
boxes at each angle represent sides that are perpendicular, meaning the angles are right angles with
segments, rays, and angles.
measures of 90º; etc.
What do you notice about all the angles of the rectangle? Answers may vary. All the angles of the
TEACHER NOTE
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Suggested
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
rectangle are right angles with measures of 90º; etc.
Is congruency another attribute that could be used to describe two-dimensional figures? Explain.
(yes) Answers may vary. The sides and angles of two-dimensional figures can be described as congruent;
etc.
Notes for Teacher
Many students have difficulty classifying
an angle when it does not have a
horizontal side. Allow these students to
use a “moveable” right angle such as
the corner of an index card (or their
5. Explain to students that they will be investigating the attributes of two-dimensional figures using the formal
geometric terms.
STAAR Grade 5 Mathematics
Reference Materials) to place at the
vertex of any angle. It should be easy to
see if the angle is less than, equal to, or
greater than a right angle.
TEACHER NOTE
Teacher Resource: Two-Dimensional
Geometric Definitions – Notes may
be used to verify student responses to
the matching activities outlined in the
instruction.
Topics:
Attributes of two-dimensional figures
ATTACHMENTS
Card Set: Two-Dimensional
Attribute Cards (1 set per 2
students)
Explore/Explain 1
Teacher Resource: Two-
Students use logic and reasoning skills to investigate, compare and contrast examples and definitions of two-
Dimensional Figures Graphic
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Suggested
Day
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
dimensional figures.
Notes for Teacher
Organizer (1 per teacher)
Handout: Two-Dimensional
Instructional Procedures:
1. Prior to instruction, create a card set: Two-Dimensional Attribute Cards for every 2 students by copying on
cardstock, laminating, cutting apart, and placing in a plastic zip bag.
2. Place students in pairs and distribute a card set: Two-Dimensional Attribute Cards to each pair.
3. Instruct students to work with their partner to match each card with its appropriate definition. Allow time for
students to complete their matches. Monitor and assess student pairs to check for understanding.
4. Facilitate a class discussion about the terms and the figures that model them.
5. Once all matches have been verified, instruct students to organize their cards into a tree-like diagram showing
how all the figures are related. For teacher reference, see teacher resource: Two-Dimensional Figures
Graphic Organizer as a sample of how the cards could be arranged. Do not display this graphic to students at
Figures Graphic Organizer (1
per student)
Teacher Resource: Polygon
Attributes KEY (1 per teacher)
Handout: Polygon Attributes (1
per student)
Handout (optional): TwoDimensional Figures Visual
Graphic Organizer (1 per
student)
Handout (optional): Polygon
Table
this time. If needed, demonstrate what a tree diagram looks like using the model below. Explain to students that
the cards are not necessarily in the correct position.
MATERIALS
Sample:
cardstock (4 sheets per 2
students)
scissors (1 per teacher)
plastic zip bag (sandwich sized)
(1 per 2 students)
TEACHER NOTE
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
Polygons with all sides and angles
Allow time for students to organize their cards. Monitor and assess student pairs to check for understanding.
congruent are called regular polygons.
Facilitate a class discussion about the diagrams they created. Allow students to adjust their graphic
For example, a hexagon with all sides
organizers based on the class discussion.
equal in length and all angles equal in
Ask:
angle measure, are considered regular
Are all two-dimensional figures polygons? How do you know? (no) Answers may vary. Some twodimensional figures have curved sides (e.g. circles); etc.
Are all polygons two-dimensional figures? How do you know? (yes) Answers may vary. All polygons
have length and width; etc.
hexagons. However, all hexagons are
not regular hexagons. These figures are
referred to as irregular figures. There are
many examples of irregular hexagons in
Are all polygons quadrilaterals? How do you know? (no) Answers may vary. Some polygons are
the real world where all of the sides are
triangles; etc.
not equal in length, and all angles are
Are all quadrilaterals polygons? How do you know? (yes) Answers may vary. All quadrilaterals are
not equal in measure.
enclosed figures with 4 straight sides; etc.
Are all quadrilaterals parallelograms? How do you know? (no) Answers may vary. Quadrilaterals only
TEACHER NOTE
have to have four sides, and those sides do not have to all be parallel and/or congruent; etc.
Teacher resource: Two-Dimensional
Are all parallelograms quadrilaterals? How do you know? (yes) Answers may vary. Parallelograms
Figures Graphic Organizer may be
must have four sides; etc.
posted in the classroom. The graphic
organizer does not include all 4- sided
6. Display teacher resource: Two-Dimensional Figure Graphic Organizer. Distribute handout: Two-
figures such as a “kite.” A kite would be
Dimensional Figure Graphic Organizer to each student. Facilitate a class discussion to summarize the
another branch off of the quadrilateral
relationships between the two-dimensional figures.
because of its attributes. A kite has two
Ask:
sets of congruent sides, but the
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
How do the attributes change when comparing the quadrilateral to the parallelogram, then to the
rectangle, and finally to the square? Explain. Answers may vary. For these connected figures, the figure
beneath contains the attributes of the figure above it, meaning the figure’s attributes move from general to
more specific if looking down the tree; etc.
Notes for Teacher
congruent sides are adjacent to each
other, not opposite of each other. A
kite’s opposite angles are congruent.
The purpose of this graphic organizer is
to help students visually organize the
Explain to students that the attributes of a quadrilateral (a four-sided polygon) are included in the attributes of
geometric figures based on their
a parallelogram (a quadrilateral with opposite sides congruent, opposite sides parallel, and opposite angles
common and distinguishing attributes.
congruent). The attributes of a quadrilateral and a parallelogram are included in the attributes of a rectangle (a
quadrilateral with four right (90o) angles (meaning opposite angles are congruent), opposite sides congruent,
TEACHER NOTE
opposite sides parallel, and adjacent sides are perpendicular because of the four right angles.). The attributes
Handout (optional): Polygon Table is
of a quadrilateral, parallelogram, and a rectangle are included in the attributes of a square (a quadrilateral with
available to assist students in
all sides congruent (meaning opposite sides congruent), opposite sides parallel, four right (90o) angles
understanding the different types of
(meaning opposite angles are congruent), and adjacent sides are perpendicular because of the four right
polygons.
angles.).
7. Distribute handout: Polygon Attributes to each student as independent practice and/or homework.
TEACHER RESOURCE
The handout (optional): TwoDimensional Figures Visual Graphic
Organizer provides a visual
representation of two-dimensional
figures along with the names in a treelike graphic organizer.
2
Topics:
Spiraling Review
Faces, edges, vertices, bases, and curved surfaces
page 13 of 74 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
ATTACHMENTS
Engage 2
Card Set: Faces, Edges,
Students use logic and reasoning skills to review examples and definitions of faces, edges, vertices, bases, and
Vertices, Bases, and Curved
curved surfaces in order to recognize them as attributes of three-dimensional figures.
Surface Cards (1 set per 2
students)
Instructional Procedures:
Teacher Resource: ThreeDimensional Geometric
1. Prior to instruction, create a card set: Faces, Edges, Vertices, Bases, and Curved Surface Cards for every 2
students by copying on cardstock, laminating, cutting apart, and placing in a plastic zip bag.
2. Facilitate a class discussion to debrief the previously assigned handout: Polygon Attributes, as needed.
3. Place students in pairs and distribute a card set: Faces, Edges, Vertices, Bases, and Curved Surface Cards
to each pair. Instruct student pairs to match each card with its appropriate definition. Allow time for students to
Definitions – Notes (1 per
teacher)
Class Resource (optional):
Three-Dimensional Geometric
Patterns (1 set per 4 students)
complete their matches. Monitor and assess student pairs to check for understanding. Facilitate a class
discussion about the terms and the figures that model them. Verify student matches are correct.
MATERIALS
Ask:
cardstock (2 sheets per 2
How is an edge on a three-dimensional figure like a side on a two-dimensional figure? Answers
students)
may vary. They are both line segments where parts of the figure meet; etc.
scissors (1 per teacher)
How is a vertex on a three-dimensional figure different from a vertex on a two-dimensional figure?
plastic zip bag (sandwich sized)
Answers may vary. Although they both show a point of intersection, the three-dimensional figure shows
(1 per 2 students)
where 3 or more edges intersect, whereas a two-dimensional figure shows where 2 sides intersect; etc.
geometric figures or solids (1 set
per teacher)
4. Display a triangular prism, hexagonal prism, and cube for the class to see. Use these prisms to discuss the
terms face and base. Explain to students that the base of a figure defines the name of the prism. Begin with the
cardstock (optional) (9 sheets
per 4 students)
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
displayed triangular prism.
tape (clear) (optional) (1 roll per
Ask:
teacher)
This figure has how many faces? (5 faces)
How could you describe the faces of this figure? (2 triangular faces and 3 rectangular faces)
TEACHER NOTE
If the bases of a prism are the two unique faces that are congruent and parallel to each other,
If geometric figures or solids are
which faces are the bases? (the triangular faces)
unavailable, use class resource
Demonstrate that the bases of a triangular prism are parallel by placing the triangular prism in the palm of
one hand and placing the palm of your other hand on top. Discuss how the two triangular faces (and your
palms) are parallel to each other.
What is the name of this figure? (a triangular prism)
(optional): Three-Dimensional
Geometric Patterns to create a set of
figures for every 4 students.
TEACHER NOTE
Teacher Resource: Three-
Refer to the displayed hexagonal prism and use the same discussion above to determine that the two
hexagons are the bases of the figure; therefore, the figure is called a hexagonal prism. Next, discuss the
displayed cube. Discuss how the cube has six congruent faces that are all squares; therefore, any two of the
squares that are parallel to one another could be considered the bases. Explain to students that this figure
Dimensional Geometric Definitions –
Notes may be used to verify student
responses to the matching activities
outlined in the instruction.
has a unique name, a cube.
5. Display a square pyramid and triangular pyramid. Use these pyramids to discuss the terms face and base.
Explain to students that a pyramid has only one base, and the base defines the name of the pyramid. Begin
with the displayed square pyramid.
Ask:
A pyramid has how many bases? (1 base)
This figure has how many faces? (5 faces)
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Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
How could you describe the faces of this figure? (triangles and a square)
Since there is only one square face, what do you think is the name of this pyramid? (a square
pyramid)
Notice, the non-base faces are all triangles. Next, refer to the displayed triangular pyramid.
Ask:
This figure has how many faces? (4 faces)
How could you describe the faces of this figure? (all triangles)
Since all of the faces are triangles, are all of the faces congruent? Answers may vary.
If the faces of the triangular prism are all equilateral triangles, then any of the faces could be the base. If one of
the triangles is not congruent to the other triangles, then the non-congruent triangle is the base.
What is the name of this figure? (a triangular pyramid)
6. Display the cylinder, the cone, and the sphere to distinguish the difference between circular surface and circular
base.
Ask:
Do all of these figures have a base? (No, the sphere has no base.)
Since the sphere has no base, the sphere is described as a curved surface.
How many bases does the cylinder have? (2 bases)
How could you describe the bases of a cylinder? (2 circular bases)
How could you describe the other surface of the cylinder? (a curved surface)
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Suggested Instructional Procedures
Notes for Teacher
The cone has how many bases? (1 base)
How could you describe the other surface of the cone? (a curved surface)
7. Explain to students that they will be investigating the attributes of three-dimensional figures using the formal
geometric terms.
Topics:
Attributes of three-dimensional figures
ATTACHMENTS
Card Set: Three-Dimensional
Attribute Cards (1 set per 2
students)
Explore/Explain 2
Teacher Resource: Three-
Students use logic and reasoning skills to investigate, compare and contrast examples and definitions of three-
Dimensional Figures Graphic
dimensional figures.
Organizer (1 per teacher)
Handout: Three-Dimensional
Instructional Procedures:
1. Prior to instruction, create a card set: Three-Dimensional Attribute Cards for every 2 students by copying on
cardstock, laminating, cutting apart, and placing in a plastic zip bag.
2. Place students in pairs and distribute a card set: Three-Dimensional Attribute Cards to each pair.
3. Instruct student pairs to match each card with its appropriate definition. Allow time for students to complete their
matches. Monitor and assess student pairs to check for understanding. Facilitate a class discussion about the
terms and the figures that model them.
Figures Graphic Organizer (1
per student)
Teacher Resource: Attributes of
Three-Dimensional Figures
KEY (1 per teacher)
Handout: Attributes of ThreeDimensional Figures (1 per
student)
4. Once all matches have been verified, instruct students to organize their cards into a tree-like diagram showing
how all the figures are related. For teacher reference, see teacher resource: Three-Dimensional Figures
MATERIALS
page 17 of 74 Enhanced Instructional Transition Guide
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Graphic Organizer as a sample of how the cards could be arranged. Do not display this graphic to the
students at this time. If needed, demonstrate what a tree diagram looks like using the model below. Explain to
students that the cards are not necessarily in the correct position.
Sample:
Notes for Teacher
cardstock (4 sheets per 2
students)
scissors (1 per teacher)
plastic zip bag (sandwich sized)
(1 per 2 students)
geometric figures or solids (1 set
per 4 students, 1 set per
teacher)
Allow time for students to organize their cards. Monitor and assess student pairs to check for understanding.
Facilitate a class discussion about the diagrams they created. Allow students to adjust their graphic
organizers based on the class discussion.
Ask:
TEACHER NOTE
Pyramids and Cones
A pyramid is a polyhedron (a threedimensional figure with faces and
edges). The attributes of a pyramid
Are all three-dimensional figures prisms? How do you know? (no) Answers may vary. Some three-
include faces, edges, and the “point”
dimensional figures are pyramids or have curved surfaces; etc.
where the edges meet, which is defined
Are all prisms three-dimensional figures? How do you know? (yes) Answers may vary. All prisms have
as a “vertex.” As the number of faces on
length, width, and height (or depth); etc.
the pyramid approaches infinity, the
Are all prisms rectangular? How do you know? (no) Answers may vary. Some prisms are triangular,
surface becomes curved, creating a
pentagonal, etc.
cone. Since a cone consists of a curved
Are all pyramids three-dimensional figures? How do you know? (yes) All pyramids have length, width,
surface, it is not considered a
and height (or depth); etc.
polyhedron. When you talk about a
cone the terms “face,” “edge,” and
page 18 of 74 Enhanced Instructional Transition Guide
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Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
5. Display teacher resource: Three-Dimensional Figure Graphic Organizer. Distribute handout: ThreeDimensional Figure Graphic Organizer to each student. Facilitate a class discussion to summarize the
relationships between the figures.
Ask:
Notes for Teacher
“vertex,” as defined by a polyhedron, do
not apply. A wide variety of resources
modify these definitions when
referencing non-polyhedrons. It is
Are all cubes rectangular prisms? How do you know? (yes) Answers may vary. All cubes have 6 square
possible to refer to the “vertex” of a cone
(rectangular) faces, 12 edges, and 8 vertices; etc.
as a “point” in elementary math.
Therefore, for elementary, TEA only lists
6. Distribute handout: Attributes of Three-Dimensional Figures to each student as independent practice and/or
homework.
the curved surface and circular base as
the attributes of a cone and do not
reference “vertex” as a defining attribute.
So, CSCOPE uses these attributes in
alignment with TEA.
Cones and Cylinders
According to TEA, a face of a threedimensional figure is defined as a flat
surface in the shape of a twodimensional figure. Since the circular
bases of a cylinder and cone are flat
surfaces in the shape of a twodimensional figure, they could also be
considered “faces.” However, for
elementary, TEA only lists curved
surface and circular base(s) as the
attributes of a cylinder and cone. So,
page 19 of 74 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
CSCOPE uses these attributes in
alignment with TEA.
TEACHER NOTE
The faces of some rectangular prisms
are all rectangles and the faces of some
rectangular prisms are rectangles and
squares. However, recall all squares are
rectangles, so refer to this prism as a
rectangular prism.
3
Topics:
Spiraling Review
Naming attributes of two- and three-dimensional figures
ATTACHMENTS
Explore/Explain 3
Teacher Resource: Naming
Students investigate and name the attributes of two- and three-dimensional figures.
Geometric Figures KEY (1 per
teacher)
Teacher Resource: Naming
Instructional Procedures:
1. Distribute handout: Naming Geometric Figures to each student. Display the top part of page 1 of teacher
resource: Naming Geometric Figures. Facilitate a class discussion regarding how to name the attributes of a
labeled geometric figure. Emphasize when naming line segments that the order of the letters within one
segment does not matter. For example,
is the same line segment as
. Also explain that when naming
Geometric Figures (1 per
teacher)
Handout: Naming Geometric
Figures (1 per student)
faces of figures, the order of the letters naming one face should be clockwise; however, the beginning vertex of
page 20 of 74 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
the face does not matter. For example, the following all name the same face: ABCD, BCDA, CDAB, and DABC.
2. Place students in pairs and instruct students to work together to complete the handout. Allow time for students
to complete the activity. Monitor and assess students to check for understanding. When student pairs have
completed the handout, invite student volunteers to display their answers. Facilitate a class discussion
encouraging students to determine all the possible ways attributes can be named.
Notes for Teacher
TEACHER NOTE
When naming faces, some resources
will name faces using a
counterclockwise order. However, the
answer keys provide sample answers in
clockwise order.
TEACHER NOTE
It is customary to name an angle with a
single capital letter or an interior number
when there is no possibility of
confusion. Angles can also be named
with three letters with the middle letter
representing the vertex of the referenced
angle.
page 21 of 74 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Topics:
Attributes of two- and three-dimensional figures
Notes for Teacher
ATTACHMENTS
Teacher Resource: Geometric
Logic (1 per teacher)
Teacher Resource: Two- and
Elaborate 1
Three-Dimensional Figure
Students extend concepts of geometric attributes of two- and three-dimensional figures.
Practice KEY (1 per teacher)
Handout: Two- and Three-
Instructional Procedures:
1. Display teacher resource: Geometric Logic for the class to see. Explain to students that special made-up
Dimensional Figure Practice
(1 per student)
words such as hulops can be used to name sets of examples. Although these are made-up names for the sets,
you can still apply what you know about two-dimensional figures to determine the characteristics a set of figures
have in common.
Ask:
What do these figures have in common? Answers may vary. The first figure is a triangle with a square
inside it, the second figure is a rectangle with a pentagon inside of it, and the third figure is a pentagon with
a hexagon inside of it; they are polygons inside of polygons; etc.
What pattern do these shapes seem to be following? Answers may vary. The inside figure has one
more side and one more vertex than the outside figure; etc.
2. Distribute handout: Two- and Three-Dimensional Figure Practice to each student. Instruct students to
complete the handout independently. Allow time for students to complete the activity. Monitor and assess
student pairs to check for understanding. Facilitate a class discussion to debrief student solutions.
page 22 of 74 Enhanced Instructional Transition Guide
Suggested
Day
4
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Evaluate 1
Instructional Procedures:
1. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned
Notes for Teacher
ATTACHMENTS
Handout: Three-Dimensional
Geometric Patterns (1 per
student)
to this lesson.
Performance Indicator(s):
MATERIALS
Grade 05 Mathematics Unit 10 PI 01
clothes hanger (wire) (1 per
Create a mobile (e.g., a decorative structure that is suspended so as to turn freely in the air) that displays models of 4
student)
different three-dimensional figures. The mobile should include 1 prism, 1 pyramid, and 2 curved surfaced figures.
yarn (6 inch strip) (4 per student)
Use the provided die-cuts or nets (cube, rectangular prism, triangular prism, cone, cylinder, triangular pyramid, and
index card (4” x 6”) (4 per
square pyramid) to represent the three-dimensional figures selected. On each net, if applicable, use different map
student)
pencil colors to highlight parallel lines and perpendicular and to shade the congruent faces of each figure.
tape (clear) (1 roll per student)
Construct each selected net to create a three-dimensional model. Using geometric attributes, create a description card
scissors (1 per student)
for each model that includes the following: (1) the formal geometric name; (2) a description of each of the two-
math journal (1 per student)
dimensional faces or curved surfaces; (3) the number of faces/curved surfaces; (4) the number of vertices, if applicable;
and (5) the number of edges, if applicable.
Complete the mobile by using yarn or string to attach each description card to the appropriate three-dimensional model
and then to a clothes hanger. The completed mobile should be similar to the sample below:
page 23 of 74 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
Observe the created mobile, and write a journal entry for each of the following: (1) describe the difference between the
number of faces, edges, and vertices of the prism and the pyramid; (2) determine examples of real-world
situations/objects in which each three-dimensional model created could be found; and (3) justify how the twodimensional attributes define each three-dimensional model.
Standard(s): 5.7 , 5.14A , 5.14D , 5.15A , 5.15B , 5.16A , 5.16B ELPS ELPS.c.1C , ELPS.c.5F
Evaluate 2
Instructional Procedures:
page 24 of 74 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
1. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned
to this lesson.
Performance Indicator(s):
Grade 05 Mathematics Unit 10 PI 02
Answer each of the following questions regarding the playhouse, using appropriate geometric language and labels:
1. identify the geometric figure that represents the roof, column, house, and top of the column;
2. identify the number of vertices, edges, and faces or curved surfaces on each of the figures
identified in step (1); and
3. name all vertices, edges, and faces for the roof and house.
page 25 of 74 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 10:
Suggested Duration: 4 days
Suggested Instructional Procedures
Notes for Teacher
Write a paragraph comparing and contrasting the attributes of the roof, column, house, and top of the column using
formal geometric language.
Standard(s): 5.7 , 5.14A , 5.15A , 5.15B ELPS ELPS.c.5B
05/17/13
page 26 of 74 Grade 5
Mathematics
Unit: 10 Lesson: 01
Lines, Angles, and Congruency Cards
Parallel lines
lines that lie in the same
plane, never intersect,
and are the same
distance apart
Perpendicular lines
lines that intersect at
right angles (90°) to each
other
Right angle
an angle that measures
90°; lines that are
perpendicular to each
other
Acute angle
an angle with a measure
less than a right angle
(90°)
©2012, TESCCC
05/14/13
page 1 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Lines, Angles, and Congruency Cards
Obtuse angle
an angle whose measure
is greater than a right
angle (90°) but less than
a straight line (180°)
Congruent
figures with the same
size, same shape
©2012, TESCCC
05/14/13
page 2 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two-Dimensional
Geometric Definitions - Notes
Angle: two rays that meet at a common endpoint
Acute angle: an angle with a measure less than a right angle (90°)
Circle: the set of all points that lie the same distance from the center and lie in the same
plane
Congruent: figures with the same size, same shape
Equilateral Triangle: a triangle with 3 congruent sides and 3 congruent angles
Hexagon: a polygon with 6 sides, 6 angles, and 6 vertices
Irregular figure: a figure with at least 2 sides not congruent or at least 2 angles not
congruent
Isosceles Triangle: a triangle with at least 2 congruent sides and 2 congruent angles
Line: a set of points that form a straight path that goes in opposite directions without ending
Line segment: part of a line between two endpoints
Obtuse angle: an angle whose measure is greater than a right angle (90°) but less than a
straight line (180°)
Octagon: a polygon with 8 sides, 8 angles, and 8 vertices
Parallel lines: lines that lie in the same plane, never intersect, and are the same distance
apart
Parallelogram: four-sided (quadrilateral) polygon with opposite sides congruent, opposite
sides parallel, and opposite angles congruent
Perpendicular lines: lines that intersect at right angles (90°) to each other
Pentagon: a polygon with 5 sides, 5 angles, and 5 vertices
Plane: a flat surface that goes on forever in all directions
Point: an exact location in space, represented by a dot
Polygon: a closed two-dimensional figure with three or more straight sides
©2012, TESCCC
05/17/13
page 1 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two-Dimensional
Geometric Definitions - Notes
Quadrilateral: any four-sided polygon
Ray: part of a line that has one endpoint and continues without end in one direction
Rectangle: four-sided polygon (quadrilateral) with 4 right (90°) angles, opposite sides
congruent, opposite sides parallel , and adjacent sides perpendicular
Regular figure: a figure with all sides congruent and all angles congruent
Right angle: an angle that measures 90°; lines that are perpendicular to each other
Rhombus: four-sided polygon (quadrilateral) having all four sides congruent, opposite sides
parallel, and opposite angles congruent
Scalene Triangle: a triangle with no congruent sides and no congruent angles
Square: four-sided polygon (quadrilateral) with 4 right (90°) angles, all sides congruent,
opposite sides parallel, and adjacent sides perpendicular
Trapezoid: four-sided polygon (quadrilateral) with exactly one pair of parallel sides
Triangle: a polygon with 3 sides, 3 angles, and 3 vertices
Two-dimensional figure: a figure with two basic units of measure, usually length and width
Vertex (plural – vertices): the point (corner) of intersection of two sides in a two-dimensional
figure
©2012, TESCCC
05/17/13
page 2 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two-Dimensional Attribute Cards
Polygon
Congruent
Sides
Noncongruent
Sides
a closed two-dimensional
figure with three or more
straight sides
Quadrilateral
any four-sided polygon
Two-dimensional figure
a figure with two basic
units of measure, usually
length and width
Parallelogram
four-sided (quadrilateral)
polygon with
•
•
•
©2012, TESCCC
05/13/13
opposite sides congruent
opposite sides parallel
opposite angles
congruent
page 1 of 4
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two-Dimensional Attribute Cards
Rectangle
four-sided polygon
(quadrilateral) with
•
•
•
•
Square
4 right (90°) angles
opposite sides congruent
opposite sides parallel
adjacent sides
perpendicular
four-sided polygon
(quadrilateral) with
•
•
•
•
4 right (90°) angles
all sides congruent
opposite sides parallel
adjacent sides
perpendicular
Rhombus
four-sided polygon
(quadrilateral) with
•
•
•
all sides congruent
opposite sides parallel
opposite angles
congruent
Trapezoid
four-sided polygon
(quadrilateral) with
exactly one pair of
parallel sides
©2012, TESCCC
05/13/13
page 2 of 4
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two-Dimensional Attribute Cards
Triangle
a polygon with
• 3 sides
• 3 angles
• 3 vertices
Equilateral Triangle
a triangle with
• 3 congruent sides
• 3 congruent angles
Isosceles Triangle
a triangle with
• 2 congruent sides
• 2 congruent angles
Scalene Triangle
a triangle with
• no congruent sides
• no congruent angles
©2012, TESCCC
05/13/13
page 3 of 4
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two-Dimensional Attribute Cards
Pentagon
a polygon with
• 5 sides
• 5 angles
• 5 vertices
Hexagon
a polygon with
• 6 sides
• 6 angles
• 6 vertices
Octagon
a polygon with
• 8 sides
• 8 angles
• 8 vertices
Circle
the set of all points that
lie the same distance
from the center (C) and
lie in the same plane
C
©2012, TESCCC
05/13/13
page 4 of 4
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two-Dimensional Figures Graphic Organizer
Two Dimensional Figures
Polygons
Triangle
Equilateral
Isosceles
Quadrilateral Pentagon
Hexagon Octagon
Scalene
Parallelogram
Rectangle
Circles
Trapezoid
Rhombus
Square
©2012, TESCCC
05/14/13
page 1 of 1
Grade 03
Mathematics
Unit: 05 Lesson: 01
Polygon Attributes KEY
Describe the number of sides and vertices of each of the polygons (1) – (10). Use the attributes
parallel, perpendicular, right angles, congruent angles, and congruent sides, where appropriate.
Then match each description to the polygon figures in the boxes below. Label each polygon figure
with the number(s) that matches its description.
(1) Hexagon
(6) Square
4 sides and 4 vertices with all sides
6 sides and 6 vertices
congruent, adjacent sides perpendicular, and
4 right (90º) angles
(2) Pentagon
(7) Trapezoid
4 sides and 4 vertices with exactly one pair of
5 sides and 5 vertices
parallel sides
(3) Scalene triangle
(8) Rhombus
4 sides and 4 vertices with all sides
3 sides and 3 vertices with no congruent
congruent, opposite sides parallel, and
sides or angles
opposite angles congruent
(4) Octagon
(9) Rectangle
4 sides and 4 vertices with opposite sides
8 sides and 8 vertices
congruent, adjacent sides perpendicular, and
4 right (90º) angles
(5) Equilateral Triangle
(10) Isosceles Triangle
3 sides and 3 vertices with all sides and
3 sides and 3 vertices with at least 2
angles congruent
congruent sides and 2 congruent angles
3
2
4
9
10
©2012, TESCCC
2
8
7
5
1
4
1
6, 8, 9
6, 8, 9
8
05/17/13
3
page 1 of 2
Grade 03
Mathematics
Unit: 05 Lesson: 01
Polygon Attributes KEY
Use the information from the table on the previous page and handout: Two-Dimensional Figures
Graphic Organizer to help answer these questions.
(11)
What attributes do a square and a rectangle have in common? How are these figures
different? Both are quadrilaterals with opposite sides parallel and congruent, adjacent
sides perpendicular, and 4 right (90o) angles. The difference between these figures is
that a rectangle need not have all sides congruent, and a square must have all sides
congruent.
(12)
Can a figure be both a rectangle and a rhombus? Explain. Yes, a square is both a
rectangle and a rhombus. A square is special type of a rectangle because both have 4
right (90o) angles, adjacent perpendicular sides, and opposite sides congruent. In fact,
the square has all sides congruent. A square is a special type of a rhombus because
both have 4 congruent sides and opposite angles congruent. In fact, the square has 4
right (90o) angles.
(13)
Do a trapezoid and a rectangle have anything in common? Explain. Yes, both are
quadrilaterals and both have at least one pair of parallel sides. Some trapezoids may
have right angles, such as in the figure labeled 7.
(14)
Can a right triangle be classified as an equilateral triangle? Explain. No. Answers may vary.
A right triangle has 1 right (90o) angle which means that the other two angles cannot
be right (90o) angles. All sides would be square, and it would no longer be a triangle.
(15)
Is a rectangle a square? Explain. No, because not all sides of a rectangle are congruent.
(16)
Is a square a rectangle? Explain. Yes, a square is special type of a rectangle because
both have 4 right (90o) angles, adjacent perpendicular sides, and opposite sides
congruent. In fact, the square has all sides congruent.
(17)
Is a circle a polygon? Explain. No, because a circle consists of a continuous curved line,
and a polygon has straight lines.
(18)
What is the attribute relationship between the quadrilateral, parallelogram, rhombus, and
square? Explain. The attributes of a quadrilateral (a four-sided polygon) are included in
the attributes of a parallelogram (a quadrilateral with opposite sides congruent,
opposite sides parallel, and opposite angles congruent). The attributes of a
quadrilateral and a parallelogram are included in the attributes of a rhombus (a
quadrilateral with all sides congruent (meaning opposite sides are congruent),
opposite sides parallel, and opposite angles are congruent). The attributes of a
quadrilateral, parallelogram, and a rhombus are included in the attributes of a square
(a quadrilateral with all sides congruent (meaning opposite sides are congruent),
opposite sides parallel, four right (90o) angles (meaning opposite angles are
congruent), and adjacent sides that are perpendicular because of the four right
angles.).
©2012, TESCCC
05/17/13
page 2 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Polygon Attributes
Describe the number of sides and vertices of each of the polygons (1) – (10). Use the attributes
parallel, perpendicular, right angles, congruent angles, and congruent sides, where appropriate.
Then match each description to the polygon figures in the boxes below. Label each polygon figure
with the number(s) that matches its description.
(1) Hexagon
(6) Square
(2) Pentagon
(7) Trapezoid
(3) Scalene triangle
(8) Rhombus
(4) Octagon
(9) Rectangle
(5) Equilateral Triangle
(10) Isosceles Triangle
©2012, TESCCC
05/13/13
page 1 of 2
Grade 03
Mathematics
Unit: 05 Lesson: 01
Polygon Attributes
Use the information from the table on the previous page and handout: Two-Dimensional Figures
Graphic Organizer to help answer these questions.
(11)
What attributes do a square and a rectangle have in common? How are these figures
different?
(12)
Can a figure be both a rectangle and a rhombus? Explain.
(13)
Do a trapezoid and a rectangle have anything in common? Explain.
(14)
Can a right triangle be classified as an equilateral triangle? Explain.
(15)
Is a rectangle a square? Explain.
(16)
Is a square a rectangle? Explain.
(17)
Is a circle a polygon? Explain.
(18)
What is the attribute relationship between the quadrilateral, parallelogram, rhombus, and
square? Explain.
©2012, TESCCC
05/02/12
page 2 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two-Dimensional Figures Visual Graphic Organizer
Two Dimensional Figures
Polygons
Triangle
Equilateral
Isosceles
Circles
Quadrilateral Pentagon
Hexagon
Octagon
Scalene
Parallelogram
Rectangle
Trapezoid
Rhombus
Square
©2012, TESCCC
05/13/13
page 1 of 1
Grade 5
Mathematics
Unit: 10 Lesson: 01
Polygon Table
Figure
Description
Triangle
• 3 sides
• 3 vertices
• 3 angles
Quadrilateral
• 4 sides
• 4 vertices
• 4 angles
Pentagon
• 5 sides
• 5 vertices
• 5 angles
Hexagon
• 6 sides
• 6 vertices
• 6 angles
Octagon
• 8 sides
• 8 vertices
• 8 angles
©2012, TESCCC
Congruent Sides
Regular
05/10/13
Non-Congruent Sides
Irregular
page 1 of 1
Grade 5
Mathematics
Unit: 10 Lesson: 01
Faces, Edges, Vertices, Bases, and Curved Surface Cards
Face
the flat surface of a threedimensional figure
Edge
a line segment where two
faces meet on a threedimensional figure
Vertex
the point (corner) of
intersection of three or
more edges of a threedimensional figure
©2012, TESCCC
05/14/13
page 1 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Faces, Edges, Vertices, Bases, and Curved Surface Cards
Base of a threedimensional figure
• prisms
—
the 2 unique faces (bases) that
are congruent and parallel to
each other unless all faces are
the same shape
• pyramids
—
the unique face (base) unless
all faces are the same shape
• curved-surface figures
—
circular base
Curved Surface
surface of a threedimensional figure that is
curved
©2012, TESCCC
05/14/13
page 2 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional
Geometric Definitions – Notes
Base of a three-dimensional figure: (1) prisms - the 2 unique faces (bases) that are
congruent and parallel to each other unless all faces are the same shape; (2)
pyramids - the unique face (base) unless all faces are the same shape; (3)
curved-surface figures - circular base
Cone: three-dimensional figure with 1 circular base and 1 curved surface
Cube: three-dimensional figure with 6 square faces (2 square faces (bases) and 4 other
square faces), 12 edges, and 8 vertices
Cylinder: three-dimensional figure with two congruent circular bases that are parallel and
1 curved surface
Curved Surface: surface of a three-dimensional figure that is curved
Edge: a line segment where two faces meet on a three-dimensional figure
Face: the flat surface of a three-dimensional figure
Hexagonal prism: three-dimensional figure with 8 faces (2 hexagonal faces (bases) and
6 rectangular faces), 18 edges, and 12 vertices
Pentagonal prism: three-dimensional figure with 7 faces (2 pentagonal faces (bases)
and 5 rectangular faces), 15 edges, and 10 vertices
Pentagonal pyramid: three-dimensional figure with 6 faces (1 pentagonal face (base)
and 5 triangular faces), 10 edges, and 6 vertices
Prism: three-dimensional figure with two congruent, parallel faces (bases) and sides that
are polygonal faces
Rectangular prism: three-dimensional figure with 6 rectangular faces (2 rectangular
faces (bases) and 4 other rectangular faces), 12 edges, and 8 vertices
Rectangular pyramid: three-dimensional figure with 5 faces (1 rectangular face (base)
and 4 triangular faces), 8 edges, and 5 vertices
Sphere: three-dimensional figure with all of its points the same distance from its center
Square pyramid: three-dimensional figure with 5 faces (1 square face (base) and 4
triangular faces), 8 edges, and 5 vertices
Three-dimensional figure: a figure with three units of measure including length, width
(depth), and height
©2012, TESCCC
05/14/13
page 1 of 2
Grade 03
Mathematics
Unit: 05 Lesson: 01
Three-Dimensional
Geometric Definitions – Notes
Triangular prism: three-dimensional figure with 5 faces (2 triangular faces (bases) and
3 rectangular faces), 9 edges, and 6 vertices
Triangular pyramid: three-dimensional figure with 4 triangular faces (1 triangular face
(base) and 3 other triangular faces), 6 edges, and 4 vertices
Vertex (plural – vertices): the point (corner) of intersection of three or more edges of a
three-dimensional figure
©2012, TESCCC
05/14/13
page 2 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Geometric Patterns
Cube
©2012, TESCCC
10/11/12
page 1 of 9
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Geometric Patterns
Rectangular Prism
©2012, TESCCC
10/11/12
page 2 of 9
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Geometric Patterns
Triangular Prism
©2012, TESCCC
10/11/12
page 3 of 9
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Geometric Patterns
Square Pyramid
©2012, TESCCC
10/11/12
page 4 of 9
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Geometric Patterns
Triangular Pyramid
©2012, TESCCC
10/11/12
page 5 of 9
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Geometric Patterns
Cone
©2012, TESCCC
10/11/12
page 6 of 9
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Geometric Patterns
Cylinder
©2012, TESCCC
10/11/12
page 7 of 9
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Geometric Patterns
Pentagonal Prism
©2012, TESCCC
10/11/12
page 8 of 9
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Geometric Patterns
Hexagonal Prism
©2012, TESCCC
10/11/12
page 9 of 9
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Attribute Cards
Three-dimensional
figure
a figure with three units of
measure
•
•
•
Cylinder
length
width (depth)
height
three-dimensional figure with
•
•
two congruent circular
bases that are parallel
1 curved surface
Sphere
three-dimensional figure with
all of its points the same
distance from its center
Cone
three-dimensional figure with
•
•
Prism
three-dimensional figure with
•
•
©2012, TESCCC
1 circular base
1 curved surface
05/14/13
two congruent, parallel
faces (bases)
sides that are polygonal
faces
page 1 of 4
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Attribute Cards
Triangular prism
three-dimensional figure with
5 faces
•
—
2 triangular faces (bases)
— 3 rectangular faces
9 edges
6 vertices
•
•
Rectangular prism
three-dimensional figure with
6 rectangular faces
•
—
2 rectangular faces (bases)
— 4 other rectangular faces
12 edges
8 vertices
•
•
Cube
three-dimensional figure with
6 square faces
•
—
2 square faces (bases)
— 4 other square faces
12 edges
8 vertices
•
•
Pentagonal prism
three-dimensional figure with
•
7 faces
—
2 pentagonal faces (bases)
— 5 rectangular faces
•
•
Hexagonal prism
15 edges
10 vertices
three-dimensional figure with
•
8 faces
—
2 hexagonal faces (bases)
— 6 rectangular faces
•
•
©2012, TESCCC
05/14/13
18 edges
12 vertices
page 2 of 4
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Attribute Cards
Pyramid
three-dimensional figure with
•
•
Triangular pyramid
1 face (base)
sides that are triangular
faces
three-dimensional figure with
•
4 triangular faces
—
1 triangular face (base)
— 3 other triangular faces
•
•
Square pyramid
6 edges
4 vertices
three-dimensional figure with
•
5 faces
—
1 square face (base)
— 4 triangular faces
•
•
Rectangular pyramid
8 edges
5 vertices
three-dimensional figure with
•
5 faces
—
1 rectangular face (base)
— 4 triangular faces
•
•
©2012, TESCCC
05/14/13
8 edges
5 vertices
page 3 of 4
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Attribute Cards
Pentagonal pyramid
three-dimensional figure with
•
6 faces
—
1 pentagonal face (base)
— 5 triangular faces
•
•
©2012, TESCCC
05/14/13
10 edges
6 vertices
page 4 of 4
Grade 5
Mathematics
Unit: 10 Lesson: 01
Three-Dimensional Figures Graphic Organizer
Three-Dimensional Figures
Prisms
Triangular
Prism
Rectangular Pentagonal
Prism
Prism
Curved
Surfaces
Pyramids
Cylinder
Hexagonal
Prism
Cone
Sphere
Cube
Triangular
Pyramid
©2012, TESCCC
Square
Pyramid
05/14/13
Rectangular
Pyramid
Pentagonal
Pyramid
page 1 of 1
Grade 5
Mathematics
Unit: 10 Lesson: 01
Attributes of Three-Dimensional Figures KEY
Describe the attributes (number of faces, describe faces and bases, edges, vertices, curved
surfaces, and/or circular bases, where applicable) for each figure. Then match each description to a
figure in the box below. Label the figure with the number that matches its description.
(1) Triangular Pyramid
(6) Triangular Prism
4 triangular faces (1 triangular face (base) and 3
other triangular faces),
6 edges, 4 vertices
5 faces (2 triangular faces (bases) and 3
rectangular faces),
9 edges, 6 vertices
(2) Rectangular Prism
(7) Cube
6 rectangular faces (2 rectangular faces (bases) and
4 other rectangular faces),
12 edges, 8 vertices
6 square faces (2 square faces (bases) and 4 other
square faces),
12 edges, 8 vertices
(3) Hexagonal Prism
(8) Square Pyramid
8 faces (2 hexagonal faces (bases) and 6
rectangular faces),
18 edges, 12 vertices
5 faces (1 square face (base) and 4 triangular
faces),
8 edges, 5 vertices
(9) Cylinder
(4) Sphere
2 circular bases, 1 curved surface
1 curved surface with all of its points the same
distance from its center
(5) Cone
(10) Pentagonal Prism
1 circular base, 1 curved surface
7
8
7 faces (2 pentagonal faces (bases) and 5
rectangular faces),
15 edges, 10 vertices
6
4
5
10
1
9
2
©2012, TESCCC
3
05/13/13
page 1 of 2
Grade 03
Mathematics
Unit: 05 Lesson: 01
Attributes of Three-Dimensional Figures KEY
Use the information from the table on the previous page to help answer these questions.
(11)
What attributes do a cube and a rectangular prism have in common? How are these figures
different? A cube has all the attributes of a rectangular prism. All the faces of a cube
must be squares, but all the faces of a rectangular prism do NOT have to be squares.
(12)
Can a figure be both a rectangular prism and a cube? Explain. Yes, a cube is both a cube
and a rectangular prism. All the faces of a cube are squares, and all squares are
rectangles.
(13)
Complete the table below to list the number of faces, edges, and vertices of a prism with a
base of 8 edges. For the figure, describe each type of face and then name the figure.
Number
of
Faces
10
Number
of Edges
24
Number
of
Vertices
Types of Faces
(number and name of
each)
Name of Figure
16
2 octagonal faces
(bases) and
8 rectangular faces
Octagonal Prism
(14)
How is a triangular prism different than a rectangular prism? Explain. A triangular prism has
2 triangular faces (bases), and a rectangular prism has 2 rectangular faces (bases).
This means that a triangular prism has fewer faces, edges, and vertices than a
rectangular prism because a triangle only has 3 sides and a rectangle has 4 sides.
(15)
How is a triangular prism different than a triangular pyramid? A triangular prism has 2
triangular faces (bases), and a triangular pyramid has 1 triangular face (base). A
triangular prism has rectangular faces, and a triangular pyramid has only triangular
faces. A triangular pyramid has fewer faces, edges, and vertices than a triangular
prism.
(16)
Name two real world objects that describe a cylinder and a cone. Describe how these two
figures are alike and how they are different based on their geometric attributes. Answers
may vary. Similar attributes include a circular base and a curved surface on both.
Differences are that a cone has 1 circular base, and a cylinder has 2 circular bases.
(17)
Name two real world objects that describe a square pyramid and a cube. Describe how these
two figures are alike and how they are different based on their geometric attributes. Answers
may vary. Similar attributes include a square face (base). Differences are that a square
pyramid has triangular faces, and a cube has square faces. The pyramid has fewer
faces, edges, and vertices than the cube.
(18)
What is true about the side faces (not the base) of all pyramids? The side faces of all
pyramids are triangular.
©2012, TESCCC
05/14/13
page 2 of 2
Grade 03
Mathematics
Unit: 05 Lesson: 01
Attributes of Three-Dimensional Figures
Describe the attributes (number of faces, describe faces and bases, edges, vertices, curved
surfaces, and/or circular bases, where applicable) for each figure. Then match each description to a
figure in the box below. Label the figure with the number that matches its description.
(1) Triangular Pyramid
(2) Triangular Prism
(3) Rectangular Prism
(4) Cube
(5) Hexagonal Prism
(6) Square Pyramid
(7) Sphere
(8) Cylinder
(9) Cone
(10) Pentagonal Prism
©2012, TESCCC
05/14/13
page 1 of 2
Grade 03
Mathematics
Unit: 05 Lesson: 01
Attributes of Three-Dimensional Figures
Use the information from the table on the previous page to help answer these questions.
(11)
What attributes do a cube and a rectangular prism have in common? How are these figures
different?
(12)
Can a figure be both a rectangular prism and a cube? Explain.
(13)
Complete the table below to list the number of faces, edges, and vertices of a prism with a
base of 8 edges. For the figure, describe each type of face and then name the figure.
Number
of
Faces
Number
of Edges
Number
of
Vertices
Types of Faces
(number and name of
each)
Name of Figure
(14)
How is a triangular prism different than a rectangular prism? Explain.
(15)
How is a triangular prism different than a triangular pyramid?
(16)
Name two real world objects that describe a cylinder and a cone. Describe how these two
figures are alike and how they are different based on their geometric attributes.
(17)
Name two real world objects that describe a square pyramid and a cube. Describe how these
two figures are alike and how they are different based on their geometric attributes.
(18)
What is true about the side faces (not the base) of all pyramids?
©2012, TESCCC
05/14/13
page 2 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Naming Geometric Figures KEY
Vertex
V
E
X
G
F
H
B
C
Face
T
Y
A
The vertices in this two-dimensional figure are:
T, V, X, and Y
The sides in this two-dimensional figure are:
D
Edge
The vertices in this three-dimensional figure are:
A, B, C, D, E, F, G, and H
The edges in this three-dimensional figure are:
VX, XY, TY, and VT
AB, AD, CD, CB, BE, AF, FH,
EF, EG, GH, GC, and HD
The face in this two-dimensional figure is:
TVXY
The angles in this two-dimensional figure are:
∠T , ∠V , ∠X, and ∠Y
The faces in this three-dimensional figure are:
ABCD, ABEF, EGHF, CGHD, AFHD, and BEGC
Note: For sides and edges, VX could also be named XV.
For faces, moving clockwise, faces could be named TVXY, VXYT, XYTV, or YTVX.
Sample answers provided for naming edges and faces
Use the geometric solids below to complete the table.
U
S
P
V
T
O
W
X
N
L
Q
R
M
(1) Name the faces:
(5) Name the faces:
QSTR, QSUW, UVXW, WXRQ, VXRT, UVTS
(2) Name the edges:
LONM, LPO, LPM, MPN, NPO
(6) Name the edges:
LM, LO, ON, NM, LP, MP,
NP, and OP
QR, QS, QW, SU, UW, WX,
XV, UV, TV, XR, TR, and ST
(3) Name the vertices:
(7) Name the vertices:
Q, R, S, T, U, V, W, and X
(4) Name a real-world object that has this
same shape.
Answers may vary.
©2012, TESCCC
L, M, N, O, and P
(8) Name a real-world object that has this same
shape.
Answers may vary.
05/17/13
page 1 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Naming Geometric Figures KEY
Sample answers provided for naming edges and faces
Use the geometric solids below to complete the table.
R
E
W
B
F
D
A
D
T
N
F
C
(9) Name two parallel faces:
G
S
(11) Name two parallel faces:
ABC to DEF
SDNT to RWGF, SRFT to DWGN,
SRWD to TFGN
(10) Name two parallel edges:
(12) Name two parallel edges:
RS to WD, RW to SD,
RS to FT, ST to RF,
WD to GN, DN to WG,
FT to GN, TN to FG
AC to DF , AB to DE, BC to
EF, AD to CF, BE to CF,
BE to AD
Use the diagram below to complete the table.
A
H
G
F
(13) Name a square:
B
C
E
D
(15) Name a parallelogram:
BCDE
ABDG or BCDE or ABEH or ACDH
(14) Name a rectangle:
(16) Name a trapezoid:
BCDE or ABEH or ACDH
ABFG or ABEG or ABFH or ACDG or
FBCD or ABDH
(17) In triangle AHG, which angle is the right
angle?
(18) ABFH is what type of quadrilateral?
∠H
©2012, TESCCC
05/17/13
Trapezoid
page 2 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Naming Geometric Figures
Vertex
V
X
E
G
F
H
B
C
Face
T
Y
A
The vertices in this two-dimensional figure are:
T, V, X, and Y
The sides in this two-dimensional figure are:
D
Edge
The vertices in this three-dimensional figure are:
A, B, C, D, E, F, G, and H
The edges in this three-dimensional figure are:
VX, XY, TY, and VT
AB, AD, CD, CB, BE, AF, FH,
EF, EG, GH, GC, and HD
The face in this two-dimensional figure is:
TVXY
The angles in this two-dimensional figure are:
∠T , ∠V , ∠X, and ∠Y
The faces in this three-dimensional figure are:
ABCD, ABEF, EGHF, CGHD, AFHD, and BEGC
Note: For sides and edges, VX could also be named XV.
For faces, moving clockwise, faces could be named TVXY, VXYT, XYTV, or YTVX.
Use the geometric solids below to complete the table.
U
S
P
V
T
O
W
X
N
L
Q
R
M
(1) Name the faces:
(5) Name the faces:
(2) Name the edges:
(6) Name the edges:
(3) Name the vertices:
(7) Name the vertices:
(4) Name a real-world object that has this
same shape.
(8) Name a real-world object that has this same
shape.
©2012, TESCCC
05/17/13
page 1 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Naming Geometric Figures
Use the geometric solids below to complete the table.
R
E
W
B
F
D
A
D
T
N
F
C
G
S
(9) Name two parallel faces:
(11) Name two parallel faces:
(10) Name two parallel edges:
(12) Name two parallel edges:
Use the diagram below to complete the table.
A
H
G
F
B
C
E
D
(13) Name a square:
(15) Name a parallelogram:
(14) Name a rectangle:
(16) Name a trapezoid:
(17) In triangle AHG, which angle is the right
angle?
(18) ABFH is what type of quadrilateral?
©2012, TESCCC
05/17/13
page 2 of 2
Grade 5
Mathematics
Unit: 10 Lesson: 01
Geometric Logic
These are hulops.
What characteristics do hulops have in common?
©2012, TESCCC
10/11/12
page 1 of 1
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two- and Three-Dimensional Figure Practice KEY
Use the clues to determine the geometric figures described.
(1)
(2)
Group A Clues
•
•
•
•
Figure B Clues
•
•
•
Same number of faces as vertices
Most of the faces are triangles
No parallel faces
Most of the faces share a vertex
Figure: Pyramid
Fewer faces than vertices
2 congruent, parallel polygonal faces
all other faces are parallelograms
Figure: Prism
(3) How are the three-dimensional figures in Group A different from those in Group B? The threedimensional figures in Group A have no parallel faces, but the Group B figures have at
least one pair of parallel faces.
Use the grouping of figures below to answer #4 and #5.
A
B
C
D
E
(4) Which of the figure(s) above does not belong to the set? Explain.
Figure C because it is the only figure with no parallel lines.
(5) Draw another figure that could be in this grouping.
Drawings may vary.
(6) These figures show the two different types of tops Josh created. The
shaded portion in each figure shows a face shared by the two threedimensional figures that makeup each top.
•
•
What three-dimensional figures are in Top A? Top B?
Top A: rectangular prism and rectangular pyramid
Top A
Top B
Top B: 2 square (or rectangular) pyramids
Compare the number of faces in Top A to Top B (including the one shaded/shared face in
each). How many more faces does Top A have than Top B? Explain. Top A has 1
additional face. Answers may vary. Top A has 10 faces (including the shaded/shared
face) and Top B has 9 faces (including the shaded/shared face). 10 – 9 = 1 additional
face.
©2012, TESCCC
05/14/13
page 1 of 3
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two- and Three-Dimensional Figure Practice KEY
Sample answers are provided for naming edges and faces.
Complete the table below based on each two-dimensional figure given. The first one is completed as an example.
Sample
Answers
Name of Figure
Use hash marks to
indicate congruent
sides, arcs to
indicate congruent
angles, and square
corners to indicate
square corners
Vertices
A
Parallelogram
D
B
A, B, C, D
Parallel
Sides
AB to DC
AD to BC
Congruent
Sides
Perpendicular
Sides
Congruent
Angles
Right
Angles
AB to DC
AD to BC
None
∠A to ∠C
∠B to ∠D
None
HK to SM
HS to KM
HS to HK
HK to KM
KM to SM
SM to HS
C
H
(7)
Rectangle
K
H, K, M, S
S
M
HK to SM
HS to KM
∠H to ∠K to
∠M to ∠S
∠H, ∠K ,
∠M, ∠S
M
L
(8)
Trapezoid
L, M, P, S
S
©2012, TESCCC
LS to MP
None
LS to SP
MP to SP
∠S to ∠P
∠S, ∠P
P
05/14/13
page 2 of 3
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two- and Three-Dimensional Figure Practice KEY
Sample answers are provided for naming edges and faces.
Complete the table below based on each three-dimensional figure given. The first one is completed as an example.
Sample
Answers
Figure
Faces that are
Parallelograms
Faces that are
Triangles
Faces that are
Rectangles
Faces that are
Parallel
Faces that are
Congruent
Faces that are
Congruent and
Parallel
ABCH, CBDE,
DGEF, GFAH,
DCHG, ABEF
None
ABCH, CBDE,
DGEF, GFAH,
DCHG, ABEF
ABCH to DGEF,
ABEF to CDGH,
AFGH to CDBE
ABCH, CBDE,
DGEF, GFAH,
DCHG, ABEF
ABCH to DGEF,
ABEF to CDGH,
AFGH to CDBE
JKNO, JKLM,
LMNO
KLN, JMO
JKNO, JKLM,
LMNO
KLN, JMO
KLN to JMO
KLN and JMO
QRST
QUT, TUS,
SUR, RUQ
None
QUT to TUS
to SUR to
RUQ
None
D
C
G
H
E
B
F
A
L
K
N
(9)
M
J
O
U
(10)
R
QRST
S
Q
T
(11) Give a real-world example of a cylinder, cone, and sphere. Describe the attributes of each of these objects. Answers may vary.
An example of a cylinder is a canned good, a cone is a party hat, and a sphere is a ball. The canned good has 2 circular bases
and 1 curved face, the party hat has 1 circular base and 1 curved surface, and the ball has 1 curved surface.
©2012, TESCCC
05/14/13
page 3 of 3
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two- and Three-Dimensional Figure Practice
Use the clues to determine the geometric figures described.
(1)
(2)
Group A Clues
•
•
•
•
Figure B Clues
•
•
•
Same number of faces as vertices
Most of the faces are triangles
No parallel faces
Most of the faces share a vertex
Figure:
Fewer faces than vertices
2 congruent, parallel polygonal faces
all other faces are parallelograms
Figure:
(3) How are the three-dimensional figures in Group A different from those in Group B?
Use the grouping of figures below to answer #4 and #5.
A
B
C
D
E
(4) Which of the figures above does not belong in the grouping? Explain.
(5) Draw another figure that could be in this grouping.
(6) These figures show the two different types of tops Josh created. The
shaded portion in each figure shows a face shared by the two threedimensional figures that makeup each top.
•
What three-dimensional figures are in Top A? Top B?
Top A
•
Top B
Compare the number of faces in Top A to Top B (including the one shaded/shared face in
each). How many more faces does Top A have than Top B? Explain.
©2012, TESCCC
05/14/13
page 1 of 3
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two- and Three-Dimensional Figure Practice
Complete the table below based on each two-dimensional figure given. The first one is completed as an example.
Sample
Answers
Name of Figure
Use hash marks to
indicate congruent
sides, arcs to
indicate congruent
angles, and square
corners to indicate
square corners
Vertices
Parallel
Sides
Congruent
Sides
Perpendicular
Sides
A
Parallelogram
D
B
A, B, C, D
AB to DC
AD to BC
AB to DC
AD to BC
Congruent
Angles
Right
Angles
∠A to ∠C
None
and
None
∠B to ∠D
C
(7)
Rectangle
H
K
S
M
M
L
(8)
S
©2012, TESCCC
P
05/14/13
page 2 of 3
Grade 5
Mathematics
Unit: 10 Lesson: 01
Two- and Three-Dimensional Figure Practice
Complete the table below based on each three-dimensional figure given. The first one is completed as an example.
Sample
Answers
Figure
Faces that are
Parallelograms
Faces that are
Triangles
Faces that are
Rectangles
Faces that are
Parallel
Faces that are
Congruent
Faces that are
Congruent and
Parallel
ABCH, CBDE,
DGEF, GFAH,
DCHG, ABEF
None
ABCH, CBDE,
DGEF, GFAH,
DCHG, ABEF
ABCH to DGEF,
ABEF to CDGH,
AFGH to CDBE
ABCH, CBDE,
DGEF, GFAH,
DCHG, ABEF
ABCH to DGEF,
ABEF to CDGH,
AFGH to CDBE
D
C
G
H
E
B
F
A
L
K
N
(9)
M
J
O
U
(10)
R
S
Q
T
(11) Give a real-world example of a cylinder, cone, and sphere. Describe the attributes of each of these objects.
©2012, TESCCC
05/14/13
page 3 of 3