Download Geometry Lesson Idea 2

Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
Unit 08: Geometry (15 days)
Possible Lesson 01 (4 days)
Possible Lesson 02 (6 days)
Possible Lesson 03 (5 days)
POSSIBLE LESSON 02 (6 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 districtapproved 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 classify two- and three-dimensional figures according to the defining attributes and use formal geometric language to describe the 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
4.8
Geometry and spatial reasoning.. The student identifies and describes attributes of geometric figures using formal geometric language.
The student is expected to:
4.8A
Identify and describe right, acute, and obtuse angles....
Supporting Standard
4.8B
Identify and describe parallel and intersecting (including perpendicular) lines using concrete objects and pictorial models.
Supporting Standard
4.8C
Use essential attributes to define two- and three-dimensional geometric figures.
Readiness Standard
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Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
Underlying Processes and Mathematical Tools TEKS:
4.14
Underlying processes and mathematical tools.. The student applies Grade 4 mathematics to solve problems connected to everyday
experiences and activities in and outside of school. The student is expected to:
4.14A
Identify the mathematics in everyday situations.
4.15
Underlying processes and mathematical tools.. The student communicates about Grade 4 mathematics using informal language. The
student is expected to
4.15A
Explain and record observations using objects, words, pictures, numbers, and technology.
4.15B
Relate informal language to mathematical language and symbols.
4.16
Underlying processes and mathematical tools.. The student uses logical reasoning. The student is expected to:
4.16A
Make generalizations from patterns or sets of examples and nonexamples.
4.16B
Justify why an answer is reasonable and explain the solution process.
Performance Indicator(s):
Grade 04 Mathematics Unit 08 PI 02
Create two 4-flap books where one booklet models 4 different two-dimensional figures (e.g., rectangle, pentagon, triangle, octagon, etc.), and the other booklet models 4
different three-dimensional figures (e.g., cube, triangular pyramid, cone, sphere, etc.) that must include a prism, a pyramid, and two curved surfaced figures.
For the figures in the two-dimensional booklet, record the following: (1) a sketch of the two-dimensional figure; (2) the most specific formal geometric name of the twodimensional figure; (3) number of sides, vertices, and other attributes, including description of sides (parallel or perpendicular) and angles (acute, obtuse, or right) in the figure;
and (4) a written justification describing how the attributes define the figure.
For the figures in the three-dimensional booklet, record the following: (1) a sketch of the three-dimensional figure; (2) the formal geometric name of the three-dimensional
figure; (3) number of faces, bases, edges, vertices, curved surfaces, and other attributes, including description of edges and faces (parallel or perpendicular) and angles (acute,
obtuse, or right) in the figure; and (4) a written justification describing how the attributes define the figure.
Standard(s): 4.8A , 4.8B , 4.8C , 4.14A , 4.15A , 4.15B , 4.16A , 4.16B ELPS ELPS.c.1C , ELPS.c.1E
Key Understanding(s):
Polygons are two-dimensional figures with specific attributes.
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Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
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.
Misconception(s):
Some students may think that the size of an angle can be determined by the length of its sides. It may help to show how extending the side of the
angle does not change the “measure” of the angle. Differently sized angle cutouts (pie shapes) can be used to demonstrate this concept.
Vocabulary of Instruction:
acute
angle
attribute
base
cone
congruent
curved surface
edges
equilateral triangle
face
hexagon
isosceles triangle
obtuse
octagon
one-dimensional figure
parallel
parallelogram
pentagon
perpendicular
plane
polygon
prism
pyramid
quadrilateral
rectangle
right
scalene triangle
side
sphere
square
symmetry
three-dimensional figure
trapezoid
triangle
two-dimensional figure
vertex
Materials List:
box (tissue box) (1 per teacher)
cardstock (1 sheet per 2 students)
cardstock (1 sheet per 2 students)
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Unit 08:
Suggested Duration: 6 days
cardstock (7 sheets per 2 students)
cardstock (optional) (7 sheets per 4 students)
construction paper (9” x 12”) (2 sheets per student)
dry erase marker (1 per student)
geometric figures or solids (1 set per 4 students, 1 set per teacher)
math journal (1 per student)
paper (plain) (1 sheet per teacher)
plastic zip bag (sandwich sized) (3 per 2 students)
scissors (1 per teacher, 1 per student)
sticky notes (optional) (2 per student)
straw (drinking, flexible) (24 per student, 12 – 32 per 2 students)
straw (drinking, flexible) (9 per student)
tape (clear) (optional) (1 roll per teacher)
tape (painter’s) (1 roll per 2 students)
whiteboard (student-sized) (1 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.
Polygon Cards
Polygon Names Chart KEY
Polygon Names Chart
Figure Search KEY
Figure Search
Dot Paper
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Unit 08:
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Quadrilateral Descriptions KEY
Quadrilateral Descriptions
Quadrilateral Cards
Triangle and Quadrilateral Practice KEY
Triangle and Quadrilateral Practice
Building Figures and Solids with Straws
Two-Dimensional Figures Graphic Organizer
Quadrilaterals Graphic Organizer
Guess the Figure
Three-Dimensional Attributes - Part 1 - KEY
Three-Dimensional Attributes - Part 1
Three-Dimensional Attributes - Part 2 - KEY
Three-Dimensional Attributes - Part 2
Three-Dimensional Figure Practice KEY
Three-Dimensional Figure Practice
Three-Dimensional Figures Graphic Organizer
Three-Dimensional Geometric Patterns
Two- and Three-Dimensional Attribute Cards
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Geometric Definitions - Notes
Geometric Logic
Geometric Logic Practice KEY
Geometric Logic Practice
Two- and Three-Dimensional Figures KEY
Two- and Three-Dimensional Figures
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
One-dimensional figures
Two-dimensional figures
Engage 1
Students discuss the difference between one-dimensional and two-dimensional figures.
MATERIALS
whiteboard (student-sized) (1 per student)
dry erase marker (1 per student)
Instructional Procedures:
TEACHER NOTE
1. Distribute a whiteboard and dry erase marker to each student. Remind students that
A plane is a flat surface that goes on forever in all directions.
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Suggested Instructional Procedures
they have learned the special names for different types of lines and angles. Instruct
students to record their responses to each of the following questions on their
whiteboard using pictures and/or words.
Ask:
What are some examples of lines in the classroom? Answers may vary.
The line created by the tiles on the floor; a pencil; the line along one side of a
desk top; the line created where two cabinet doors meet; etc.
What are some flat objects in the classroom? Answers may vary. A desk
top; book cover; chalkboard; the face of the clock; etc.
Notes for Teacher
A plane figure is also called a two-dimensional figure with
two basic units of measure, usually length and width. A
polygon is a closed two-dimensional figure with 3 or more
straight sides.
TEACHER NOTE
A circle is a two-dimensional figure whose length and width
can be measured through the center of the circle (diameter).
2. Explain to students that the lines they just named are all examples of onedimensional figures, and the flat surfaces they just named are all examples of twodimensional figures.
3. Facilitate a class discussion about the differences between one- and twodimensional figures:
Ask:
Using the examples on your whiteboard, how could you describe the
difference between a one-dimensional figure and a two-dimensional
figure? Answers may vary. A one-dimensional figure can be a straight or curved
line that does not form a closed figure. A two-dimensional figure is formed by
straight or curved lines that form a closed figure; etc.
4. Explain to students that a dimension is a measure in one direction. A one-
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Notes for Teacher
dimensional figure has only one dimension, length. Straight and curved lines are
examples of one-dimensional figures.
5. Explain to students that a plane is a flat surface that goes on forever in all
directions. A plane figure is a two-dimensional figure with two basic units of
measure, usually length and width. Two-dimensional figures are comprised of onedimensional figures, which can have straight or curved lines.
Topics:
Attributes of polygons
Explore/Explain 1
Students define a polygon as a closed figure with straight sides. Students examine and name
polygons by identifying the number of sides and types of angles within each figure.
Instructional Procedures:
1. Prior to instruction, create a card set: Polygon Cards for every 2 students by
copying on cardstock, cutting apart, laminating, and placing in a plastic zip bag.
ATTACHMENTS
Card Set: Polygon Cards (1 per 2 students)
Teacher Resource: Polygon Names Chart
KEY (1 per teacher)
Teacher Resource: Polygon Names Chart
(1 per teacher)
Handout: Polygon Names Chart (1 per
student)
Teacher Resource: Figure Search KEY (1
per teacher)
Handout: Figure Search (1 per student)
2. Facilitate a class discussion about attributes.
Ask:
MATERIALS
What is an attribute? Can you give examples? Answers may vary. A
characteristic that helps define a figure; etc.
3. Explain to students that they will be investigating the attributes of geometric figures,
cardstock (1 sheet per 2 students)
scissors (1 per teacher)
plastic zip bag (sandwich sized) (1 per 2
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Suggested Duration: 6 days
Suggested Instructional Procedures
beginning with two-dimensional figures.
2. Place students in pairs. Distribute a card set: Polygon Cards to each group.
Instruct student pairs to sort the figures into 2 or more groups and be ready to
explain how they sorted the figures. Allow time for students to complete the activity.
Monitor and assess student pairs to check for understanding. Facilitate a class
discussion to debrief the possible groupings.
Ask:
What are the groups you created from the sort? Answers may vary. Groups
of polygons with right angles and those without; groups of polygons by the
number sides (3, 4, or more than 4, etc.); etc.
Notes for Teacher
students)
TEACHER NOTE
An attribute is a characteristic that helps define a figure. A
two-dimensional figure is comprised of at least 3 onedimensional figures and has two basic units of
measurement (usually length and width).
TEACHER NOTE
On handout: Polygon Names Chart, students may only
provide the specific name of each quadrilateral, such as
square, rectangle, parallelogram, or trapezoid. The
3. Explain to students that each figure from their card set: Polygon Cards is a
polygon.
Ask:
relationships between the multiple ways to name each
quadrilateral will be discussed in Explore/Explain 2.
How do you know that each figure is a polygon? Answers may vary. Each
figure is a closed figure; each figure has straight sides; etc.
4. Explain to students that one way to sort polygons is by number of sides.
5. Distribute handout: Polygon Names Chart to each student.
6. Display teacher resource: Polygon Names Chart.
Ask:
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Unit 08:
Suggested Duration: 6 days
Notes for Teacher
How many sides does each of these polygons have? (3, 4, 5, 6, and 8
sides)
7. Demonstrate recording the number of sides on the displayed teacher resource:
Polygon Names Chart. Instruct students to replicate these numbers on their
handout: Polygon Names Chart.
8. Explain to students that polygons are named by their sides.
Ask:
What are polygons with 3 sides called? 4 sides? 5 sides? 6 sides? 8
sides? (triangles; quadrilaterals; pentagons; hexagons; and octagons)
9. Instruct students to examine the figures on their handout: Polygon Names Chart,
determine the number of angles in each, and record the number of angles and
polygon name for each figure. Allow time for students to complete the activity.
Monitor and assess students to check for understanding. Facilitate a class
discussion to debrief student solutions.
10. Collect handout: Polygon Names Chart to be redistributed in Explore/Explain 2.
11. Distribute handout: Figure Search to each student as independent practice and/or
homework.
2
Topics:
Spiraling Review
Triangles
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Unit 08:
Suggested Duration: 6 days
Suggested Instructional Procedures
Quadrilaterals
Explore/Explain 2
Students identify, describe, and build triangles and quadrilaterals using straws.
Instructional Procedures:
1. Prior to instruction, create a card set: Quadrilateral Cards for every 2 students by
copying on cardstock, cutting apart, laminating, and placing in a plastic zip bag.
2. Facilitate a class discussion to debrief the previously assigned handout: Figure
Search.
3. Place students in pairs. Distribute 9 flexible drinking straws, a pair of scissors, and
handout: Dot Paper to each student. Remind students of the terms acute, right,
and obtuse angles. Facilitate a class discussion about how the straws can be used
to create triangles.
Ask:
How many triangles can you make with 9 straws? How do you know? (3;
because each triangle has three sides and 3 x 3 = 9.)
4. Instruct students to use their flexible drinking straws to create triangles with different
types of angles, record the triangles they made on their handout: Dot Paper, and
list the different combinations of acute, obtuse, and right angles that can make a
triangle. Allow time for students to complete the activity. Monitor and assess
students to check for understanding. Facilitate a class discussion to debrief student
Notes for Teacher
ATTACHMENTS
Handout: Dot Paper (1 per student)
Teacher Resource: Quadrilateral
Descriptions KEY (1 per teacher)
Teacher Resource: Quadrilateral
Descriptions (1 per teacher)
Card Set: Quadrilateral Cards (1 per 2
students)
Handout: Quadrilaterals Graphic
Organizer (1 per student)
Teacher Resource: Triangle and
Quadrilateral Practice KEY (1 per teacher)
Handout: Triangle and Quadrilateral
Practice (1 per student)
Handout (optional): Building Figures and
Solids with Straws (1 per student)
Handout (optional): Two-Dimensional
Figures Graphic Organizer (1 per student)
Teacher Resource (optional): Guess the
Figure (1 per teacher)
MATERIALS
cardstock (1 sheet per 2 students)
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Suggested Duration: 6 days
Suggested Instructional Procedures
solutions and for students to share their findings.
Ask:
Can a triangle have more than one right angle? Explain. (No, there can
only be one right angle in a triangle because the other two have to be less than
a right angle to close the figure.)
Can a triangle have more than one obtuse angle? Explain. (No, there can
only be one obtuse angle in a triangle because the other two have to be less
than a right angle to close the figure.)
Can a triangle have more than one acute angle? Explain. (Yes, a triangle
can have all three acute angles or two acute angles and the third angle either
obtuse or right.)
Notes for Teacher
scissors (1 per teacher, 1 per student)
plastic zip bag (sandwich sized) (1 per 2
students)
straw (drinking, flexible) (9 per student)
math journal (1 per student)
TEACHER NOTE
Handout (optional): Building Figures and Solids with
Straws may be used to assist students with creating the
triangles in this lesson.
TEACHER NOTE
5. Instruct student pairs to create an example of each type of triangle: one with a right
angle, one with an obtuse angle, and one with all acute angles on their handout:
Dot Paper. Allow time for students to complete the activity. Monitor and assess
student pairs to check for understanding.
6. Facilitate a class discussion about classifying triangles by their sides.
Ask:
Can a triangle have three sides of the same length? Explain. (Yes and no,
because a triangle can have three sides of equal measure, at least two sides of
equal measure, or no sides of equal measure.)
Could you describe a triangle based on its sides? Explain. (yes) Answers
may vary. If a triangle has 3 sides that are equal in length, then it is an
Students identified triangles as equilateral, isosceles, or
scalene in Grade 3 (TEKS 3.8).
TEACHER NOTE
Although the word “trapezoid” has been used at previous
grade levels, Grade 4 is the first grade where students are
held accountable for the attributes of a trapezoid.
TEACHER NOTE
Polygons with all sides and angles congruent are called
regular polygons. For example, a hexagon with all sides
equal in length and all angles equal in angle measure, are
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Suggested Duration: 6 days
Suggested Instructional Procedures
equilateral triangle; if a triangle has at least 2 sides equal in length then it is an
isosceles triangle; if a triangle does not have any sides that are equal in length,
then it is a scalene triangle; etc.
Notes for Teacher
considered regular hexagons. However, all hexagons are
not regular hexagons. There are many examples of
hexagons in the real world where all of the sides are not
equal in length and all angles are not equal in measure.
7. Explain to students that they have learned how to identify and classify triangles
based on their sides and that now they will be looking at the attributes of
quadrilaterals to identify and classify them as well.
Ask:
TEACHER NOTE
Teacher resource (optional): Guess the Figure and
handout (optional): Two-Dimensional Figures Graphic
Organizer are available to assist students in understanding
What is the same about all polygons that are quadrilaterals? (They all
have 4 sides and 4 angles.)
the different types of polygons and quadrilaterals. The
graphic organizer can be posted in the classroom and/or
individual copies can be made for students, as necessary.
8. Display teacher resource: Quadrilateral Descriptions.
9. Distribute a card set: Quadrilateral Cards to each pair. Instruct student pairs to
find a quadrilateral to match each description from the displayed teacher resource:
Quadrilateral Descriptions and record the quadrilateral and description in their
math journal. Allow time for students to complete the activity. Monitor and assess
student pairs to check for understanding.
10. Invite a student volunteer to draw an example of the figure that matches the first
description from the displayed teacher resource: Quadrilateral Descriptions for
the class to see. Facilitate a class discussion about how the figure drawn has only
one pair of parallel sides. Explain to students that the special name for this
quadrilateral is “trapezoid.”
The graphic organizer does not include all four-sided
figures such as a “kite.” A kite would be another branch off
of the quadrilateral because of its attributes. A kite has two
sets of congruent sides, but the congruent sides are
adjacent to each other, not opposite of each other. A kite’s
opposite angles are congruent. This graphic organizer is as
a tool designed to help students to begin organizing the
attributes polygons have or do not have in common.
State Resources
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Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
Notes for Teacher
MTR 3 – 5: Two-Dimensional Figures Important Book
11. Repeat the activity for the next 4 descriptions on the displayed teacher resource:
Quadrilateral Descriptions. Explain the special names for each quadrilateral as a
“parallelogram,” “rectangle,” “rhombus,” and “square.”
TEXTEAMS: Rethinking Elementary Mathematics Part II:
Developing Deep and Complex Geometric Knowledge;
Sorting Shapes; Missing Shapes
12. Facilitate a class discussion about the characteristics of the quadrilaterals.
Ask:
What characteristics do you look at when comparing quadrilaterals?
Answers may vary. The lengths of the sides, angles, and if the sides are parallel
or not; etc.
Is it possible for a quadrilateral to have a right angle and an obtuse
angle? How do you know? (Yes; a trapezoid can have both a right angle and
an obtuse angle.)
Is a trapezoid a parallelogram? Explain. (No; because a trapezoid has only 1
set of parallel lines and a parallelogram has 2 sets of parallel lines.)
Is it possible for a quadrilateral to have no pairs of parallel sides?
Explain. (yes) Answers may vary.
13. Instruct student pairs to hold up the card from their card set: Quadrilateral Cards
that they think represents a quadrilateral with no parallel sides.
Ask:
What do you think this quadrilateral is called? Answers may vary.
14. Explain to students that because this it is a four-sided figure with no pairs of parallel
sides, it is called an “irregular quadrilateral.”
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Suggested Duration: 6 days
Suggested Instructional Procedures
Notes for Teacher
15. Display teacher resource: Quadrilateral Graphic Organizer. Redistribute
previously completed handout: Polygon Names Chart to each student. Facilitate a
class discussion about the relationship that exists among different types of
quadrilaterals, as well as the different names for each type of quadrilateral. Instruct
students to add additional names that describe the quadrilaterals on their handout:
Polygon Names Chart.
16. Distribute handout: Triangle and Quadrilateral Practice to each student as
independent practice and/or homework.
3
Topics:
Spiraling Review
Two-dimensional figures
Three-dimensional figures
Explore/Explain 3
Students identify, describe, and build two- and three-dimensional figures using straws.
ATTACHMENTS
Teacher Resource Three-Dimensional
Attributes (Part 1) KEY
Handout: Three-Dimensional Attributes
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Enhanced Instructional Transition Guide
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Notes for Teacher
Instructional Procedures:
(Part 1)
Handout (optional): Building Figures and
Solids with Straws (1 per student)
1. Display a sheet of paper and a tissue box.
Ask:
What are the two dimensions of the paper you can measure with a ruler?
(length and width)
How many dimensions of the box can you measure? (3; length, width, and
height)
MATERIALS
paper (plain) (1 sheet per teacher)
box (tissue box) (1 per teacher)
straw (drinking, flexible) (24 per student, 12 –
32 per 2 students)
tape (painter’s) (1 roll per 2 students)
scissors (1 per teacher, 1 per student)
sticky notes (optional) (2 per student)
2. Remind students that when they were finding the area of a figure, they were working
in two dimensions—length and width. Additionally, when they were finding the
volume of a figure, they were working with three dimensions—length, width, and
height.
3. Place students in pairs. Distribute a roll of painter’s tape to each pair and a pair of
scissors and 24 flexible straws to each student. Remind students that they have
used the straws to make triangles.
4. Instruct students to make a square with their flexible drinking straws. Allow time for
students to complete the activity. Monitor and assess students to check for
understanding.
Ask:
TEACHER NOTE
Handout (optional): Building Figures and Solids with
Straws may be used to assist students with creating the
figures in this lesson.
TEACHER NOTE
Approximate number of straws needed to construct each
How could you change this two-dimensional figure into a three-
figure:
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Suggested Instructional Procedures
Notes for Teacher
dimensional figure? Answers may vary.
5. Instruct students to make 5 more squares with their flexible drinking straws. Allow
time for students to complete the activity. Monitor and assess students to check for
understanding.
Ask:
Are these figures two-dimensional or three-dimensional? How do you
know? (Two-dimensional; because they can only be measured by length and
width.)
Could you connect these figures to create a three-dimensional figure?
Explain. (yes) Answers may vary. Taping each square together could create a
cube; etc.
TEACHER NOTE
For students who have difficulty drawing a three-
6. Instruct students to lay the squares on their desk and use the tape to connect the
sides of the polygon faces together to create edges as shown below. Allow time for
students to complete the activity. Monitor and assess students to check for
understanding.
dimensional figure, allow them to use dot paper and
demonstrate by drawing a cube starting with overlapping
squares and then connecting the corners of both squares.
TEACHER NOTE
For students who need a stronger visual for the terms face,
edge, and vertex, have them trace a square the same size
as the square face of their cube onto a sheet of paper.
Then, have them write the word “face” onto the paper and
tape it to the front face of their cube. Instruct them to use
Ask:
small sticky­notes labeled “edge” and “vertex” to tape to one
of the edges and one of the vertices on their cube.
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Notes for Teacher
How does a two-dimensional square differ from a three-dimensional
cube? (It has another dimension.)
How many squares do you need to make the cube? (6 squares)
Explain to students that each square represents a face of the cube.
7. Instruct students to fold the faces of the figure up to create the cube, tape each
edge together, and also tape each vertex of the figure. Allow time for students to
complete the activity. Monitor and assess students to check for understanding.
Ask:
A cube has how many vertices? (8 vertices)
A cube has how many edges? (12 edges)
8. Distribute handout: Three-Dimensional Attributes (Part 1) to each student.
Instruct students to complete the row for the cube by recording the number of faces,
vertices, and edges. Allow time for students to complete the activity. Monitor and
assess students to check for understanding. Facilitate a class discussion for
students to name the two-dimensional figures that make-up the faces of the threedimensional figure.
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Notes for Teacher
Ask:
What are the names of the faces for the cube? (squares)
9. Assign each student pair one of the remaining 4 three-dimensional figures from
handout: Three-Dimensional Attribute (Part 1). Distribute 12 – 32 straws to each
pair, depending on the assigned figure. Instruct student pairs to use their flexible
drinking straws to create their assigned three-dimensional figure. Allow time for
students to complete the activity. Monitor and assess student pairs to check for
understanding. Facilitate individual group discussions about the three-dimensional
models.
Ask:
How will the model of the rectangular prism be like the model of the
cube? How will it be different? Answers may vary. The cube has 6 congruent
faces that are squares, while the rectangular prism has 6 faces, 2 of which are
rectangular faces (bases) and 4 other rectangular faces. The cube has 12
edges of equal length, while the rectangular prism has 12 edges some of which
are different length; etc.
How are these two types of pyramids different? How are they alike?
Answers may vary. They are different because the shapes of their bases are
different and the number of edges is different. They are alike in that they both
have some triangular-shaped faces; etc.
10. Facilitate a class discussion for students to share the models they have built.
Instruct students to complete their handout: Three-Dimensional Attributes (Part
page 19 of 75 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
Suggested Instructional Procedures
Notes for Teacher
1) based on the models shared. 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, as needed.
4
Topics:
Spiraling Review
Three-dimensional figures
Explore/Explain 4
Students identify and describe three-dimensional figures by their attributes.
Instructional Procedures:
1. Place students in groups of 4. Distribute a set of geometric figures or solids to each
group.
Ask:
Why are all of these figures called three-dimensional figures? Answers
may vary. The figures all take up space and have another dimension besides
just length and width; etc.
2. Instruct students to sort the three-dimensional figures and be prepared to describe
the attributes they used to do so. Allow time for students to complete the activity.
Monitor and assess student groups to check for understanding. Facilitate a class
discussion about the sorting activity.
Ask:
ATTACHMENTS
Teacher Resource: Three-Dimensional
Attributes (Part 2) KEY (1 per teacher)
Teacher Resource: Three-Dimensional
Attributes (Part 2) (1 per teacher)
Handout: Three-Dimensional Attributes
(Part 2) (1 per student)
Teacher Resource: Three-Dimensional
Figure Practice KEY (1 per teacher)
Handout: Three-Dimensional Figure
Practice (1 per student)
Class Resource (optional): ThreeDimensional Geometric Patterns (1 set
per 4 students)
Handout (optional): Three-Dimensional
Figures Graphic Organizer (1 per student)
page 20 of 75 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
Suggested Instructional Procedures
How did your group sort the geometric figures? Why? Answers may vary.
Grouping spheres, cones, and cylinders together because they have curved
surfaces; grouping prisms and pyramids because they all are composed of
faces; etc.
3. Display all of the prisms, except the rectangular prism, from a set of geometric
figures for the class to see.
Ask:
What are the flat surfaces of each geometric figure called? (faces)
What type of two-dimensional figures are these faces? (polygons)
Why are these three­dimensional figures called “prisms”? (They are
three-dimensional figures that have 2 congruent parallel faces (bases) and sides
that are polygonal faces.)
How do you determine the special name for each prism? (You look at that
shape of the 2 congruent parallel faces (bases) to determine and name the type
of prism.)
Explain to students that the shape of the base of the prism names the prism.
Notes for Teacher
MATERIALS
geometric figures or solids (1 set per 4
students, 1 set per teacher)
cardstock (optional) (7 sheets per 4
students)
scissors (optional) (1 per teacher)
tape (clear) (optional) (1 roll per teacher)
TEACHER NOTE
If geometric solids are unavailable, use class resource
(optional): Three-Dimensional Geometric Patterns to
create a set of solids for every 4 students.
TEACHER NOTE
Pyramids and Cones
A pyramid is a polyhedron (a three-dimensional figure with
faces and edges). The attributes of a pyramid include faces,
edges, and the “point” where the edges meet, which is
4. Display the rectangular prism from a set of geometric solids for the class to see.
Ask:
defined as a “vertex.” As the number of faces on the pyramid
approach infinity, the surface becomes curved, creating a
page 21 of 75 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
Suggested Instructional Procedures
Is this figure a prism? How do you know? (yes) Answers may vary. It is a
three-dimensional figure with at least two congruent faces (bases) and sides that
are polygonal faces; etc.
How would you name this prism? Answers may vary.
Notes for Teacher
cone. Since a cone consists of a curved surface, it is not
considered a polyhedron. When you talk about a cone the
terms “face,” “edge,” and “vertex,” as defined by a
polyhedron, do not apply. A wide variety of resources modify
these definitions when referencing non-polyhedrons. It is
possible to refer to the “vertex” of a cone as a “point” in
5. Instruct students to examine the square bases of the prism. Because a rectangular
prism could have two square faces (bases), the student may refer to this figure as a
square prism.
Ask:
What do you know about squares and rectangles? (All squares are
rectangles.)
elementary math. Therefore, for elementary, TEA only lists
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 three-dimensional figure is
6. Explain to students that because all squares are rectangles, it can be inferred that
this is a rectangular prism even though some of the faces are “squares.”
7. Display the pyramids from a set of geometric figures for the class to see.
Ask:
defined as a flat surface in the shape of a two-dimensional
figure. Since the circular bases of a cylinder and cone are
flat surfaces in the shape of a two-dimensional 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, CSCOPE uses these
What are these three-dimensional figures called? (pyramids)
8. Explain to students that like prisms, the shape of the base of a pyramid names the
pyramid. The difference is that a pyramid has only one base and a prism has two
bases.
Ask:
attributes in alignment with TEA.
TEACHER NOTE
Handout (optional): Three-Dimensional Figures Graphic
Organizer is available to assist students in understanding
the different types of polygons. This graphic organizer can
page 22 of 75 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
Suggested Instructional Procedures
Excluding the face of the pyramid that is the base, what type of polygons
are the other faces of the triangular pyramid? (triangles)
Are these faces of a pyramid always a triangle? How do you know? (yes)
Answer may vary. No matter what the base of the pyramid, the faces connect to
the edges of base and one common endpoint at the top of the pyramid, which
creates a triangular face; etc.
What do you notice about the shape of the base and the name of the
pyramid? How do you know? (The shape of the base names the pyramid.)
Answers may vary. A square pyramid has a square for a base; a triangular
pyramid has a triangle for a base; etc.
Notes for Teacher
be posted in the classroom and/or individual copies can be
made for students, as needed.
9. Distribute handout: Three-Dimensional Attributes (Part 2) to each student.
10. Display teacher resource: Three-Dimensional Attributes (Part 2). Facilitate a
class discussion about the attributes of spheres, cones, and cylinders. Instruct
students to record the attributes as they are discussed on their handout: ThreeDimensional Attributes (Part 2).
11. Distribute handout: Three-Dimensional Figure Practice to each student as
independent practice and/or homework.
5
Topics:
Spiraling Review
Two-dimensional figures
Three-dimensional figures
Geometric logic
ATTACHMENTS
page 23 of 75 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
Suggested Instructional Procedures
Elaborate 1
Students extend concepts of two- and three-dimensional figures by formalizing geometric definitions
of these figures. Students determine common characteristics and attributes of a set of figures.
Instructional Procedures:
1. Prior to instruction create a card set: Two- and Three-Dimensional Attribute
Cards for every 2 students by copying on cardstock, cutting apart, laminating, and
placing in a plastic zip bag.
2. Place students in a pairs and distribute a card set: Two- and Three-Dimensional
Attribute Cards to each pair. Instruct student pairs to separate the picture cards
from the attribute cards into 2 piles, shuffle each pile, spread the picture cards face
up on the desk, and place the attribute cards in a stack face down on the desk.
3. Explain to students that they will take turns drawing an attribute card from the pile
and trying to match it with the correct picture card. Instruct students to begin the
game. Allow time for students to complete the activity. Monitor and assess student
pairs to check for understanding.
4. Distribute handout: Geometric Definitions—Notes to each student. Instruct
students to verify their matched cards with the definitions. The student with the most
correct pairs of cards wins.
Notes for Teacher
Card Set: Two-and Three-Dimensional
Attribute Cards (1 per 2 students)
Handout: Geometric Definitions – Notes
(1 per student)
Teacher Resource: Geometric Logic (1 per
teacher)
Teacher Resource: Geometric Logic
Practice KEY (1 per teacher)
Handout: Geometric Logic Practice (1 per
student)
Teacher Resource: Two- and ThreeDimensional Figures KEY (1 per teacher)
Handout: Two- and Three-Dimensional
Figures (1 per student)
MATERIALS
cardstock (7 sheets per 2 students)
scissors (1 per teacher)
plastic zip bag (sandwich sized) (1 per 2
students)
5. Display teacher resource: Geometric Logic. Instruct students to examine the
figures.
Ask:
page 24 of 75 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
Suggested Instructional Procedures
Notes for Teacher
What do these figures have in common? (They are either squares or
triangles; they are all shaded; they all have a single white dot in them.)
6. Explain to students that special made-up words such as roopeets are used to name
sets of examples, and that they can apply what they know about two-dimensional
figures to determine the characteristics a set of figures have in common.
7. Distribute handout: Geometric Logic Practice to each student. Instruct student
pairs to list the characteristics each of the figures has in common. 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.
8. Distribute handout: Two- and Three-Dimensional Figures to each students as
independent practice and/or homework.
6
Evaluate 1
Instructional Procedures:
1. Assess student understanding of related concepts and processes by using the
Performance Indicator(s) aligned to this lesson.
MATERIALS
construction paper (9” x 12”) (2 sheets per
student)
scissors (1 per student)
Performance Indicator(s):
page 25 of 75 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 4/Mathematics
Unit 08:
Suggested Duration: 6 days
Notes for Teacher
Grade 04 Mathematics Unit 08 PI 02
Create two 4-flap books where one booklet models 4 different two-dimensional figures (e.g.,
rectangle, pentagon, triangle, octagon, etc.), and the other booklet models 4 different threedimensional figures (e.g., cube, triangular pyramid, cone, sphere, etc.) that must include a prism,
a pyramid, and two curved surfaced figures.
For the figures in the two-dimensional booklet, record the following: (1) a sketch of the twodimensional figure; (2) the most specific formal geometric name of the two-dimensional figure;
(3) number of sides, vertices, and other attributes, including description of sides (parallel or
perpendicular) and angles (acute, obtuse, or right) in the figure; and (4) a written justification
describing how the attributes define the figure.
For the figures in the three-dimensional booklet, record the following: (1) a sketch of the threedimensional figure; (2) the formal geometric name of the three-dimensional figure; (3) number of
faces, bases, edges, vertices, curved surfaces, and other attributes, including description of
edges and faces (parallel or perpendicular) and angles (acute, obtuse, or right) in the figure; and
(4) a written justification describing how the attributes define the figure.
Standard(s): 4.8A , 4.8B , 4.8C , 4.14A , 4.15A , 4.15B , 4.16A , 4.16B ELPS
ELPS.c.1C , ELPS.c.1E
04/22/13
page 26 of 75 Grade 4
Mathematics
Unit: 08 Lesson: 02
Polygon Cards
©2012, TESCCC
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Polygon Names Chart KEY
Figure
©2012, TESCCC
Number of Sides and
Angles
Polygon Name
3 sides
3 angles
Triangle
3 sides
3 angles
Triangle
3 sides
3 angles
Triangle
4 sides
4 angles
Quadrilateral/Square/
Rectangle/Parallelogram
4 sides
4 angles
Quadrilateral/Rectangle/
Parallelogram
4 sides
4 angles
Quadrilateral/Parallelogram
4 sides
4 angles
Quadrilateral/Trapezoid
4 sides
4 angles
Quadrilateral/Trapezoid
4 sides
4 angles
Quadrilateral
5 sides
5 angles
Pentagon
6 sides
6 angles
Hexagon
8 sides
8 angles
Octagon
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Polygon Names Chart
Figure
©2012, TESCCC
Number of Sides and
Angles
11/09/12
Polygon Name
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Figure Search KEY
Use the descriptions below to write the letters of the figures that fit that description. You may use
each figure more than once. Hint: some figures are polygons, some are not.
B
C
A
E
I
F
J
G
H
K
L
(1)
A figure with at least one pair of parallel lines B, E, F, G, H, I, J, L
(2)
A quadrilateral E, G, I
(3)
A hexagon H, L
(4)
A polygon with more than 3 sides B, E, G, H, I, K, L
(5)
A figure with at least one right angle A, F, G, I
(6)
A triangle A, D
(7)
A figure with at least one obtuse angle B, E, H, K, L
(8)
A figure that is not a polygon C, F, J
(9)
A figure with more than 4 vertices B, H, K, L
(10)
A figure with at least one acute angle A, D, E
©2012, TESCCC
11/09/12
D
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Figure Search
Use the descriptions below to write the letters of the figures that fit that description. You may use
each figure more than once. Hint: some figures are polygons, some are not.
B
C
A
E
I
F
J
D
G
H
K
L
(1)
A figure with at least one pair of parallel lines_______________________
(2)
A quadrilateral ____________________________________________________
(3)
A hexagon _______________________________________________________
(4)
A polygon with more than 3 sides _____________________________________
(5)
A figure with at least one right angle ___________________________________
(6)
A triangle ________________________________________________________
(7)
A figure with at least one obtuse angle _________________________________
(8)
A figure that is not a polygon _________________________________________
(9)
A figure with more than 4 vertices _____________________________________
(10)
A figure with at least one acute angle __________________________________
©2012, TESCCC
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Dot Paper
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©2012, TESCCC
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Quadrilateral Descriptions KEY
(1) Only 1 pair of parallel sides
(2) Four right angles; only 2 sides the same length
(3) Four right angles; all sides the same length
(4) Two pairs of parallel sides; no right angles
(5) Opposite sides parallel; all sides the same length
(6) No pairs of parallel sides
Possible answers:
(1)
(2)
(3)
(4)
Trapezoid
Rectangle
Square
Parallelogram (for it to be a rhombus, all sides have to be
congruent)
(5) Rhombus (for it to be a square, all angles must be right
angles)
(6) Irregular Quadrilateral
©2012, TESCCC
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Quadrilateral Descriptions
(1) Only 1 pair of parallel sides
(2) Four right angles; only 2 sides the same length
(3) Four right angles; all sides the same length
(4) Two pairs of parallel sides
(5) Opposite sides parallel; all sides the same length
(6) No pairs of parallel sides
©2012, TESCCC
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Quadrilateral Cards
Trapezoid
Square
©2012, TESCCC
Rectangle
Rhombus
Parallelogram
Quadrilateral
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Triangle and Quadrilateral Practice KEY
Draw a sketch and name each triangle in the space provided.
1. Has 3 sides
All three angles are acute.
Sketches may vary.
Acute triangle
2. Has 3 sides
One angle is a right angle.
Sketches may vary.
Right triangle
3. Has 3 sides
One angle is an obtuse angle.
Sketches may vary.
Obtuse triangle
Draw a sketch and name each quadrilateral in the space provided.
4. Has 4 sides
Sketches may vary.
Opposite sides are congruent.
Opposite sides are parallel.
Rectangle, Rhombus,
Opposite angles are congruent.
Parallelogram, Square
5. Has 4 sides
All sides are congruent.
Opposite sides are parallel.
All angles are right angles.
©2012, TESCCC
Sketches may vary.
Square
05/14/13
page 1 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Triangle and Quadrilateral Practice KEY
Draw a sketch and name each quadrilateral in the space provided.
6. Has 4 sides
Sketches may vary.
Opposite sides are congruent.
Opposite sides are parallel.
Rectangle, Square
All angles are right angles.
7. Has 4 sides
Only 2 sides are parallel.
Sketches may vary
Trapezoid
8. Has 4 sides
All sides are congruent.
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Sketches may vary.
Rhombus
(9)
Can a figure be both a rectangle and a rhombus? Explain. Yes, a square is both a
rectangle and a rhombus.
(10)
Does a trapezoid and a rectangle have anything in common? Explain. Yes, both are
quadrilaterals and both have at least one pair of parallel sides.
(11)
Can a right triangle be classified as an acute triangle? Explain. No; Answers may vary; An
acute triangle must have all angles less than 90º. So, a right triangle cannot be an
acute triangle because it has a 90º angle; etc.
(12)
What kind of angles are the other two angles on a right triangle? acute angles
©2012, TESCCC
05/14/13
page 2 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Triangle and Quadrilateral Practice
Draw a sketch and name each triangle in the space provided.
1. Has 3 sides
All three angles are acute.
2. Has 3 sides
One angle is a right angle.
3. Has 3 sides
One angle is an obtuse angle.
Draw a sketch and name each quadrilateral in the space provided.
4. Has 4 sides
Opposite sides are congruent.
Opposite sides are parallel.
Opposite angles are congruent.
5. Has 4 sides
All sides are congruent.
Opposite sides are parallel.
All angles are right angles.
©2012, TESCCC
05/14/13
page 1 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Triangle and Quadrilateral Practice
Draw a sketch and name each quadrilateral in the space provided.
6. Has 4 sides
Opposite sides are congruent.
Opposite sides are parallel.
All angles are right angles.
7. Has 4 sides
Only 2 sides are parallel.
8. Has 4 sides
All sides are congruent.
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
(9)
Can a figure be both a rectangle and a rhombus? Explain.
(10)
Does a trapezoid and a rectangle have anything in common? Explain.
(11)
Can a right triangle be classified as an acute triangle? Explain.
(12)
What kind of angles are the other two angles on a right triangle?
©2012, TESCCC
05/14/13
page 2 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Building Figures and Solids with Straws
Materials:
flexible drinking straws
masking tape
scissors
Procedure:
To create a polygon
Use scissors to slice the short end of the straw up to the bend in the straw (see dotted line on
diagram)
Slice along dotted line
To make the geometric figures, squeeze the short end together and insert it into the long end of the
straw. Always insert a short/sliced end into a long end.
Continue inserting until you have created the desired polygon.
To create a solid
Use the polygons you have created to serve as the face of each solid figure. Example: a cube would
need six square faces.
Lay the polygon faces on a table to create a net. Use masking tape to tape the edges of the polygon
faces together to create the net.
Bring the faces of the net up to create the 3-dimensional figure. Tape the remaining edges together.
A good idea is to have the students put tape on each edge and vertex as reference “touching points.”
©2012, TESCCC
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two-Dimensional Figures Graphic Organizer
©2012, TESCCC
05/14/13
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Quadrilaterals Graphic Organizer
Quadrilaterals
Parallelogram
Rectangle
Trapezoid
Rhombus
Square
©2012, TESCCC
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Guess the Figure
Materials:
1 set of quadrilateral pieces per student or pair of students
Procedure:
Teacher selects one piece from his/her set of pieces and hides it.
In order to determine which piece the teacher has hidden, the groups take turns
asking “yes/no” questions about which piece they think is hidden, or they can make
an actual guess as to which piece is hidden.
This is a good strategizing game and the teacher should take advantage of
opportunities that arise to discuss these strategies. Some questions, the teacher
may ask are:
 What is the best question to ask first? Why?
 Is there another question that is equally as good? Why or why not?
 If you were left with a square, a rhombus, and a rectangle, what would be a
good question to ask?
©2012, TESCCC
05/14/13
page 1 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Guess the Figure
©2012, TESCCC
05/14/13
page 2 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Attributes (Part 1) KEY
Figure
Name
Cube
Rectangular
Prism
Sketch
Number
of
Faces
Number
of
Vertices
Number
of
Edges
Names
of
Faces
6
8
12
Squares
12
Rectangles
OR
Rectangles
and
Squares
6
8
Triangular
Prism
5
6
9
Triangles
and
Rectangles
Triangular
Pyramid
4
4
6
Triangles
8
Square
and
Triangles
Square
Pyramid
©2012, TESCCC
5
11/09/12
5
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Attributes (Part 1)
Figure
Name
Sketch
Number
of
Faces
Number
of
Vertices
Number
of
Edges
Names
of
Faces
Cube
Rectangular
Prism
Triangular
Prism
Triangular
Pyramid
Square
Pyramid
©2012, TESCCC
11/0912
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Attributes (Part 2) KEY
Figure Name
Model
Attributes
All points are the same
distance from its center
Sphere

Cone


Cylinder

©2012, TESCCC
11/09/12
1 circular base
1 curved surface
two congruent circular
bases that are parallel
1 curved surface
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Attributes (Part 2)
Figure Name
Sketch
Attributes
Sphere
Cone
Cylinder
©2012, TESCCC
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Figure Practice KEY
These groups show different types of three-dimensional figures.
Name the group in which the following items should be placed. Then name the 3-dimensional
figure the item best represents.
(1) Baseball: Group C; Sphere
(5) Basketball: Group C; Sphere
(2) Funnel: Group C; Cone
(6) Can of soup: Group C; Cylinder
(3) Cereal box:
Group A; Rectangular prism
(4) Refrigerator:
Group A; Rectangular prism
(7) The moon: Group C; Sphere
(8) Egyptian pyramid: Group B; Pyramid
Describe and write 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.
(B) Triangular Prism
(A) Cube
6 square faces (2 square faces (bases) and 5 faces (2 triangular faces (bases) and 3
4 other square faces), 12 edges, 8 vertices
rectangular faces), 9 edges, 6 vertices
(C) Triangular Pyramid
(D) Cone
4 triangular faces (1 triangular face (base)
and 3 other triangular faces), 6 edges, and
1 circular base, 1 curved surface
4 vertices
(E) Sphere
(F) Cylinder
1 curved surface
2 circular bases, 1 curved surface
©2012, TESCCC
05/14/13
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Figure Practice
These groups show different types of three-dimensional figures.
Name the group in which the following items should be placed. Then name the 3-dimensional
figure the item best represents.
(1) Baseball:
(5) Basketball:
(2) Funnel:
(6) Can of soup:
(3) Cereal box:
(7) The moon:
(4) Refrigerator:
(8) Egyptian pyramid:
Describe and write 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.
(A) Cube
(B) Triangular Prism
(C) Triangular Pyramid
(D) Cone
(E) Sphere
(F) Cylinder
©2012, TESCCC
05/14/13
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Figures Graphic Organizer
Triangular
Prism
Rectangular
Prism
Square
Pyramid
Triangular
Pyramid
Cylinder
Cone
Sphere
Cube
©2012, TESCCC
05/14/13
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Geometric Patterns
Cube
©2012, TESCCC
11/09/12
page 1 of 7
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Geometric Patterns
Rectangular Prism
©2012, TESCCC
11/09/12
page 2 of 7
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Geometric Patterns
Triangular Prism
©2012, TESCCC
11/09/12
page 3 of 7
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Geometric Patterns
Square Pyramid
©2012, TESCCC
11/09/12
page 4 of 7
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Geometric Patterns
Triangular Pyramid
©2012, TESCCC
11/09/12
page 5 of 7
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Geometric Patterns
Cone
©2012, TESCCC
11/09/12
page 6 of 7
Grade 4
Mathematics
Unit: 08 Lesson: 02
Three-Dimensional Geometric Patterns
Cylinder
©2012, TESCCC
11/09/12
page 7 of 7
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three- Dimensional Attribute 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 (90º) to each
other
Right angle
an angle that measures
90º; lines that are
perpendicular to each
other
Acute angle
an angle with a measure
less than a right angle
(90º)
Obtuse angle
an angle that measures
greater than a right angle
(90º) but less than a
straight line (180º)
©2012, TESCCC
05/14/13
page 1 of 8
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three- Dimensional Attribute Cards
Polygon
a closed twodimensional figure with
3 or more straight sides
Quadrilateral
any four-sided polygon
Congruent Figures
figures that are the same
size, same shape
Two-dimensional figure
a figure with two basic
units of measure, usually
length and width
four-sided (quadrilateral)
polygon with
• opposite sides
congruent
• opposite sides parallel
• opposite angles
congruent
Parallelogram
©2012, TESCCC
05/14/13
page 2 of 8
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three- Dimensional Attribute Cards
Rectangle
four-sided polygon
(quadrilateral) with
• 4 right (90°) angles
• opposite sides
congruent
• opposite sides parallel
• adjacent sides
perpendicular
Square
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
05/14/13
page 3 of 8
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three- Dimensional Attribute Cards
Triangle
a polygon with
• 3 sides
• 3 angles
• 3 vertices
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 and lie in
the same plane
C
©2012, TESCCC
05/14/13
page 4 of 8
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three- Dimensional Attribute Cards
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
Edge
a line segment where two
faces meet on a threedimensional figure
the point (corner) of
intersection of two sides in
a two-dimensional figure
and the point (corner) of
intersection of three or more
edges of a threedimensional figure
Vertex
Face
©2012, TESCCC
the flat surface of a
three-dimensional figure
05/14/13
page 5 of 8
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three- Dimensional Attribute Cards
Three-dimensional
figure
a figure with three units
of measure:
•
•
•
length
width (depth)
height
• prisms
Base of a threedimensional figure
—
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
—
Prism
circular base
three-dimensional figure
with
•
•
two congruent, parallel
faces (bases)
sides that are polygonal
faces
three-dimensional figure
with
Rectangular prism
•
6 rectangular faces
—
2 rectangular faces
(bases)
— 4 other rectangular faces
•
•
©2012, TESCCC
05/14/13
12 edges
8 vertices
page 6 of 8
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three- Dimensional Attribute Cards
Cube
three-dimensional figure
with
6 square faces
•
—
2 square faces (bases)
— 4 other square faces
12 edges
8 vertices
•
•
Triangular prism
three-dimensional figure
with
5 faces
•
—
2 triangular faces
(bases)
— 3 rectangular faces
9 edges
6 vertices
•
•
Pyramid
three-dimensional figure with
•
•
Square pyramid
1 face (base)
sides that are triangular
faces
three-dimensional figure
with
•
5 faces
—1
square face (base)
— 4 triangular faces
•
•
©2012, TESCCC
05/14/13
8 edges
5 vertices
page 7 of 8
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three- Dimensional Attribute Cards
Triangular pyramid
three-dimensional figure
with
•
4 triangular faces
—
1 triangular face (base)
— 3 other triangular faces
•
•
6 edges
4 vertices
Curved Surface
surface of a threedimensional figure that is
curved
Cylinder
three-dimensional figure
with
•
•
Cone
three-dimensional figure
with
•
•
Sphere
©2012, TESCCC
two congruent circular
bases that are parallel
1 curved surface
1 circular base
1 curved surface
three-dimensional figure
with all of its points the
same distance from its
center
05/14/13
page 8 of 8
Grade 4
Mathematics
Unit: 08 Lesson: 02
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°)
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; and (3) curved-surface figures – circular
base.
Circle: the set of all points that lie the same distance from the center and lie in the same plane
Cone: three-dimensional figure with 1 circular base and 1 curved surface
Congruent: figures that are the same size, same shape
Cube: three-dimensional figure with 6 square faces (2 square faces (bases) and 4 other square
faces), 12 edges, and 8 vertices
Curved Surface: surface of a three-dimensional figure that is curved
Cylinder: three-dimensional figure with two congruent circular bases that are parallel and 1 curved
surface
Edge: a line segment where two faces meet on a three-dimensional figure
Equilateral Triangle: a triangle with 3 congruent sides and 3 congruent angles
Face: the flat surface of a three-dimensional figure
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 parallel, opposite sides
congruent, 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
©2012, TESCCC
05/17/13
page 1 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Geometric Definitions—Notes
Point: an exact location in space, represented by a dot
Polygon: a closed two-dimensional figure with three or more straight sides
Prism: three-dimensional figure with two congruent, parallel faces (bases) and sides that are
polygonal faces
Pyramid: three-dimensional figure with 1 face (base) with sides that are triangular faces
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, adjacent sides
perpendicular, opposite sides congruent, and opposite sides parallel
Rectangular prism: three-dimensional figure with 6 rectangular faces (2 rectangular faces (bases)
and 4 other rectangular faces), 12 edges, and 8 vertices
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) with all sides congruent, opposite sides parallel, and
opposite angles congruent
Scalene Triangle: a triangle with no congruent sides and no congruent angles
Sphere: three-dimensional figure with all of its points the same distance from its center
Square: four-sided polygon (quadrilateral) with all sides congruent, opposite sides parallel, 4 right
(90°) angles, and adjacent sides perpendicular
Square pyramid: three-dimensional figure with 5 faces (1square face (base) and 4 triangular
faces), 8 edges, and 5 vertices
Trapezoid: four-sided polygon (quadrilateral) with exactly one pair of parallel sides
Triangle: a polygon with 3 sides, 3 angles, and 3 vertices
Three-dimensional figure: a figure with three units of measure including length, width (depth),
and height
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
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 and the point (corner) of intersection of three or more edges of a three-dimensional
figure
©2012, TESCCC
05/17/13
page 2 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Geometric Logic
These are roopeets.
What characteristics do these roopeets have in common?
©2012, TESCCC
11/09/12
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Geometric Logic Practice KEY
List the characteristics each of these figures have in common.
Each figure is made-up of a shaded quadrilateral and an unshaded triangle
sharing one side (or attached on one side).
Use the space below to draw another example with these same
characteristics, and then to draw a non-example.
Example
Non-Example
Drawings may vary but
should adhere to
characteristics listed above.
Drawings may vary but
should NOT adhere to
characteristics listed above.
©2012, TESCCC
05/14/13
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Geometric Logic Practice
List the characteristics each of these figures have in common.
Use the space below to draw another example with these same
characteristics, and then to draw a non-example.
Example
©2012, TESCCC
Non-Example
05/14/13
page 1 of 1
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three-Dimensional Figures KEY
A description is given for each polygon. Write the name of the polygon described and then match
each polygon name to the correct figure in the box below. Label the polygon with the number that
matches its description and name.
(1) Polygon with six sides
(2) Four-sided polygon with opposite sides
parallel and no right angles
Hexagon
Parallelogram
(3) Four sided polygon with opposite sides
(4) Polygon with three sides
parallel, all sides congruent, and opposite
angles congruent
Triangle
Rhombus
(5) Polygon with five sides
(6) Four-sided polygon with only one pair of
parallel sides
Pentagon
Trapezoid
(7) Four-sided polygon with opposite sides
(8) Polygon with eight sides
parallel, opposite sides congruent, and 4
right angles
Octagon
Rectangle
(9) Polygon with four sides
(10) Four-sided polygon with all sides
congruent and four right angles
Quadrilateral
Square
(11) Three-sided polygon with one right angle (12) Three-sided polygon with one obtuse
angle
Right Triangle
Obtuse Triangle
©2012, TESCCC
05/14/13
page 1 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three-Dimensional Figures KEY
Describe and write 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
4 triangular faces (1 triangular face (base)
and 3 other triangular faces), 6 edges, and
4 vertices
(3) Rectangular Prism
6 faces (2 rectangular faces (bases) and 4
other rectangular faces), 12 edges, 8
vertices
(5) Cone
1 circular base, 1 curved surface
(7) Sphere
(2) Triangular Prism
5 faces (2 triangular faces (bases) and 3
rectangular faces), 9 edges, 6 vertices
(4) Cube
6 square faces (2 square faces (bases) and
4 other square faces), 12 edges, 8 vertices
(6) Square Pyramid
5 faces (1 square face (base) and 4
triangular faces), 8 edges, 5 vertices
(8) Cylinder
1 curved surface
©2012, TESCCC
2 circular bases, 1 curved surface
05/14/13
page 2 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three-Dimensional Figures
A description is given for each polygon. Write the name of the polygon described and then match
each polygon name to the correct figure in the box below. Label the polygon with the number that
matches its description and name.
(1) Polygon with six sides
(2) Four-sided polygon with opposite sides
parallel and no right angles
(3) Four-sided polygon with opposite sides
(4) Polygon with three sides
parallel, all sides congruent, and opposite
angles congruent
(5) Polygon with five sides
(6) Four-sided polygon with only one pair of
parallel sides
(7) Four-sided polygon with opposite sides
parallel, opposite sides congruent, and 4
right angles
(8) Polygon with eight sides
(9) Polygon with four sides
(10) Four-sided polygon with all sides
congruent and four right angles
(11) Three-sided polygon with one right angle
(12) Three-sided polygon with one obtuse
angle
©2012, TESCCC
05/14/13
page 1 of 2
Grade 4
Mathematics
Unit: 08 Lesson: 02
Two- and Three-Dimensional Figures
Describe and write 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) Cone
(6) Square Pyramid
(7) Sphere
(8) Cylinder
©2012, TESCCC
05/14/13
page 2 of 2