# 3 D Shape Templates

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```					                                        The CROSSROADS Project
Summer 2005

UNIT COVER PAGE

Subject:      Mathematics                  Grade Level (Circle): K 1 2     3   4   5

Unit Title: Groovy Geometry

Description: Hands-on activities to enhance student understanding of two-and three- dimensional objects.

Math Standard: GEOM

Grade Level Indicator: (2) Describe, classify, compare, and model two-and three-dimensional objects using
their attributes.

Duration: 7-10 days

Creators (Design Team Members): Please print or type

Name                                               School/District
Janice Fiorello                                    Clarendon Elementary, Canton City Schools
Judy Orchard                                       Waynesburg Elementary, Sandy Valley Schools
Shelly Pilsitz                                     Avondale Elementary, Plain Local Schools
Unit Test Template

Unit Title: Groovy Geometry                         Grade Level : 3 4 5
Math Standard: Geometry and Spatial Sense           Indicator Number: 2

Teacher’s Name ________________________________ Building _________________________
District ________________________________________ Date of Testing ___________________

Skills & Concepts: Pre-Test
Student’s Name ____________________________________               Total Score: _____/20

A. Multiple Choice (2 points each; 10 points total)
Directions to the student: Show how you solve each problem in the box provided. Use words, pictures, or
numbers. Then circle the LETTER of the correct answer.

1. I’m thinking of a shape that has four sides. It is closed with at least one right angle. Opposite sides are
parallel. Adjacent sides are not equal in length. What shape am I thinking of?

How did you find your answer?                          a.     square

b.     rectangle

c.     trapezoid

d.     rhombus

2. Think about the shape of a can of soup. It has curved sides and two congruent circular bases. What
name is given to the three-dimensional object with this shape?

How did you find your answer?                          a.     triangular prism

b.     cylinder

c.     circle

d.     sphere
2
3. What shape fits the rule? Rule: The shape has four sides. None of the sides is the same length.

How did you find your answer?                        a.

b.

c.

d.

4. Which of the following statements is true?

How did you find your answer?                        a. Every parallelogram is a rhombus

b. Every rectangle is a square

c. Every rhombus is a parallelogram

d. Every trapezoid is parallelogram

5. Which shape shows the base of the            ?

How did you find your answer?                        a.

b.

c.

d.

Objective Test Sub-Score: _____/10
B. Multiple-Step Problem Solving (3 points)
Directions to the student: Find the answer to this question. Be sure to finish the WHOLE question. You may
use words, pictures, or numbers. Be sure to show your work.

Draw three triangles about the same size. Each triangle should be different in some way from those

Explain why each is different.

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

Score: _____/3
C. Try It Another Way! (3 points)

Directions to the student: Read the question below. Then draw, write about, or show TWO DIFFERENT
ways to find the answer.

Examine the shapes below. How can these be sorted? Show one way these shapes can be sorted in the
first box. Now, in the second box, show ANOTHER way to sort them.

B                                           E
A                            C              D                               F

Box #1                                               Box #2

Explain the attributes you used to sort the shapes for each answer.
__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

Score: _____/3
D. Extended Response (4 points)
Directions to the student: Use sentences to answer this question.
Compare the cube and the rectangular prism. List at least two similarities and two differences.

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________
Score: _____/4
Unit Pre-Test

Multiple Choice (2 points each; 10 possible)

1. B

2. B

3. B

4. C

5. B

Multi-Step Problem Solving (3 points each)
Scoring Rubric:

3=Communicates effectively and clearly through their drawing and writing, using correct math terms.

2=Incorrect drawing OR incorrect explanation

1=Drawing is correct, but no explanation

0=No attempt shown

Try It Another Way! (3 points)
Scoring Rubric:

3=Two groups are correctly sorted and explained

2=Two groups are correctly sorted, but not correctly explained

1=Made an attempt, but did not show clear understanding

0=No attempt shown

Extended Response (4 points)
Scoring Rubric:

4=Two similarities and two differences listed correctly using geometric terms (Four correct responses)

3=Three correct responses

2=Two correct responses

1=One correct response

0= No attempt shown
LESSON PLAN #1 Build What I’ve Created
Unit Title: Groovy Geometry
Math Standard: Geometry & Spatial Sense Standard
Math Indicator: (2) Describe, classify, compare, and model two-and three-dimensional objects using their
attributes.
Objective: Each fourth grade mathematics student will:
-Construct a geometric design from oral directions.
-Use precise geometric vocabulary in giving directions.
-Recognize geometric shapes and patterns in quilt designs

Materials: Two identical sets of pattern blocks, each containing from six to twelve blocks and a variety of
shapes for each pair of students. (A template for pattern blocks can be found on the CD in the Navigation
through Geometry)

Procedures:
*This activity can be used for pre-assessment at the beginning of a unit on geometry. By observation, teachers
can determine students’ familiarity with the geometry terms.

Begin this activity by reading Sweet Clara and the Freedom Quilt, by Deborah Hopkinson (1993), or Sam
Johnson and the Blue Ribbon Quilt, by Lisa Ernst (1983). Discuss the quilt patterns in the book encouraging
students to determine how they are alike and how they are different and note the connection to mathematics.
While reading, review two-dimensional shapes and discuss their properties.

On a separate sheet of paper one student designs a “quilt patch” from pattern blocks without the partner seeing
it. Then the creator of the design gives directions to the partner so that the partner can re-create the design
without looking at it. The re-creator then explains to the designer what the design looks like. Remember that if
the partners are facing each other, place a divider between them so that the builder cannot see the pattern being
described. Be sure to encourage students not to use color or identify a block but rather to use its
mathematical name. Finally the quilt designs are compared visually, and the students’ together record answers
to the following questions.
 What words or phrases helped you re-create the design?
 What words or phrases confused you? Why?
 Can you think of better ways to explain the directions for making this design?

The activity is then repeated with partners switching roles. Follow the activity with a classroom discussion that
develops the geometric vocabulary used by the students. Record these on chart paper for all to see. Have the
students then examine the designs and see if they can rearrange the pattern blocks to find new shapes with five,
six, or seven sides. They should record which blocks make up the new figure, trace around the new shapes, and
verify the number of edges by counting the sides in the diagram. They can also discuss the number of angles in
their diagram and compare that number with the number of sides.

Product:
The quilt patch designed by the students.

Assessment Criteria:
To assess students’ performance, ask them to design a quilt patch and then write directions for another student
to re-create the design. Their success is determined by the quality of another student’s re-creation of the design.
This approach encourages self-assessment as students modify their directions on the basis of the outcome.
LESSON PLAN #2 Shape Discovery Sort

Unit Title: Groovy Geometry
Math Standard: Geometry & Spatial Sense Standard
Math Indicator: (2) Describe, classify, compare, and model two-and three-dimensional objects using their
attributes.
Objective: Each 4th grade mathematics student will:
 Construct polygons using 4 congruent triangles
 Use precise geometric vocabulary
 Classify two-dimensional objects using their attributes.

Materials:
Scissors
30 3” x 5” squares per students
Tape
Chart paper

Procedures:
1. Each small group of students will be given a bag with thirty 3in. x 3in. squares.
2. Members of the group should fold and cut each square on the diagonal to make two congruent triangles.
3. The group’s task is to find all the unique shapes made by putting four triangles together according to the
following rules.
 Each triangle must touch the side of at least one other triangle.
 Sides of triangles that touch must be the same length and match exactly.
 Congruent shapes in different positions are considered the same shape.
4. Students should compare arrangements in their group to be sure they are finding different shapes.
5. Once the group has agreed that a shape is unique, tape the sides together.
6. While students are working, walk around and encourage student to find many different shapes. (14
possible)
7. While students are working, walk around the room and listen for geometric terms that you hear the
students using. Write them on chart paper.
8. When students reach a good stopping point, have each group hand the teacher a shape and discuss the
make up of the shape (sides, angles, name etc…) while the teacher attaches it to the chart paper.
9. Continue to do this until you have all 14 combinations.
10. Using these combinations, create a rule for sorting. As the teacher, sort a few shapes into groups. Have
students try to guess the rule. Student then begin to sort shapes according to your rules.
11. Continue sorting shapes into different groups. (You can sort by angles, sides, name etc…)

Product: The fourteen shapes created by the group.

Assessment Criteria: To assess students’ performance, teachers will observe students use of vocabulary while
constructing shapes, as well as differentiating shapes using their attributes.

Attachments None
LESSON PLAN #3 Tangrams

Unit Title: Groovy Geometry
Math Standard: Geometry & Spatial Sense Standard
Math Indicator: (2) Describe, classify, compare, and model two-and three-dimensional objects using their
attributes.
Objective: Each 4th grade mathematics student will:
 Discover the attributes of two-dimensional objects
 Construct a set of tangrams
 Review geometric vocabulary

Materials:
One computer for each pair of students
One rectangular piece of construction paper per student
Scissors

Procedures:
Direct students to the website www.linkslearning.org Once students are here, click ENTER at the bottom of the
screen. Find Kids, and click MATH. Click Illustrated Lessons on the left of the screen. Click Tangrams.
An animated screen will appear and students need to listen to the directions presented on the screen. Be sure to
explain the use of the buttons at the bottom of the screen to the students.

Product: A completed set of tangrams

Assessment Criteria:
To assess students’ performance, teacher will observe students creating their tangram shapes. Teacher can
question students about the attributes of the shapes they created.

Attachments NONE
LESSON PLAN #4 It’s a 3-D World Out There

Unit Title: Groovy Geometry
Math Standard: Geometry & Spatial Sense Standard
Math Indicator: (2) Describe, classify, compare, and model two-and three-dimensional objects using their
attributes.
Objective: Each 4th grade mathematics student will:
 Build a variety of solids from materials supplied
 Discover the relationship among the number of faces, edges and vertices of solids
 Discover relationships between two-and three- dimensional figures

Materials:
 A set of 16 “sticks” (toothpicks, pretzels, straws or coffee stirrers)- each of four different lengths (two to
eight inches) – for each pair of students
 A variety of “fasteners” (gumdrops, (stale) miniature marshmallows, pipe cleaners or clay)
 One copy for each pair of students of the black line master “Two and Three-Dimensional Shapes” and
“Counting Parts of Solids.” (See Attachments)
 For each pair of students, a set of three-dimensional wooden or plastic shapes- including one each of a
cube, square pyramid, a cylinder, a cone, and a sphere-and a variety of prisms such as a rectangular
prism, or a triangular prism etc…

Procedures: *Might take more than one class period
You might want to set the stage with this introduction:
 Today we enter into a different dimension in mathematics-the third dimension. It is hardly new to you,
since we live in the third dimension. But in class, we have been exploring shapes only in two
dimensions. Two dimensional shapes lie flat on a tabletop, and they can be drawn on a piece of paper.
But three-dimensional shapes can stand up—they have height.
1. With the students’ input, make a list of two-dimensional (2-D) shapes (triangles, squares,
rectangles, circles etc…) Show the students the set of solid shapes. Ask pairs of students to
explore the following questions: How are these three-dimensional (3-D) shapes like the ones we
have written down? How are they different? Make a list of the similarities and the differences.
Bring the class together to discuss their findings.
2. Next, distribute copies of “Two-and Three-Dimensional Shapes” and assign the following task to
pairs of students: Select one 3-D shape and compare it to one or more 2-D shapes. Write down
on this activity sheet all the things that are alike about the shapes and all the things that are
different. Again summarize the exploration with a class discussion of the task.
3. Pass out to each pair of students a set of “sticks” and a supply of “fasteners.” Ask the students to
create as many of the solids as they possibly can. You might suggest to them that they may find
some solids that cannot be created. Remind students to build at least a cube, a rectangular prism,
a triangular prism, and a square pyramid and to turn and flip their constructions to make sure
they are truly different. You can refresh the students’ understanding of congruence by referring
to two-dimensional shapes if needed.
4. Next review the terms faces, edges, and vertices by referring to the terms used for two
dimensional shapes. Have the students count the number of faces, edges and vertices in each of
the shapes they constructed. They can use the blackline master “Counting Parts of Solids” as a
recording sheet.
5. Have the student take their shapes to an open area in the classroom. Have students stand in a
circle and place their shapes in the circle. Select a student to pick up someone’s shape (other
than their own) that he or she can name.
6. Have the student name the shape. Pass the shape to the person on the right. Have that person
give one of the following:
---Attribute of the shape
---another name for the shape
---real world example of the shape
7. The shape continues moving to the right in round-robin style until students are stumped.
8. The next student picks a new shape. Continue for about 15-20 minutes. Students will learn from
each others’ observations and the quality of responses will improve as the activity continues.
Tell students that they will each complete this activity with a single shape on their own.
9. Give a shape from the floor to each pair of students along with a large sheet of paper and instruct
students to make a two-dimensional line drawing of the three-dimensional shapes they have been
assigned. Using crayons they will need to color the edges of the shapes. On the large paper,
they will need to make room for three titles Names, Attributes, and Real World Examples. They
will begin their poster by listing information in the three categories on their paper.
10. Have students share their poster with others and discuss lists.
11. Select a few posters to review with the class, and encourage students to ask questions.

Product: The three-dimensional objects created by the students and the completed poster created by the pair of
students.

Assessment Criteria: To assess students’ performance, teacher will observe students creating their three-
dimensional shapes. Teacher will also check student understanding by evaluating their completed poster and
presentation.

Attachments “Two- and Three- Dimensional Shapes” and “Counting Parts of Solids”
Two- and Three-Dimensional
Shapes
Names:___________________________________

The three-dimensional shape we chose is a __________________________.
The two-dimensional shape we chose is a ___________________________.

Here is a picture of the two-dimensional shape:

List all the ways these two shapes are alike.     List all the ways these two shapes are
different.
Counting Parts of Solids
Name:_____________________________

Figure               Number of   Number of   Number of
Faces       Vertices    Edges
LESSON PLAN #5 Guess My Shape

Unit Title: Groovy Geometry
Math Standard: Geometry & Spatial Sense Standard
Math Indicator:
Objective: Each 4th grade mathematics student will:
 Describe two- and three-dimensional objects using their attributes
 Classify two- and three-dimensional objects.

Materials:
Bag with a variety of two- and three-dimensional shapes
Variety of solid figures and pattern blocks
Attachment “Solid Figures”

Procedures:
1. To review two- and three- dimensional object students will play a simple game.
2. One student reaches into a bag and pulls out a shape and doesn’t show it to anyone but the teacher.
3. The remainder of the students can ask 10 (yes/no) questions about the shape’s properties to help
determine what figure it is. (Does it have 4 edges? Does it have one base? Does it have 4 sides?)
Encourage students to ask quality questions without repeating something that has already been
4. Play several rounds to review shapes.
5. Once students have grasped the understanding, gather all shapes from the bag and set them out on the
table. Have students brainstorm examples of these in real life.
6. Randomly distribute 2-3 shapes to each pair of students. Have students list everything they notice about
these figures. Discuss the lists.
7. Using three dimensional shapes only, have the students examine the figure to decide where its base
would be. Have student complete the chart (“Solid Figures”). As you name each figure, have them fill
in the data. As students are filling in the data have them look for patterns that would help them name
any new figure. (Ask them what is the same about all pyramids? What is the same about all prisms?
etc…)
8. Have students collaborate in small groups (4-6 people) bringing their shapes with them. Now, using
their 6-9 shapes have the students classify their objects into groups. Students will need to record how
they sorted the shapes, and draw the shapes they included into the group on large paper. Students
continue to repeat this to find out how many different ways they can sort their shapes. They need to
continue to record how they are sorting them, but they don’t necessarily have to draw each sort.
9. Bring students together in a large circle. Have one group place their shapes into a sort they had
previously recorded without telling the whole group how they sorted them. Other students will try to
guess which attribute was used to sort the objects. Continue until each group has a chance to share.

Product: Completed chart paper explaining sort.

Assessment Criteria: : To assess students’ performance, teacher will observe students participating in the Guess
My Shape game as well as working in groups to sort objects.

Attachments “Solid Figures”
SOLID FIGURES
Name:_______________

Name           Base Shape      Face Shape
square Prism (cube)     square          square

triangular prism      triangle       rectangle
RECOMMENDED UNIT RESOURCES

Print Resources

Navigating through Geometry in Grades 3-5 (p.11) (p.26)
Investigations: Seeing Solids and Silhouettes 3-D Geometry (p.74-75)
Activity Math: Using Manipulatives in the Classroom (p. 201-202) By: Anne M. Bloomer, Phyllis A.
Carlson
“Activities That Promote Geometric Thinking” (p.7 of Mike Mikusa Handout)
“How Many Shapes Can You Make?” (p.10 Carolyn Borrow Handout)
Janice Van Cleaves’s Geometry for Every Kid by: Janice Van Cleaves

Internet Sites for Teacher Reference

Internet Sites for STUDENT Use

Unit Test Template

Unit Title: Groovy Geometry                         Grade Level : 3 4 5
Math Standard: Geometry and Spatial Sense           Indicator Number: 2

Teacher’s Name ________________________________ Building _________________________
District ________________________________________ Date of Testing ___________________

Skills & Concepts: Post-Test
Student’s Name ____________________________________              Total Score: _____/20

A. Multiple Choice (2 points each; 10 points total)
Directions to the student: Show how you solve each problem in the box provided. Use words, pictures, or
numbers. Then circle the LETTER of the correct answer.

1. I’m thinking of a shape with four equal sides. It is closed, and has no right angles. Both pairs of
opposite sides are parallel. What shape am I thinking of?

How did you find your answer?                         a.     square

b.     rectangle

c.     trapezoid

d.     rhombus

2. Think about the shape of a box of cereal. The sides, top, and base are all rectangles. What name is
given to the three-dimensional object with this shape?

How did you find your answer?                         a.     cube

b.     triangular prism

c.     rectangular prism

d.     rectangle
3. Which shape fits the rule? Rule: The shape has 6 faces. The faces are all congruent.

How did you find your answer?                        a.

b.

c.

d.

4. Which of the following statements is true?

How did you find your answer?                        a. Every trapezoid is a parallelogram.

b. Every square is a rectangle.

c. Every parallelogram is a rhombus.
.
d. Every rectangle is a square.

5. Which shape shows the base of the             ?

How did you find your answer?                        a.

b.

c.

d.

Objective Test Sub-Score: _____/10
B. Multiple-Step Problem Solving (3 points)

Directions to the student: Find the answer to this question. Be sure to finish the WHOLE question. You may
use words, pictures, or numbers. Be sure to show your work.

Draw three quadrilaterals about the same size. Each quadrilateral should be different in some way from

Explain why each is different.

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

Score: _____/3
C. Try It Another Way! (3 points)

Directions to the student: Read the question below. Then draw, write about, or show TWO DIFFERENT
ways to find the answer.

Examine the shapes below. Show two different ways to sort these shapes. Show one way these shapes can
be sorted in the first box. Now, in the second box, show ANOTHER way to sort them.

B                                               E
A                                    C              D                                F

Box #1                                               Box #2

Explain the attributes you used for each sort.
__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

Score: _____/3
D. Extended Response (4 points)

Directions to the student: Use sentences to answer this question.

Compare the triangular prism and the square pyramid. List at least two similarities and two differences.

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________
Score: _____/4
__________________________________
Unit Post-Test

Multiple Choice (2 points each; 10 possible)

1. D

2. C

3. B

4. B

5. C

Multi-Step Problem Solving (3 points each)
Scoring Rubric:

3=Communicates effectively and clearly through their drawing and writing, using correct math terms.

2=Incorrect drawing OR incorrect explanation

1=Drawing is correct, but no explanation

0=No attempt shown

Try It Another Way! (3 points)
Scoring Rubric:

3=Two groups are correctly sorted and explained

2=Two groups are correctly sorted, but not correctly explained

1=Made an attempt, but did not show clear understanding

0=No attempt shown

Extended Response (4 points)
Scoring Rubric:

4=Two similarities and two differences listed correctly using geometric terms (Four correct responses)

3=Three correct responses

2=Two correct responses

1=One correct response

0= No attempt shown

Enhancing Mathematics Education,
Stark County, Ohio
UNIT TEST
Composite Data Record
Unit Title: ______________________________________________ Grade Level : 3 4                  5
Math Standard: ___________________________ Indicator Number: __________

Teacher’s Name ________________________________ Building _________________________
District ________________________________________
Date of Pre-Testing ___________________     Date of Post-Testing ___________________
Number of Students Tested _____________     Number of Students Tested __________

POINTS AWARDED
Pre-Test Class Average Post-Test Class Average                  Change (+/-)
Part A (Multiple
Choice)
10 points possible
Part B (Multi-Step
Problem Solving)
3 points possible
Part C (Variant
Methods)
3 points possible
Part D (Extended
Response)
4 points possible

TOTAL Score
20 points possible

Please write 1-3 paragraphs describing your experiences with this unit, what the test results suggest to you, and
how you plan to use this information in your teaching practices. Attach this response along with the student test
set described below to this page for submission.

PAYMENT awarded with submission of: (1) this completed form, (2) paragraph(s) as described, and (3) ONE
student’s pre- and post-test set. Please white-out the student’s last name to protect his/her identity.

CROSSROADS Validation ________ Date __________

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