LER 4331
Ages Grades
+
+
3
8
®
Activity Guide
Cube
Sphere
Cone
Cylinder
Hemisphere
Square pyramid
Rectangular prism
Pentagonal prism
Triangular pyramid
Triangular prism
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Volume is expressed in cubic units of measurement: inches, feet, yards, miles,
milliliters, centimeters, decimeters, meters, kilometers, etc.
Using the funnel, fill the 1-liter graduated cylinder with plastic fill.
Remove the base of the chosen solid and fill it with the plastic fill. Note the
amount of fill required. Repeat two or three times to ensure accuracy.
Repeat the process with all of the shapes.
Have the students evaluate their data by listing the solids in descending order
from most volume to least volume. Compare completed list with original
estimation.
Discuss:
What other materials could be used for the measurements?
What relationships exist between the various solids? How does the volume
of the cube compare to the volume of the square pyramid? Explain any other
comparisons derived from the data.
Characteristics of Geometric Solids
Work with the students to create a chart like the one below to record their own
observations:
View-Thru®
Geometric Solids
Shape
of Base(s)
Number
of Faces
Number Number
of Vertices of Edges
1
2
3
4
5
6
7
8
9
Large Cube
Small Cube
Large Rectangle
Small Rectangle
Pentagonal Prism
Large Triangular Prism
Small Triangular Prism
Square Pyramid
Triangular Pyramid
10 Large Cylinder
11 Small Cylinder
12 Cone
13 Sphere
14 Hemisphere
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Euler’s Formula
Euler’s Formula is named after Swiss mathematician Leonard Euler. In the mid-eighteenth
century, Euler discovered that for any polyhedron, F + V = E + 2. In the formula, F represents
the number of faces, V represents the number of vertex points, and E represents the number of
edges. For example, a cube has 6 faces, 8 vertex points, and 12 edges.
F + V = E + 2
6 + 8 = 12 + 2
Have the students use their data from the preceding chart to discover Euler’s Formula. Euler’s
Formula is true for the first nine solids listed in the table.
Intervention Strategies
Scaffolded Instruction: Before providing formulas to students, instead provide the
definitions of perimeter and area, and opportunities to solve problems that allow students
to gain data leading to the use of a formula. Begin with two-dimensional shapes before
advancing to three-dimensional solids.
Directed Orientation: Use different household items that resemble a cube, cone, sphere,
cylinder, pyramid, or prism. Have students sort the items by different attributes you provide.
Then, introduce the formal shapes and have students match the shapes to the corresponding
household items.
Free Exploration: Have students fill the solids with rice or water to explore properties of
volume. Encourage students to make estimations and compare which shapes are able to hold
more or less than the others.
© Learning Resources, Inc., Vernon Hills, IL (U.S.A.)
Learning Resources Ltd., King’s Lynn, Norfolk (U.K.)
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Made in China.
LRM4331-GUD
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