Learning Resources LER 7630 User Manual
TM
LER 7630
ACTIVITY GUIDE
A Hands-on Approach to Learning About Area and Volume
3
3
3
x 2.3) x 4.6 V = 63.5 cm
2
/
3
x (4.2 x 3.6) x 4.6 V = 34.8 cm
2
/
1
3
3
3
x (1.5 x 1.3) x 4.6 V = 4.5 cm
(4.6 x 4.6) x 4.6 V = 32.5 cm
2
3
/
/
1
1
3
x 4.3 x 3.8) x 4.6 V = 12.5 cm
2
/
1
(
π x 2.33 V = 50.9 cm
3
3
/
/
1
4
3
3
x 4.6 V = 25.5cm
2
x π x (2.3)
3
/
1
3
) V = 25.5 cm
3
x 4.6 V = 76.4 cm
π x 2.3
2
3
/
4
x (
2
/
1
V =
) V =
3
Volume Table
™
x s) x H V = (4 x
2
/
3
x b x h) x H V =
x b x h) x H V =
2
2
/
/
1
1
x b x h) x H V =
2
/
1
(1 x w) x H V =
(
3
3
/
/
1
1
) x H V =
2
3
π x r
(π x r
3
3
/
/
4
1
π x r
3
/
) x H V = π x (2.3)
4
2
x (
2
/
1
V =
) V =
3
Power Solids
A x H V =
3
/
1
V = A x H V = (s x s) x H V = (4.6)(4.6)(4.6) V = 97.3 cm
Large Square Prism
V = A x H V = (1 x w) x H V = (2 x 2) x 4.6 V = 18.4 cm3V = A x H V = (1 x w) x H V = (2 x 4.6) x 4.6 V = 42.3 cm3V = A x H V = (w x
Large Rectangular Prism
Small Rectangular Prism
V = A x H V = (
V = A x H V = (
V =
Hexagonal Prism
Large Triangular Prism
Square Pyramid
Small Triangular Prism
3
A x H V =
π x r
3
/
1
V =
A x H V =
3
3
/
/
4
1
V =
V =
Cone
Sphere
Triangular Pyramid
π x r
3
/
4
x (
2
/
1
V = A x H V = (π x r
V =
Cylinder
Hemisphere
2
Introduction
The transparent Power Solids™ set includes 12 plastic three-dimensional
shapes that allow for hands-on study of volume. Power Solids can be integrated
easily with daily math lessons for introducing, teaching, and reviewing math
concepts effectively. They allow students to make concrete connections
between geometric shapes and their associated formulas for volume, and to
observe volumetric relationships between the geometric shapes as well.
Most shapes in this set are variations of a prism or a pyramid, both of which
are polyhedrons. Polyhedrons are solid figures with flat sides, or faces. Faces
may meet at a point, called a vertex, or at a line, called an edge. A prism has
two congruent bases; the remaining faces are rectangles. A pyramid has one
base and the remaining faces are triangles.
Three shapes in this set have curved faces rather than flat ones; the cylinder,
cone, and sphere. Technically, they are not polyhedrons. Even so, a cylinder
can be thought of as a circular prism: a figure with congruent circular bases
and a single, rectangular face. A cone can be thought of as a pyramid with a
circular base and a face that is a wedge. A sphere is a unique shape with no
parallel to prisms or pyramids.
At the outset, learning formulas for the volume of more than a dozen geometric
shapes may seem daunting to your students. Formulas become much easier to
remember when students recognize that only the method for calculating the
area of a base changes from formula to formula; the other variables are
calculated the same way, regardless of shape.
Getting Started With Power Solids
Allow students to become familiar with the manipulatives before beginning
directed activities. You may want to explore prisms and pyramids on separate
days. Encourage students to handle, observe, and discuss the Power Solids. Ask
them to write down their observations as they make the following comparisons:
How are the shapes similar? (All shapes have the same height. They are all
three-dimensional. They all have empty spaces inside them.) How are the
different? (Some have flat sides; some have curved sides. Some are boxshaped; some are round, and some are triangle-shaped.) Where have students
seen these shapes in the world around them? (Great Pyramids of Egypt, traffic
pylons, film canisters, soccer balls, pieces of chalk, boxes, lipstick tubes, and
so on.)
Introduce and identify the following terms: face, edge, vertex or corner, and
base. Mention to students that the base of each Power Solid can be identified
by the hole in the face.
™
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