Technology Integration Lesson Plan
Name: Michael Plocher
Date: February 11, 2012
Lesson Title: Understanding nets and surface area of geometric solids
Subject/Topic: Mathematics - Geometry
Source of Plan: Geometry with Geometer's Sketchpad
http://wps.prenhall.com/wps/media/objects/7027/7196251/lesson_plans/Instructional_Plannin
g/Geometry_with_Geometer_s_Sketchpad.pdf
Brief Teacher demonstrates a GeoGebra sketch and with guided observations, questions, and
Description: student use of software, leads students to understand the underlying concepts of nets and how
they relate to surface area. Instead of using Geometer’s Sketchpad like in the original lesson
plan, the freely available and open source GeoGebra software will be used.
Relative Using software to manipulate nets and geometric solids frees up class time that would
Advantage: normally be spent cutting out nets. This allows more time for students to observe the
relationship between nets and their geometric solids. The addition of technology also
motivates students to spend more time on the topic thereby gaining a deeper understanding of
the relationship between nets and the surface area of geometric solids.
Objectives: 1. Create a geometric solid when given its net.
2. Create a net for a given geometric solid.
3. Understand how nets are related to formulas for surface area.
Standards: ISTE-NETS Student Standards
1. Creativity and Innovation
 Apply existing knowledge to generate new ideas, products, or processes
 Use models and simulations to explore complex systems and issues
2. Communication and Collaboration
 Interact, collaborate, and publish with peers, experts, or others employing a variety of digital
environments and media
3. Research and Information Fluency
 Process data and report results
5. Digital Citizenship
 Exhibit a positive attitude toward using technology that supports collaboration, learning, and
productivity
6. Technology Operations and Concepts
 Understand and use technology systems
 Select and use applications effectively and productively
NCTM: The National Council of Teachers of Mathematics Standards
Geometry
GM.4b Use two-dimensional representations of three-dimensional objects to visualize and
solve problems such as those involving surface area
Measurement
ME.2d Develop strategies to determine the surface area of selected prisms, pyramids, and
cylinders
Representation
RE.5c Use representations to model and interpret physical, social, and mathematical
phenomena
Grade Levels: Grades 6, 7, 8
Time Frame: Fifty minutes
Technology GeoGebra files, computer, SMARTBoard (SB), projector, JAVA, notebook computers
Used:
Understanding nets and surface area of geometric solids
© 2012 Michael D. Plocher
Permission is granted for use as an example in EDT5001
Other
resources:
Preparation
Prior to Class:
Developing
Background:
Detailed
Lesson
Procedure:
Saxon Math Course 3 textbook, student math notebooks, scissors, tape, surface area formula
sheet, dimensions of geometric solids sheet
1. Create webpage with links to GeoGebra files students will be using.
2. Divide students into groups of two.
3. Make sure notebook computers are charged.
4. Verify the GeoGebra files work on each notebook computer and the SMARTBoard
connected computer. Java needs to be updated to Java 6.
5. Copy/paste a net model of a cube on 8 ½ x 11 in. paper and make enough copies for each
student.
6. Create enough surface area formula sheets for each student.
7. Create enough measurement sheets for each student.
1. Ask students to explain how to find the area of a circle, square, rectangle, and triangle and
list on the SB, the formulas they mention.
2. Display plastic geometric solids such as a cylinder, cone, pyramid, and triangular prism
and ask students to name each solid.
3. Ask students to name the shapes of the faces that make up a cylinder, cone, pyramid, and
triangular prism.
1. Today, using GeoGebra software files you will explore geometric solids by manipulating
their faces to create something called a net. You will also manipulate a net to create a
geometric solid. Finally, you will use area formulas to help you calculate the surface area
of each geometric solid.
2. Discuss the fact that there is no one formula for the surface area of a prism. This is
because a prism can have a square, rectangular or triangular base. Show students a flat
pattern (net) of a cube and discuss how they might be able to come up with the surface
area by analyzing the net.
3. Separate students into groups of two and give them two sheets of paper with a cube net
printed on it and a role of tape. Students are told to number the squares one through six
and then write the formula for the area of a square on each square of their net.
4. The students are then told to cut out their net using their scissors, and with the numbers
facing outward, construct a cube using the provided tape. They should be encouraged to
discuss with their partner how to accomplish this and are allowed to work collaboratively.
5. After the students have constructed their cube, they should calculate its surface area. They
should come to the conclusion that there are 6 squares that make up the 6 faces or sides.
This means they can take the area of one side and multiply it by 6. The end result is the
total surface area of the cube.
6. If they struggle to do this, allow them to open their cube and lay it flat and calculate the
area of each square then add up each area.
7. When done, the teacher explains that using paper to construct nets can be time consuming
and slows down learning. Construction of nets of geometric solids using software allows
nets to be created quickly and without the errors normally associated with paper models
of nets. These digital nets can then be manipulated to create a 3D geometric solid more
efficiently than when using paper nets.
8. The teacher then displays the GeoGebra file of a cylinder and asks students to name the
solid.
9. Using the Geogebra file, the teacher then displays the cylinder’s net and asks students to
list the shape of the faces they see and write down the formula showing how to find the
area of each face.
10. Through questioning, the teacher confirms that what the students have written down is
correct.
Understanding nets and surface area of geometric solids
© 2012 Michael D. Plocher
Permission is granted for use as an example in EDT5001
11. Manipulating the cylinder’s net in the GeoGebra file the teacher will create its geometric
solid.
12. The students will then be directed to calculate the surface area of the cylinder with
dimensions provided by the teacher.
13. The students will now get their notebook computers so they can begin exploring the
relationship between the geometric solids of prisms, cylinders, pyramids, and cones and
their nets.
14. Once the notebook computers are turned on and online, the students will click on the
previously created GeoGebra file links listed on the class math web page. This will run
JAVA files on their notebook computers allowing students to unfold digital geometric
solids to create nets and fold nets to make geometric solids.
15. When students have had time to explore the relationship between various geometric solids
and their nets, they will be given a sheet with measurements for five different solids for
the purpose of practicing calculating surface area. The students will also be given the
Surface Area Formula sheet. When calculating surface area, the students will show all
their work in their math notebook.
16. The students will create a Spreadsheet in GoogleDocs to record their surface area results.
Within the spreadsheet the students will list the name of the geometric solid they are
finding the surface area of, the dimensions used for each calculation and the surface area
they calculated. They will share the link to their spreadsheet with the teacher so he can
view the student’s results as they record them.
17. Within their math notebook, the students will draw and label the net and geometric solid
of a cylinder, cone, pyramid, and triangular prism.
URL List: http://www.splnewulm.org/school/academics/mathcourse3.html
http://www.geogebra.org/cms/
http://www.geogebra.org/en/upload/files/english/Knote/Nets/cube.html
http://www.geogebra.org/en/upload/files/english/Knote/Nets/Pyramid.html
http://www.geogebra.org/en/upload/files/english/Knote/Nets/cylinder.html
http://www.geogebra.org/en/upload/files/english/Knote/Nets/conenet.html
Assessment: 1. Each correct answer students record in their spreadsheet receives one point.
2. Student’s notebooks will be collected to observe their calculations. Students receive one
point for showing their work.
3. Drawings of nets and geometric solids that are correct receive one point each.
Understanding nets and surface area of geometric solids
© 2012 Michael D. Plocher
Permission is granted for use as an example in EDT5001
Cube Net
Understanding nets and surface area of geometric solids
© 2012 Michael D. Plocher
Permission is granted for use as an example in EDT5001
Dimensions of Geometric Solids
Below are the dimensions of five rectangular prisms; choose three rectangular prisms and find their
surface area:
Dimensions of a rectangular prism
A. side = 2, height = 9, length = 3, width = 4
B. side = 12, height = 4, length = 1.8, width = 6
C. side = 1.8, height = 6, length = 10, width = 0.5
D. side = 10, height = 0.5, length = 5, width = 5
E. side = 2, height = 9, length = 3, width = 4
Below are the dimensions of five triangular prisms; choose three triangular prisms and find their surface
area:
Dimensions of a triangular prism
F. side = 2, height1 = 9, height2 = 3, base = 4
G. side = 12, height1 = 4, height2 = 1.8, base = 6
H. side = 1.8, height1 = 6, height2 = 10, base = 0.5
I. side = 10, height1 = 0.5, height2 = 5, base = 5
J. side = 2, height1 = 9, height2 = 3, base = 4
Below are the dimensions of five cylinders; choose three cylinders and find their surface area:
Dimensions of a cylinder
K. radius = 2, height = 9
L. radius = 12, height = 4
M. radius = 1.8, height = 6
N. radius = 10, height = 0.5
O. radius = 5, height = 5
Below are the dimensions of five regular pyramids with a square base; choose three pyramids and find
their surface area:
Dimensions of a regular pyramid with a square base
P. side = 2, Slant height = 9
Q. side = 12, Slant height = 4
R. side = 1.8, Slant height = 6
S. side = 10, Slant height = 0.5
T. side = 5, Slant height = 5
Below are the dimensions of five cones; choose three cones and find their surface area:
Dimensions of cones
U. radius = 2, Slant height = 9
V. radius = 12, Slant height = 4
W. radius = 1.8, Slant height = 6
X. radius = 10, Slant height = 0.5
Y. radius = 5, Lateral height = 5
Understanding nets and surface area of geometric solids
© 2012 Michael D. Plocher
Permission is granted for use as an example in EDT5001
Surface Area Formulas
Surface Area of Rectangular Prism
(Area of Base x 2) + [(Perimeter of Base) x Height of the prism]
(2 [l w]) [(s
x
x
+
+
s + s + s) x h ]
s
s
l
s
s
w
h
Surface Area of Triangular Prism
h1
(Area of Base x 2) + [(Perimeter of Base) x Height of the prism]
{[½ (b
x
x
h1)] 2} [(s
x
+
+
s + s) x h2]
s
s
s
b
h2
Surface Area of a Cylinder
(Area of Base x 2) + [(Circumference of Base) x Height of the cylinder]
[(π
x
2
r
) 2] [(2
x
+
x
r
π x r) x h]
h
Understanding nets and surface area of geometric solids
© 2012 Michael D. Plocher
Permission is granted for use as an example in EDT5001
Surface Area of a REGULAR Pyramid – Triangle Base
(Area of Base) + (One-half times the perimeter of the base) x (slant height)]
B (usually given) [½ (s
+
x
+
s + s)
x
l
l]
s
s
s
Surface Area of a REGULAR Pyramid – Square Base
(Area of Base) + (One-half times the perimeter of the base) x (slant height)]
(s2) [½ (4 s) l ]
+
x
x
x
l
s
s
Surface Area of a Cone
(Area of Base) + (Lateral surface area of the Cone)
(π
x
r2
) (π
+
x
r
x
l)
l
h
r
Understanding nets and surface area of geometric solids
© 2012 Michael D. Plocher
Permission is granted for use as an example in EDT5001