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Teacher:
David Cochrane
Grade Level: Grade 8
Subject:
Pre-Algebra
Lesson:
Drawing Three-Dimensional figures
Unit:
Three-Dimensional Figures
Class Length: 96 min.
Day of Unit: 1
I.
Introduction
Goal: The goal of this lesson is for students to know and draw three-dimensional
figures.
Rationale: Students must know how to draw three-dimensional diagrams because many
real-world problems do not provide diagrams, which are important problem-solving tools.
Also, students must be able to interpret information from diagrams of three-dimensional
figures when presented with a problem containing only a figure.
Multicultural Issues
 Use a variety of pictures for examples and guided practice;
 Use of real-world problems;
 Use of objects in the students’ environment to make learning personally
meaningful.
Standards:
 ACOS: 11, 15, 23
 NCTM: 24, 32, 33, 35
 SAT10: 15, 23.2, 23.3, 23.4, 23.5, 23.6
 AHSGE: 7-4
 NETS: 1-6
Interdisciplinary Connections
 Egyptian pyramid anticipatory set.
II.
Objectives
Teacher Objectives
I want my students to know:
1. Three-dimensional figures;
2. Three-dimensional figure terminology definitions;
3. How to properly draw three-dimensional figures;
4. How to summarize the lesson’s “big ideas”;
5. How to communicate problem solving ideas;
6. How to use a variety of technologies to solve problems;
7. How to use manipulatives to solve problems.
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Student Objectives
Students will be able to:
1. Define the concept of a three-dimensional object/figure (cognitive/know.);
2. Give examples of three-dimensional objects/figures (cognitive/comp.);
3. Give non-examples of three-dimensional objects/figures (cognitive/comp.);
4. Define prisms, pyramids, cylinders, and cones (cognitive/know.);
5. Give examples of prisms, pyramids, cylinders, and cones (cognitive/comp.);
6. Define a net (cognitive/knowledge);
7. Construct a net as a prism model (psychomotor/mech.);
8. Save a Microsoft Paint ® diagram to a floppy disk (psychomotor/mech.);
9. Define the parts of three-dimensional figures (cognitive/know.);
10. Label the parts of three-dimensional figures (cognitive/know.);
11. Explain why drawing three-dimensional figures is important (cognitive/eval.);
12. Draw diagrams of three-dimensional objects/figures on isometric dot paper
(cognitive/synth.);
13. Draw a diagram of a three-dimensional object/figure using Microsoft Paint ®
software (cognitive/synth.);
14. Appreciate technology by using Paint to create a crisp diagram
(affective/valuing);
15. Volunteer to summarize the lesson’s “big ideas” (affective/responding);
16. Explain how to draw diagrams of three-dimensional figures (cognitive/comp.).
III.
Pre-Class Preparation
Prerequisites
Students must know:
 Basic computer skills (keyboarding, mouse usage);
 How to use Microsoft Paint ® software;
 How to compute the area of polygons.
Required Materials
 Anticipatory set handouts (150)
 Isometric dot paper (1 sheet per student)
 Overhead projector
 Isometric dot paper transparency
 Isometric dot paper activity follow-up questions
 Large cube prop for drawing a three-dimensional figure activity
 Laptop computer with Microsoft Paint software installed
 At least (7) computers with Microsoft Paint software installed
 (6) 3.5 inch floppy disks
 (30) rulers or straightedges (optional)
 Computer and printer to print out group Paint activity work
Materials Acquisition
1. Teacher will supply the (150) self-created anticipatory set handouts
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2.
3.
4.
5.
Teacher will supply (150) sheets of isometric dot paper
Overhead projector is part of the classroom equipment
Teacher will provide the isometric dot paper transparency
Teacher will provide (150) handouts of isometric dot paper follow-up questions
with isometric dots on the reverse side
6. Teacher will supply the cube prop
7. Teacher will furnish the laptop computer for in-class Paint demonstration
8. Computers will be available in the Media Center. Computer time will be reserved
one month in advance
9. Teacher will provide (6) 3.5 inch floppy disks
10. Teacher will supply (30) rulers for students who do not have one
11. Teacher will provide the class computer and printer to print out group Paint
activity work
Resources
 Geometer’s Sketchpad ® software (for isometric dot paper);
 Microsoft Paint ® software (for Paint activity);
 Glencoe Mathematics Applications and Connections Course 3 (1999 Edition)
textbook (for three-dimensional figure drawing ideas);
 All other materials and ideas are teacher-created.
Set Up
 Turn computers on and check to make sure the Paint program works properly on
all computers;
 Check to make sure the overhead projector functions correctly at least one day
prior to the lesson;
 Place cube prop next to the projector cart;
 Place transparencies on the projector cart;
 Place math journal prompt on the overhead projector and turn the projector on
before students walk into the classroom;
 Place the grouping assignment sheet on the clipboard by the door.
Class Management (Disp. 5.4)
 Students will follow the daily routine for entering the classroom;
 Students will turn in homework upon entering the classroom following the correct
procedure;
 Students will check the “groups” sign above the door and follow the procedure for
forming groups;
 Students will collect their journals from the bin and begin working immediately
from the projected prompt;
 At the end of the last class meeting, students were assigned reading material in the
textbook and to prepare questions.
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IV.
Instructional Procedures
A.
On-Task Activity
 Transition: Good [morning] students.
 Directions: Please follow the procedure for obtaining your journal and begin
writing.
Math Journal Entry (5 minutes)
 Teaching Strategy: Journal Writing
 The journal prompt will be: “How might you use mathematics while shopping
at Wal-Mart?”
 Transition: Thank you for your journal entries.
 Directions: Please pass your journals to the left so that the student helper can
put those away. Now, the last time we met I asked you to read the section on
“Three-dimensional figures” in our textbook. Are there any questions
concerning the reading material? Good. Let’s take a look at today’s
anticipatory set.
B.
Introduction to Lesson Content
Lesson Springboard (5 minutes)
 Teaching Strategy: Advanced Organizer
 Teacher will select a student helper to pass out anticipatory set handouts.
Students will read the handout problem as the teacher reads it aloud. Students
will ask questions as needed.
 Transition: We will be studying the properties of three-dimensional objects
and figures today, as well as learning how to draw them properly. When
might we need to know how to draw an accurate diagram of a threedimensional object? [Students will volunteer answers] What if we’re given a
word problem involving three-dimensional figures without a diagram?
Diagrams are important tools to help us think through problems. What if we
are only given a diagram and are told to solve a problem? We would
certainly have to know things about three-dimensional objects in order to use
the diagram correctly and solve the problem.
 Directions: Now let us introduce some terminology associated with these
figures.
C.
Instruction
Introduction, Terms, and Definitions (15 minutes)
 Teaching Strategy: Informal Lecture
 Review two-dimensional figures, such as polygons and circles;
 Three-dimensional shapes are shapes that have length, width, and height;
 Students will give examples and nonexamples of three-dimensional figures;
 Definitions:
 Prism – a 3D shape with at least one pair of bases;
 Cylinder – a 3D shape with circular bases and one face;
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


Pyramid – a 3D shape with a polygonal base and triangular faces that
meet at an apex;
 Cone – a 3D shape with a circular base and one face that comes to an
apex
 Face – a flat surface of a 3D figure;
 Vertex – where three or more edges meet;
 Edge – where two or more faces meet;
 Bases – parallel and congruent faces.
 Apex – the top of a pyramid or cone
Transition: Now we have a pretty good idea about what these shapes are and
how to spot them.
Directions: Let’s use apply our knowledge of three-dimensional figures to
some real-life objects by classifying them and giving some examples, as well
as some nonexamples.
Classification, Examples, and Non-examples (10 minutes)
 Teaching Strategy: Informal Lecture
 Present a montage of pictures on the overhead projector and ask students to
classify each object, figure, or shape, including attributes such as faces, bases,
edges, vertices, and apexes.
 Teacher will ask the students to give examples of prisms, pyramids, cylinders,
and cones.
 Transition: We seem to understand the concept of these three-dimensional
figures in regard to the world around us.
 Directions: But what if we don’t have the object or a picture of it? How can
we communicate the shape of the object to another person? Well, we could
try to put our ideas into words, but have any of you heard the saying, “a
picture is worth a thousand words?” Also, what if we need to solve a word
problem and need a picture to help us solve it? Let’s find out how we can
draw an accurate representation of a three-dimensional object or figure.
Drawing Three-Dimensional Figures (15 minutes)
 Teaching Strategy: Informal Lecture
 A cube prop will be used to model a generic three-dimensional figures
 Class, look at this cube. Notice that by looking at only the top of the cube, or
even just two sides, it’s not as good as looking at three sides of the cube. Can
we ever see all of the cube’s sides from just one angle? Why? Because there
will always be part of the shape that is hidden from us. Drawing this hidden
part is the trickiest part. We will first draw the parts we can see and then
tackle the hidden parts.
 Each of you has been given a sheet of isometric dot paper. Here is where we
will draw a picture of the cube. First we will draw the visible edges. For the
hidden edges we used dashed lines instead of solid lines.
 Transition: So now we can accurately draw three-dimensional figures just by
looking at a three-dimensional figure. Remember, we will need to create
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
drawings such as these when we need a drawing to solve a problem. Now
let’s put those sheets away in our notebooks …
Directions: … and turn our attention to our next activity, which will be to
build a net model. Our helper will pass out the activity sheets. Now, since the
activity is called a “net” activity, look at your sheets and tell us what you
think a “net” might be. [Answers will vary] A net is a two-dimensional
shape, such as a sheet of paper, that can be folded up into a three-dimensional
shape, such as a prism. Nets are special because we can’t always take just
any two-dimensional shape and fold it up so that it makes a three-dimensional
shape.
Net Activity (15 minutes)
 Teaching Strategy: Discovery
 By creating nets, students will make kinesthetic connections with
mathematics.
 Transition: We will be working with nets such as these in our next lesson, so
it is important for us to understand nets and how they can help us to model
certain three-dimensional shapes.
 Directions: Now please take out your anticipatory set sheet that we discussed
at the start of class. We will use this sheet to complete the next activity. All
groups should prepare to start the activity now by assembling at your group’s
computer. [Groups will assemble now.] Let’s read the instructions together.
[Student’s name] please read the activity introduction. Thank you. [Student’s
name] please tell us what we need to remember for this activity and what our
goals are. Thank you. [Student’s name] please read the questions to be
answered at the bottom of the page. Thank you. If you have any questions,
please follow the procedure for asking questions. You may begin.
Paint activity (25 minutes)
 Teaching Strategy: Cooperative Learning
 This activity will allow students to make connections to mathematics by
creating a diagram using technology. Cooperative learning will occur because
all group members will contribute to the diagram.
 Transition: Time is up students. Please save your diagram on the floppy disk
that is already in the disk drive. Please name your file according to the
period and group color you are in. Well, I think this activity was a great
success. Your Paint drawings looked very good. I will print them out and
post them on the hall tomorrow where you will really be able to appreciate the
power of the computer to help create diagrams.
 Directions: Now all groups need to answer the follow-up questions on the
bottom of the activity sheet.
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Closure (6 minutes)
 Teaching Strategy: Review
 Teacher will remind students that all work must be handed in at the beginning
of the next class meeting. This will be the follow-up questions regarding the
three-dimensional figure activity, and the anticipatory set questions.
 Students will volunteer to briefly summarize the day's activities, to include
how to draw three-dimensional figures and why drawing three-dimensional
figures is important. Teacher will ask students if they have any questions.
Students will ask questions as needed. Teacher will remind students that
questions can also be e-mailed.
 Student helper will hand out homework sheets. Students will read over the
problems and ask questions as necessary.
 Transition: Class, please get ready to be dismissed by cleaning up around
your work area. Thank you. When everyone is quiet and seated, I will dismiss
you. Thank you. Class, you are dismissed.
V.
Evaluation
A.
Assessment
1.
Did the students participate in the classroom interactions?
2.
Did the students understand the main points of the lesson?
3.
Did the students participate in the Paint activity?
B.
Remediation
1.
Dependent on individual student needs
2.
Accommodations will be made for special needs students
3.
Plan B: allow the students to use individual manipulatives at their
desks.
C.
Short-Term Assessment of the Lesson’s Content
1.
Teacher will assess student comprehension regarding drawing
three-dimensional figures by observations during guided practice.
2.
Teacher will assess student comprehension and application of these
skills when grading group activity work.
D.
Long-Term Assessment of the Lesson’s Content
1.
Teacher will assess long-term learning when students must use
these skills in order to solve word problems in which no figure is
given, and to solve problems when only a figure is given.
2.
Long-term assessment will be performed via the weekly quiz, the
unit quiz, the mid-term exam, the final exam, and the SAT-10
normative assessment exam.
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VI.
Self-Evaluation
What worked well?
What did not happen according to what I wanted to happen?
Did I meet my teacher objectives?
Did I maintain the students’ interest?
Did I make learning relevant and meaningful to all students?
Did I use varying activities?
Discuss how this lesson could be improved.
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TRANSPARENCY
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Drawing 3D Figures Anticipatory Set
You are a member of an archeological team that has discovered a lost
pyramid deep in the African jungle. While most Egyptian pyramids are
square-based, this pyramid is pentagonal-based, meaning that the base is in
the shape of a pentagon. Your team has not measured the sides or height of
the pyramid yet, but you must send a diagram of the pyramid back to
America right away.
Here’s what you need to remember:
 How to draw polygons;
 How to use Microsoft Paint software;
 How to save a drawing to a 3.5 in. diskette.
Here’s what you will be able to do after this activity:
 Draw a three-dimensional figure using isometric dot paper;
 Create a three-dimensional figure using Microsoft Paint.
Help your team sketch what you think the pyramid might look like on a
sheet of isometric dot paper. Then create a diagram of the pyramid using
Microsoft Paint software. Color will help, but too many different colors can
make your diagram confusing. Make sure your diagram contains the names of
your group members, the date, and class period. Save your diagram on a 3.5
in. diskette. When you are finished, answer the following questions
individually on a separate sheet of paper.
1. Did this activity help you to better understand how three-dimensional
figures are drawn? Explain.
2. What did you like about this activity?
3. What did you dislike about this activity?