NTTI
NTTI
NTTI Media-Rich Lesson
Millicent G. McCaskill
NAME
What’s Your Dimenision? 2D or 3D
LESSON TITLE
Fourth - Fifth Grades
GRADE LEVELS
One Hour Class Period
TIME ALLOTMENT
OVERVIEW
What is a two-dimensional figure? A two-dimensional figure, also called a plane or
planar figure (flat) is a set of line segments or sides all lying in a single plane. The sides
are called the edges of the figure. The edges are one-dimensional, but they lie in the
plane, which is two-dimensional (See figure I – examples).
What are three-dimensional figures? A three-dimensional figure, sometimes called a
solid figure, is a set of plane regions and surface regions, all lying in three-dimensional
space. These surface regions are called the faces of the figure. Each of them is twodimensional. The arcs of curves that are the edges of the faces of the figure are called
the edges of the figure. They are called one-dimensional. The endpoints of the edges
are called its vertices. They are zero-dimensional (see figure II – examples). Solid
geometry is concerned with polyhedron, spheres, three-dimensional solids, lines in
three-space, planes, and so on.
The focus and essential questions for this lesson is “How can we make two- and three
dimensional figures?” How are they alike? How are the different? Students will create
a polyhedron from different polygons. Identifying and building three- dimensional
objects from a two- dimensional shape will allow students to determine the relationship
between 2D and 3D figures.
SUBJECT MATTER
Mathematics
Geometry (2D & 3D -- solid geometry)
LEARNING OBJECTIVES
Students will be able to:
•
Identify and create two- and three- dimensional figures (i.e., rectangle, triangle,
trapezoid, rhombus, square, triangle, hexagon, and pentagon) using manipulatives.
•
Compare and contrast plane and solid figures according to one or more attributes
(e.g., faces, edges, vertices, and shape).
STANDARDS
Georgia’s Standards
www.glc.k12.ga.us
Mathematics (5th & 6th Grades)
Standards matching this resource:
QCC 18:
Topic: Solid Figure, Plane Figure, Geometric Properties, Classifying
Standard: Contrasts and classifies simple plane and solid geometric figures by their
properties.
MEDIA COMPONENTS
Video(s)
1. The Kay Toliver Files – Polygons (This video reviews polygons while introducing and
guiding students in an investigation of the third dimension, as they transform
polygons into polyhedron.)
Web site(s)
Lois Terms – http://www.loisterms.com/polyquiz.htm
This site helps students and teachers immediately see how much they know about
polygons.
The site consist of ten questions of varying nature about polygons.
MATERIALS
•
Internet Access
•
Videos (The Kay Toliver Files) – 1 copy
•
Television, VCR or DVD needed to view videos.
•
Physical models of the 3D shapes – (12 different examples are needed for this
lesson). Construct your models using either card stock or foam board. You can
purchase the foam board at any arts and craft store.
•
20 – 30 sheets of Poster board (varied colors)
•
scotch tape (1 roll for every 2 students)
•
•
•
trays needed for polygonal shapes (5)
cut-outs of each polygonal shapes (4” – 5” in size) – {20 cut-outs of each shape}
clear overhead sheets
PREP FOR TEACHERS
Before teaching this lesson, make certain that all of your Web sites are bookmarked on
all of the computers in your classroom, and that all of the necessary links are still valid
and running. CUE your videotape to the first segment you are going to use in the
Learning Activity, at the visual cue of where Kay Toliver says, “What name can we give
to these figures?
Make sure that you have pre-cut all polygonal shapes that students will use in the
creation of their physical model. (ex: square, hexagon, pentagon, trapezoid, rhombus)
Make your demonstration models at least a week before the lesson. Prepare all
materials at least two-three days prior to teaching the lesson.
When using media, provide students with a FOCUS FOR MEDIA INTERACTION, a
specific task to complete and/or information to identify during or after viewing of video
segments, Web sites, or other multimedia elements.
Students should know the definition of the following concepts::
•
Rhombus
•
Square
•
Hexagon
•
Parallelogram
•
Pentagon
•
Rectangle
•
Trapezoid
•
Polyhedron
•
Quadrilaterals
•
triangles
Media Components
•
Overhead projector (Optional) – (make sure you have a spare bulb)
•
VCR with remote
•
LCD Panel with remote
•
Television with remote
•
Video
Web site(s)
Computer Resources:
•
Modem: 56.6 Kbps or faster.
•
Browser: Netscape Navigator 4.0 or above or Internet Explorer 4.0 or above.
Macintosh computer: System 8.1 or above and at least 32 MB of RAM.
•
Personal computer (Pentium II 350 MHz or Celeron 600 MHz) running
Windows® 95 or higher and at least 32 MB of RAM
•
Software: Excel (optional)
INTRODUCTORY ACTIVITY: SETTING THE STAGE (Engage)
Step 1
Explain to your students that they live in a three- dimensional world. Tell them that
everything around them has length, width and thickness. Explain to them that even
though our world is three- dimensional, we often communicate in two dimensions: with
pencil and paper.
Remind your students what the difference is between two- dimensional and threedimensional figures. Discuss this by having volunteers point out examples found in
classroom. On a clear overhead sheet record, your class’s answers to the question you
posed. (Student reactions will vary.)
Step 2
Tell the students that they are now going to take a pretest quiz to determine their
knowledge about the different type of shapes that are two-dimensional. Take your
students to the following Web site: How Much Do You Know About Polygons? Quiz
at http://www.loisterms.com/polyquiz.htm. Provide your students with their first FOCUS
FOR MEDIA INTERACTION, asking your students to take the quiz to see what they
know about polygons. (This site consists of ten questions of varying nature about
polygons. Each participant is graded on their responses and is afforded the opportunity
to view their correct and incorrect responses. Each question is also given a brief
explanation in regards to the correct responses. To see the questions and correct
answer responses for each question see Appendix A at the end of this lesson.)
Step 3
After your students have completed the Easy Polygon pretest and show you the results
of their efforts (make sure you document their scores in your grade book), explain to
your class that they are going to be learning about how these two- dimensional figures
will be used to create three- dimensional figures called polyhedral. Ask your students if
any of them know how to identify polyhedrons. Record their answers on the overhead.
Tell you students that they will find out more as they create a polyhedron using different
polygonal shapes.
Pair students:
•
Media Interaction Worksheet
•
1 physical model of a polyhedron
•
1 writing journal per student
LEARNING ACTIVITIES
Learning Activity 1
Step1
Insert THE KAY TOLIVER FILES – into your VCR.
Step 2
Provide your students with a FOCUS FOR MEDIA INTERACTION, asking your
students if they know the definition of a polyhedron. Allow your students a few seconds
to write down their definition in the journals. When they hear the answer, they are to
raise their hands. PLAY the videotape. PAUSE the videotape when the Kay Toliver
says, “What are these faces everyone?” Answer is Polygons. It is now time to take out
the physical example of a polyhedron (You can select any example you have). Showing
your example have student go to their journals and write down the polygonal shape they
see. Examples: Trapezoid, square, triangle, etc. Discuss with your students if they can
tell you the difference between the polygonal faces and the polyhedron. Refer back to
the segment just viewed to check for understanding. FORWARD videotape back to
when Kay Toliver says, “So what is the difference between polygons and a polyhedron?
Provide students with a FOCUS FOR MEDIA INTERACTION. PLAY the videotape
until it reaches the point when Mrs. Toliver says, “Guest what you are making today? A
polyhedron.” and STOP videotape.
CULMINATING ACTIVITY
Step 1: Creating a polyhedron from different polygons – Hands-on creation of
polyhedrons
Explain to your students that today they will construct a polyhedron using different
polygons. Hand out to each pair of students 1 physical model of a unique polyhedron.
Tell your students to examine their polyhedron to determine what polygonal shapes
make up their polyhedron.
Step 2
Hand out tape and have one student from each pair come to the front of the room to
collect their polygons to construct their polyhedron.
Step 3
Teacher will rotate throughout the classroom monitoring students as they complete the
task. Answer any questions that students may have during your rotation.
Step 4 – Sharing your Creation
Explain to your students that at this time they are to share to the class their polyhedron.
Students will need to give a clear description of what polygons make-up their
polyhedron. Once every group has finished sharing their creation, have each student
then write in their journal a list of where they could find their polyhedrons in everyday
life. Using your overhead as student share, their ideas make a list of those ideas.
Step 5 – Closure of activity/lesson
Using the information they obtained today along with teacher, students/teacher will
recap what they learned today about two- dimension vs. three- dimensional shapes.
Teacher will ask the following questions:
1.
What are the properties of a polygon? Answer: They are flat figures with many
sides and vertices. They are two- dimensional figures.
2.
Could you name several different polygons? Answer: trapezoid, square,
rhombus, hexagon, triangle
3.
What is a polyhedron? Answer: A polyhedron is a 3- dimensional figure, made
up of many faces, edges, vertices and has space.
4.
How are they alike? Answer: They both have vertices and edges.
5.
How are they different? Answer: Polygons are flat plane shapes, twodimensional, and have many sides. A polyhedron has many faces made up of
polygons, and has space.
Assessment: You are able to assess the students during and after this lesson through
teacher observations and though questioning.
CROSS CURRICULAR ACTIVITIES
Folding Origami Shapes - Paper-folding activities can be used to involve students in
exploring geometric concepts such as congruency, symmetry, and area. Origami
activities are especially appealing to students, since the resulting figures are threedimensional and resemble familiar animals and objects. In this project students use
paper folding to learn about angles and polygons. They also develop a better intuitive
understanding of congruency, symmetry, area, and geometric figures.
Geography -- Students can use maps to identify states or countries shaped like
polygons.
Writing – The student will assess the importance of geometry in real life and write to
explain real-life applications of two geometric principals from this unit.
Art – The student will design a stained glass window incorporating a minimum of ten
two-dimensional shapes and include a key to identify the shapes.
COMMUNITY CONNECTIONS
Invite an architect to your class to speak on how they use polygonal/polyhedron shapes
in the design of buildings and other structures.
Take your class on a field trip to a museum to view Artwork that appears to be 3D in
content.
(Appendix A)
HOW MUCH DO YOU KNOW ABOUT POLYGONS?
Dear Students: Polygons are all around us. They help us understand our
world and how to get around in it. Think about a stop sign. You probably
already know that a stop sign has eight sides. Because we have become
used to a stop sign having eight sides, we may think STOP! whenever we
see an eight-sided polygon even if it doesn't have the word, STOP, painted
on it.
http://www.loisterms.com/polyquiz.htm.
How much do you know about polygons? Check out your knowledge by
taking the Quickie Quiz below.
<>Question 1: Which of these figures is a polygon?
Figure #1
Figure #2
Figure #3
Figure #2 is a plane (flat), closed figure made up of line segments.
Therefore, it is a polygon.
____________________________________________________________________________<>Questi
on 2: Which figure is a quadrilateral?
Figure #1
Figure #2
Figure #3
A quadrilateral is a polygon with four sides. Figure #1 has four sides; therefore, it is a
quadrilateral.
<>Question 3: What is the name of this polygon?
pentagon
octagon
hexagon
A hexagon is a polygon with six sides. This figure has six sides; therefore, it
is a hexagon.
_________________________________________________________________________
___
<>Question 4: Which figure is a dodecagon?
Figure #1
Figure #2
Figure #3
A dodecagon is a polygon with twelve sides. This figure has twelve sides;
therefore, it is a dodecagon.
<>Question 5: Which figure is a type of parallelogram?
Figure #1
Figure #2
Figure #3
A parallelogram is a quadrilateral with both pairs of opposite sides parallel. A
rhombus is a quadrilateral which has both pairs of opposite sides parallel.
Therefore, it is a type of parallelogram.
_________________________________________________________________________
___
<>Question 6: Which figure is a concave polygon?
Figure #1
Figure #2
Figure #3
Figure #3 is a concave polygon since it appears to "cave in" in places.
_________________________________________________________________________
___
<>
Question 7: Which figure has seven sides?
A hexagon
A nonagon
A heptagon
A heptagon is a polygon with seven sides.
_________________________________________________________________________
___
<>Question 8: An n-gon has how many sides?
n-sides
nine sides
no sides
Polygons with 3, 4, 5, 6, 7, 8, 9, 10, and 12 sides all have special names like
triangle or hexagon. All other polygons can be called n-gons. You can think
of n-gon as meaning "any" number of sides, or whatever number of sides
your current polygon has. The polygon shown with the question has 13
sides, so it can be called a n-gon or a 13-gon.
_________________________________________________________________________
___
<>
Question 9: Which figure is a regular polygon?
Figure #1
Figure #2
Figure #3
Regular polygons have congruent sides and congruent angles. That means
that all their sides are the same length and all their angles have the same
degree measure.
The square has four congruent sides and four congruent, right (90 degree)
angles. Therefore, it is a regular polygon.
_________________________________________________________________________
___
<>Question 10: Which description matches this figure?
Concave decagon
convex decagon
congruent decagon
This figure has ten sides. Some of the sides appear to "cave in." Therefore, it
is a concave decagon.
_________________________________________________________________________
___
<>SCORING
Score one point for each question that you got correct.
Score a Bonus Point if you took the time to read the answers and
explanations.
1 - 3 points - You're are just beginning. Study the answers and explanations
to learn more about polygons.
4 - 8 points - Keep working. You'll get there!
9 - 11 points - You've mastered polygons, and you have great study habits.
I hope that you have enjoyed this Quickie Quiz.
Figure II
Comb
Sphere
Cube
Polyhedron