Prep for Teachers
Prior to teaching this lesson, bookmark all Web sites used in the lesson.
Lesson activities require a Java capable browser.
- Windows 2000 Internet Explorer 5.5
- Windows 2000 Netscape 4.08, 4.75, 6.1
- Windows 95 Internet Explorer 4.72
- Mac OS 8.6 Internet Explorer 5.0
- Mac OS 8.6 Netscape 4.61
- Mac OS 9.1 Internet Explorer 5.0
- Mac OS 9.1 Netscape 4.76, 4.79
| If you are experiencing difficulties from a Macintosh,
please download, install, and try the latest MRJ available at http://developer.apple.com/java/download.html.
Download and load the Shockwave plug-in available at http://www.shockwave.com.
CUE the videotape to the appropriate starting point. Prepare the student
organizers and handouts for the lesson by copying them for each student.
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.
Explorations with Area and Perimeter
Announce to students that a new city ordinance requires that schools must
cover a minimum area, regardless of how tall the buildings are, in order
to be certified as adequate space for students. How would they go about
figuring out how much space their school building occupies? (Elicit responses
from students that help them distinguish between the distance around the
building, perimeter, and the property covered by the building, area. Discuss
units of measurement.)
Working with a partner and using the Interactive Area Explorer
students will explore the relationship between area and perimeter. Be
sure to read the "What?" "How?" and "Why?"
sections, which will provide background information on using this tool
in instruction. The "Area Explorer Discussion" at http://www.shodor.org/interactivate/discussions/area.html
and the "Perimeter Explorer Discussion" at http://www.shodor.org/interactivate/discussions/perimeter.html
will help the teacher to guide the discussion of strategies that can be
Provide students with a FOCUS FOR MEDIA INTERACTION, asking students
whether they think different shapes can have to same area. Why or why
not? Explain that they will discover the answer by using the Area Explorer
Web site at http://www.shodor.org/interactivate/activities/perm/index.html.
Distribute the "Area Explorer" handout found in Student Materials.
Working with a partner on the Web site, students will determine the perimeter
of different shapes with the same area. Guide students through setting
the slide for different areas and encourage them to figure out different
strategies for determining the perimeter. Though it is relatively easy
to count the number of units with smaller, simpler shapes, as the area
increase new strategies must be tried.
As no hints or answers are provided, monitor students closely and provide
support as needed.
To encourage communicating about mathematics, have students record their
observations about this activity and any strategies they used to tackle
the more difficult challenges. When students are finished have them share
Consult the "Area Explorer Discussion" for strategies and sample
student responses (see above). Students should understand that shapes
with the same perimeter can have different areas and that some pattern
may exist. In addition, they should recognize different strategies for
determining area, counting square units, "boxing in" a shape,
and breaking down irregular shapes into rectangles whose are can be calculated
"Sensible Flats," a Cyberchase episode, will prepare
students for a lesson on area calculation of regular and irregular shapes.
If your students are not familiar with the series, introduce the show
to them using the Cyberchase Web site at http://pbskids.org/cyberchase/index.html,
clicking on "How it All Started" and "Meet the Cybersquad."
Depending on computer access you may have students explore the site individually,
with a partner, or use a large-screen monitor or projection device and
display the Web site for the whole class to review. Provide students with
a FOCUS FOR MEDIA INTERACTION, asking them to look at this page
and list the main characters and the main idea of the show. After students
have explored the site their list of characters should include:
Inez, Matt and Jackie, the Cyberchase kids;
You may optionally choose to dedicate an additional class period to Cyberchase
#101 that introduces the series in greater detail.
Digit, their Cyberchase sidekick;
Motherboard and Dr. Marbles, guardians of Cyberspace;
Hacker and his two sidekicks, Buzz and Delete, who are out to destroy
Motherboard and gain control over Cyberspace.
CUE Cyberchase #105: Sensible Flats to the beginning of
the tape for a brief synopsis of how the Cyberchase story began.
If students are familiar with the Cyberchase storyline, CUE
Cyberchase #105: Sensible Flats to just after the opening theme
song. Provide a FOCUS FOR MEDIA INTERACTION, asking students to
listen for the land rush rules. START the tape.
PAUSE the video when Hacker is called, "that no good cyber
scoundrel." CHECK for student understanding about the land
rush rule by asking what it was. (The land rush is a race for the last
available property in Sensible Flats. The only rule is that no one can
have a larger piece of property than Judge Trudy.) Then ask what shape
the Judge's property appeared to be. (The property is a rectangle, a regular
Provide a FOCUS FOR MEDIA INTERACTION, asking students to be prepared
to describe the shape of the property Hacker takes for himself. RESUME
PAUSE the video when Hacker says, "Any fool can see it's not
bigger," and the outlines of the homestead properties are visible.
Ask students to describe Hacker's property and tell if they think he has
broken the rule or not. (The property is an irregular shape. Students
may provide various descriptions.)
FAST FORWARD to the scene after the Cyberkids leave the jail and
you hear Hacker say, "Never, never." The Cyberkids are on the
cliff looking down at the homestead properties. Provide a FOCUS FOR
MEDIA INTERACTION, asking students to watch for three strategies the
Cyberkids use to figure out the size of Judge Trudy's property. RESUME
PAUSE the video when the Cyberkids are covering the property with
orange tarps and Inez says, "Finding these tarps in the gold mine
was sheer genius, Digit." CHECK for understanding of the first
strategy, dividing the land into same size squares by covering the area
with equal size square units. (Students should begin to understand the
basic definition of area as the number of square units needed to cover
a surface) RESUME PLAY.
PAUSE the video when Inez says, "There is another way to mark
off squares on the land." CHECK for understanding of the second
strategy, marking the area with a grid and counting the resulting squares.
(Students should understand that square units can be mapped on a surface
by creating a grid.) Repeat FOCUS and RESUME PLAY.
PAUSE the video when Matt says, "Tumblin' Tumbleweeds! I just
realized something." Ask students to predict the third strategy.
What does Matt have in mind? (Multiplying length times width.) Repeat
FOCUS and RESUME PLAY
PAUSE the video when Digit says, "Which would you prefer?
Length times width or counting squares?" CHECK for understanding
by reviewing the methods the Cyberkids used. (Covering the property with
square units the tarps making a grid and counting the squares;
using the grid but multiplying length times width.)
FAST FORWARD to the courtroom scene after the kids make a deal
with Hacker. Inez says, "The evidence please," and Jackie hands
her two sheets of paper. Provide a FOCUS FOR MEDIA INTERACTION,
asking which one of the techniques students think the Cyberkids will use
to calculate the area of Hacker's property. (Answers may vary.) What problems
might they have? (Because the property is an irregular shape the Cyberkids
may have to use other strategies to figure out the area. Encourage students
to predict what some of those strategies might be.) RESUME PLAY.
STOP the video after Judge Trudy says, "Case dismissed!"
CHECK for student understanding of the Cyberkids' solution. (Jackie
demonstrates how to break down the shape into small rectangles. In order
to create some rectangles, triangular shapes need to be moved and combined.
An important point for students to remember is that cutting and moving
pieces of an irregular shape does not change the area as long as the pieces
are moved to another part of the same shape.)
The National Library of Virtual Manipulatives for Interactive Mathematics
is a Web site that provides uniquely interactive, Web-based virtual manipulatives
or concept tutorials, mostly in the form of Java applets. Be sure you
have a Java capable browser (see Prep for Teachers.)
At the interactive Geoboards site students can create shapes using
virtual geobands, fill the shapes with color, and get measures of shapes
and lines. Click on the "Instructions" link at the top of the
window for a detailed explanation of the tools. As with hands-on manipulatives,
students will be able to investigate, describe, and reason about the results
of subdividing, combining, and transforming shapes using models and representations.
Introduce students to Virtual Manipulatives Geoboards at
The Java applet might take a minute or so to load depending on the speed
of your connection. Demonstrate how to create a one-unit square and then
a multiple unit square using a large screen monitor or LCD projector.
Distribute copies of "Judge Trudy's Property" handout and "Hacker's
Property" handout. Each handout is a schematic of the properties
with a grid.
Provide a FOCUS FOR MEDIA INTERACTION, asking students to work
with a partner and use this Web resource to recreate the Cyberkids' proof
of Hacker's innocence. These interactive Geoboards provide students with
the ability to create shapes and measure them without having to cut and
rearrange by clicking on the "Measure" button.
An additional offline alternative would be to distribute one copy of the
"Judge Trudy's Property" handout and two or more copies of the
"Hacker's Property" handout, then ask students to rework the
Cyberkids' solution and see if they can come up with a different solution
of their own. Encourage students to try and find a solution that uses
different and/or fewer shapes to describe Hacker's property and still
prove it equal to Judge Trudy's.
Given the opportunity to do both online and offline culminating activities,
students should be able to readily apply the concepts learned from watching
the video. To extend the learning, invite students to create regular and
irregular shapes of their own that have the same area to provide classmates
with new challenges.
For fun, and to reinforce the concept that different shapes can have the
same area, be sure to have students try their hand at digital tangrams
available on the Cyberchase Web site, http://pbskids.org/cyberchase/games/area/tangram.html.
This site provides a free self-study activity about area that will open
in a separate window. This activity requires the Shockwave plug-in available
This site requires the Shockwave plug-in available at http://www.shockwave.com.
"Minimize Perimeter" and "Maximize Area" are interactive
activities that enable students to manipulate the size of regular rectangles.
These activities include algebraic and graph components for more advanced
Cyberspace is a term that has real meaning beyond the animated series,
as do the names of characters and technology concepts presented in each
episode. Provide students with a starter list of words from the lesson
episode including cyberspace, motherboard, digit,
and hacker. Have students research the meaning of each term using
Webopedia at http://www.webopedia.com,
an online dictionary for computer and Internet terminology. Each Webopedia
entry includes links to other related terms that students can add to their
own personal glossary.
Using their personal technology glossaries, have students write their
own Cyberchase episode. Have them create a new scenario for the
Cyberchase kids, perhaps one that challenges the Cyberchase
kids to understand perimeter and the area of other regular shapes (triangles,
circles, other parallelograms.) They might want to create and draw new
characters in the style of the Cyberchase cast using their glossary
as a source for character name.
How many dollar bills would it take to wallpaper the Washington Monument?
How much fabric would it take to make a bathrobe for a groundhog? These
and other questions are posed on the Fermi Off-the-Wall Math League
Web site at http://www.int287.k12.mn.us/gifted/fermileague.html.
A Fermi question is posed with limited information given and requires
that students ask many more questions. Examine the archived "Sample
Fermi Problems/Unique Solutions" from prior competitions for questions
that will challenge students to apply their knowledge of area, perimeter,
- How much area is required for a Little League field, a Pop Warner
football field, or a youth soccer field? Have students do the research
and design a community athletic complex to include one field that
could be used for baseball and football, two soccer fields, as well
as areas for spectator seating.
- Using their knowledge of area and perimeter, have students plan
a community or school garden. Coordinate with community leaders to
find an appropriate location and contact a local nursery or garden
supplier for materials and support.
- Learn more about how knowledge of area and perimeter calculations
is used in accomplishing real tasks. Invite a landscape artist, architect,
contractor, or builder in to provide students with hands-on examples
of math in the real world.