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Lesson Plans
Gotcha Covered, Pardner!
OverviewProcedure for teachersStudent Resources and Materials
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

Download and load the Shockwave plug-in available at 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.

Introductory Activities: Setting the Stage

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 at, 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 and the "Perimeter Explorer Discussion" at will help the teacher to guide the discussion of strategies that can be used.

Step 1:

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

Step 2:

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.

Step 3:

As no hints or answers are provided, monitor students closely and provide support as needed.

Step 4:

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 their conclusions.

Step 5:

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 more easily.

Learning Activities

"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, 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;

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.
You may optionally choose to dedicate an additional class period to Cyberchase #101 that introduces the series in greater detail.

Step 1:

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.

Step 2:

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 shape.)

Step 3:

Provide a FOCUS FOR MEDIA INTERACTION, asking students to be prepared to describe the shape of the property Hacker takes for himself. RESUME PLAY.

Step 4:

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.)

Step 5:

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 PLAY.

Step 6:

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.

Step 7:

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.

Step 8:

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

Step 9:

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.)

Step 10:

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.

Step 11:

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.)

Cross-Curricilar Extensions

The National Library of Virtual Manipulatives for Interactive Mathematics at 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.

Step 1:

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.

Step 2:

Distribute copies of "Judge Trudy's Property" handout and "Hacker's Property" handout. Each handout is a schematic of the properties with a grid.

Step 3:

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.

Step 4:

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,

Cross-Curricilar Extensions

Math Realm
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 at
This site requires the Shockwave plug-in available at "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 students.

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, 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 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, and measurement.

Community Connections
  • 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.