Students are asked to recognize that rectangles can have the same perimeters but different areas. They also are asked to calculate the perimeters and areas of different rectangles, to find the entire set of rectangles (with whole-number side lengths) of a given perimeter, and to find the corresponding rectangle with the maximum area. This CYBERCHASE activity is motivated by an episode in which the CyberSquad competes against Hacker's team in a Skate-Off competition in which the field only has to be rectangular and have a perimeter of 26 standard fence sections. When Jackie performs in the competition, she runs out of room and falls over the wall. The CyberSquad tries to figure out a) if the practice and competition fields are different, and b) if the competition field is legal.
Part I: Learning Activity
1. Have the students work individually for this activity.
2. Give each student a piece of graph paper. Read the following statement: There is going to be a Skate-Off competition between the CyberSquad and Hacker's Team. In this skating, skateboarding, and biking competition, there are two rules: 1) the outside edge of an official Skate-Off field is 26 standard fence pieces around. 2) The field has to be a rectangle. Using the length of a grid square as equivalent to one standard fence piece, draw one possible Skate-Off field.
3. Tell the students that they will see a video clip showing the first round of the competition.
4. Read the students the following statement: The CyberSquad has practiced and practiced on the practice field. But when Jackie performs in the competition, something unfortunate happens. What happened, and why did it happen?
5. Show the students the Skate-Off: Round One QuickTime Video , but pause it after Jackie scores low and says "I felt like I ran out of room out there!"
6. On the board, copy the different fields drawn by the students, and ask them to compare the different fields.
7. Distribute the Handout: Skate-Off Fields, by the Rules , which shows the practice field and the competition field, and a table.
8. In class discussion, compare the fields the class drew to the drawings on the handout of a) the practice field and b) Jackie's competition field. Has something changed? Are all the fields legal (official), according to the rules?
9. Show the students the rest of the first video clip, in which the CyberSquad conclude that Hacker has manipulated the size of the competition field.
10. Then ask the students to complete the table at the bottom of the handout, "Skate-Off Fields, by the Rules," and list all the different fields they can make that meet the rules, by listing the length and width of each possible field. In the next column, use the formula for perimeter to check each field's perimeter. In the next column, use the formula for area to see if the amount of competition room is the same for each field.
11. Show the students the Skate-Off: Final Round, Inez vs. Rimm QuickTime Video, in which Inez competes in skating against Rimm. If Inez loses, the CyberSquad lose, and Inez has to be Hacker's cheerleader. In the end, the CyberSquad use the rules to their favor, narrow the field (and decrease the area) even more, and the CyberSquad win after all.
12. Ask the students to complete the table in the handout.
13. Ask the students to consider and write down how they would change the rule for the size of the field to make a fairer and more consistent competition.
Part II: Assessment
Assessment: Level A (proficiency): Students are asked to find the perimeter and area of four different rectangles, with progressively more basic information provided about the rectangles' dimensions.
Assessment: Level B (above proficiency): Students are asked to list all the possible rectangular fields with a perimeter of 36 and to calculate their areas. They are asked to find the one with the maximum area and to give their opinion on the best shape for the competition field.