# Square Off Game Lesson Plan: Area & Perimeter of Polygons

In this lesson plan, which is adaptable for grades 3-8, students use BrainPOP resources to learn to calculate the area and perimeter of a given polygon. Students will also explore the relationship between area and perimeter of various spaces through both virtual game play and hands-on activities.

### Students will:

1. Calculate the area and perimeter of a given polygon
2. Explain the relationship between area and perimeter of various spaces
3. Explore area and perimeter concepts and relationships through virtual game play and hands-on activities

### Materials:

• Graph paper and scissors for each student
• Computers for students to use in game play
• Internet access for BrainPOP and GameUp

### Vocabulary:

area; perimeter; polygon; base; height; parallelogram; altitude; perpendicular; trapezoid; parallel

### Preparation:

Familiarize yourself with the Square Off Game. The objective is to capture alien spaceships and cover the greatest area with force fields. The game board is a 20 × 20 grid which is initially occupied by five spaceships. More spaceships are added as the game progresses. On each turn, engineers from mission control will provide players with four numbers. These numbers represent the perimeters of various force fields that you can create. On the grid, create a rectangular force field with one of the given perimeters that surrounds as many spaceships as possible.

Points are based on the number of spaceships you capture as well as the amount of area you cover. You'll earn an efficiency rating for each turn, which is based on the maximum possible area that you could have covered. The closer your area is to the maximum possible for the given perimeter, the greater your efficiency rating for that turn. Your overall efficiency rating is an average of your efficiency rating for all turns. At the end of the game, you’ll get a bonus based on your efficiency rating. So, it might be in your best interest to capture fewer spaceships but cover greater area to boost your efficiency rating. The game ends when all spaceships have been captured, or when it is impossible for either player to make a move. The winner is the player with the most points.

### Lesson Procedure:

1. Activate students' prior knowledge about area and perimeter by showing the BrainPOP movie Area of Polygons. Younger students may benefit from viewing BrainPOP Jr.'s movies/activities for Area and Perimeter.
2. Pass out graph paper and challenge students to draw a figure with an equal area and perimeter, such as 16. Give students several minutes to experiment. Is it possible for a figure to have a perimeter and area of 16? Is it possible with other numbers? What causes a figure to have a perimeter that is greater than its area?
3. Address student misconceptions about how area and perimeter change proportionally. Help them understand, for instance, that a 3 × 3 square has an area of 9 square units and a perimeter of 12 units, but a 1 × 8 rectangle has an area of 8 square units and a perimeter of 18 units. That is, the area decreased, while the perimeter increased.
4. To explore this idea, have students cut out eight squares from their graph paper. Ask them to create various arrangements of rectangles using just their eight squares. Allow students to discover that all of the arrangements will have an area of 8 units, but all of the figures don't have the same perimeter.
5. Project the Square Off Game for students to see and introduce the basics of game play. Provide modeling as needed for students, and then allow them to play with a partner for 10-15 minutes.
6. Debrief about game play. Guide students to understand that the greater the area surrounded, the more points they earn. Students realize that more points are earned for a square than any rectangle with the same perimeter.
7. Give students several more minutes to explore the game again on their own, using the strategies they learned during the debriefing session.
8. Have students apply their new understandings about the relationship between area and perimeter to a new project. Challenge them to design a zoo, amusement park, or other space with specific perimeter and area guidelines. For example, you may specify that all animal areas or rides must have a perimeter of 20, and see how many different shaped areas students can design for their zoo or park.

### Extension Activity:

Be sure to check out our other Math Games in GameUp!