Square Off Directions

Object: To capture alien spaceships and cover the greatest area with force fields.

Set-Up: The game board is of a 20 × 20 grid. Initially, the grid is occupied by five spaceships. More spaceships are added as the game progresses.

Play: On each turn, the engineers from mission control will provide you 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.

Winning the Game: 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.

Math Concepts: Area, Perimeter

What You Can Do: At home or in the classroom, kids can be exposed to area and perimeter in a variety of ways. Young children can cover flat surfaces with congruent squares to determine their areas: “The area of my bedroom floor is 64 red squares,” or “The area of my desktop is 15 blue squares.”
Kids often make the mistake of thinking that area and perimeter change proportionally, but that isn’t always the case. For instance, 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. To explore this idea, give students eight squares and ask them to create various arrangements of rectangles. All of the arrangements will have an area of 8 units, but do all of the figures have the same perimeter? The answer is no, and it can be powerful for kids to discover this on their own.

Math in the Game: The greater the area surrounded, the more points you earn. Students quickly realize that more points are earned for a square than any rectangle with the same perimeter. Consequently, this game can teach kids about the relationship between perimeter and area.

Related Resources:

Planning a Playground
Students have to think about area and perimeter as they place equipment on a playground that they create.

Go with Green Rectangles
This lesson allows students to investigate similar rectangles. It focuses on the relationship between the scale factor and the ratio of perimeters as well as the scale factor and the ratio of areas.

Fair and Square: Using Concrete-Pictorial-Abstract Activities to Maximize Area
This lesson helps students understand the math of area and perimeter by creating human-sized rectangles and working with geoboards. These activities provide concrete experiences before moving on to pictorial and abstract work with area and perimeter of rectangles.