Each student will work on their own 15×15 grid. The goal of round one is to surround as many 1×1 grid squares as possible.
Player 1 will roll both dice and determine their sum. The player will draw a shape on the board so that the length of the perimeter is equivalent to the sum of the two die. If the sum of the die is equal to two, the player misses their turn.
Player 2 will repeat the above steps. Players take turns rolling the dice and drawing shapes on their own grid paper. Play continues until each player has rolled 15 times.
After the first shape is drawn, only the vertices of additional drawn shapes can touch.
For every 1×1 grid square surrounded, a point is gained.
Record how many points each player receives below the grid.
As an additional challenge, suggest students record the area of the shapes they made.
Round 2: Area
Have each player work on a new 15×15 grid. In this round, the numbers on the dice represent area. Rolling a two no longer means missing a turn.
In this round, shapes can be placed wherever the student wishes. The goal is to cover the entire grid, leaving as few spaces as possible.
Player 1 will roll both dice. On the grid, Player 1 will draw a shape using the sum of the numbers on the dice as the area.
Player 2 will repeat. Players will take turns rolling the dice and drawing shapes on their own grid paper.
When students have rolled twice in a row and are unable to proceed, the round is over.
Every square left blank results in the deduction of one point. Each player records their score below the grid.
Calculate the total points between the two rounds.
The player with the greatest number of points wins.
As an additional challenge, have students record the perimeter of the shapes they made.
Do students create different shapes on the grid if they roll the same dice combination as they did during a previous round?
In the first round, do students connect the shapes by the vertices?
What strategies do students implement to cover the grid in the second round?
Do students recognize shapes can have similar area and perimeters, yet look very different?
Use additional dice to explore shapes with greater perimeters and areas.
Have students collaborate by taking turns to work on the same grid.