In the first lesson, students were invited to create a new game based on the four-square pieces used in TETRIS. Using five identical squares, groups explored possible arrangements and clarified guidelines for piece creation along the way. Part 2 continued as students kept track of possible pieces by cutting them out of a 1-inch grid on cardstock.

As collections grew, quite a few groups had several pieces that were duplicates. I anticipated this, and so prepared a few slides to challenge their spatial reasoning and sharpen their skill at finding these duplicates.

After groups were convinced we had found all 12 unique pentominoes, I reminded students that what made someone really exceptional at TETRIS was an understanding of how the game pieces fit together. I explained how

*clearing lines*was related to*making rectangles*and challenged them to practice making rectangles by putting together various pentominoes. I used this handout to help structure their exploration.I suggested that students treat this part of the lesson as a tutorial, similar to the TETRIS tutorials. It’s not the real game, but exploring how the pieces fit together would certainly support their gameplay. We spent about 10 minutes on this task before getting to the real deal.

I asked students, “What do we do with these new game pieces? How does the 5-square game work?” These questions led us to take a closer look at what makes the TETRIS game tick. Together we brainstormed some of the game features:

Students immediately pointed out the constraints we were dealing with that would prevent a TETRIS-like experience. We didn’t have unlimited pentominoes and clearing lines wasn’t possible with physical pieces. I decided to use this opportunity to present them with the challenge of actually putting together a new game. Here’s what I said:

Groups got to it and after a few minutes a whole class discussion yielded these results:

I asked students, “What do we do with these new game pieces? How does the 5-square game work?” These questions led us to take a closer look at what makes the TETRIS game tick. Together we brainstormed some of the game features:

- What’s the goal?
*Fit pieces together, clear lines, and keep the screen from filling up.* - How does game play work?
*Player vs. Computer* - How are pieces chosen?
*Computer chooses randomly and presents next piece to player.* - What’s the game board like?
*10 x 18 grid.*

Students immediately pointed out the constraints we were dealing with that would prevent a TETRIS-like experience. We didn’t have unlimited pentominoes and clearing lines wasn’t possible with physical pieces. I decided to use this opportunity to present them with the challenge of actually putting together a new game. Here’s what I said:

*In order to create a working game, you’ll need to come up with precise responses to the four questions we just discussed.*Groups got to it and after a few minutes a whole class discussion yielded these results:

Answers to questions 1-3 were worked out pretty easily, but defining the game board size left us stumped. We ended up creating several sizes and ran some game trials.

Gameplay using these two boards led us to think about how many squares we really needed.

From their work building rectangles during the tutorials earlier in the lesson, students knew it was challenging to create a rectangle using all of the 12 pentominoes. And from their gameplay using the two trial boards, they knew there needed to be some extra squares for those times pieces didn’t fit together perfectly. Thus, a board with exactly 60 squares was ruled out. We settled on trying an 8×9 and an 8×8.

Based on these results, most groups decided to use the 8×8 board for future play. A few explained that the extra row on the 8×9 board made play easier and they preferred it over the 8×8. Overall I found this activity to be a motivating context for student use of mathematical practices and an inexpensive way to get a great game in kids’ hands during the last few days of school.