How many unique pentominoes can you generate with five squares?
Exploring that question is a great way to introduce a unit on pentominoes. Using pentominoes improves spatial skills. Generating them is also a great way to practice flexible thinking. To do this activity you will need:
- Five identical squares for each child (could be plastic or cut from tagboard)
- Graph paper
- Five teacher squares for demonstrating (can be the same as students if using a projector; magnetic ones work well on whiteboards)
- A set of Pentomino pieces
Explain that a pentomino is a shape made from 5 squares. Each square must touch at least one edge of another square, and the edges must all be lined up evenly.
Ask students to guess how many unique shapes they think can be made. Record the guesses.
Allow students to use their squares to create pentominoes. As pentominoes are discovered, students should record them on their graph paper.
Allow students to share their pentominoes with the class. As students share each shape, show them the identical shape from your pentomino set and identify its letter name. Note that sometimes a shape seems to be unique, but it is actually another shape flipped or rotated. Have students record shapes they are missing on their graph paper.
You should end up with all 12 pentominoes. Compare initial guesses to the actual number of pentominoes possible.
Here are some Pentomino Puzzles.