Pentomino Activities for the Classroom

Create a pentomino puzzle.

Pentominoes are shapes formed by putting five squares together. The squares must be the same size and must be connected to each other along at least one side. The interesting shapes are intriguing to most students. Pentominoes lend themselves well to a wide range of classroom activities, from illustrating mathematical concepts to geometrical puzzles.

Exploring

Introduce your students to pentominoes by having them discover on their own what they are. Pass out some plastic linking cubes or wooden blocks and ask the students to work in small groups to come up with as many shapes as they can. Tell them that the shapes have to use five squares that are all connected on at least one side. Once they form the shapes, have them draw them on a piece of 1-inch graph paper. See which group can come up with all 12 possible pentominoes. Point out that even if you flip a pentomino over, it is still the same shape because you did not move the squares out of position. If you don't have wooden blocks or unifix cubes, you can use small square pieces of paper.

Puzzles

The classic puzzle game "Tetris" is based on tetrominoes, which are shapes made from four squares, but you can play a similar puzzle game with pentominoes. Give each student a piece of graph paper that features 1-inch squares. Have them color and draw all 12 pentominoes on the graph paper, and then cut them out. Then, ask them to fit the pieces together into preset boundaries. For example, you may ask the students to fit as many pieces as they can into a square that is 15 inches (or squares) in diameter. Take it a step further and ask the students to predict which of the pentominoes can be folded into a three-dimensional box. Record the predictions, and then pass out some scotch tape and have the students try to fold them to see if they predicted correctly.

Geometry

Teach a lesson on symmetry using pentominoes. Each student or small group will need two copies of each of the 12 pentominoes. Use paper or unifex cubes to create them. Then, talk about and define what symmetry means. Have the students use the pairs of pentominoes to create symmetrical and asymmetrical shapes. Discuss mirror images and why flipping and turning one of the pentominoes can change a shape from symmetrical to asymmetrical.

Measurement

Use pentominoes to reinforce the measurement concepts of area and perimeter. This activity is best done after a lesson on area and perimeter. Give each student a set of pentominoes. Point out that each is composed of five 1-inch squares, so each has the same area of 5 square inches. Show them that each pentominoe vaguely (or not so vaguely) resembles a letter of the alphabet. The letters are F, L, I, P, N, T, U, V, W, X, Y and Z. Ask them to try to identify each pentominoe by which letter they think it represents. Then, have the students determine the perimeter of each pentominoe by writing down the letter it represents, along with the perimeter in inches. Ask them to identify the pentominoes with the largest and smallest perimeters in inches, and discuss why those particular shapes ended up with those figures.

References

• University of North Carolina School of Education: Flipping Around Pentominoes
• The SEDL National Center for Quality Afterschool: Geometry - Finding Pentominoes