The Foundation for a Meaningful Life
Kindergarten - Grade 9 in Southborough, MA
Serious Fun

Puzzling with Pentominoes

Fourth graders designed pentomino animal puzzles to learn about congruence and spatial relations.
Recently, fourth grade mathematicians explored congruence and spatial relationships as they worked with pentominoes. Pentominoes are sets of twelve polygon pieces, each composed of five equal-sized squares. The pieces can be arranged in multiple ways to form a rectangle, a mind-boggling concept for students used to math problems with one correct answer. Students have to flip, turn, and swap out the geometric pieces as they test for congruence and try to figure out if they have discovered all the possible constructions. 

Students build their understanding by starting with two-tile dominoes with the constraint that a whole side must always touch a whole side. “The fewer the tiles, the easier it is for students to start seeing which ones are alike and which are different,” says Math Department Chair Maura Oare. “That’s the beginning of understanding congruence.” Once students have found all the ways in which those tiles can be arranged to make a rectangle, they are ready to move on to three-tile tromino constructions, four-tile constructions, called tetrominoes, and finally, to pentominoes. For visual thinkers, these tasks can feel easy, while students who usually excel in calculating can find it unexpectedly challenging. “We’re always mindful of student frustration when doing an exploration like this,” says Maura. The unit meets each student where they are. Students can go at their own pace to cement their understanding or extend their learning with various pentomino games.

To finish the unit, each student chose an animal from the “pentomino zoo” and used their pentominoes to create an animal. The final designs will be laser cut in the Center for Creativity and Design with individual acrylic pentomino pieces and a matching wooden board to create a keepsake puzzle.
main number 508-490-8250
admission 508-490-8201