Pentominoes are wonderful creatures. They are fun to create, they can be colored by students, and there are a multitude of questions that can be posed, and many activities to pursue to stimulate and strengthen students’ minds.
This activity asks students to use a single pentomino to tessellate the plane. In other words, can you use only one shape as a floor tile and fit it together to cover the entire floor of a room? Some of the pentominoes can be tessellated quite easily, like the letter I, while others, like the letter F, may take awhile to fit together into a repeatable pattern.
This activity is best used after students have explored and discovered all 12 pentomino shapes. Depending on the age of the students, use 1cm, 1/2″, or 3/4″ grid paper to record results. Coloring the shapes gives a nice touch to the work. Once students find a way to tessellate a given pentomino, consider challenging them to find a different way to arrange the given shape to cover the plane. Students who are good at spatial visualization are better problem solvers. Presenting material in a visual way is always a good approach since it gives the class a common reference point when reviewing.
Here is a link to some tessellations my students created. This can be viewed as a slide show: Pentomino Classroom Tessellations
Related Posts:
Polyominoes: Puzzles, Patterns, Problems, and Packings, by Solomon Golomb
Pentomino Puzzles; Spatial Sense, Geometrical Visualization, and Reasoning Skills
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i found this website very useful, but i think if you had tessellated perfect shapes like crosses and others that would be a great help