Bringing together the young artists and the young organizers in your class, this lesson takes that popular topic of tessellations and gives it algebraic roots. After covering a few basic properties and definitions, learners attack the task of determining just which regular polygons actually can tessellate. Spiraling in algebraic concepts of solving inequalities and interpreting the results really drives home those links between geometry and algebra. A novel twist to add to your standard tessellating a plane repertoire.

Concepts

tessellations, regular polygons, interior angles

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Additional Tags

math

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Instructional Ideas

• Link with art department to create larger scale projects, possibly extending into irregular tessellations
• Consider using the lesson-suggested extension investigating art of MC Escher
• Developing the formula for the measure of an interior angle of a regular polygon might make a good lesson-opening refresher
• Those interested in non-Euclidean geometry could apply this same activity to tessellating the sphere

Classroom Considerations

• Last page is blank if copying costs are a concern
• Learners that have not practiced algebraic skills recently (especially solving inequalities) might need a quick brush-up lesson

Pros

• Serious math theory presented in an approachable, discovery-learning way
• Multiple approaches to solving covered in the teacher notes

Cons

• Student worksheet not separated from teaching notes
• Tessellation misspelled on the top of page 2 (student activity), and pages 4 and 5 (answer key)

Common Core

HSA-CED.A.2 HSG-MG.A.1 HSG-MG.A.2 HSG-MG.A.3