Unit 9 · Tessellation
Tessellation
Mathematics · Grade 7
What You Will Be Able To Do
🧩Decide whether any regular polygon tiles, using one line of arithmetic
3️⃣Prove that exactly three regular polygons work, and the list can never grow
📐Explain the surprise: EVERY triangle and EVERY quadrilateral tiles
🍯Say why a honeycomb is hexagonal rather than square
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At any point where tiles meet, the angles round that point must add up to exactly 360 degrees. That single fact decides everything in this topic.
Presenter notes: Open with the floor of the classroom, or a brick wall outside the window, and ask why floor tiles are square. Someone will say because they fit. Push further: would pentagonal tiles fit? Almost everyone thinks they would, because a pentagon looks perfectly reasonable. Say that by the end of the lesson they will be able to prove that a pentagonal floor is impossible, and that the proof is one line of arithmetic.