Chris hoped to work as an apprentice at a pottery shop near his home, and his art teacher, Ms. Glenn, had agreed to help him improve his skills. One day, as Chris worked hard forming an unusually shaped vase, Ms. Glenn suggested he try something even more ambitious. "You seem to have mastered the basics of vase building really well," she said. "Tomorrow, I'll show you how to make a similar vase but with a tessellation pattern."

Chris stared blankly at Ms. Glenn. He wasn't even sure what she said.

"Do you know what tessellations are?" Ms. Glenn asked. When Chris shook his head, Ms. Glenn continued. "You can find plenty of information online about them. Why don't you do some research tonight? And, to give you ideas for your vase pattern, find some images or take some photos of tessellations and bring them in tomorrow."

After dinner, Chris did a quick Internet search to find out the meaning of the word tessellation. Then, he read a bit more about them before setting out to gather some images for the next day. Study the slides below to see what Chris learned about tessellations.

Chris used his phone to snap a picture of the wall in his parents' bathroom. What shapes do you see in this photo? How are the shapes in the photo arranged? Regular squares are set right next to each other, in a repeating pattern of rows and columns. Next, Chris saw this drawing in his family's kitchen, created by his talented younger sister and attached to the front of the fridge with scotch tape. What does this drawing have in common with the bathroom wall? It consists of identical shapes placed side by side, right next to each other, in a way that doesn't leave any gaps. The next example of a tessellation that Chris found was right in his own room. His mother had bought him a few new folders for school, and one of them looked like honeycomb. Chris wondered briefly how bees could be smart enough to create exactly this shape over and over. Then, he added another photo to the collection on his phone. What shape gets repeated in a honeycomb pattern? a hexagon Chris felt he was on a roll and would soon have lots of ideas for his vase pattern. He decided to look for tessellations using other shapes besides the ones he'd found already. Chris looked all over his house for more tessellations. However, he found no patterns like the ones he'd seen. Chris even tried creating a pattern of his own. Look at his sad attempt to create his own tessellations, using first pentagons and then octagons. What prevents these drawings from being tessellations? There are gaps between the shapes in one drawing, and overlaps in another. Chris had to do a little more research to find out why. What do you think he learned? Chris learned that only three regular polygons can form tessellations on their own--squares, triangles, and hexagons.