# Introduction to 3-D with Polyhedron Nets and Islamic Design

A couple weeks ago, I was planning for our last unit in geometry which is 3 dimensional solids, and as I was measuring nets and counting vertices, edges, and faces, I suddenly realized I was really bored. If I was bored, my students definitely would be! I knew I needed to amp up my curriculum to still teach nets, relationships between 2-D and 3-D, and constructions (TEKS G.6B and G.2A), but somehow make it more engaging.  What eventually fell out of my plans was a new connection between math and World History.

I started thinking that students could choose a 2-D net, decorate it, and then fold it into the 3-D polyhedron. However, this was not very exciting and required little critical thinking. Also, I knew I wanted students to decorate their models, but I didn’t want them to just draw flowers or smiley faces or simplistic designs with no reason behind it. So, I asked the World History teacher if there were any connections he thought I could make between our two classes. He told me they were about to start Islamic culture and history which was perfect because Islamic art incorporates a lot of geometric design. We talked about some questions to prompt some thinking for his class. By asking students to pre-think, my geometry students were able to be the experts the next day in World History.

Here’s the basic outline of the lesson plan.

1. Pass out the Islamic Art and Polyhedron student worksheet and talk with the students about the fact that we are going to make a connection between World History and geometry…yet again!! 🙂

2. Show this video (or any other video you find) and ask students to jot down anything they see that answers #1 (What patterns do you see in Islamic art?).

3. After the video, have students pair up and talk about what they saw. Then call on students to share out whole class. (Think, Pair, Share model)

4. Then, we went on to the questions #2-4 which talks about the history of the region and asks students to compare Islamic design to Chinese, Eurasian, and African Art, but you can add or take out any other questions that would be relevant to their World History class.

5. Show students the net templates they can choose from. Some chose simple nets like cubes, rectangular prisms, while others chose more complex such as octahedrons and stellated dodecahedrons. (There are many templates online…I decided to use this website. Warning: Some models are very tricky, but I think if students get to pick, they will have the buy in and motivation to complete it.)

6. After they have chosen their template, found the number of vertices, edges, and faces, we used the rest of the class to design their Islamic artwork. Remind students that they must use rules and compasses when drawing lines, circles, and arcs, because Islamic art focuses on very precise designs.

7. The next day, we came back and started class by having a chalk talk with this question: “What is the main focus of Islamic art…what does it include/not include?”

8. Then after a 3-5 minute chalk talk, I let them work on their design and fold their 3-D nets.

Overall, students enjoyed this hands on activity. One change I would make is to print out the larger nets rather than the single page nets, especially for the more complex types (anything larger than an octahedron) because folding and taping those got quite tricky! My plan is to hang these up with fishing wire between my room and the World History room as a visual connection between the two classes. Thanks, Mr. Sprott, for helping me dream up this mini-project!