I’m really terrible at producing nets. It’s a huge challenge for me to be able to look at a 3-D image and visually imagine what it would look like in a 2-D net. Last week in class, we created three nets that together, made a cube. The shapes were a triangular prism, triangular pyramid, and square pyramid, making up 1/2, 1/6, and 1/3 of the cube respectively. Below is a photo of our nets we created in our group. Being in a group of three, we each constructed a net and placed them all together at the end. I wanted to revisit this activity to ensure I understood how each of the other two nets were created.
When we created the nets, we decided to use a 1cm x 1cm cube, making the dimensions for our squares 1cm x 1cm, so I decided to stick with that when reviewing the mathematics for each net. I began with the triangular prism. With my 1cm x 1cm square, I knew the dimensions of the two triangles as well, because these were essentially just a square cut in half. I then had to find the hypotenuse of the triangles, where I used the Pythagorean Theorem to get 1.4cm. I knew my bottom most square was a 1cm x 1cm square, and my rectangle was 1cm x 1.4cm, because of the hypotenuse of the triangle.
Next, I worked on the square pyramid. Since this is the one I made in class, I was pretty familiar with this one. I started with another 1cm x 1cm square since this too would be a face of the cube. The two smaller triangles were again, a 1cm x 1cm square cut in half, so I used my calculations from the triangular prism in order to label its hypotenuse. For the other two triangles, I knew that one side would have to be the hypotenuse from the smaller triangles, so from there I needed to find the hypotenuse. Using the Pythagorean Theorem, I found the hypotenuse to be 1.73cm.
Last, I worked on the triangular pyramid. It made more sense to me to put the other two pieces together and then try and visualize the sides of this net and what their measurements then had to be, based on the measurements of the other nets. I realized that the two triangles that create a rectangle at the top is the same measurements as my rectangle in the triangular prism. I just needed to find the hypotenuse which again, is 1.73cm. Based on this, I knew the other two triangles had hypotenuses of 1.4 cm.
It made sense with the numbers that one builds off the other. I also thought it was cool to see the other ways the nets could have been drawn. It may have been easier to figure out the math to each of them, depending on how you drew the nets. In a classroom, I think creating nets for 3-D objects could be extremely valuable. I hope to incorporate this as much as possible. It can really help students to learn and thoroughly understand geometry, while also giving them hands on activities where there isn’t just one right answer. Like we’ve seen, there’s many ways to do this and I think students can find much value in that. It was definitely an enjoyable activity that I think is important to have experience with.