When teaching online, I was on a constant search for interactive websites to use with my students. This became even more important as I was working with my grade 6 students on measuring angles with a protractor. In the classroom, it is easy to walk around and see how students are holding and lining up the protractor, but this is obviously more challenging over Zoom. First, many of many students did not bring home their geometry sets as they were collecting locker supplies before we went online. Second, even if they had, I would not have been able to see how they were holding and using those physical protractors, even with screen sharing options. I found a few good activities on Desmos (this one and this one), but I was looking for additional practice. I then came across this selection of activities from Transum. This first one is from their Starter of the Day selection and involves estimating and then checking. This second one offers more questions of varying types of angles. Using these activities allowed me to model by sharing my screen, and then have students share their screens so I could watch how they were manipulating the online protractor and lining it up with the angle. There are many interactive activities on Transum’s website. I haven’t even begun to explore all of their offerings, but I plan to do so this summer.

# geometry

## Playing with Platonic Solids

This week I am starting to explore platonic solids with my grade 8 students. The key question that I want them to answer is “Why are there only five platonic solids?” (For a brief explanation, see the MathsIsFun website. For a more detailed explanation, read this entry from The University of Utah.)

I want this to be a true exploration activity, and as such, I will give my students limited information. I will not volunteer this information, but I will give it only after they determine the right questions to ask.

First, the students will be given nets of the platonic solids so that they can build them and use them in their exploration. I will be giving them the copy from the learner.org interactives.

They will also get scissors and a handout with the regular polygons. They may cut out the polygons and use them as manipulatives. There are eight copies of each polygon, from three-sided to eight-sided figures.

I have also created a Notebook file for the Smartboard. This will be open for the students to come and explore with, as well. It is not fancy. On one side of the page are the platonic solids for the students to see. On the other side of the page are the regular polygons, set up as infinite clones. In the middle of the page is a play area. Students can thus pull out copies of the polygons, turn them around, and see how they fit together. (The polygons were created from the tools in the program, and the platonic solid images were taken from Wikipedia. If you click on each image on the second page of the file, you will be taken to the home site for that image. )

Platonic Solids Notebook File (Unfortunately, this is what the Notebook file looks like as a PDF. WordPress will not allow me to upload the Notebook file. Help anyone?)

Should students get frustrated, I will begin to lead them through the following thought process:

- Consider the regular polygons. Starting with the triangle, what is the measure of each interior angle? Continue for the rest of the polygons.
- What do you notice about the sum of the interior angles of the polygons, as you go from three-sided figures up to eight-sided figures?
- Which of these polygons are able to tessellate? Why are they able to tessellate?
- Which of these would be able to be constructed into a polyhedron? Why wouldn’t all of the regular polygons be able to be constructed into a polyhedron?

They can then go play on the Learner.org website.

The final task will be for them to submit an explanation as to why there are only five platonic solids. I will accept written work or digital work – students can choose which method suits them best.

Have a great week.