## Exploring Geometry By Discovering Angle Relationships

*Wed Apr 8, 2015* – The Explain Everything Project File has been updated to correct an error.

The Geometry portion of the grade 9 applied course is one that I have always struggled to make meaningful for my students. The curriculum has students exploring angle theorems, but really never goes deep enough for finding these angles to be interesting or useful. While I’ve spent a significant amount of time trying to improve other areas of the course, this is one that I haven’t moved forwards as much as I would like. It probably doesn’t help that I usually teach this portion of the course last when everyone (including myself) is pretty burnt out. With the spiralled approach I’ve been taking this semester, I have been focusing a lot of attention to this portion of the curriculum with some high hopes for more opportunities for inquiry and curiosity.

Here’s a video summary of what I’ve created in Explain Everything for a portion of my lesson tomorrow. Feel free to jump down to screenshots if you’d prefer.

In order to allow students to do some exploration, I have created an Explain Everything project file that is preloaded with slides for students to work on like you see below:

Students are prompted to find some angles using a transparent protractor. They are later asked to record their solutions and justify as if they are creating their own tutorial video. I have *tried* to get my students to create tutorial videos in the past, but always found that there is a much steeper learning curve than I had anticipated – especially when dealing with secondary students. In order to scaffold students to a place where they are more comfortable creating their own videos from scratch, I am hoping these project files will slowly move them closer to gaining some confidence recording their thinking.

Throughout the Explain Everything project file, students are encouraged to ditch the protractor by finding rules (or theorems) that could help them save time and effort. This is my whole focus on inquiry – to get students to want the more efficient method.

At the end of the exploration, the “New Browser” option in Explain Everything allows me to embed a web browser right inside the project file. In this case, I’m going to try a Socrative multiple choice assessment that students will include in their screencast video to promote consciously verbalizing why they are selecting each response.

My hope is that students will not only make connections related to angle theorems, but I will also gain some insight as to how deeply each student understands the concepts. Often times this portion of the course can have students jumping to solutions without clearly communicating their thinking. Are they on track or are they simply guessing/estimating? If that isn’t enough, I’m hoping this will be a great screencasting ice-breaker for my students moving forward. With the progress we are making due to the spiralling of content, it is my hope that students will have some time at the end of the semester to compile their own MFM1P Grade 9 Applied Tutorial Resources site that students around the world can access.

Grab the project file here and Explain Everything on the App Store.

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## About Kyle Pearce

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

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