Mini-Lessons – Polygons & Angle Explorations on Geoboard

My hope every day for the next couple of weeks is to provide some mini-lessons, focused on specific content and/or grade bands. My goal is to create 3-4 lessons on the FREE online math software, These lessons will be freely available for anyone to use – parents, teachers, students. If you create your own free account on, you can save the activities and modify them to fit your own needs. If you use them with students, they can also create accounts and create their own versions that they can then share with you as well.  There are many options for how you can use these free lessons, with my goal to support remote learning with some resources that keep students thinking and working with math.

Today I have created three different elementary-focused mini-lessons. For each lesson, I have also created a short video that talks about using the lesson. I have provided the link to the activity itself as well as the accompanying video so you have some support if you plan to use them. For just the first one, Geoboard Explorations – Polygons, I have included an image of the activity and the full mini-lesson walk-through video so you get an idea of what these activities entail and their learning goal (s).

  1. Geoboard Explorations-Polygons Activity This lesson explores what polygons are and how polygons get their name.
    • Video About the Geoboard Explorations-Polygons Activity:

Here are the other two activities for today (click on them and it takes you to the activity), all elementary focused, along with the links to the mini-lesson walk-through videos:

2. Geoboard Explorations – Square & Rectangle Activity This lesson explores similarities between squares and rectangles through manipulation and observation on a geoboard.

3. Measuring Angles – Protractor Activity This lesson helps students understand what angles are, where they can be found, what ‘degree’ measurement is and how it connects to understanding of circles, and finally, how to use a protractor to measure angles.

NOTE: I will be back tomorrow with a focus on linear relationships, graphing, and equations. We will explore data collection, slope, rate of change, equations, and lines of fit.

Remember – if you want to save and/or modify any of these activities, create a free account.  Some useful links below:

The STEM Around Us

NCTM Innov8, the new team-based conference that NCTM is sponsoring, is going on right now in St. Louis, Missouri. Our team is there of hqdefaultcourse, supporting math teachers with our technology and a great team-building session based on the Wheel of Fortune and the probabilities of winning (session is Friday, November 18 at 10:45 am in Room 265/266). St. Louis brings to mind the very famous St. Louis Gateway Arch, something math teachers attending will probably be exploring and trying to mathematically represent – is it a parabola? (In fact, it is NOT a parabola, but rather a flattened catenary). (Cool 3D mathematical model here).

This idea of looking at real objects and connecting mathematics to them is something math teachers do often. It makes complete sense, and, as I have been teaching a geometry course for Drexel these last several weeks, I have really deepened my appreciation for this idea of looking at our constructed world to find the mathematical connections and relationships. What I think we tend not to do with students, and what we should do much more of, is go beyond the obvious “shape” explorations and function fitting to explore the STEM connections.

What I mean is after we identify the inherent shapes and/or functions in ‘real-world’ objects, start asking questions that get students thinking about the why behind those shapes. The why questions lead to investigation and research by students into science, technology, engineering, and math applications that would take them much deeper into understanding the world around them. And, I wager, this type of questioning will engage students in learning and applying what they learn in a much more relevant and interesting way.  Giving them purpose for learning. And, as a result, we might have more students going into STEM fields.

Some examples:

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Why, for example, are most buildings polygon shapes, particularly triangles and rectangles? Why don’t we see more circular or cylindrical shapes for buildings, besides the grain silos or water towers? Is there a reason? This is where engineering would come into play – are certain shapes stronger from an engineering perspective?



Why are science and medical tubes cylindrical? Is their a scientific reason for these shapes/containers? Why not use a prism shape, so then you could set the vials down on a table versus having to store them in special holders so they don’t roll away? Is the shape somehow connected to the way molecules or blood cells behave – i.e. science factors that might determine the tools used.  2791136-image-of-the-motherboard-without-a-pc-processor-closeup

Look at all the different shapes on a computer motherboard – there are cylinders, rectangles, squares, networks of curves/lines of wires, prisms…so many things going on. Students could ask whether certain shapes provide better conductivity? Or heat control? How does the height of a component impact it (notice the different heights of the cylindrical components). I don’t even know the questions to ask here, but this is a great example of where technology comes into play.

I feel that if we allowed students to explore beyond simple things like fitting a function to a curve or identifying shapes in a picture, and really focused on STEM applications and reasons behind the use of those specific shapes, we would be encouraging students creativity, curiosity, and developing research capabilities in order to find solutions. It would be so engaging and really get students interested in those STEM careers, but more importantly, a better understanding of the STEM around them.