# Engaging students: Using the undefined terms of points, line and plane

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Alec Bui. His topic, from Geometry: using the undefined terms of points, line and plane.

C1. How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

This topic appears in a game that I play called League of Legends. To give context, in the game there are a total of 10 players with 5 players on each team. Within each team, they must work together to achieve the goal of destroying the enemy team’s Nexus, which is their base. Most games are not usually this straightforward. You must work with your team to take objectives such as towers, special buffs, and secure kills. This video provides a great summary as to what this game is https://www.youtube.com/watch?v=BGtROJeMPeE.

This topic appears in the game in a very dynamic way, specifically with the champion’s abilities. Each champion’s abilities have different interactions with the game and how it is used. It depends on your cursor placement, which decides what point in the plane you’re aiming at. Also the distance and position of your cursor from your champion can dictate the line in which the ability is casted towards. All of this is conducted on a plane in which the game is played on. These terms are very basic and is inherently understood when playing the game. These inherent concepts depends on the champions and their abilities. Basically the position of the cursor dictates the path and location in which the ability is used on the plane. In terms of the game, this is how you aim and move depending on your character.One specific champion that comes to mind is Thresh. This video (https://www.youtube.com/watch?v=Sv95nBi7ulQ) goes over the champions abilities. Death Sentence, Dark Passage, and Flay all clearly makes use of points (the position in which the cursor is related to the plane) and lines (in relation to where the cursor is respective to the champion, what path & direction will the ability follows).

My background with League of Legends:

●Played the game for about 3-4 years
●I played for our school at UNT (Esports Club)
●What role I played – ADC (Attack Damage Carry)
●In the U.S, I was ranked top 1.87% (in season 8)
●In the world top 2.1% (in season 8)
●Favorite champion: Lee Sin

D5. How have different cultures throughout time used this topic in their society?

This question and topic reminded me of a YouTube channel which I think uses the undefined terms without explicitly saying so. The channel is called “Primitive Tool” which you can search on YouTube. The channel has a multitude of construction videos of different structures such as pools and houses built back with primitive tools. It makes you think how basic knowledge of lines, points, and plane were naturally used without a mathematical explanation or background. It was very natural to consider this vocabulary in normal day to day life which was continuously used. You can see the progression and advancement of this simple vocabulary in our architecture over human history. Different cultures have used this topic expressed through art, architecture, etc. One that sticks out in my head are the Egyptians. It’s clear that basic mastery of the topic is needed to construct the phenomenal pyramids that stand today.

E1. How can technology be used to effectively engage students with this topic?

Geometer’s sketchpad would be a great way to engage this topic. It would be a great way for students to explore the different tools with little to no explanation needed. Student’s can play around with the tools up until guided practice is needed up to the discretion of the teacher. It would be far more engaging than simply explaining what these terms are and going through examples. It provides a dynamic way for the students to interact with all of the terms. This allows them to see the relationship between the terms. They can further their exploration by creating shapes and different polygons with the tools. Overall it’s great dynamic way to learn what the terms are instead of a static manner.

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