POTW – First Parallel Proof

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What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: This was an opener problem I used the first day after I taught parallel lines.

What is it: This is a proof that practices using formal two column proof with parallels. It forces students to practice their reasons.

Why I like it: I like that students have to first practice the congruent complements theorem because even my honors students want to say substitution. Then, they have to prove the lines parallel using a converse to the original statements we learned the class before. Then, they end the proof using a straightforward statement. I think it is important that students have to practice and wrestle with knowing when to end their reasons with parallel or end it with an angle pair congruent.

Let me know if you used this and how it went!

POTW – Polygon Intro

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What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here. I am taking no claim that these are necessarily original as I might have stolen them from many of you reading this!

How I used it: Before I taught students what a polygon was, I just showed them some examples and some non-examples.

What is it: I used this in a powerpoint and had students, on their own, create their own definition of what an example was. As I revealed one example and then a non-example, I could see students constantly erasing and changing their definitions. Then, I had them work together and challenge each other’s definitions. Then, we moved on to practicing their definition. Only after, I told them that these were called polygons.

Why I like it: Instead of me telling my students what they need to know, they figured it out on their own. It appeared that everyone had the correct way to define a polygon before class was over and I did not have to do anything but guide them in the right direction and allow for discussion. So much more engagement than just telling them what the definition is and telling students to apply it.

Here is a link to the powerpoint if you want to try it out. Let me know if you used this and how it went!

POTW – Transversal Angle Challenge

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What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here.

How I used it: After students learned about the different types of angle pairs, they got to complete this challenge.

What is it: Students all went to the board with a partner and drew the diagram. With a marker and an eraser in hand, they had to try and put the numbered angles in the diagram so every statement was true.

Why I like it: So much discussion! Students were arguing (in the best way possible) over which angle goes where and why something was or was not a type. It was tricky because we had just learned the basics on a diagram with one transversal and now their were three! They learned that certain angles could be interior or exterior depending on what transversal they were looking at (or at least that is what they told me when we had a class discussion after the activity). I just acted as an answer key and when students asked me if it was right, I would just point out a counterexample and walk away. It was lots of fun and a nice way to get students up and engaging with the ideas.

Let me know if you used this and how it went!

POTW: Beginning Proof – Angle Bisector

I have been slacking on this lately so here is hoping I can pick right up and keep going…

What this is: I am going to highlight problems I used with my honors geometry students that I thought were valuable. You can see all posts in this series here.

How I used it: This was a question we completed in class together as students were practicing proofs.

What is it: This involves students using the congruent complements theorem and angle bisector definition.

Why I like it: My students were tripped up about how to prove something is an angle bisector since they had to use the converse to the definition of an angle bisector (which I make my students write everything in if-then form at the moment). It was great discussion about how to use it and since it was our first problem that involved using a converse, now many are much more careful in checking.

Let me know if you used this and how it went!