POTW – Crook Problem

Crook problem

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 a problem I threw at my students during class while we were working on parallel lines.

What is it: This is a classic crook problem but initially stumped a lot of students immediately.

Why I like it: Anytime I can give a problem nobody knows how to solve right away is great. Many of them drew some crazy triangles and could eventually reason it out. I liked that I could draw in an auxiliary line and introduce that idea that since two points determine a line, I can draw one in parallel to the other two anywhere I want in the diagram. It was great because they immediately asked if I could make up another one for them to complete.

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

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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!

POTW: Segment Ratio Problem

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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 my first post in this series here.

How I used it: This was a question on a review activity we were completing in preparation for our Chapter 1 Test.

What is it: This involves the idea of the segment addition postulate and ratios.

Why I like it: The idea of how students calculate lengths with the ratios always brings up interesting viewpoints like using 2x and 3x and some students doing it in their head and visualizing how to break it. The best part about this problem is how their can be more than one solution. Very few found that out at first glance.

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

POTW: Segment Addition Postulate

If you had asked me before I started teaching, I would have told you their would be one subject I never want to teach: Geometry. I did not really get what it was all about doing an integrated curriculum in high school and I though proofs were annoying so I vowed to just stay away from it. Fast forward to now where I have taught some form of geometry every single year of my career…and I freaking love it!

I could tell you why I love geometry but I think showing you is better. I am always on the lookout for great problems that can lead to some really interesting discussions. I have decided this would be a good year to share some of my favorites I have collected over the year in my segment called POTW = Problem Of The Whenever.

I was going to call it problem of the week but what if I do not have a problem I really like, what if we are testing, what if I just don’t feel blogging, what if…..this just works out better for me but still encourages me to share. I feel like finding good geometry problems can be difficult sometimes so hopefully this will give some people an extra problem or two as well as convince others to share!

In the future, I won’t bore you with all this text above so now lets get into a problem. Here are a couple of segment addition problems. Note: I teach honors geometry classes this year so these are geared towards them but I have had success using these with other geometry classes as well.

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How I use it: I give this when students have just discovered what the segment addition postulate is and now need to practice a few. This is the first of 3 in a row I like to use.

What I like: Students usually approach it a couple of different ways and we get at what the midpoint is. Gets them to really describe to each other how they are convinced B is or is not a midpoint.

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What I like: Students tend to assume the points always go in the order of A, B, and then C. This shakes it up a bit.

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What I like: This allows students to practice their factoring skills and lets us discuss what occurs when you obtain two answers. The idea of a value being extraneous in the geometric world is always fun to have them debate over, especially in a problem like this where you can ask questions like: Does it matter if the variable is negative?

 

Hopefully, I will continue doing this throughout the year. Let me know if you use them and how it goes as well as any problems you would like to share!