POTW: Segment Ratio 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 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.

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.

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.

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!