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!
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!
So a little behind here on #sundayfunday challenge but that is okay because the goal is just to #pushsend.
I will be teaching geometry honors and algebra 2 studies (Learners who have struggled). In geometry I will be doing the same activity to build up a need for geometry vocab I have done before which you can read here. I will also be using my school fever activity that I have used before and you can read about that one here.
I have decided to try and get out of my comfort zone a little and instead of just reviewing how to plot coordinate points with my algebra 2 students, I thought it might be great to try and incorporate some sort of desmos activity instead. I am hoping that this will excite them instead of bore them to death on the first day of class. Students will be using the mini-golf coordinate activity with a few extra slides that I have added/modified at the beginning and at the end to lead some discussion about scatterplots. After being at #tmc17 and being involved in #desmoscamp I really love the idea of pausing and being able to restrict parts of the activity. This will be my first time trying all of this out on a new group of students day 1 but I am thinking it will lead to great success! If you want to see what it looks like and try it out then go here.
Regardless of what you are doing, I encourage you to think of ways to try and take a risk and go for something new. This has made me even more excited for the start of the year!
The other day in my geometry honors class, I had to teach special right triangles. I knew that I just needed time for them to practice and didn’t have time to create some type of interesting way for them to practice. I grabbed a couple of worksheets to bring with to class. I decided at the last minute to make copies of the answer keys. As students worked on the practice problems, I placed my answer key copies up around the room. To my surprise, my students were working really well and only asked me a question when they critically needed it. My last block of the day would probably have kept going if I didn’t stop them to move onto something else.
One thing that made this more effective than I thought was also having two worksheets. One was simple practice with the special right triangles and the other was tougher with application problems. It was nice that students could use this and differentiate a little. Allowing them some movement didn’t hurt either. I think that I just need to give my students time to work and ask questions and I don’t always need something flashy and exciting to help them learn. I was feeling kind of bad about this and now I feel, even though I could still always update the worksheets for next year, that it was pretty solid and the students seemed pretty strong on the homework that I assigned. I needed to write this to remind myself of these things.
With my regular geometry class, I wanted to have an activity that they can get started with right way on the first day of school. I came up with them dividing shapes into similar figures using this worksheet below:
I think some students will divide into four congruent shapes while others will divide into four similar shapes. It can generate discussion about what the difference is and motivate some discussion on how these will be two huge concepts for the rest of the year.
Enjoy your remaining summer while it lasts!
I have been trying to structure my geometry classes this year with a problem to think about so that they can discover something. I believe that if they learn something without me, they take ownership of it and actually remember it. I gave them this triangle midsegment problem the other day in class:
As you can tell, it is nothing fancy. Maybe because I have been doing things like this all year long but my students dove in and tried to figure out a whole bunch of stuff. After they made their conjectures, I drew another one on the board and they had to figure out everything again and see if their conjectures worked. Some did and some didn’t…which lead to some great discussions. After 30 minutes, we were done discussing and everyone was convinced that this always worked. I threw a sketchpad up on the board and played around with it and they double checked it always worked (they love watching these things fly around on the screen).
I could have easily just told the students to accept this fact and do 10 practice problems on it but instead, I thought that this would be much more beneficial. I then proceeded to give them a few practice problems in different contexts involving midsegments…they rocked through all of them. Love it when kids tell you that this concept was easy when reality, they think it is “easy” because they worked hard to understand the idea behind and not just memorize that it is parallel and half the measure of the base. I need to remember to do more of this as it is so powerful!
Last week I worked on writing proofs with my regular geometry students. Some of them have a difficult time coming up with reasons and statements as well as knowing how to proceed to the next step. I wanted something that would help them review for their upcoming quiz as well as help to get them thinking about the logical flow of a two-column proof.
We did the activity below where they had to cut up the pieces and paste/tape them into the appropriate spots. Some of the pieces were not used to add a little bit of a challenge. They were really engaged and loved it.
This is short because I just needed to blog to hopefully get me back into it!