Posts Tagged ‘Geometry’


I Made a Thing!

September 23, 2017

One of my favorite sessions at TMC17 was the CO+DE=MATH session by Tamar McPherson (@teachme124) and Stephanie Reilly (@reilly1041). They introduced me to, which I really like because you can write code on the left side of the screen and run it on the right side of the screen. I am going to be attempting to do a couple of classes with my Pre-AP Geometry classes this week on coding. We’re going to do some of the Hour of Code problems on on the first day, and then I’m going to attempt to introduce them to Python using trinket on the second day. In the process, I decided I’d have some fun and try to write a program to simplify radicals. I wish I could embed it, but WordPress won’t do frames.

Enter a square root you want to simplify (ex. \sqrt{75}), and it will give you the simplified radical (ex. 5\sqrt{3}). Here it is: Simplifying Radicals


Been Away, But Now I’m Back — Reflections on 2014-2015

June 7, 2015

One of the reasons that I haven’t posted anything this year is directly related to one of my favorite tools this year: One of my main purposes for writing this blog is to allow me to reflect on lessons that I have taught, and with planbook, I set up a tab called “Reflection”, that allowed me to do that and have all of the lesson information right there. As far as a year-end overall reflection, I felt that a blogpost would be more helpful, so thus…

In almost every way, this school year was a lot of fun. I had four PAP Geometry classes and two Astronomy classes. My PAP kids were great (I also had about 16 8th graders who were generally adorable), and it was a blast finally being able to teach Astronomy. My schedule even worked out so that I did not have to have “Freshmen Lunch” (35 minutes). With that being the case, I will mention the few minor annoyances just to get them out of my system, and then go on to what I think worked, and what I’m changing for next year.

To summarize:

  • Astronomy is great!
  • Not just a flipped classroom, but a flipped-mastery learning classroom!
  • Canvas is a really good tool for the aforementioned classroom.
  • Having students make a Kahoot quiz for their presentations is a great way to ensure engagement.

Read the rest of this entry ?


2013-2014 In Review

July 1, 2014

Man, this was a crazy year! In addition to the stuff listed below, I had a house fire on Sept. 16th, and I was out of my house until Thanksgiving!

The Freshman Center

  • My 9-12 high school decided that the freshmen needed to be segregated as much as possible from the rest of the student population. Since the district wasn’t going to build us a separate building, we moved all of the freshmen teachers to one end of the building (for the most part). This meant that a school which had been organized around departments was now organized around grade levels. I’d say about 80% of the school had to change rooms. Fun.
  • Trying to force a separate freshmen center on a system designed for 9-12 created some interesting challenges. Our poor counselors ended up having to toss out the computer-generated course schedules and schedule about 800 freshmen manually about two days before school started.
  • Because I wanted the opportunity to teach Pre-AP Geometry, I volunteered to join the freshmen center to teach PAP and Regular Geometry. I ended up with three PAP classes and three regular classes, with all 9th graders.
  • For various reasons, my new room wasn’t with all of the other freshmen teachers. At first, this bugged me, but upon reflection, I decided I didn’t mind being downstairs in what amounted to the senior hall.
  • Everything was working fairly well until a school board member was upset that the biology students were in a regular classroom and not in a lab. Because of this school board member, all of the biology teachers (except one who refused to move because of the mold in the old part of the building where the labs were) moved back to their old rooms and traded places with the teachers who had moved there. The worst part was that our nice little 9th grade enclave was now broken.

PAP Geometry

  • Failures
    • I know Dr. Epperson insists that students can learn skills through problem-solving, but I have not yet figured out how to do it. As the year progressed, I stopped trying to force them to work on problems, and instead we did a lot of worksheets.
    • While I really liked my homework and my homework policy this year (see “Successes”), I did not follow through on the online homework that I assigned. The students figured out pretty quickly that they didn’t have to do it, and they generally weren’t mature enough to realize that they needed to do it.
    • Because I got in a rut of using worksheets for skill practice, we almost never got to spend the time to really develop the conceptual knowledge that I had wanted to. That’s probably my biggest disappointment.
    • Our school district has decided on a “BYOT” policy for electronic devices, but my freshmen cannot handle free access to their cell phones in class.
  • Successes
    • I flipped my classroom, and it was wonderful! In order to make things simple, I just decided to upload pdfs of my existing PowerPoint slides. I first was using, and while they were nice, they were a little clunky to use and their format was more designed for portrait files than landscape. I eventually found, which worked out really well. Slideshare will also let you upload and sync audio files, which I did a few times.
    • After I had uploaded my powerpoint pdf, I pasted the url in my school blog ( Students were required to take notes over the powerpoint for homework. For the first semester, I also assigned problems from Khan Academy or As I said above, I didn’t check on whether students were doing them, which was a big mistake.
    • I decided to take the meaning of “Geometry” to heart, and I took my kids outside the class for several measuring projects. I plan to do separate posts on these:
      • Proportional Measuring — I broke them up into teams, gave them mirrors and rulers, and had them measure tall things around the school. It was a little disconcerting to have a student try to tell me that the hallway was only 6 feet tall, but overall, I think it went well. The only drawback was that it was very cold outside, so we couldn’t measure outdoors as much as I wanted.
      • Inclinometers — During our trig unit, I came up with a printable inclinometer that I had them make, and we went out and measured tall things again. This time the weather was nicer, so we were able to measure goal posts and flag poles.
      • Eratosthenes Experiment — I got permission to take my students out of their last period classes on March 21st, and we calculated our latitude and the circumference of the Earth. In a moment of inspiration, I realized I could have them use their phones and a Google form to collect the data, so that worked out really well.

Regular Geometry

  • I ended up following the same schedule for my regular kids as for the PAP kids. The only differences were in how I weighted the grades and that the regular kids could re-assess up to a 4 (100%) as opposed to a 3 (75%).
  • For the most part, I liked my regular classes, but I had one class that combined the worst of being below-level and being freshmen. We went round-and-round all year. In fact, I had seven (7!) students in that class cheat on their final exam.
  • If my PAP kids couldn’t handle access to their cell phones, the regular kids really weren’t mature enough. This was enough of an wide-spread phenomenon that we have already decided that freshmen may not “BYOT” next year.

Quick Idea from #TMC13

August 4, 2013

I just thought of this as I was reading some recaps of TMC13: During “My Favorites”, Chris Lusto offered the idea of having students work out the definition of a circle.

What just struck me was one of the activities challenged the students to come up with an example that fit a classmate’s definition but was not a circle. COUNTEREXAMPLE!! Counterexamples (especially geometric counterexamples) are so tricky for students to get. Here’s a built-in example of why they’re a big deal. Love!


Geometry Curriculum 2013-2014

July 16, 2013

The Texas Geometry EOC exam is essentially kaput. The new guidelines (which only require Algebra I, English I, English II, US History, and Biology) don’t officially go into place until 2014-2015, but the bill says that any student who is a freshman before 2014-2015 (i.e. all of my students) can graduate under the new plan instead of needing to pass 15 EOC exams.

Because we will be getting new standards in a couple of years, I’m sure someone somewhere will come up with some sort of assessment that I will need to administer, but right now, I’m kind of basking in the idea that I can space out my curriculum over the entire year (and with the kids I will be teaching, they should have all passed the Algebra I EOC, so I don’t have to worry about reviewing for that).

As I wrote in an earlier post, M was going to be the other PAP Geometry teacher with me (she decided she’d rather live closer than 3-1/2 hours from her boyfriend–go figure). Before she got her new job, she and I sat down and worked on a new Geometry curriculum sequence. I liked it so much that I’m probably going to propose it for our regular Geometry sequence as well unless I get some serious pushback from the district.

When M and I started talking how we wanted to sequence things, we both agreed that starting the year off with geometric reasoning (inductive, deductive, conditionals, etc.) was not what we wanted. We ended up with what I think is a really great plan–review/practice solving equations while we introduce the idea of algebraic proofs. These kids should already be comfortable with the mechanics of solving equations, so we planned to start asking them to justify each step. From there, we move to reviewing/deepening their understanding of slope and equations of lines. From there we can move into actual Geometry with points, lines, and planes.

PAP Geometry Sequence

I’m thinking about adding a unit on at the end for PAP for non-Euclidean geometry, just to blow their minds.

Since my master plan for the year is to have the students (a) work harder than I am and (b) learn by problem-solving, I am going to flip the notetaking part of my class as much as possible. Since most of these kids should have some sort of internet connection, I am going to post my notes online (either on my school blog or a LiveBinder, I can’t decide). I will then usually have a short Khan Academy practice assignment on a purely mechanical, low-level skill, and I’m thinking 5-6 3-leaved problems to show mastery.

Once students come back to class, they will have a short quiz over the homework. That will then give us the rest of class to work on problems either extending the topic, tying the topic to previous topics, or totally unrelated because sometimes math just works that way. The unit tests will be written at a deeper level than the quizzes, but not as deep as the problems.

Part of me really just wanted to issue every student a copy of the Exeter Math 2 curriculum and say, “That’s it! Now go do.” Unfortunately, I think I’d spend the rest of the year fighting with parents to keep my head attached to my shoulders. I’ve also been concerned about how to supply the foundational instruction that some of these problems require, and how to supply that in an organized fashion. Maybe after I’ve taught this class for a year the way I’ve laid it out, I can feel more comfortable jettisoning the training wheels.


Cool Midpoint and Distance Idea

September 14, 2012

via Lisa:

The Radical Rational had an idea to put a grid on top of a map of her school. The questions she proposed asking her students:

•Calculate the distance between Room 137 & Room 114.
•Find the coordinates between Room 137 & Room 114. What room are you closet to at this point?
•Connect Ag, Kitchen, Cafeteria & Workshop. What type of quadrilateral have your formed? How do you know? Prove it. We have not covered types quads – but they can use their BYOD to find this information if needed, right?
•Connect Library, Room 128, Room 116 and Room 114. Is it a rectangle? Or a square? (LOL) How do you know. This always comes up in discussion – I must say I love the “disagreements”.
•Connect Room 145, Room 142 and Band. What type of Triangle have you created? How do you know? Prove it.
•Connect the Gym, Library and Tan Hall – Find the perimeter & area of this triangle.
•What about having them “map” out their schedule and calculate “as the crow flies” distances between their destinations.


Made4Math #10

September 3, 2012

Sometimes it’s nice when necessity kicks us in the rear and makes us come up with different ways to do things.

I have always dreaded the “Points, Lines, and Planes” section of Geometry because it’s so text- and definition-heavy. (Reference this post for my original format.) Because the district has switched things up on us, PL&P is not the first section, and I need to teach it on the same day as their first quiz. I quickly decided to make this into a holey-notes foldable, but what format to use? It’s too much text for a 2-page booklet and not really enough text for a 4-page booklet. That size usually lends itself to a tabbed booklet, but how to arrange it?

My good scanner is up at school, but here is the result:

In all three classes, we got almost all the way through, and it was a lot less mind-numbing than it has been in years past.