Discovering Triangle Shortcuts and Breaking Desmos #Teach180

Today in geometry we looked into Triangle congruency shortcuts hat involve combinations of sides and angles. Here is some student work for why the SSA shortcut doesn’t work.

I’m hopeful future-them will remember this day when they’re in PreCal and doing the ambiguous case of Law of Sines.

In AFM I had such grand plans for our third day of modeling with functions. Then the Internet Gods smited us…smote us…what ever the past tense is for smite.

I have no idea what happened. But Desmos wasn’t showing a line of regression for all my students, and a lot of them were getting negative growth factors in regression when it should have been positive.

All and all 23 of my 38 students couldn’t get a regression line to populate. I have some ideas about what could have gone wrong. I plan to test them this weekend. My thoughts are:

  • Maybe because we had 3 regression lines going and all use the letter b that it made Desmos refer to a previous thing?
  • Maybe our schools internet is blocking something
  • The “log mode” option disappeared this week on my app, so maybe there was an update I don’t know about?

Who knows family. I’ll get it figured out cause my next 3 weeks are all Desmos-regression-heavy.


Congruence Shortcut Work #Teach180

Today we formally started to look at Triangle congruency shortcuts in Geometry. We, by the end of class, established the following conjectures:

  • 1 congruent side is not enough to make 2 congruent triangles
  • 2 congruent sides is not enough to make 2 congruent triangles
  • 3 congruent sides always makes congruent triangles
  • Some 2 sides congruent and 1 angle combinations work, but we haven’t found a pattern for when.

Good progress was made with our math family today

Day 3: playing with AngLegs #Teach180

Today was the first real day of our triangle unit in geometry. So after the students pulled most of the weight in a proof of the Triangle Interior Angle Sum conjecture (wooooot!) we didn’t have enough time to start the next investigation. So I just turned the students loose with the AngLegs to play.

Ps. This is my class of 6. So we just sit in one big group and I sit on a desk near by.

Day 2: Stand and Talk #teach180

My morning AFM class, who I love dearly, hate talking. Like. HATE talking. I spent all of last semester trying every thing I could think of to increase whole class discourse. Most of it with limited success. Part of the issue is it’s early in the morning by teenage standards –9am. It is either their first or second class of the day. The other part of the problem is I have a few very vocal kids who, bless their hearts, love to answer questions so the quiet ones defer to them. And for the sake of “keeping the class moving forward” I let the vocal kids do the talking, thusly perpetuating the cycle. Shame on me.

I wanted to work on being better this semester with these morning class kids. So today, on a whim, I decided to try a Stand and Talk for the intro to modeling activity. I gave them a zoomed in screen shot of a Desmos window with 3 functions. And I asked them to state what functions they thought they were and then to prove it to the best of their ability. Here’s a screen shot of the paper they had:

It was the first day of the modeling unit. They hadn’t learn how to prove a function is linear, or quadratic, or exponential. And they thought I was being evil when I had them working with their group. I was at one point accused of “throwing [them] in the deep end and watching them not swim.” To be honest this was intentional. I needed the student to realize they didn’t know what characteristics define the shape of their parent functions. I needed them to want a tool. To steal a Dan Meyer-ism, I needed a headache. So I made one.

Right as I could tell they were seconds from giving up I asked them to stand up with their paper and go and find a peer with whom they hadn’t talked to at all today. Then to discuss their thoughts and strategies.

Look at that glorious talking. ❤️

I have never been so excited about a noisy classroom in my career. I contained my glee but did sneak one picture. They were having such wonderful math conversations about what they were thinking.

In the end we walked away with 100% certainty that there was a linear function. And no clue what the other ones were.

We returned to seats. I pulled up the Desmos with the zoomed in graphs and I asked if zooming out would help. They said yes, and 3 zooms later a class of quiet teenagers were not-so-quietly voicing their feelings to their group on what the other two graphs had to be and why.


Semester 2 day 1 #teach180

Yay for the start of second semester. Aside from the absolute displeasure that was a 5am wake up after weeks of sleeping in I had a wonderful day with students. We focused on review from first semester in geometry by playing trashketball. In AFM I did a Formative Assessment of review of quadratic and linear graphs before we officially start the modeling unit tomorrow.

Here are students working on the kinematic quadratic review.

Day “I don’t know but it’s two days until exams” #Teach180

I fell off the teach180 wagon hard towards the end of this semester. Between me and the toddler catching every cootie and school stuff this was just an easy ball to drop.

But I’m back! With two days left in the academic marking period before exams to bring you:

Geometry’s Transformations Wallpaper tracing day

Students made an 8.5″x11″ paper filled with transformations and then cut the page in half twice and filled in the empty space to create a repeating pattern than could be tessellated into a 24″x36″ print. These beauties go to the printer tomorrow.

AFM has the group portion of their final today, working on mortality data from hurricanes.

Day 46: Transformations and Play Table #Teach180

Today in geometry we continued our exploration of transformations, doing a MAP transformations card sort with connecting transformations, as it was day 2 of the unit I really just wanted to see what the kids already knew. The hardest part of teaching at my school, since the kiddos come from all over, is I NEVER know what they know, so Formative Assessment is my best friend!




We then had some time in my afternoon class to play with the math play table and the end cuts from my dad’s wood picture frame business. It is a lot of fun to play with creating patterns with these!