# Cold Season = Increased Absences

It’s cold season in Massachusetts (I’m even writing this while surrounded by cough drops and tissues).  Cold season means my students miss class more often and come back to school overwhelmed by make-up work.

In our 1:1 environment, I write out my examples in Notability and my students take their notes in Notability too.  When a student is absent, he/she typically asks a classmate to share the notes from class before coming back to school.  While this doesn’t make up for the missed class, when absent students come to see me the next, they have already seen the notes and are prepared to ask questions other than the dreaded “did I miss anything?

Note: Students typically “share” their notes with each other by sending their Notability file via email to another student.

# Desmos Graphing App

Graphing calculators are good, but the Graphing Calculator app by Desmos is better.  Graphing calculators are expensive. (The Desmos app is free).   Graphing calculators require several clicks to change the ‘window’ of a graph.  (The Desmos app is interactive and I can zoom in with my fingers).  Graphing calculators can be finicky when entering complicated equations. (The Desmos app points out your error).

I could go on an on about why I think Desmos makes a better graphing calculator for my students, but instead I’ll tell you about my Trigonometry students.

We are headed towards proving trigonometric identities, but before start simplifying them by had, I had them graph pairs of equations whose equations looked very different but graphs were identical.

Two equivalent equations graphed at the same time.

Imagine their surprise when only one graph showed up!  Several were concerned that they had done something wrong, but au contraire, they are equivalent equations!  We had a lot of fun entering pairs of equations and deciding whether or not they were equivalent.

My students have started calling these trigonometric identities “same, same, but different” because they look the same on the graph, but they have different forms when written.

When I did this same activity last year with graphing calculators, it took forever to enter the equations and then find their mistakes if they forgot parentheses.  The Desmos app saved us a lot of time and therefore allowed us to try lots of different pairs of equations.

Entering complicated equations is easy with this list of functions.

You can change the x- and y-axis to radians too!

Desmos also has a web based calculator that is just as fun!

# Geometry Proofs: So Many Ways!

I teach Geometry.  My students struggle with the idea that there are lots of different ways to prove something.  What they really hate is that there isn’t one right answer.  I on the other hand get the most frustrated when a student is looking at a proof I have projected saying,  “I did something different … am I wrong?”

Prior to our 1:1 iPad environment, I would have said, “well let me come take a look” or “how about you write it on the board and we’ll look at it?” Oh the time I wasted waiting for kids to write on the board … oh the time I wasted looking at one kid’s work while the rest of the class stared off into the distance.

Enter Apple TV and students doing their homework in Notability on their iPads. Now I say, “could you mirror your iPad and we’ll look at your proof together as a class?”  Within seconds, the whole class is looking at an alternative method of proving something.  Sometimes  it’s right.  Sometimes it needs to be tweaked.  Other times, it’s way off.  But regardless, we get to look at several different proofs for each problem and still have class time left to do something else!

When my students are working on a particularly difficult topic, I like to know if they’re on the right track.  If I don’t get questions via email or see students in my room the next morning, I begin class without knowing where my students stand with yesterday’s material.  This isn’t exactly ideal.  (I realize I could scrap the idea of homework, but that’s not where I’m headed.)

Instead, I have my students enter the answers to their homework problems into a Google Form.  They’re not submitting all of their work, so it doesn’t take much for me to scan through their answers and quickly get an idea of whether each student is on the right track.

I tried this for the first time last week when my trigonometry students.  I created a Google Form asking for identifying information (first and last name, email address, and class period) and answers to each of the five homework questions.  Since my students do their homework in Notability on their iPads, it was easy for them to quickly enter their answers and submit the form when the were finished with their homework:

I checked in on the responses a few times, emailed students who seemed to be way off track and offered some hints based on which problems were wrong.

I sent emails to students in lines 1 and 3 when I noticed their answers were incorrect.

Then, before class, I used Flubaroo, a script in Google Forms, to “grade” the homework and email students their grade (out of 5) as well as the answer key.  Below is the summary of the grades.  [Note: I did not use this grade, but rather, I gave full credit to students for completing the assignment.]

Instead of starting class by asking what questions my students had, I was able to target the one question that  most students struggled with.  Another nice thing about using forms to collect homework responses is the ability to project all of the responses at the beginning of the class period.  When I ask an open-ended question, I like for my students to see all of the different responses and discuss which ones are better explanations.  Thank you Google!