Finishing Up Unit 1 of Pre-AP Algebra 2

One afternoon toward the end of summer, I got a phone call while at the orthodontist with my youngest daughter. I was a little surprised to see the call was from the head of the math department at my school.  The call was to ask me if I would consider taking on one of the Pre-AP Algebra 2 classes. I was actually delighted to take on another math class, although it meant an overload in an already busy year for me. My class load already included AP Environmental Science, which is brand new for me, and AP Precalculus which is a brand new curriculum. The only prepped and familiar class for this year is AP Biology. 

One of the benefits of Pre-AP Algebra 2 is that the curriculum is primarily put together, although I'm finding that it still takes some time to prep the lessons. Fortunately, unit 1 had lessons for each of the topics except for the last one. Key concept 1.3: Graphing Absolute Value as Piecewise Defined Functions didn't have a lesson. Before the year started I decided to teach the concept through a Desmos activity. I'm still about a week away from using this lesson, but wanted to share it in case it may be helpful to someone else. Feel free to let me know if you catch any errors. I'll also make adjustments as my students try it and help me find any issues.

Here's the link to Absolute Value as a Piecewise Function.

Desmos Activities for Precalculus Polynomial and Rational Functions

Made by Desmos.com

We came so close to finishing the first quarter face to face, but had to transition to remote learning for a week and a half starting on the last day of the quarter. Fortunately, I had been preparing my classes for this from the beginning of the year. They have been scanning and submitting all of their work in Google Classroom and we have been using Desmos on a regular basis. I would use Desmos wether we were face to face or remote, but I love Desmos even more when we have to go to remote learning. 

I found some great activity builders on Desmos for this unit that I didn't have last year. I even went to a virtual math seminar on using the computational layer in Desmos to add special elements to Desmos Activity Builder this past weekend and tried my hand at it for an activity we did this week. I must confess I made a couple of mistakes that my students helped me to realize and fix as we did it. It's not fancy, but it gave my students the group practice I wanted them to have with graphing rational functions with slant asymptotes. 

Here's the link to my whole collection: Precalculus Unit 3

Here are the individual activities:

Polynomial Equation Challenges

Constructing Polynomials

Polygraph: Polynomials (My students LOVE polygraphs!)

Polygraph: Rational Functions

What's Your End Behavior

Sketching Polynomials...without Desmos

Polynomials and Roots

Horizontal and Slant Asymptotes (I love the use of "which one doesn't belong" in this activity.)

Graphing Rational Functions (This is my creation...not fancy, but it accomplished what I was looking for.)

Power, Polynomial, and Rational Functions Activities

 

In my folder for unit 3, I only had one question stack that I made using homework questions.  I used a template from Math = Love. I also converted that template into a Google Doc, since I do all things Google, which is here.

The rest of the time, we either did jigsaws with chosen homework questions or Desmos activites. I love Desmos. My students were particularly fond of the polygraphs in Desmos. 

With polygraphs, once students input the class code for the activity, Desmos begins to pair students up. One student picks a graph out of 16 choices, and the other student asks questions trying to narrow down the choices until they think they have figured out the chosen graph.  Once they have either guessed correctly, or run out of guesses, Desmos will pair them with another student. Even with an odd number of students, the guesses go pretty quickly, so no one is waiting for a partner for very long.

I do give students particular vocabulary that I want to see them using. In the teacher dashboard, I'm able to see all of the interactions from each guessing session. This gives me a picture of how students are really understanding the concepts we are working with. It also keeps them accountable, since I can see all the questions they are asking.

Here are the links to the activities in the picture at the top:

Polynomial Equation Challenges

Constructing Polynomials

Polygraph: Polynomials

Polygraph: Rational Functions

By the way, some of the activities that are put out by Desmos also have a teacher guide that may really help you step up your game if you print it out and work through it before the students start it in class. When I first started using Desmos, it was tough to keep up with what students were doing and answering questions. I didn't have time to take shots of student work to showcase solid or creative thinking. Sometimes, I would do that after class and show them the next day. I have to guess that the more I use Desmos, the better I will get at using all the tools available to teachers. I did also grow to love the pacing feature that only lets students have access to certain slides. This helped encourage some students to take their time instead of just rushing through the activity without thinking about what they were doing. I love hearing student exclaim, "she's released more slides!" when I'd allow them to go on to more frames of the activity.