Quadratics and Polynomials on Desmos AB

My Algebra 2 class is largely student-paced through Desmos Activity Builder. Before starting polynomials, we did a small unit on solving quadratics. Below is a collection of Desmos activities  I created for my quadratics unit and the start of my polynomial unit. A lot of these  Desmos activities are created using CPM curriculum.

Quadratic Formula: Students review and practice using the quadratic formula (song included)

Using Roots to Create Quadratic Equations: Students learn how to use roots to create a quadratic equation.

Interactive: Using Roots to Create Quadratic Equations: Practice using roots to write quadratic equations by flying angry birds, catching Pokemon, and going scuba diving!

Projectile Motion – Quadratic Application: Students learn to apply their knowledge of quadratics for projectile motion problems.

Polynomials

Polygraph Polynomials (Jim Baumgart) – Started off playing polygraph to see what vocabulary they could apply before starting the unit.

What is your end behavior? : Students explore the beginning and end behavior of polynomials.

Graphing Polynomials: Students learn how to graph polynomials by using their roots and dilation/compression.

Match my Polynomial: Coaster Edition (Interactive): Match my polynomial – Roller-coaster edition. Students practice writing equations of polynomials with an added bonus 🙂

Socratic Seminars for Math Review

We are preparing for midterms, and for my Algebra 2 class, I decided to do a Socratic Seminar to review the all of the material. Instead of giving my students a list of topics that would be on the midterm, they created their own list by looking through their notes and tests and discussing the past semester.

My students were set up into two circles. Students on the inside circle had to discuss the questions prompted on the board. All students on the inside circle had to talk once before anyone else in the circle could speak again. This had all students looking through their notes and past test and participating in the review. They were coming up with what was important and narrowed down the topics that they struggled with the most. I added in a few questions in verbally when I felt they got stuck or could push the topic further.

Being able to verbalize the concepts they needed to know and the concepts they needed to work was extremely helpful for my students.

While the inside circle was discussing the prompted questions, the outside circle was discussing the questions on a back channel chat. They were writing down the topics that they needed to know/work-on and went into more detail about the concepts than the inner circle.

For backchanneling, I have used

They both work really well and are extremely teacher/student friendly.

For this seminar, I used Today’s Meet. If you would like to embed your backchannel into your class page, it is extremely easy. By clicking class tools at the bottom of your chat, it allows you embed the live stream or transcript to your page.

This back channel chat was embedded “live stream” into their Haiku page, so it was easy to get to and they can refer back to it to study.

For this seminar, I had students switch circles for every chapter. I asked the same questions for each chapter. I had questions appear one at a time.

I love doing Socratic seminars in my classes.  Talking about concepts and explaining them to their peers really helps students truly understand the concept. This activity also had them reflect on everything they learned this year. I think reflecting on their past test, instead of just looking at them, was also really beneficial.

A video of my seminar can be found here.

I would love to hear if you have any suggestions or ways to improve and use Socratic Seminars. I also love trying new back channeling sites, if you have tried one that works well I would love to hear about it!

More than a Worksheet… with Desmos!

Typically, I use Desmos Activities at the beginning or end of a lesson. I have found it as a great tool to introduce or wrap up a class. However, recently I have been using activity builder more in my classroom every day.  A new thing I have been doing is  pairing Desmos Activites with  worksheets.

Pros of pairing them together

• Students are writing more!
• After students complete one problem on their sheet, they follow along with the Desmos Activity until they are told to stop and move to the next problem.
• Problems go more in depth after they solve it on their paper. Students are asked to explain their answers.
• Students can check their answers.
• Instead of being called over to ask if “they did it right” students can check their answers on their own and move at their own pace.
• Students can also compare their answers with other students all around the room
• You know how ALL of your students are doing at all times
• You can see if they are doing it correctly all in one place. I’ll walk around with my iPad as I help students.
• If you realize that a lot of students are struggling with a certain problem you can put the activity on teacher mode  and talk about it as a class.
• You get immediate Feedback!
• This is a great space to give an “exit ticket”, see where students are, and how you can help them!

Here is an example of a worksheet and the Desmos Activity that goes along with it about graphing and solving systems of equations.

This example is practice graphing systems of equations: Worksheet & Desmos Activity.

Simplifying Rational Expressions: Mafia Edition

When simplifying rational expressions, students always seem to want to simplify TOO much (and incorrectly) !! Below are a few common”over simplifications” that I’ve seen.

This is where #lifelessonswithFinney kicked in. We started talking about the Mafia. Yes, the Mafia. Not only were we talking about the Mafia, but we were talking about killing off family members of the Mafia.

The polynomial is our numerator is a family. The Mafia Family. The denominator is our hitman.

I asked my students what they thought would happen if they tried to kill only one member but not the rest of the family.

“We’d be in trouble!!!! They’d come after us!!!!!!!!!”

Exactly. So we if we want to kill off one member of the family then we have to kill them all! This is the only way that you’d make it out alive! If you can’t kill them all then it is fully simplified. Killing doesn’t mean you have to get rid of it completely. However, you must “hit” every member of the family.

Making Percents Real : Apple Edu

I just finished my first week of teaching Algebra 2 ever. On one of the first days, I wanted to dive in and do math, but I didn’t want to intimidate my students so early in the year. Julie Reulbach gave me the great idea of reviewing percents by looking at Apple Computers.

I handed out the sheet I created with no other instructions or introduction than they could work with a partner to figure out the answers.

The worksheet I created explored the 13-inch MacBook Pro. First, I had students find the tax  on the computer and then justify how they found it.

Next, we looked at the price of the 13-inch MacBook Pro compared to the price of the same computer from the Apple Education Store. Students had to find the percent discount.

Third, students had to apply that percent discount to the cost of the 15 inch Macbook Pro to figure out what education price would be.

This is where the conversation became interesting. After everyone was finished, I revealed the actual education price of the Macbook. They were outraged!!! The price was about \$100 more than they calculated it should be!!!

This then prompted the question “Do you think this happens for every Apple Product?”

Each group then picked an Apple product. We looked at Macbook Air, Ipads,  and Imacs (I have a class of 8 students).

Students picked what size they first wanted to look at and then found the percent discount from the original price to the education price. Once they found the percent decrease they wrote their percent on the board. They then looked up a different size of the same product to see if they discount remained the same!

This lead into a discussion about which product receives the biggest discount and why. Also what we thought affected the discount, and how sales aren’t always as straightforward as they seem.

This was a fun, easy, and real-world lesson that helped students review percents without sitting through a review lesson or by doing practice problems.

We did go over the worksheet to address any class misconceptions before we broke out to look up different products.  Originally, many students found the percent tax by finding the tax and then adding it to the original. This was a great opportunity to introduce original(1+percent) which they see for growth and decay later in the chapter.