Creating a Polynomial Function

One thing that I have been looking forward to trying in Advanced Algebra is more tasks. One of my goals for this year is doing more mathematical talking and orchestrating better discussions in the classroom. One task I created recently that still needs work is this creating a polynomial function from zeros task. Previously students have only factored and solved polynomials with P's and Q's. I was thinking they could work their way backwards from the previous days material.

Here is a link to a better looking version.

I gave them the task to work on for 15 minutes and I went around the classroom getting students started and answering questions.  If I had more time I would have done a better job of calling students up and presenting their work, but I was running short on time. I was hoping their thinking would help them think backwards especially with day before lesson.

Some places they might have gotten stuck at that I had posed responses for:

• Students will have a hard time getting started (it feels like a high entry task)
• I will ask them to go through an example problem we have done before, such as x^2-4x+3
• Multiplying the "i's" together, it has been about a full quarter since they have seen imaginary numbers multiplied together.
• I will ask them what i squared is? What do they remember about imaginary numbers?
• Distributing correctly.
• Ask them how they would distribute (x+2)(x+2)?

If you are really digging this lesson, you can view 28 minutes of the lesson here. 

I still feel like the entry to the task is too high, I would love comments on how this could be a better lesson.

Are You Looking for Piece-wise Functions

Doing piecewise functions this year? Here’s my latest @Desmos activity called Lava Piecewise Functions.#mtbos #iteachmath

Avoid the lava!https://t.co/TvMm8knYKo pic.twitter.com/latZBLBZqt

— Andrew Stadel (@mr_stadel) September 26, 2018

In today's @desmos activity, I asked my stus to break my piecewise function - that was fun to watch! Wanted to impress how much engineering goes into making continuous piecewise fn: #mtbos #flipclass https://t.co/pMQ7BKb8qu pic.twitter.com/gi0CKwZj8C

— Audrey McLaren (@a_mcsquared) November 21, 2018

Walking limits! #amtnys2018 pic.twitter.com/aqdjD2NlTB

— Caitlyn Gironda (@Caitlyn_Gironda) November 3, 2018

Algebra 2 Ss applying piecewise functions by creating a coloring book to send to elementary schools to show the amazing things you can do with math! We are interested in sending our book to multiple schools, so if you are interested lmk! #TMSLeaveATrail #ITeachMath pic.twitter.com/Bejse3Njr4

— Sarah Plain (@mrs_plain_LCPS) October 25, 2018

Representations of Relations

This is going to be my fifth year teaching Algebra 2, this year I am changing schools so it will be called Advanced Algebra. I was doing some curriculum writing with my new team of teachers and the first section we are going to cover as a class is Representing Relations my first reaction was...



At this point with just coming back to school students may not remember what relations are, what functions are, or domain and range.

I thought back to Dan Meyer's talk of headaches and aspirin and why do students need to know there are different ways to represent relations: ordered pairs, tables, graphs, and mapping.

I took the second graph from New York Times: What's Going on in this Graph?  and re-organized the information differently.

Give the students the following information:
This data is organized from by: country (guns per 100 people , mass shooters per 100 million people).
United States (85, 28)
Canada (26, 9)
Afghanistan (2, 20)
Iraq (37, 4)
France (35, 15)
Yemen (55, 40)

Ask the students what they notice? what do they wonder? As the teacher write down everything they say. One question I have is what is the data saying? Is there a different way to represent the data?

Give the students the following information:



What do they notice and wonder now? What has changed? You can show them mapping as well, but eventually you will need to introduce other things, but the last one is the graph from The New York Times.




How do the three representations differ, do they all tell the same story? Do some tell the story better? I'm not sure if this is the way to start the year out, but nothing is perfect. I want students to feel that there is some context to mathematics other than its day 1 therefore we do lesson 1.

Is it Linear? With Fidget Spinners

Fidget spinners are all the rage right now. At my school I would say maybe 10% have them, one thing with fidget spinners that my students are using right now is an app called Finger Spinner. The point of the game is you get 5 tries to reach the highest number of spins. With each number of spins you get certain coins which you can upgrade your fidget spinner such as increasing speed or greasing the wheels.

Introduce the topic is by having out an actual fidget spinner and spin it twice and ask the students were there the same amount of spins both times? Some will say yes since it is the same fidget spinner and some will say no, because it determines how hard you spin it.

Then do the same thing with the app, projecting it on the whiteboard. Spin it once and then twice. Since it counts the number of spins it will be easier to ask if they were the same.

The next question is how many times would I have to spin it to get to 100 spins?

 

I have been using this handout from Estimation180: http://www.estimation180.com/blog/estimation-180-handout to have students record their answers in one place.

I want students to look at the data and see that each one is about the same in number of spins and looks linear. Using the whiteboard I want to project some student work start from the basic ones to the student work where they have a linear graph sketched (w/ average). Then have the student explain the processes they went through.

The last part is to get students using the app. My question to them is once you upgrade a part of the fidget spinner does it stay linear? What if you keep upgrading? What if you alternate upgrading? How does it effect the number of spins?

My goal next year is to incorporate more modeling and more hands-on uses of math concepts.

Financial Literacy in Math

Financial literacy is the ability to understand how money works in the world: how someone manages to earn or make it, how that person manages it, how he/she invests it, and how that person donates it to help others.

I believe that my past Algebra 2 students understand the material.  I don't think that they could go out and apply those concepts (for example in a job environment.)

Looking at exponential functions, for example, students can look at the depreciation of a new or their old car in terms of re-sale value.  Students can enter the data and draw a scatter plot on a sheet of graph paper.

If students didn't have a car they could search for one.  For example I searched my wife's car a 2015 Chevy Cruze.

The MSRP is $16,170

After the first year it depreciates: $7,904
After the second year: $1,200
After the third year: $1,000
After the fourth year: $875
After the fifth year: $675

Students could then plot this and look for the exponential line of best fit through that data on Desmos. You could then prompt follow up questions, what will the value be 8 years from now? Is $8,456 a good price now for a 2015 Chevy Cruze?

For slope and finding slope of a line, give them real-world data to extrapolate.  This data below came from the Nebraska Department of Roads.

What is the slope of each year from January to May?  What is the slope of each year from May to December?  What causes this?

What do you expect June to look like? Can we determine what the price will be December?

Having students know the concepts is one thing.  Having them use the concepts beyond the classroom is what we are looking for as math teacher.