#16

On Monday I'll start my 16th year of teaching.  Where has the time gone?!?  I honestly can't believe I'm that old!

I'm going to continue using Standards Based Grading and Interactive Notebooks this year.  I'm also going to get serious about my flipped class.  I kind of dropped the ball on it last year - I just took on too much and something had to give.  I'll finish my Master's degree on October 26th, so I'm hoping I'll be able to do a better job keeping up with the videos.  When I quit making the videos last year my students would ask if I was going to start back up again because they loved them!

I've been crazy busy this week with staff development and trying to finish up my classroom makeover, but I thought I'd go ahead and share a couple of things.

First off, my classroom!  It makes me so happy to walk in and see my chevron wall and cheery yellow paint.  And I finally had them replace my stinky dirty carpet with tile.

A close up of my desk

I'm going to spend the first few days of school setting up Interactive Notebooks and introducing my students to my TI Nspire calculators (I'll also be talking up my beloved Desmos).  Here is a basic calculator reference sheet I made for their notebooks.  I plan on making calculator guides like this anytime they learn how to do something new with them.

I really wanted to buy a set of radian protractors for my classroom, but I just can't spend the money on something that we really won't use for long.  Luckily inspiration hit and I came up with my own version printed on old transparencies (I mean who even uses an overhead projector anymore?!?).  When we first start talking about radians and I'm trying to get them to understand what a radian is and how it relates to degree measure I'm going to have them use these to measure and draw angles in both radians and degrees.  I'm pretty stoked about it!  I made a little pocket by sealing an envelope and cutting it in half.  They can store their protractor in the pocket.  It's just so cute!

Polynomials and Rational Functions

My polynomials and rational functions unit has passed me by and I didn't stop to post about it!  So here it all is in one post.

I started polynomials with the end behavior activity that I blogged about before.  After the activity, I gave them this foldable to summarize what they'd discovered:

End Behavior Foldable

The next day I gave them this to put in their notebook and we did this activity.

Zeroes and Multiplicity for INB

The next day we did this worksheet

Multiplicity Worksheet

We then took our first assessment over polynomials.  Up to this point, all of the polynomials we had worked with were already factored and had rational zeroes.  To prepare to work for polynomials that weren't factored and that had irrational or imaginary zeroes, we took a day to talk about synthetic division (something they have already done in Algebra II).  I gave them this for their notebook and we did a worksheet from Kuta over synthetic division.

Synthetic Division Handout

Next I gave them this to put in their notebook and we did a worksheet from my Nasco Joke Worksheet book:

Finding All Zeroes of a Polynomial

We then took our second assessment on polynomials.

Next up was Rational Functions.  Day 1 was a foldable and a little worksheet to practice using the foldable.

Rational Functions Foldable

Rational Functions Flower Activity

Our second day with rational functions found us doing this activity I got from Rebecka Peterson.  I <3 Desmos!
Rational functions day 3 was this matching activity I found on Teachers Pay Teachers.  Students worked in pairs to match up all of the cards.
Day 4 was this asymptotes sudoku puzzle, also from Teachers Pay Teachers.
Day 5 - Rational Functions Assessment

So there's a quick and dirty rundown of what's been going on in my class the last couple of weeks.  I REALLY like how I did this unit this year.  With the graphing technology available to students, I feel like things like Descartes Rule of Signs and the like are just outdated and unnecessarily confuse what should be a simple concept like the Fundamental Theorem of Algebra.  My students really seem to get that the number of zeroes a polynomial function has is determined by its degree.  They get how to determine end behavior and they get what effect the multiplicity of each zero will have on the graph.  Their first line of attack in finding zeroes is to use graphing technology and then they know they can use synthetic division and the quadratic formula if they can't get the whole picture just from their calculator.
Following polynomial functions with rational functions let them further see the value of being able to find zeroes of polynomials as the zeroes of the numerator and denominator are used to find holes, x-intercepts, and vertical asymptotes.  They were such pros at finding zeroes at this point that analyzing and graphing rational functions was a piece of cake!

Converting Polar Coordinates and Polar Graphing Foldables

Converting Polar Coordinates Foldable

Polar Coordinates WS

Polar Graphs Foldable

I got this worksheet from the Master Math Mentor website.  If you've never check it out, do it!  He has an entire Pre-Cal course complete with notes, assignments, quizzes, and tests and it's really good!

Polar Graphs Matching WS

Zombie Attack - Integration using U-Substitution

The fabulous Janelle Graham over at The Dog Days of Math posted this Zombie Attack power point game on her blog.  She was kind enough to e-mail it to me and I modified the questions to be about integration using u-substitution.  I'm so excited to try this out with my AP Calculus students today!

Zombie Attack - U-Substitution

Intro to Polar Coordinates

We first made this foldable and worked out the examples together.

Polar Coordinates Foldable

I then had them try figuring out a few coordinates in this Geogebra Activity.

Once they felt comfortable enough, I turned them loose to play Polar Coordinate Battleship with a partner.  I was shocked at the number of kids who had never played or even seen the board game battleship before, so we had to take a few minutes to explain the basics, but then they were off.   Calling out the coordinates was a slow go at first, but those who stuck with it quickly got much better at it.

Polar Coordinates Battleship

Kahoot!

I recently found this amazing website called Kahoot!  Kahoot! is a game based classroom response system.  You can create your own quizzes, surveys or discussions and your students can access them on their device.  It's completely web-based so it works on all platforms and the best part is it's free!  Don't have time to make your own quiz?  Browse the over 30,000 public quizzes to see if there's one that will work for you.  I made my own Kahoot! over finding area of oblique triangles and my students LOVED it.  Once you create your own account, you can play my Kahoot! by clicking the link below:

Area of Oblique Triangles Kahoot!

Area of Oblique Triangles Foldable

Area of Oblique Triangles Foldable

Flippity

I just discovered this amazing site called. Flippity.  You can use a Google Docs spreadsheet to create a set of virtual flashcards!  Here's a set I made:

Flippity AP Review

And a link to the virtual version online: Flippity AP Review

How cute is that?!?

Riemann Sums Foldable

Riemann Sums Foldable

Biorhythms

This is another activity we did to reinforce trig graphs.  It was fun, the kids loved it, and I did it on Digital Learning Day, so that was a plus!  I originally only planned on doing it in my Pre-Calculus classes, but my AP Calculus kids heard about it and insisted on doing it during their class, too!

*UPDATE - the day after we did this was the first day of the Winter Olympics, so I had my students chart the biorhythms for several different athletes. We're going to monitor how those athletes perform during the Olympics and compare their actual performances with their biorhythms.

Biorhythms Activity

Here's Shaun White's biorhythms for February 2014.  The red line marks the day he got 4th in the half pipe.

Ferris Wheel Math

I'm having my students relate what they've learned about amplitude, period, phase shift and vertical shift to a real world scenario involving ferris wheels.  I started  by having them read chapter 15 of the book, The Joy of X which I've blogged about before.  It's a chapter about the ubiquitousness (is that a word?) of the sine curve.  It's a great read!  We then focused in on the example of the Ferris wheel that he gives in the chapter.  I started by working through the first problem on the worksheet with them.  I then turned them loose to do the card match and work the second problem.  The conversations they had and the observations they made were amazing!  And I love love love the card match - it really forces them to see the connection between the graphs, the equations, and the descriptions of the Ferris wheels.  One of the graphs doesn't have a matching equation, so they have to write that equation themselves, and two of the descriptions get used twice, which brings up a great conversation about how that can happen.  I loved this activity!

Ferris Wheel Activity

Note - I didn't realize that the problem was in meters, so on the last question you can either ask them for meters/min and km/hr or you can have them change meters to feet in the problem.  Sorry about that!

Ferris Wheel Card Match

Basic Integration Rule Foldables

Foldables I made for Basic Integration rules.  I had a mistake on the power rule, but I fixed it in the digital file posted below.  Before I gave them these, I had them intuitively find the integrals of some basic functions.  They were able to figure the power rule out on their own, which was awesome!

Basic Integration Rules Foldable
Trig Integration Rules Foldable

Graphs of Sine and Cosine Foldables

Foldables I made for graphing Sine and Cosine.  I'm not completely happy with them, so I'm sure I'll modify them for next year.  I'd like to add a description of what amplitude, period, phase shift, and vertical shift actually are in terms of how they're represented on a graph, not just how to find them from an equation.

Graphs of Sine and Cosine Foldable

Translating Sine and Cosine Foldable

Function Behavior Card Match for AP Calculus AB

I love these card matching/sorting activities! The discussions that go on between students as they try to figure things out are amazing! This one has students match up four sets of cards. When they're done, they have 8 sets containing 4 cards each - 1 function graph, 1 derivative graph, 1 function description, and 1 derivative description. It's a great activity to reinforce the vocabulary and basic concepts associated with functions behavior. I like to use it before I introduce the algebraic approach of the First Derivative Test.
Function Behavior Card Sort Activity

Function Behavior Foldables for AP Calculus AB

We're starting Function Analysis in my AP Calculus AB class.  Here are a few foldables that I came up with to help students keep things straight.  I've included links to the PDF's below.

Increasing/Decreasing Foldable

Concavity Foldable

Max/Min and POI Foldable