Find Student-Taught Math Lessons and Riddles on Padlet #StudentTeachingStudents

I blogged about my Ted-Ed Project here, but I used Padlet to create a visually pleasing and easy way to sort the student-made videos. Click below to get a glimpse at all of them. 

Hello my name is x+3--activities for teaching polynomial and rational functions, by A. Mosaad

This is a quick post to tell you all about an easy and fun activity to use for polynomial and rational functions. I learned of it by attending a workshop of the same name as the title at the Rutgers "Good Ideas in Teaching Pre-Calculus and..." workshop that I also blogged about here. Here is the abstract:

It began with the presenter, Amro Mosaad, giving everyone a nametag with a factor on it, like “x-1” and x+3” and have them pair up and give them one of the following worksheets. They have many tasks, such as find the zero and graph their product and then graph their quotient...this is so good after you’ve taught polynomial graphs and rational functions. They can switch papers with another group and have them check work on Desmos.

This can also be done with zeros and complex zeros. Amro said, "Find your twin," meaning, find your complex conjugate.

Amro also suggested the "mystery polynomial" activity: Get into groups of 2 or 3 with no one you have been in a group with yet. Give your group the polynomial you just came up with and your “name” and your new partner(s) that you never worked with before will need to figure out who your other partners were. Awesome!

Here are the links. Thanks to Amro for sharing them with me!

Rational Functions activity
Polynomial Functions activity
Complex Zero activity

I thought this was a great formative assessment activity.

One attendee I was working with suggested that students check work on www.mathway.com wow!! I have never seen this website before, but I will definitely be using it in the future!

Desmos to the Rescue

It's midterm time here already, and I am tutoring a student in Pre-Calculus Honors. He texted me this question from his quiz last night when he was studying:

Given that the point (-3, 6) is on the graph of f(x), where does this point move to 

given that h(x) = -f(2x+5) +3?

He had a wrong answer, and the teacher corrected it to (-11/4, -3).

We took horizontal stretches PLUS translations out of the curriculum except with trig (which we teach in a different way, using quarter- and half-periods) and except for in Pre-Calculus Honors. So I was trying to remember my way of doing it. 

I factor out the 2 to get: h(x) = -f(2(x + 5/2)) + 3, and then make a rule. (x,y) --> (1/2x - 5/2, -y+3). Essentially, after explaining and using Desmos for discovery, students see that what happens on the outside of the function happens to "y" in the correct order (i.e., multiply by a -1 and then add 3--or reflect over the x-axis and shift up 1--see the "blue"), and what happens to the "x" happens oppositely (i.e., divide x by 2, then subtract 5/2--see "purple)"). So I took (-3, 6) and substituted into my rule (1/2x - 5/2, -y+3) and got the transformed point (-4, -3). Not the x-value my excellent colleague got. 

So of course, I think I'm wrong. I text two other colleagues in the department. They both get x = -11/4. I am really confused at this point. I remember another way a former colleague used to teach the horizontal transformation. He would say, let x' be the transformed value, and let x be the original value. so 2x' + 5 = x and solve for x'. You get x' = (x-5)/2. This is the same thing that I got, but I just distributed the 1/2. So I'm really thinking I'm right because I got my answer two different ways. Still, for my highly esteemed colleagues to all agree on a different answer...I'm stumped. They are, too. 

So out comes Desmos. The first equation I enter is f(x) = -2x, because the point (-3 6) lies on the graph. The next equation I enter is h(x) = -f(2x+5) + 3. .

And now I have proof that this method is correct. The orange point is not on the transformed function, but (-4, -3) is. 

So thanks, Desmos. And it's not about being right, because I would have been satisfied knowing I was wrong, too. It's about being able to prove how to do it, so that we can collaborate on the answer and determine, perhaps the best way to teach it. And to know that at 10 pm, we can sleep peacefully and not stay stumped :)

Even though I was right, I find this one of the most difficult topics to teach. Students can understand it momentarily, but they really can't recall it after the test. If anyone has any ways that work for them, please leave a response at the bottom of this post. I would love to hear it!

The Unit Circle of Life

Math~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Our math department is divided. Some like teaching the trig ratios with the Unit Circle, some don't. Since I hate  conflict, I teach both methods--one where students will draw a triangle in a quadrant and use what they know about 30-60-90 or 45-45-90 triangles to solve, and one where they learn the first quadrant of the unit circle and then reflect into other quadrants to get the answer.

For years, I have assigned a unit circle project, where students design a unit circle to wear or bring with them all day...the crazier, the better. I give bonus points to the top 3. Some of my favorites have involved printer tattoos that students wear, Shrinky Dink jewelry, Unit Circle Togas...so many more...

But one day earlier in the year I came across Unit Circle Art, a blog by Miss Rudolph. I loved her guidelines and rubric, and I used it in my Pre-Calculus and Algebra 2 Honors classes, and I have never been more pleased with the results. So this year, students were told not to use pre-made circles...that was a game changer. In the past, I have gotten some very lame projects where students cut out unit circles and paste them on circular shapes. I also said that they could not use the site http://www.embeddedmath.com to have a pre-made circle. So students worked really hard (for the most part...and if not, their grades suffered.) Here are some of the best ones.

Coolest thing ever!!

The Unit Circle of Life!

 

The rules were: Do not use a circle to begin with, but you may draw a circle. You must include degrees, radians, sine, cosine, and tangent of each special angle. You may not use a pre-drawn unit circle. According to the blog mentioned before which I pinned on Pinterest here: unit circle project, and I used Miss Rudolph's rubric exactly.

VERTICAL TEACHING:
I have been fortunate enough to have a new classroom since spring break, where 3 walls are wallpapered with white board paper. I tried to think how I could do something different after teaching the unit circle that would involve students going to the board. On the fly (usually the best way it works--organically), I asked students to go to the board in pairs, each having a different marker. Here were the directions:

partner 1: draw a circle
partner 2: draw the lines
partner 1: label quadrant 1 in degrees
partner 2: label quadrant 2 in degrees
continue for quadrants 3 and 4 alternating, and then continue for radians, (cosx,sinx) and tanx

The kids were definitely talking it through...it was a million times better than when I have had them fill in the unit circle on their own in the past...they loved drawing it on the board, and they helped each other and talked it out. Students that were confused had a partner to help them. If a pair was stuck, they could look at what another pair was doing.

Geek of the Week competition

My students love vying for Geek of the Week, and they asked to see who could draw the unit circle fastest...of course we had to use the Theme from Rocky...I got this idea from a blog but I can't find it...if you know where I got it from, please let me know so I can give credit to the owner!

Play~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Mu Alpha Theta States was so much fun...the poster competition was "Math and Movies." Seven girls worked so hard to create this poster...some stayed up all night, in fact! We did not win, but they definitely won in my eyes! It's a combination of Mean Girls and Good Will Hunting and DaVinci Code.

Eat~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I was told by family members that this was the best dessert ever, so here is the recipe of Flourless Chocolate Cake by King Arthur...very rich and decadent!

~Lisa