Sunday, December 27, 2015

30 Days of Tech and...

Thanks to Meg Craig for this idea, which she posted about here.

With the start of the new year, here are 30 days of tech and..., to try something new. I'm hoping to blog this out to the faculty once we get back from break. It's all different levels, so even if you have been on twitter for years, there is something for everyone.
Here is the actual link: Link for 30 days of tech and...

My Log B(log)

I'm starting logs in my Algebra 2 Honors class upon return from winter break. There's been a few great posts that I've found on these blogs from Wendy Menard, Julie Reulbach, and Kate Nowak. They are all fantastic, and I've used much of their ideas in my here's notes, links, etc. for exponentials and logarithms, that could go with any text, though I use Larson Algebra 2 and Trigonometry, 9e. Keep in mind that I teach in 90 minute blocks. Each note packet is for a day, but I haven't used them yet and so some could go over. These are linked to my dropbox, so you will need an account to open them.

--First, I am using this Desmos intro to exponential growth and decay. This is a play on the doubling pennies idea and the m&m's exponential decay problem along with graphs.

Then I will give out these Exponential Notes.

When I find the time, I am going to throw in these two videos:

-- a Ted Ed video on how many folds of paper can get you to the moon

-- a Mythbusters video on paper folding

On Day 2, I will give them these Intro to Logs Notes.
--includes the Need for Logs (click on Wendy's and Julie's link, above)

--includes the fun puzzle from Kate (click on her link, above)

My plan is to use this Kahoot! as a good brain break that day.

On Day 3, I will hand out Laws of Logs Notes (nice way for students to figure out the laws in groups, by Kate.) We have a week of immersion before these notes (and no class), thus the big review in the beginning.

On Day 4, they will get A Huge Review of Logs and Exponents (I haven't checked answers! The last half is a review sheet that I once found, but I don't know where to give the credits to. The latter is for them to do on their own, if they want to)

What did I miss? Please send anything my way :)

Wednesday, December 23, 2015

The 30 Day Happy Teacher Challenge from Presto Plans

I came across this on Pinterest yesterday and decided to give it a try for the 30 days after we get back from winter break. Maybe you will too? It's also a free download here.

Then I saw it on twitter, here...

I am going to give this a try. If all goes well, maybe we in the MTBoS can come up with another 30? Or maybe we can start it all over again. 

Thanks, @prestoplans!

I hope you have a fantastic rest of the year, and an even better 2016.


Thursday, December 17, 2015

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!

Saturday, December 12, 2015

Math Club T-shirts Designed by Students; We've Come a Long Way in 5 Years

Every year, our math club and math honor society, Mu Alpha Theta (MAO), designs a T-shirt for the year. When we compete in South Florida, we enjoy wearing them and looking at all of the other designs that the other schools have made.

Yesterday, we unveiled our secret design, created by 3 seniors:

This was a play on Watch Me Whip, Watch Me Nae Nae, which is a popular song and dance out right now. So cool when on twitter, @pamjwilson tweeted this within days after the students and I came up with the idea "watch me flip, watch me translate." 

Great minds think alike. 

My students and I whipped and nae-nae'd for a while with excitement when we finally came up with the idea. OK, so they whipped and nae-nae'd...I would try, but I can't dance. At all. (My friends always tell me "less is more," but I don't get it, so I often refrain...especially in front of students!) 

We are lucky to have talented artists in the club, and that we have a great local company that makes the shirts for us at an affordable price. The color is beautiful and the shirt is soft this year, as we used a different brand. We always have our school mascot, Scotty, on the shirt in some way, and we usually take some pop culture idea and go with it. 

Last year, a senior came up with the idea "AB/BC" (Calculus), a play on words with AC/DC. We had SO much fun coming up with mathematical names for their songs. Here's how that shirt came out: 
In 2013 - 2014, we did a parody with Monsters University: 
Here's the artist's rendition..and how it turned out...we also make a digital scrapbook each year...the cover is the bottom left picture.
This was on the back of the T-shirt. At that time, we had student names on the back at that time, which I did not add.
In 2012 - 2013, "Oppa Gangnam Style" was big. My son, a freshman at the time, came up with idea "Cosine Tangent Style." The math club went to the mall after a competition once, and we were stopped constantly. People wanted to buy our shirt!
And below is our first shirt--we have come a long way! It says, in math symbols, "I'm Mathy and I Know it!," a parody of "I'm Sexy and I know It!" with a line from the song on the back, "I workout"...Problems.

We never know what we will come up with until we meet with the kids and come up with an idea after the summer. "Taylor Swift Series" was a close one this year, but I'm glad we came up with something specific to 2015. 

If you are not part of, which I have written about herehere, and here, what are you waiting for? It has made a huge difference in my life as a teacher, and I think it has made a difference in the lives of my students. Maybe it will make a difference in your and your students' lives as well. 

Friday, December 4, 2015

Got time to do something outside the box? Ted-Ed is the answer!

I have posted about the Einstein problem before, but this time it just got real!
Dan Van der Vieren (Mr. VDV) is the teacher who recently Skyped with my class twice for an hour and a half each time just so we could learn how to solve the Rubik's Cube (by the way, 63% of us in the class can do it without looking at any video or notes--so far!) just created an awesome Ted-Ed video called "Can you solve 'Einstein's Riddle'?"

It is awesome. I have given this problem before, but this was a great little video that was very fun to watch. The characters, script, and editing make it all the more fun. I played it this morning for my students and paused at the exact moment so they could begin working. This is NOT a puzzle for the meek...but it certainly is a fun one. I don't know if it's true, but the internet boasts that only 2% of people can get the answer to this riddle.

Here's the version I have given:
But Dan's twist is that the fish is stolen...who took it?

Here's some of my students' work:

There's more, but I don't want to show you the answer. It will be fully explained, after the pause when students do work on the problem. It's a great activity, but I do recommend a full class period. If a student wants to give up, do it with them on the board...very fun!!

Great job, Dan!

I blogged about the bridge riddle here--we love Alex Gendler and the narrator! It's another great problem.

And my students enjoyed this variation on the Prisoners Hat Problem.
I hope these keep coming. They are fun and counterintuitive in many cases. They open my students' eyes to problems that I was exposed to at some point, but that they have never seen. I know your students will love them as much as mine did.