Angry Parabolas

As a way of connecting quadratic functions to something my students would  be familiar with I decided that we should play a game. Not just any game. I wanted to focus on one of the most popular games available for mobile devices. So I hooked my phone up to a projector and fired up Angry Birds. Most, if not all, of my students were familiar with the game and couldn't believe that we were playing it in math. I heard comments such as "Are we really going to play this?", "Is this a joke?", "What's the catch?", "You're going to link this to math aren't you?".  If nothing else they were interested in what the link to math was.

I had a couple of students come up and try the game. Once they had a chance to play I gave it a try and fired the bird high into the air so that it made a beautiful arch. I didn't hit a single obstacle and my students thought I was completely incompetent at the game. They sincerely offered suggestions about how I could improve. Eventually they realized that I had no intentions of hitting anything. I explained that the interesting part about the game is that it leaves behind a nice trail showing where the bird had been.

I took a screen shot and fired it up on the computer. We labelled the parabola and discussed some terminology. I didn't feel the need to write out any definitions. They seemed to get the ideas. It was funny to hear students helping each other by referring to the game in their explanations.

The game provided a good introduction to the unit and I wondered how I could take it further. My first thought was how cool would it be to have students write a simplified version of the game? They would learn the math, a whole ton of problem solving and some programming.  I wasn't prepared to do this since I thought it would take up too much time. I may however consider using Sam Shah's technique of modifying a program in the future. Perhaps I could write the program and they could modify it so that it worked properly.

My second thought was to have students determine the equation that modelled the path of the bird. I created a Geogebra file with the image as the background and a grid laid on top of the image. I had students determine the equation at their seats first, then I had a student come up to board and move the sliders around to reveal the equation.You can find a link to the Geogebra file here.

I'd like to find a good way of determining the equation of the function that will allow the bird to hit a certain location and use this information to improve game play. I can see some technical challenges here. I'll have to think about this for next time.


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Quadratic Functions With Video

There are some lessons that I know students are just going to hate. Often times they'll put up with it but I feel like I'm doing them a disservice. I want to find a way to make these lessons more engaging.

One such topic is having student determine the function that models some form of quadratic data. I find that many students get lost in the wording of such questions and get bogged down by the details. I thought I would introduce a video to see if it helped with their understanding. I showed my class the video below and asked them to determine the function that models the height of the ball at any given time.

I played the video on the interactive white board and had a student come up to the board and put dots on the board to show the location of the ball. Once the video was finished he drew a smooth curve through the points. My question to the class was how do we determine the function that models the situation? I was amazed how engaged the students were. I received a ton of answers: We need to find the vertex. We need a set of axes. We need the 'a' value.

The video and the one question I asked produced the buy-in I was after. It was great. The nice thing about this lesson is that later in the unit when students struggled and asked for help they would say things like "Oh right, this is what we did with the video isn't it?".

As an added bonus we were able to practice a couple of times just by shifting axes around, which also reinforced the idea that the 'a' value was the same because we were talking about the same curve.

I realize that the problem is still somewhat contrived. Ideally I'd like to have a situation where students feel compelled to solve the problem and end up using the math to do it. Nobody really wants to know the function that models the path of the ball, but it was a situation they could relate to and was a step in the right direction.

How Not To Teach Statistics

I had to teach statistics to my unmotivated grade 11 students. I thought I'd try to make things interesting. Textbook questions for a unit like this are typically boring and unrealistic. I decided that as a class we would create a survey that was interesting to teens, post the survey online, have everyone share the link then analyze the results. To me this was a good way to make the material interesting and relevant and was also a way to teach some digital media skills.

We created a Google form that would house the questions. The survey answers we're automatically dumped into a spreadsheet, where in theory they could easily be analyzed. I shared the link to the survey with my students through Moodle and they could share it using their preferred methods.

The trouble with data sets is that they are rarely very clean. Many of the questions generated by students in the class used a scale (poor, good, very good, excellent). This data was clean and would provide good graphing opportunities. I also wanted students to have numerical data. How else can you find measures of central tendency or measures of spread?  We did create some questions where the answer should have been numerical (How many hours of television do you watch per week?). The trouble is that many of the survey participants either didn't enter a number or entered numbers that were unrealistic. After the first day of releasing the survey we had 16 responses, six of which were unusable. I decided to scrap the project and we headed back to the textbook. We discussed the problems with surveys so that we could all learn from the situation.

I'll have to rethink this activity for next time. Ideally, we'd have a Wii in class and could generate a ton of data for a given game: scores, time played, levels reached, points/second, player biographics, etc. We could then analyze that data. Add a Wii to the wish list.

Mortgages

While listening to the radio last night there were a ton of stories about the hike in long-term interest rates here in Canada. These stories generated a lot of buzz around mortgages. Many experts were saying that homeowners should lock their variable rate mortgages into a fixed rate mortgages.

One of these brokers caught my attention. He suggested sticking with a variable rate but making the payments as if you were on a five year fixed mortgage. This would pay down principal a lot faster. Here's the math...He said that on a $300 000 mortgage this method would result in a savings of $8000/year. My first thought was 'I wonder if that means that on a $150 000 mortgage your savings would be $4000'. It was a very simple question as I was driving, but I quickly realized how useful it could be when talking about exponential functions and to see how much students have understood. It's also a nice way to show students how the math they're learning relates to everyday life.

The question could simply be: Would a mortgage of $150 000 (or $600 000) result in a savings of $4000 (or $16 000)? Why or why not?