BTW: I have been snooping around on Mathalicious for a while with the free lessons, but after attending the NCTM conference in Baltimore and attending the Mathalicious presentation, we were given a username and password to use for a month. Score! You cannot get me off the site now. Hmmm. I still need funding from my district for the rest of the year.
Back to my post. In my Algebra 1 classes, we finished solving multi-step equations and I thought this lesson would be a perfect wrap-up to it all. The lesson starts by giving the students an opportunity to discuss different traffic violations and then moves on to the formal lesson. I love they there seems to be some hook for each of these! Next, it gives the students information about how the fine for speeding tickets are calculated in Virginia. What I love about the next part is that it doesn't give boring word problems to solve, mathalicious gives videos and pictures where some piece of information is missing and the students have to solve. I like that the question is intuitive rather than forced.
This lesson took about two days and we had some quality discussions about speed, equations, flow of traffic, fairness, and even a story about a woman who got a speeding ticket while riding a horse.
When the lesson was over, I felt that something was missing. I believe that the information in the lesson was real and not contrived, but I'm not sure that the students were completely convinced. I have a bff since 7th grade who happens to be a police officer (Sergeant actually) who would have information for us for Pennsylvania (where we live). So, I call him and he is more than willing to be of assistance. He kindly wrote out 3 fake speeding tickets using PA information.
You can view/download the fake speeding tickets here. (Original Speeding Tickets)
You can view/download the fake speeding ticket here. (John's ticket is modified for linearity)
To begin, I gave the students two of the fake speeding tickets. Jane and John's. I asked students to look at the information for how fast the person was driving, what the speeding ticket was, and the correspond fine or total due. Then I gave them the information for one fake Samantha Miller who was driving 67 mph in a 45 mph speed zone. What would her total fine be?
I was a bit skeptical about this because we have never talked about writing an equation from two points, we aren't even close to that. I figured the worst that could happen is that I have to hand-hold them through the entire process.
Here is the work of one student. When she excitedly jumped out of her seat to volunteer to show her work, her neighbor say, "Gee, you never want to go to the board."
Some students started by finding the difference in Jane and John's information. You can see one students work for this above.
One group of students decided to try guess and check, starting with the mph over. They estimated that it would probably be a single digit number and started with 8. They kept working until they found that the base fees were the same and then knew they had their answer.
Another group of students decided to try guess and check, starting with the base fee. Since we already completed the VA problem, they assumed that the PA base fee was close to that. They spent about half the period with guess and check and were unable to find a solution.
In Pennsylvania, when you are between 16 and 25 mph over the speed limit, the base charge is $122. For all speeding the fine is $2 for every mile per hour over the limit. *Note* I did have to fudge some information (the base fee) on the students papers to make sure it was linear. Don't worry, after the lesson I told them the truth.
When we did the Mathalicious activity, we found that in Virginia, speeders are charged $6 for every mile per hour they are over the speed limit, plus another $61. When the students were working with the PA information and found that speeders are charged $2 for every mph over the limit, one student said, "I'd rather be speeding in Pennsylvania." That's when it hit me that this problem wasn't over yet. We have the opportunity to revisit this in our next outcome that deals with variables on both sides of the equation. And then AGAIN when we begin talking about inequalities. And AGAIN when we study absolute value equations and inequalities. Whew!
Variables on both sides: At what speed over the limit do you have to drive to get the same fine in VA and PA? 6x + 61 = 2x + 122
Inequalities: For what speeds over the limit will your fine be higher in VA? 6x + 61 > 2x + 122
Absolue Value Equations and Inequalities: Since the students and I already had a conversation about flow of traffic, the idea is in their heads. Perhaps we could write our own speed maximums and minimums using absolute value equations and inequalities.
Don't forget Algebra II and Piecewise Functions. The base fee of $122 is only for speeds of 16-25 mph over the speed limit (Do I hear Domain and Range for Algebra I?). There is a different base fee for other speeds as well.
Back to Mathalicious:
I am so excited to have a problem that I can revisit again and again with my students. It will certainly help with making connections between different math topics that so many students assume are isolated symbol manipulation punishments.
I found that I kept forgetting to talk about certain things while on a particular slide in Mathalicious. Because they were worthy conversations to have with the students I would continuously back track in the presentation to have those conversations. It was annoying to me and I felt so unorganized. Therefore, I decided to create note cards for each slide. I do like the Lesson Guide that comes along with each lesson, but I need the note cards to keep myself a little more organized.