At Twitter Math Camp this summer, I got the opportunity to work with a small group of amazing Algebra I teachers on planning a linear functions unit. While the crazy of school has thwarted me from following through on all the plans, I still got in a thrown together version of one today.
So, the idea was to compare pizza companies and see who had the best deal. But each company provides us with different info about their prices. Check it:
To get things started, we all did Pizza Hut as a class. We decided on the function c(t) because cost depends on toppings. We wrote the equation c(t) = 10 + .85t. We used the function to generate a table using the domain [0,5] because some people might want cheese pizza and 5 is a good max number of toppings. Then we graphed y = c(t) using the same domain and we were done! They did most of the work, I was just there to prod them along if they didn’t know what to do next.
Next, I told one half of the class they were to be my “Papa John’s Experts” and the other half they were my “Domino’s Experts”. If someone had an issue figuring out one of the representations, they were to see an “expert” from the other side of the aisle. It worked great most of the time; they found help on their own when they needed it.
I thought the best part was finding the cost per topping for Domino’s. Since they were only given two points, it was really like asking them to find the slope of the line between (2 , 10.7) and (5 , 14). But in context, it was not a scary math problem, just “well, there’s three more toppings there and it costs $3.30 more, so it’s $1.10 per topping”(their words). Later I showed them (out of context) that they had done the good ol’ (y2-y1)/(x2-x1). One kid even seemed mad that I had “tricked” him into calculating slope, as if he was proud of not being able to do it and I ruined all that for him. Weird.
Note: It is fun being able to refer to the y-int as a cheese pizza all day! (Also, it was a great follow up to the 100×100 burger problem from Kaplinsky in which the y-int is a bun and dressings.)
Next class, we’ll choose a company and make whiteboards to defend the choice. Is Domino’s really always the cheapest? Is cost all we care about? Tune in next time to find out. 🙂
Oh yeah, and I started class with a pizza themed counting circle! We started at 10.5 and counted up by 1.25 at a time. It was a good one, it went pretty fast. And we did the “toss the ball and make a prediction” game, where I call “stop” and whoever has the ball tosses it across and we have to predict what that person will say. I ❤ Counting Circle!