Got a good project going and I'm curious to know what you came up with. As a suggestion what about having students classify functions vs non-functions? Create an input output table of cars/vehicles driven by age groups. And then determine to see if there's a correlation between age groups and insurance rates. Is this situation a representation of a mathematical function? What model(s) would you use to describe this connection? Also, have students investigate traffic and times in an intersection. What about some connection between students that buy lunches in hash lines and menu items? And then there's periodic functions.

Alicia G

01-16-2013 09:50 PM

When I teach functions, I draw a big box on the board, complete with gears, dials, needles, and buttons. I show a big funnel on the left going into it and then there's a little slide on the right that the empties out. The input (parameter) of the function goes "in" the function and the output (result) comes out the slide. I explain that there are workings inside the box that I drew that does the same thing to every input ("every legal input" is more accurate, but that's not the purpose here). I put a 10 in and an 8 comes out. I put a 85 in and an 83 comes out. Then, I ask, "If I put in a 54, what comes out?" And they shout out "52." I tell them that my machine is a "subtract 2 machine" and it's a function. I emphasize that for any value going in, there is only one value of the output. Now there may be more than one input that causes the output, but there is never more than one output for a certain input.

What sort of functions can you show?

I like Paul's conversion idea. This can be done with distances, temperature, etc.

How about 25% percent-off sales? You put in $100 and out pops $75.

Or, sorting girl and boy? When you put in Tom, out comes "male." When you put in Sally, out comes "female." Put in Peter, out comes "male" again. It's okay that two (or more) inputs spit out "male," but any one input can only be male OR female.

Or a letter-grade assigning function? You put in a 53 and out comes an F. Put in a 94 and you get an A.

Project? A quick one would be for the kids to dream up functions and have kids guess what the function is.

GPaulC

01-16-2013 09:30 PM

Maybe the function that changes degrees F to degrees C? Maybe the function that changes Kilometers to Miles? Maybe cut and paste the last month of data from, say, Google Inc. stock or equity value for each day of the month in Dec? Then compare that to a "wild" sort of penny stock, so students can see a "stable" function vs. an "unstable" or erratic penny stock equity value that changes much more drastically? Just draw a F(x) "box" and talk about how the Market opens in the morning and closes at the end of the day (input price, output price--however this may be confusing if the stock changes in overnight trades). If you find nice stock charts that are approximated by simple linear or second order polynomials, that might be cool.

There is always simple projectile motion, if you give them the equation and talk about angle of shot, initial velocity and vertex or highest point reached (maybe too complicated?). I bet there is a youtube video on this, and maybe an applet to play with by changing the initial values or constants.

Maybe have students take data in the LUNCH LINE--say, cost of meal vs. a "popular vote" on the "most enjoyable" OR the "most nutritious" lunch (main course, two sides, and drink)--and plot these two functions using the cost as the ordinate.

PT

01-10-2013 05:52 PM

We have just finished 2-step equations/ functions/ graphing functions, and I would like my kids to see how functions work in the real world. Any project ideas?