Function Machines

A couple months ago I posted about teaching functions and using the function machine analogy.  I'm working on the same thing again now with a different class and am taking the function analogy and running with it.

First they worked on some practice and did fantastic with it.  I kept the pictures of the machines on there which actually seemed to help I think.

On this too we spent some time talking about how -x doesn't mean negative, it means the opposite of x. We discussed that the f(x) machine switches the sign of the number and then adds 5.

So today I had something else planned but got inspired all of a sudden and changed up everything that I was doing because I thought the new idea was way better.

About a year ago the Math Midway was at the Liberty Science Center and I really wanted to go check it out.  In particular, I was extremely excited to see the Organ Function Grinder in action.  Unfortunately though, it was gone when I finally got to the Liberty Science Center for teacher appreciation day.  I was really sad to have missed the function machine.

Today it occurred to me that I should try to make something similar.  I did some searching and came across the activity guide for the function machine and it gave me all the information that I needed to run with the idea.

I made this to use with the activity:

Now what I really want is something cooler that actually spins.  But for throwing it all together in about 20 minutes, this is as far as I've gotten.  I'm still considering it a work in progress though. (update on this here)

I gave the kids the activity sheet right from the activity guide.  To introduce the idea, I had the kids work on the first part which only uses one of the dials.  So one operation only.

As for the inputs, they had numbers to choose from.  I just took the numbers from the answer sheet included and gave them out.  I decided to separate them into the ones that they would need for each part, but I think in the future I would just hand out one list of inputs to use for the entire activity.

This is a completed one:

I enjoyed this a lot for a few reasons.  For one, it wasn't just problems where they plugged in numbers and got an answer.  They had to think more and use some common sense and reasoning which is always fun.  Also I really liked that some of them got the same answer different ways and they realized that both of their answers were correct.

I liked this too:

Technically my directions were to use only one operation, but that actually made me enjoy seeing this way more.  This kid didn't do two operations because the directions said to, he did it because it was what he needed to do to get 8 as his output.  I plan to use this as a perfect tie in to tomorrow's part of the activity where we use two and then three operations which I expect to be much more challenging.

Now as if that wasn't enough fun, I also made this:

I plan to have it as an ongoing activity, perhaps for extra credit I think.  On the side I will have different inputs on the index cards...negatives, fractions, decimals..whatever.  Kids will pull a given input, evaluate it for the given function and toss the card into the slot on the top of the box.  I will regularly change the function on the front.  I plan to differentiate this using the inputs.  I am going to let the kids pick their card, but for kids who are struggling either I can pick the card for them or I will make them one with a number of my choosing.  I'm not planning this for an actual class activity, but just to sit in my room and have the kids work on it when they have a free minute.  It'll be for extra credit points so I hope that should be enough motivation to get them over there.  We'll see how it goes.