Organ Function Grinder Machine

This is an activity that I really like but forgot about for awhile. One of my projects for this summer was to clean up all my files and I recently rediscovered this. After starting this post, I even rediscovered that I blogged about this awhile ago right after I made it. 

Since then I've refined it a bit so I thought it was worth sharing again.

A bit of background is that this idea came from the Math Midway exhibit which was here at the Liberty Science Center awhile ago. My favorite was the Organ Function Grinder. This is the activity guide that goes along with the exhibit. 

This activity is my attempt at recreating the exhibit. 

The basic idea is a three function machine where the kids needs to play with the dials and choose input numbers to try to make goal numbers. I really like that they include some interesting functions, especially invert. I also like that there are more than one way to get the answers, that's always a huge plus.

The activity gives a list of available numbers that can go into the machine, and a list of goal numbers. The students choose an input number and decide what functions to use in order to make the target number. The activity begins by having them only use one function and then progresses to using all three. Using multiple functions starts to get especially interesting and leads to good conversation about how the order of the functions used changes the output.

Below are the tables that can be used for the activity, or this could easily be split up a ton of different ways. On the handouts (download link at the bottom of this post), I also included a picture of the machine above each table.

Use only one function

Use two functions

Use three functions

Just a word about the layout of these- I originally had the goal outputs filled into the output column instead, but I changed it thinking that especially in the more complex ones that I wanted the kids to go across the row and apply the functions in order to calculate the output for themselves and check that it worked.

This could easily be modified a bunch of different ways. Some of the ideas I had were:

• Changing the inputs to create different problems.
• Choose one goal number and challenge kids to find as many ways possible to make it.
• Choose one input number and have kids choose 3 functions. Investigate what happens when the functions are applied in different orders.

If anyone else has other ideas I'd love to hear them.

Download