*Your teacher will give you a set of four function machines. Your team’s job is to get a specific output by putting those machines in a particular order so that one machine’s output becomes the next machine’s input. As you work, discuss what you know about the kind of output each function produces to help you arrange the machines in an appropriate order. The four functions are reprinted*

*below.*

*In what order should you stack the machines so that when 6 is dropped into the first machine, and all four machines have had their effect, the last machine’s output is 11?**What order will result in a final output of 131,065 when the first input is 64?*

There was another activity - a scavenger hunt of sorts to use when identifying key vocabulary for relations and functions. The document linked above has links to the materials needed. The gist of the ideas is that there are 10 relations/functions posted around the room in various formats. The class is in teams. Each team receives a clue (there are four different sets of clues). As a team decides on the answer to a given clue, they return to the teacher to defend their answer and if successful to receive the next clue. In the end there is one function that is the "treasure."

i love this, but i would also ask the kids to do some writing about why they chose what they choose. this could also be done informally by asking the students to present their reasoning. still, i'm a big fan of writing reflections and writing for understanding in math. so i might add some questions like:

ReplyDeletewhen you approached the first problem (input 6, output 11), which function(s) did you know could not be the last one. why not?

likewise, which function is probably not a good choice for the first one? why?

in general, is there any order that the functions could never go in? why not?

also: could there ever be two different orders that give you the same output? i don't know the answer to this, but i'm curious how students might approach this.

lastly, i'd probably ask the students to identify each type of function and give a sketch of it because i'm nuts about trying to keep reinforcing this idea that we can understand so much about what a graph looks like just by looking at its equation's form.

thanks for this; i'll definitely use it! :)