The second session we chose was called Fun Functions by CPM.
The Bug Problem
We began the session by checking our understanding of what a function is. I took a picture of the PowerPoint slide, but it didn't come out readable at all. So, you'll have to put up with my re-creating the slide in Microsoft Paint...
|Image Source: Buel P. Colton, Zoology: Descriptive and Practical(Boston:D.C. Heath & Co., 1903) 18|
I was shocked at just how many teachers in the room voted that this was most definitely not a function. Then, I started thinking about what my students would say if I gave them this question. The thought was not pretty. My kids need to know more about functions than just the vertical line test!
The first activity we did was to order function machines.
Here were our four functions:
Of course, they were printed on function machines and laminated for durability. (And, for the record: laminated papers are really hard to photograph in a bright classroom!)
CPM has posted these function machines as a free PDF on their website if you're interested.
Our task was to arrange the functions so that when a 6 was dropped in the first function machine that the last machine's output would be 11. This led to some good conversation in our group about which functions couldn't be last.
CPM also has a PDF version of this activity with an easier set of functions that I plan on using with my Algebra 1 students this year.
Silent Board Game
Next, we moved on to an activity called silent board game.
When we entered the room where the session was held, this laminated sheet was taped to the wall:
The idea is that the teacher puts up an incomplete input/output table.
Here's the one we used in our session:
I got this image from page 8 of this file from CPM that features several pre-made Silent Board Game tables.
As we played the game, I realized it truly was a silent board game. The facilitator would hold up her dry erase marker until someone raised their hand. Then, she would hand them the dry erase marker. They would walk to the board and fill in an output value. If the output value was correct, there would be silence. IF the output value was incorrect, there would still be silence. But, the teacher would walk to the board and erase the incorrect value.
This continued until the board was filled. Then, we moved on and silently filled in the rule for the function and the functions' growth rate.
I'm honestly not sure how this activity would play out in my classroom. Would my students stay silent and engaged the entire time???
One participant in the session suggested a tweak to this activity: have a graph where students plot each point after adding it to the table. This could help students see if the function was linear, exponential, etc.
After the Silent Board Game, it was time to get out of our seats and do a function walk. Our facilitator suggested that this was a great activity to get students outside. If doing it outside, she suggested that we could draw the axes of our coordinate plane with chalk.
Since she works for CPM and does this presentation frequently, she had taken two rolls of ribbon and written the values on them to serve as axes. I thought this was quite ingenious!
We were each given a laminated index card with an input value filled in. Different people received different colored index cards. I was in the red group.
The purpose of the color-coding became clear when we got our handouts. As a person with a red card, I would be helping to graph the equation y = 2x + 1.
We took turns graphing different functions.
Here's my spot on the x-axis before we moved to our appropriate spots.
And, here's a picture of the rest of the red group in action:
If I end up teaching trig again this year, I think I'd definitely like to do some kinesthetic graphing of trig functions.
There were several other activities in the handout that we didn't get to. A copy of the handout for this presentation can be found here.