Math = Love: OCTM Recap: Fun Functions

## Friday, June 17, 2016

### OCTM Recap: Fun Functions

This is my second blog post recapping sessions Shaun and I attended last week at the Oklahoma Council of Teachers of Mathematics Summer Conference.  Be sure to check out my previous post on High Yield Geometry Routines!

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!

## Function Machines

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.

 Source: http://pdfs.cpm.org/stuRes/CCA2/chapter_01/CCA2%20Lesson%201.1.1%20RP.pdf

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.

## Function Walk

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.

1. wondering on the silent board game...what if there were a few different boards posted around the room and make it a "chalk talk" still silent, but students are critiquing the reasoning of others as they rotate around the stations? the idea of a graph is great too.

2. I have done the silent board game in my pre-algebra classes. My 7th graders generally do very well with it. My only modification is to keep a mental list of who I have called on and I try make everyone go up (especially after we have done a few rounds).

1. Good reminder!

3. Thank you so much for sharing! My teaching keeps improving because of your great ideas :)

1. You're welcome, Kirsten!

4. Love this post because there are some great ideas!!! Thank you for posting these!

1. You're welcome!

5. I completely agree that there needs to be more kinesthetic activities and hands on activities to ensure math is equally accessible and obtainable to all different types of learners. This is a great way to increase differentiation in the math classroom. Whenever I have taught functions I always try to relate it to a machine where something is going in, runs through the machine, and a product comes out. Although this seems like a simple concept to me, some students still do not understand or are unable to picture exactly what I mean. However, the activity you provide here with the function on an actual illustration of a machine gives students a visual and something to remember functions by. Giving students an input, 4 different functions, and an output allows for them to practice the skill of evaluating functions while instilling some logic and puzzle-like enjoyment into math than just having students evaluate functions from a textbook.

I like the silent board game with inputs and outputs but am also unsure if my students would stay completely engaged the whole time. I would also worry about them just guessing random outputs. The idea of having students plotting the points on a graph afterwards is a really valuable suggestion so students can see the nature and behavior of the function.

Lastly, my favorite activity is definitely the function walk. I am always trying the think of reasons to take my students outside on beautiful days and this is perfect for just that! I could also bring them into the gymnasium. Anything to get them out of the classroom always peaks their level of interest and engagement. The idea of having each person represent a point on a specific function according to color helps each student practice evaluating an output for a given input as well as see how the function looks in 3D. You are absolutely right that this activity can be used for a variety of mathematical contents such as pre-algebra, algebra 1, algebra 2, trigonometry, and even pre-calculus/calculus. I think that having students work together to model functions in real-life using human beings will be both fun and informative.

Thanks so much for sharing! I can not wait to use all of these fun, engaging, and innovative ideas to get my students to learn and love mathematics.

6. Everything I have seen from CPM has been wonderful. I really like the function walk idea! Thanks for posting!

1. You're welcome!

7. Hi Sarah, Would you be willing/able to quickly explain why the bug line is a function? Thanks! ~ Sophie

1. Deborah has a great answer below!

8. The bug problem is a function because we are seeing a 'picture' of it's trail, not the graph of the bug's location vs. time. The bug can only be in one location at a time, so it is a function. (One of those sneaky picture fails vertical line test, but the picture is not a graph and the situation is a function.)

1. Thanks for answering this, Deborah!