Thursday, January 22, 2015

Function SET Game

My junior class study hall (made up of kids who are not math students of mine), are a bit of an active bunch.  In order to get them to concentrate on actually getting homework done, I have bribed them with games on Fridays.

Last Friday, I brought out SET.  None of them had played this game before, and I have only played a few times (I know, I know: and I call myself a Math teacherA??).  Anyway, several of them really got into it once I played a few rounds with them, and because they were getting excited and arguing over whether something was a set or not, others began to come and look over their shoulders.

(Did you know you can play this on line?????)

So all of THIS got me thinking about transformations of functions, families of functions and the like, so I made this

My co-teacher and I are going to try it out tomorrow as a warm up with a Pre Cal class that has really mixed ability levels.  We'll put them in groups of 3 or 4: make them each responsible for justifying what makes a set.  We won't give them any rules, just:  "Make a set, but be able to explain why these 3 can make a set."  

I did make a SmartNotebook with the same table in it AND some sample pix of what makes a set in the actual SET game.  If they are really stuck, we will show those to see if we can't make some progress!

Would love feedback if you try this:  what went well, what suggestions for change?
Keeping my fingers crossed that this doesn't bomb!

Friday, January 9, 2015

My Love Fest with the Standards of Mathematical Practice: Episode 1

There may be much about the Common Core that I have issues with, but I absolutely LOVE the Eight Standards of Mathematical Practice.

I find myself becoming more and more aware of making sure I am including these in every day lessons, not just those really FAB lessons (yes Mr. Kaplinsky, I am taking about you, since we just finished the In and Out Burger lesson!). Two of my favorites Standards are MP3 and MP6.

Yesterday, rather than going through the homework (a review of solving equations that included fractions, distributive property, combining like terms), I put the students in groups of 4 or 5.  Each group got 2 different colored chips.  This is what they did:

FIRST:  They had to assign roles.
  • Yellow chip meant you were the speaker.  
  • Red chip meant you were the responder.
  • The other 2 or 3 in the group were the Active Listeners.
  • Yellow chip Speaker explained what THEY did as the first step in solving the equation. "First I added 2x and 5x."
  • Red chip Responder gave a reason for Speaker's action:  "You combined 2x and 5x because you wanted to combine like terms on the left side of the equation".
  • Yellow chip Speaker stated what they did next.  "Next I divided both side by 7."
  • Red chip Responder gave the reason for that step.  "You did that so you could isolate the variable.  You are allowed to do it because of the division property of equality."
  • The Active Listeners did not speak until Speaker and Responder were done.
  • The Active Listeners verified correct responses.
  • The Active Listeners were responsible for pointing out any errors in process or in arithmetic.
  • The Active Listeners corrected or helped supply appropriate vocabulary and/or properties (they were allowed to check their Interactive Notebooks).
  • The Active Listeners shared alternate methods for solving the problem (the Responder was allowed to share at this stage, too).
  • Group members passed the chips to the left, and worked on the next problem.
  • We chose a couple of the more complicated problems, ones which caused a lot of difficulty, and shared different approaches.  That way we could all see the different ways in which the problem could be solved.
  • Students demonstrated the 4 different ways to approach problems that had fraction coefficients, or contained a fraction containing a variable.
What my aide and I noticed:
  • Students were good at being Speakers, but not quite as good at being Responders, especially if the Speaker and Responder approached solving in a different manner.  Responders were kind of thrown off.  We had to point out that they needed to listen carefully what the Speaker actually said, and give a reason for that action. When we saw this difficulty happening in multiple groups, we gave the Speaker a white board and had them write the problem, showing and speaking one step at a time.  This had the added benefit of giving the Active Listeners the ability to see arithmetic errors as well as hear process errors.
  • There were times when all group members had a different answer!!  They really got in to finding out which was the right answer and where the mistakes were made. The most frequently heard exclamation was, "OH!  I see what I did wrong!"
  • Most common errors:  Combining like terms across an equal sign.  Subtracting integers such as -5-3.    Dividing with negatives such as -8/-2.   Losing the subtraction sign after getting rid of the variable term ( 2x - 5 = 3x +2  results in 5 = x +2).
NOTE:  My aide and I modeled how to do the Speaker and Responder roles before we let the kids go at it.  We had the students all be the Active Listeners and share how some of them would have approached the problem Mr. D and I modeled.  I believe this was a REALLY important part of the success of this activity.

After this activity I gave the Term Benchmark Test.   It involved everything from 1st Trimester.  It had eight "solve for x" questions.  They did remarkably well (on these 8 questions) ESPECIALLY on problems involving fraction coefficients.  I was over the moon.