I was lucky enough to be able to attend Twitter Math Camp 2013 in Philly last week. Part of TMC was a session called "My Favorite..." This was a fantastic entry point for those who had a "small" idea to share that wasn't really enough for a full session (or, if you were too chicken (like me) to sign up to present a full session!)
Never have I been so nervous to get up in front of a room of teachers!
So on to my favorite! Imagine you have a store that sells only oranges and marshmallows.
Give the bag a good shake, and ask your volunteer "what's in the bag?". Of course they will look at you like you are a little crazy, and in this case, say "3 oranges and 2 marshmallows." Ponder this thoughtfully, and ask for another volunteer.
This time, tell them to pick up two sets of marshmallows and put them in the bag.
Shake it up, and ask again "what's in the bag?" In this case they will probably tell you "5 marshmallows". Usually they don't look in the bag, so ask them to check and make sure.
This is where I like to look very confused...so if 3 oranges plus 2 marshmallows equalled 3 oranges plus 2 marshmallows, how did 3 marshmallows plus 2 marshmallows equal 5 marshmallows?
Using that reasoning, shouldn't 3 oranges plus 2 marshmallows equal 5 "orangamallows"?
So do this a few more times, and then ask what would happen if we put 2 "x"'s and 3 "x"'s in the bag?
Or 4 "x"'s and 3 "y"'s?
Somewhere in the conversation you can bring in vocabulary like "combining like terms", and model what the different algebraic expressions look like.
All year long, whenever someone makes a combining like terms error, you can hear a cry of "orangamallows" in the room!
Thanks, TMC and the general twitterbloggersphere for the forum to share!