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!)
Ask a volunteer to take a few of each and toss them in a bag.
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!
Nicole
I'm so glad you blogged about this! I loved hearing your presentation at TMC, it was so great to meet you!
ReplyDeleteThanks! Your recap post was fantastic- that is next on my to-do list!
DeleteThis is such a fun and unexpected combination. I had a student last year who just could not wrap his head around the idea that 6 and 3x aren't like terms, no matter how many analogies, pictures, and scenarios I shared with him. I wonder if this might have helped. :)
ReplyDeleteThanks Kathryn- I very much enjoy reading your blog- I'm glad I could share something back!
ReplyDeleteI love it. Fun. Engaging. It makes sense. Conceptual. Fantastic.
ReplyDeleteNicole, I didn't get to see your presentation at TMC13 - probably some family 'emergency' that required me to step out and make a call - but I love this idea. Do you find that in the students' minds this understanding extends naturally from this activity to terms with the same base but different exponents? In my 'gifted' Algebra 2 class, more than a few students are still combining like bases with different exponents by adding the exponents. Yikes! I would love to use this to illustrate unlike terms, but I'm wondering how to stress the terms are unlike even when the bases are the same (if they don't already understand that at this late stage).
ReplyDeleteWe definitely come back to this when we get to adding polynomials
Delete...many students bring it up when I show it as a "favorite mistake". I haven't tried it with "the bag" at this level but I am thinking of a large version of algebra tiles cut out of craft foam. Strips labeled "x" and squares with each side the same length as the strip labeled x^2. Julie Reubach shared a video of her class where she had a stack of items and students added them to a bag and took some out and added more, wrote the expression as they went, simplified their answer and then checked the bag, I could see a pile of strips, squares, and maybe even cubes being a fun activity with just enough concrete reinforcement. Thanks for commenting!
Nicole — I loved your presentation at #TMC13, but I think I love this writeup even more. We just had our first expressions and equations test, and I think this would be a great activity for remediating with students about identifying and combining like terms. Thank you for blogging about this!!!
ReplyDelete- Elizabeth (@cheesemonkeysf)
Thanks for reading and commenting...if you haven't seen them, you should check out what Julie did with it at
Deletehttp://ispeakmath.org/2013/09/25/algebraic-expressions-with-6th-grade/
, what Nora did with it at
http://simplifyingradicals2.blogspot.com/2013/09/pennies-paper-clips-buttons-and.html
and what Kathryn did with it at
http://iisanumber.blogspot.com/2013/10/distributive-property-and-combining.html
Sorry, nothing is linking for me!