In an ongoing process to better teach the boring bits I have worked out a new way to introduce adding polynomials. I feel like I should justify what I have been doing over the last… 7 months… but lets just say I have been busy in the classroom. Anyways; here are goods.
Start off by asking students to evaluate the following:
Walk through it to make sure they totally understand, this should be easy peasy for them.
Then throw this up:
Tell ’em you will race them and give ’em a 30 second head start, keep in mind that the previous problem has set them up to plug 2 into EVERY. SINGLE. X they see, so it is going to take them forevvvvvvvvvveeeeeeeeeeeerrrrrrrrrrrr to evaluate this expression.
After the 30 seconds is up announce that you are starting the problem (do this on a scratch sheet of paper by your desk, so they can’t see what you’re doing). Combine like terms, get this thing down to a trinomial (or possibly binomial) and then plug in 2 for x.
Announce to the class that you have finished the problem (in all my classes this was before they had even finished writing it down) then let student sit, perplexed, as to how you solved the problem so dang fast.
This gives at least some reasoning as to why mathematicians would ever want to add like terms.