I have often complained (mostly to myself) that when you teach upper level math like PreCal, there just aren't many real world projects that you can do that will help kids learn the standards. There are real world connections that can be made but finding hands-on projects for the kids always eluded me. Just like most other connected math teachers, I have searched the web for these magic bullets that would teach factoring or trig identities so that I didn't have to just stand up and work problems with my students. You can find all kids of cool stuff on slope, geometry, etc. but the higher you go, the tougher it gets. (Confession: I have always been jealous of every other subject because I can think of a million cool, hands-on ways to teach anything from the Civil War to Lord of the Flies to Newton's Third Law.)
@ddmeyer has clearly come closer on this than anyone with his #graphingstories, #3Acts and #MakeoverMonday. Many have followed in his footsteps and there are many twitter math rockstars that I could mention here. So it finally occurred to me to look for problems in my text that maybe could be made over, or at the least turned in to something my kids could get their hands dirty with instead of expecting someone else to do the work for me. (Another confession: I have taken way more than I have given to the MTBoS folks).
I looked but I got no inspiration for the first few days but then I got lucky. There was a problem on factoring out the greatest common factor from an expression. Here was the problem
But the Flash Sale is an extra 20% off after the 40%, so I thought it would be a great way to intro this problem in Makeover fashion of the text problem and help them learn to factor. So I gave the kids this slide on their Edmodo page (we are completely 1:1)
I told them my wife makes me go to figure out how much the clothes will cost and I NEED you guys to figure out a way for her to calculate the 40%/20% deal so I NEVER have to go there again. I asked them to define all variables, write your formula in a general form and see if you can factor it.
Then it was like the Beastie Boys song "Paul Revere." Hands went up and people hit the floor. Luckily, no kids ran for the door. I just told them to figure it out, that's all you get. I didn't even do a real makeover and develop the problem, the perplexity, and any supporting material. I just winged it. I knew only a few might actually get the answer the way it was intended, factored and all, and a few might find another way, but it was what happened next that blew my mind.
In three sections of PreCal that day, I had at least 5 different correct solutions where kids figured out the discount really equaled 52% off and that I could just tell my wife to cut the price in half. They figured it out in ways I had never even thought of and they were totally correct. One group figured out the discount for about 5 different prices, then divided the original by the discount and found a common ratio of about 2 and said I could just divided by 2 every time. I was high fiving kids and thanking them because I don't ever have to go to Justice again!!!
I completely forgot about factoring and writing the factored form. I didn't even make them turn anything in. I could have cared less. Of course I showed them the "proper solution" but I also told them how impressed I was by their effort and solutions and that the only thing that would matter to me this year was that they got a solution, no matter how they arrived there. I think it gave most of them the confidence to try anything instead of shutting down and trying nothing at all.
Even though they probably learned nothing about factoring with the GCF, I count it as a victory because factoring may only be something you need if you are going to continue on down the math road. Most kids in regular PreCal are smart, but not in Math and Science. They are AP Lit smart and will go on to become teachers and writers and won't ever take Calculus and probably won't ever factor anything again.
As usual, there won't be one of these for every section of every chapter for every standard and the sooner you realize that as a math teacher, the better off you will be. Your job is to give kids the opportunity to be wrong and creative and to think for themselves. It's an opportunity they rarely get in this day and age.