Slope, y-intercept, slope, y-intercept. Over and over and over again until I think I must repeat those words in my sleep. Maybe THAT is the key to getting my kids to GET IT? They need math 3 times a day, every day, until those words dance in their dreams!
We learned slope early on, when we studied rate of change. Some got it, some didn't, despite spending about 2 weeks on it. But move on we must, and did.
Now that the time of the year for linear functions is upon us, we are revisiting slope, and now y-intercept, and the ever popular y=mx+b form. We've looked at the functions themselves, setting up function charts, solving them, learning about 'solutions'. We've picked out the slope and y-intercept from the equation itself. We've counted boxes on line after line, rise over run, rise over run. Go up, go over... which is x, and which is y. We've solved for slope from a table, using 2 points, calculating the difference in their y values, over the change in their x-values.
We've looked at multiple problems applying slope and y-intercept to real life situations from pledges for a walkathon, to different rates of phone companies, to today's problem (MY favorite) comparing buying yearbooks from 2 companies: Gorgeous George's :) and Outrageous Rathje's (my language arts sidekick). We've made BIG graphs on supersized graph paper. We've worked in small groups. We've worked in partners. We've worked in large groups. We've used the wireless chalkboard. We've used the document camera. We've done them alone. We've done them together.
and still....... there are those among them who look as if I am speaking Greek or Vulcan when I ask them to find the slope of a line drawn on the board, or suggest they start by putting a point on the given y-intercept.
and onward we move... towards inverse relationships, those dreaded y=k/x situations.
and I focus on the positives:
RL who answered every single question I asked in class today, even when I tried to shhhusssshhh him so someone else could have a chance. RL who is a rough character, from a rough family, but bless his sweet little algebraically blessed mind, he got every answer correct but one! He was THE one everyone wanted for a partner when it came time for partner work. He KNEW he knew how to do it all and so did everyone else. Then, I had to laugh when his partner couldn't read what RL had written because spaces between words, or even letters, is not a skill evident in his hen-scratched printed words. But all three of us knew the words written were right on target.
CH who is this tiny little guy who looks like he should be in maybe 2nd grade, and always struggles with everything we do in math. He yells out at someone up count from their y-intercept up for the slope, "NO!! IT'S A NEGATIVE SLOPE. GO BACKWARDS!! Make your line go DOWN!"
LF, the new girl with the jetblack spikey hair they call porcupine girl, who didn't want to go to the document camera, swearing she couldn't do it. But all of them rallied and encouraged her, walking her through, step by step, until her line was sketched perfectly, as she walked back to her seat with a huge smile of satisfaction across her face, beneath the jetblack eyeliner rimmed eyes sparkling her pride.
and I know..... tonight I will hear the same words over and over again, dancing like sugarplums in my head, rise over run, slope and y-intercept, rise over run, slope and y-intercept.