So today was day 3 of "Line Week." (insert proper theme music here) We were in the computer lab again using our self-made excel sheets to graph different lines and look for relationships (see day 2 post). We tried a Jeopardy game where I graphed a line and we identified the slope & y-intercept. It worked okay with me graphing on the computer and projecting for the class, but did not work well when the students broke into groups of 2 and 3 to do with themselves. We worked through it, but it is not something I will do again.
We then discussed a graph about money and days! I graphed the line y = 3x + 12 in the first quadrant, with the x-axis being days and the y-axis being money. They quickly saw the y-intercept of $12 and the end total at day 7 of $33. I then asked how much money I was paid --- and the shout of $33 with quickly yelled! Then I got to say "Nope, why?" That was awesome! We worked our way thru the problem - starting with the slope of $3 per day, or the fraction $3/day. That led to the discussion that $12 was the amount of money I had prior to the seven days, leading to the answer of $21 for 7 days. This was a great entry into the mx and b having to be like terms to add discussion.
I asked for units on m, x and b --- without much effort the class was all able to explain the units of m-$/day, x - days and b - $. I then worked thru mx -- $/day times days -- which is $! The same as b! That then lead to the discussion of what is y = mx + b.
y is the vertical point, m is RISE/RUN (from our day 1 work with the stairs), x is RUN and b is a RISE.
So y = mx + b is RISE = RISE/RUN*RUN + RISE, where the RUN cancels, so RISE = RISE + RISE! Like terms. This lead into a couple minutes of talking about how we should think of m. Again big ideas and fairly good returns.
As always - when the really good learning started it seemed the class ended, but will pick up with Day 4 tomorrow and Day 5 on Monday! A weekend will allow for some good review of the previous week on Monday.....