*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*= 3

*x*+ 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.....