I'm starting to jump around the Estimation 180 site. My students still enjoy it so we keep doing it. Today we did a variety - one song length, one number of carts, one distance between two cities and one number of pennies to form a shape. I realize that they can't use previous estimations to help with the new ones when I do this, but I will go back and do more of each.
Back to equations of lines. We worked on slope last week and today we started by writing the equation of a line given its slope and y-intercept. We had to back up and define y-intercept first (several times) and doing this exercise abstractly was likely not a great idea. I'm not sure that everything needs to be in context, but I think I could have done a better job of tying it all together. The next examples were graphical - again, finding the equation of the line. At least this gave some meaning to the slope and y-intercept.
Next, we tackled our first "solving by substitution" question:
This took a long time. The rest of the period, in fact. We came up with equations, looked at some data, sketched graphs, made sure we understood what we were trying to find, then had to use algebra to solve. Algebra. Sometimes it seems like they have never done it before. But we did get through it and may be in good shape to try more similar problems tomorrow.