To Start: We've got 8 coins. One of them is heavier than all the others, but looks just like the other 7. You got an old school scale. What is the minimum number of times you will need to use the scale in order to guarantee finding the heavier coin? How can you prove this to others?
Next: homework. Where did we run into trouble?
Then: There's a sheet online of some Class 4 Problems. Let's start on those and see how far we get.
The goal here is to think of equations as, perhaps, something a little different than we had before. There's lots of different ways for us to describe the movement of an object or of the way two things interact. We tend to pick the one that is the easiest for us to work with and manipulate. In the case of most of the ones I've selected, parametric thinking is probably the easiest.
If time permits, we will consider some ideas about lines that we might be more comfortable with, such as -- what is a system of equations? How and why does it work? How can lines interact? But I'm not sure this will happen.
Outro: Nim -- how does it work? Why does it work?