Kim addressed the burning questions. We discussed how important it is to be constantly learning and it is good to realize the proof of some of these properties is very complex and require the use of variables and logic. Luckily we don’t have to prove the properties an theorems over and over – someone did that for us but if we are going to use them it is good to have an idea of how it was proven.

Here are the websites for different ways to show multiplying two negative numbers with manipulatives and the number line:

- One way (around 3:51)
- ice cube and box idea
- Flipping over the origin (3:10)
- walking forwards and backwards (2:10)

We also reviewed that dividing by zero never gives a numerical answer. 6/0 is undefined. 0/0 is indeterminate.

Charles answered some multiplication questions and then headed into the division.

There was some good discussion about the difference between partitive and quotative division.