I was a little surprised to see the negative numbers pop up again. We played with those a while back, when he discovered them, but he hasn't brought them up for a long time. Today, he did them spontaneously. He needed a little assistance, which looked like this:
Hero: What's 3-4?
Mom: If I owe you $4, and I give you $3, how may more do I need?
Hero: $1. [Writes 3-4=1]
Mom: We write it this way. [3-4=-1]
Looking at the conversation now, I think I may need to come up with a better way of explaining what is going on. I think maybe we could use our abacus, and use that to make things more visual. We'll probably do that tomorrow.
For the other negative problem it went like this:
Hero: [writes] -9 + 4 + 3 + 2= 9
Mom: [puts out blue rod] Let's say I owe you $9. This blue rod is how much debt I have. I pay you $4 [purple rod below the blue], and I pay you $3 [add the green one], and then I pay you $2 more [add the pink rod. Have I given you enough to get to $9 extra? At that point he could see what I was getting at, so he added the slash through the equal sign.
The other cool thing that came out of this exercise is we had a chance to discuss how it is ok to put an equation on both sides of an equal sign. We use shapes at this point, because that's what they do in Miquan when there is an unknown.
 +  = O + O
However, if you're going to use an equal sign you have to make sure both sides are actually equal, or use the not-equal sign.