*Math 8* – All my grade 8’s had their timetables changed so I was essentially starting with a new class today. About 2/3 of my students were new to me. Having already done a constructivist review lesson with adding integers, today I took a faster more direct route because the first half of the class was spent going over class business (books, course outline, expectations, etc).

I quickly reviewed two methods for adding and subtracting integers, using modeling and a number line. From what I saw on Wednesday, almost all kids are comfortable with this.

The situation that is hardest for them to understand and the hardest for me to explain is when you subtract a negative number. For this, I had students fill in the 6 – n table shown above. Students were confident that the pattern was correct and would hold for subtraction. From this, we reasoned then that 6 – (-1) = 7, 6 – (-2) = 8, etc.

I get kids to explicitly state their reasoning each time. It’s repetitive but I want to reinforce that answers come from reasons, not tricks.

From the data table and the equations we developed, I asked students to write down a rule on how to subtract a negative. Most students give rules #1 and #2. I ask around until we get to rule #3 (we had already covered the definition of an “additive inverse”). I then asked the students to give the pros and cons of each rule and we generally agree that rules 1 and 2 don’t give any explanation and they can also be confusing.

Most kids do have a rule for this situation. They say you turn one negative around and put it on top of the other negative, which makes it a positive. Excuse me while I gag…

Next day I will offer an analogy for adding and subtracting integers:a hot air balloon where positives are helium and negatives are weights. It’s the best analogy I’ve come across that fits with subtracting a negative (if you remove a weight, the balloon rises / gets more positive / does the same thing as if you added helium). I might make a Scratch game/simulation for this.

**One last note…** I had students return some Plickers voting cards since they weren’t going to be in my class anymore. One student was walking away when she stopped, turned around and said, “I really liked your class. It’s the most fun math class I’ve ever had.”

So that goes in the win column.