First, we spent a couple days adding positive and negative numbers. We used green counters for positive numbers, and red for negative. We use these two colors throughout our unit. I really putting an emphasis on the fact that adding is PUTTING TOGETHER. This would later help with differentiating between the rules for adding negative and the rules for subtracting negatives. After doing a few sample problems, the students were able to come up with their own rules for adding positive and negative numbers. They quickly caught on and all was well in the world! (Don't worry.....subtracting is next....that's a WHOLE different ball game!) Here are our notebook entries for adding:
Next, we began working on subtracting. This time, I used a clear bucket to show what we had in the container, and what we needed to subtract, or take out. Before giving them any tricks, we practiced many many times with counters. For example, if the problem read: 8- (-4), I would fill the container with 8 green tiles, or 8 positives. Then, I would ask if we were able to take out 4 red tiles. Obviously, there were only green tiles in the container, so I couldn't take any out. We had discussed earlier how the opposite of every number added together equals zero, so I demonstrated putting in groups of one red and one green tile at a time, until I had 4 reds to take out, all the while emphasizing that I wasn't changing the value of the container since I was just adding zero to it. Then, I was able to take out the red counters, leaving only green behind. This was not an easy concept to teach, and there were some frustrating looks around the room, but we kept at it until it slowly started clicking. That's when I introduced Mr. Minus.
Who is Mr. Minus, you ask? It's more of a "what". Mr. Minus is a poem my mother, Mrs. McHugh, also a 5th grade math teacher, made up years ago. I owe her A LOT this year! It goes like this:
Mr. Minus, Mr. Minus
Learn you I must
But I think I’m going to turn you into a plus,
Now change the second number to its opposite sign,
Add them both together and life will be fine! Yeahhhhh!
It's catchy and the kids love it! Here is our notebook page on subtracting. Again, the pictures are of containers holding what we need to take out and the step by step change it goes through.