My favorite lesson from the last few weeks was one that addressed understanding the concepts of ordering integers, finding the opposite of a number, and finding the absolute value of a number. We had already discussed the meaning of the terms opposite and absolute value. When students came into class that day, I handed each kid a sticky note with an integer written on it. I made sure that someone got zero, and that there was at least one pair of numbers that were opposites.
Out we went to the courtyard, for a variety of reasons. The weather was nice, it gave us more space, and it prevented us from disrupting other classes on the hall. With no instruction on how to order integers, I instructed students to make a number line. They talked and compared and lined up. The discussions were productive. When they were all in line, I asked if anyone wanted to move. Most often kids looked to each neighbor to decide, but in one class a student came out of the line to check everyone’s position!
When that task was complete, I instructed them to make a number line if they were equal to the opposite of their number. Some discussion ensued and a line formed. All was well. Now came the rub. “Make a number line if you are equal to the absolute value of your number.” They weren’t sure about the difference between opposite and absolute value. Some moved, some didn’t, discussion ensued. Eventually, the correct definition of absolute value came out, and the line formed. I had to ask the two people who were opposites if they should be lined up next to each other or not. We agreed they should stand one in front of the other, to represent the same spot on the number line.
As the day progressed, I added more tasks. “Opposite of the opposite of your number.” “Opposite of the absolute value of your number.” “Absolute value of the opposite of your number.” I especially recommend opposite of the opposite. It makes things go much more smoothly when you start talking about multiplying integers and they can think about flipping from one side of the number line to the other repeatedly.
This was a fun activity allowed them to think, discuss, move, and seems to have produced fruit in their understanding of integers. I recommend it for students beginning their work with negative numbers.