How do we help students build greater competence and confidence in adding and subtracting with negative numbers? Many use a thermometer but may not approach it like this.

The most important thing to remember is, do not explain this to your students.  Use a thermometer and guide their discovery and experience of it. Have them start at zero and move in the direction of more hot, still more hot, more hot and then less hot, less hot, and less hot. Start back at zero and now move in the direction of more cold, colder, and still more cold and now less cold, less cold and less cold.

Now, think of + as more and (+) as hot, so +(+) is more hot. And – as less and (-) as cold, so  -(-) is less cold. Ask them, more hot or +(+) goes which way on the thermometer? They respond, up! Less cold or  -(-) goes which direction on the thermometer? They respond again, up!

Then what about more cold or  +(-), which way is that on the thermometer, down! And likewise, less hot or  -(+) is which direction on the thermometer, down!

So simply start with the thermometer having the students show which direction +(-), -(-) is and so on. Then slowly introduce numbers. Ask how far and in which direction, +(+3) or +(-2). When they are comfortable with this, finally give a starting number, 3 + (4), or 5 – (-2) or (-5) + (-2) and so on.

You can slowly introduce nomenclature, without making a big deal out of it, as the experience is settling in. With the problem, +(+3) we are adding a positive going how far in which direction? Or with (-5) + (-2) we’re starting where and adding a negative going how far, which way, and ending up where? Introduce the terms as they continue to experience on a thermometer what is starting to become familiar to them.

Watch the second half of our podcast on Guided Discovery for some ideas on how to set up this lesson by orienting students to the concept and a thermometer.