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.

http://www.masterylearningsystems.com/Podcasts/CNR-GD.mp4

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May 29, 2010 at 4:58 pm

Because my students have such a hard time with negative numbers (ie: solve for y in y + 25x = 3x + 7), I started thinking about what the problem was. I would get answers like “y = -28x + 7” or “y = 22x + 7” so it was obvious there was a lack of understanding of negatives.

For my thesis, I began looking into when negative numbers are taught- 7th grade! What?? That’s too late in my opinion. Then I began to look into HOW they are taught- with a number line. But at the very beginning of the first lesson in 7th grade, there is a picture of a boy with a caption above his head reading “I owe my dad $4. I have -$4”

So this idea of owing is tied directly into negatives. So I thought about owing someone some money, paying some back, and figuring out how much more I owed.

If I borrowed $12 and paid you back $7, the problem would look like “-12 + 7” but I would solve the problem, in my head, by counting from 7 to 12. This is not the way we are taught in school. The way we are taught in school is to “find -12 on the number line, count 7 to the right, see what number you land on.” But this isn’t what we do in real life!

Absolute value is the answer. Although “take the difference between the absolute values of the two numbers” is a bit of a mouthful, it is the way to go. This way both numbers, -12 and 7, are treated as real numbers instead of -12 being treated as a number and 7 being treated as a movement. I really think that if we teach kids this way they will begin to see the relationship between positives and negatives and no longer make mistakes when they get to me!