MathChat

Making Sense of Negative Signs

If you’ve ever seen students struggle with expressions that have a negative sign in front of parenthses (I sure do!), expressions like this:  – (8x – 5)

then this blog entry is for you!

I’ve developed a new way to help students get this concept right — and to remember the concept so they continue to get it right, week after week. I’ll explain the basic approach in this entry, then give more details in the next entry.

The big problem with the typical textbook presentation for this concept is that it is filled with math gobbledygook. I’ve found that you can cut out the gobbledygook and instead relate this kind of problem to everyday life. Once students learn it this way, they’ll never forget it!

MAIN IDEA: encourage students to think of the negative sign as the as the everyday word, OPPOSITE.

So start out by asking simple questions, but writing them in a pseudo-math format.

Example:

Write:  opp (black)

while you ask:  What is the opposite of black?

When students give the answer, what you write now looks like this:

opp (black)

= white

————————

Continue with other examples, like this:

opp (tall)

= short

————

opp (down)

= up

———–

Once students get the basic idea, expand on the idea by telling students they can take the opposite of two concepts, not just one. Show this by writing expressions like:

opp (white, short)

Students should answer:

opp (white, short)

= black, tall

and: 

opp (left, slow)

= right, fast

————-

Once students master this idea, extend the lesson to NUMBERS, first by pointing out that all numbers (except 0) and MONOMIALS have opposites. e.g., that the opposite of + 3 is – 3; the opposite of – 5 is + 5, the opposite of – 8x is + 8x, the opposite of 6ab is – 6ab, etc.

Now challenge students to do problems like this:

opp ( + 5x, – 7 )

They should get:

opp ( + 5x, – 7 )

=     – 5x, + 7

——————–

Then simply explain that in math, we express the idea of opposite by using a “–” sign in front of the (    ), and that we write the terms inside (    )  without commas.

Give students this problem:

– ( 7x + 4 )

See if they can get the answer, which should look like this:

–  ( + 7x – 4 )

= – 7x + 4

——————-

I hear a lot of: “Oh, that’s easy,” when I explain it this way. I think that’s because opposites is a concept students know “cold.” Plus, using the opposites concept connects the algebra to non-math concepts, and students often find that refreshing. I’m sure you’ve noticed that, too.

Then give students a set of problems, like these:

1)  – ( – 7a – 4 )

2)  – ( – 3x + 7 )

3)  – ( + 8y – 3 )

4) – ( 4p – 6a + 12 )

5)  – ( 9x + 4y – 3 )

Have fun with this lesson. If you think of any ways to extend it, or if you find any tricks that make it work especially well, feel free to share them by sending them to:  josh@SingingTurtle.com