## Kiss those Math Headaches GOODBYE! ### ANSWER: July Problem of the Month

a)  How much is the discount, under the terms of this sale, for a bundle of clothes with retail value of \$250?

Discount = \$130. You get this as follows:

1st)  Take a 20% discount off \$250 by multiplying 250 by .8.

Answer is a \$50 discount, making the new selling price \$200, \$250-\$200.

Take a 40% discount off the new selling price of \$200 by multiplying 200 by .6.

Answer is an \$80 discount, making the new and final selling price \$120, \$200 – \$80.

Total discount is the sum of the two discounts:  \$130 = \$50 + \$80.

b)  How much would the discount be if Al’s had just run a straight 60% discount sale?

At a straight 60% discount, the dollar value of the discount would be \$150, which you get by multiplying \$250 by .6.

c)  Why do you think that Al’s is running the sale in this way?

Many possible answers, but the main point is that Al’s strategy is to make customers think they are getting 60% off, while he actually gives them less than 60% off. He actually gives them a 52% discount.

### Algebra mistakes due to Negative Signs? Use COLOR to EXPLAIN.

Have you ever noticed how much trouble students have figuring out the difference between these two kinds of expressions: The key, I’ve found, is to use the Order of Operations to decode the meaning of each expression.

Ask your students to think through how many Order of Operation steps there are in each expression.

If they’re on the right track, they’ll see that the top expression has just one operation:  working out the exponent by multiplying (– 3) by itself twice. This looks like this: As for the bottom expression, this is more difficult because of that “loose” negative sign, a negative sign that is not enclosed inside parentheses. Just like a “loose canon” can be a danger in the military, a “loose” negative sign can spell trouble on the algebra playing-field. Students will make all kinds of weird mistakes in trying to figure out what to do with this little varmint.

But if you tell students to view that “loose” negative sign as meaning (– 1) times the expression that follows it, they can use the Order of Operations again to do the right thing first.

Specifically, they notice that there are two operations to be performed: multiplication and exponents, and they remember that they do exponents before multiplication, following the Order of Operations.

Following these steps, the simplification looks like this: And while this is fine and correct, notice that you can “kick it up a notch” by using color to separate out the two operations. I use blue for decoding the negative sign and working it out; I use red for the 3-squared term. Check it out: I’ve yet to meet a student who cannot follow this procedure, when color is used.

Try it out and see what kind of results you get.