Extra Help

Today (Sat.) i was tutoring a student like i usually do on Sats for the past 33 years. It always amazes me what goes through these kids minds as i try to help them. This particular student is a college student. A very successful businessman and very much liked by everyone he meets. I would say he has a very HIGH social IQ. But

He just does not get math.

Today we were working on the equation of a line... y = mx + b.

If just seeing that gets your palms sweating, you are in good company.

Why does the education world think people need to know Algebra to succeed in this world. Percents, yes ! maybe some simple ideas of discounts, yes ! getting the correct change at the store, absolutely. But unless a student is going to college, why waste everyone's time and energy. It could be better spent on learning a trade or real life skills. Remember only 50% of the population TRIES to go to college. My generation it was 20% and my parents generation only 10%....

with 50% NOT making it through college...that leaves only 25% of the new 20 and 30 something population with a college degree. And many only learned how to drink and failed at that too...lol

So this college student in what they are calling Calculus but really is only Algebra 2 at best, is struggling with the words Cost, Revenue and Profit. They also throw in there marginal cost, fixed cost and breakeven point, and Supply and Demand to make the word problems sound impressive.

But like i tell all my students, no matter how many fancy words they are using, they are basically giving you 2 points !! and with those 2 points, you need to find the slope and where it crosses the y axis. Something most schools teach in 6 or 7th grade and reinforce all through algebra and geometry.

Today's problem was Juan Valdez (yes, most textbooks are published in California) is making t-shirts. It cost him $3.50 to buy the t-shirts and a fix amount of $90 to set up his shop. He sells the shirts for $9.00. What is his "break-even" point ?

Let me know when you get the answer. And yes, you all got A's and B's in algebra because they do not give out C's anymore.

(For a discussion on slope, check out my other blog on "Fun Math" and Thales.)

So the book ask first to find the Cost linear function. Right off the bat, my student does not know what "linear" means. The biggest problem with word problems in the public schools is that the students do not know how to read. Many in the 10th grade are at a 4th or 6th grade level reading wise.

Ok so we need to remember that Slope is Rise/Run (rise over run). How much did the line rise divided by how much the line ran. In this case with our boy Juan, the slope is $3.50. (of course the selling price of $9 a shirt gets in the way. We call this "white noise"...or too much information.)

Since the book asked for the cost equation, we do not need to worry about the selling price for a little while.

At this point when helping a student, they need a plan of attack that will work with ALL word problems of this type, not just cost and profit problems. (Sometimes this is a double edge sword. I have learned over the past 30 years of tutoring struggling students especially with limited tutoring time, that to "get through the test" sometimes you just have to memorize certain problems and hope the teacher just puts those certain problems on the test. In my classes I call them "classics" and yes, the t-shirt problem is a classic in Algebra 1 classes and sometimes in Prealgebra at the prep schools.)

So i teach my tutorees to put down 2 points. Always go back to the 2 points. And then memorize the slope formula (change in y over the change in x). Struggling students can memorize better than think. Of course the downside of this strategy is that they forget what they have learned when they memorize something else. But who needs algebra in the real world anyways.

Ok the first point is x=0 then y=90 (what we call the "fixed" cost....if you sell 0 t-shirts you will still have to shell out the $90 to set up the shop or operation.)

At this point my college student who has passed precalculus in college (probably more of review of algebra one and geometry) asks me:

y = C(x) = mx + b

"that extra C(x) gets in my way !!", "I am stuck, i do not know what to do ?"

So i have to simple say..."get rid of it"...do you know y = mx + b ?

Now we go onto our second point of the problem...what if you sell 1 shirt ?

The cost is $90 plus $3.50 for the shirt.

The student says, "so is the cost of the first shirt $93.50 ?" good question.

Well that would be one expensive shirt, but true...if you sell no more shirts, that first shirt would have cost Juan $93.50...the reason most small businesses (95% in fact) go out of business in the first year. I wish we could have a nice discussion about the real world, but our time together is limited. (Most businesses goal should be to breakeven by the third year...that is why you have to have DEEP pockets to make a small business work. Most people blow ALL their money on the first year and then lose it all.)

So again we need to get AWAY from the wording and back to the 2 points (0,90) and (1,93.50).

therefore the slope is (93.50-90)/(1-0) = 3.50. The book tries to call this marginal cost, but this only confuses struggling students. m = 3.50 they understand.

(My student says...."oh, M in y = mx + b stands for marginal cost"...and I have to think for a second...in 33 years no one has made that connection to me...i told you he was a successful businessman. (Ok, Dr. Mead is that correct ? Dr. Morris ? how about you Dr. Zerla my math history prof ? Or Mr. Blount my trusty sidekick who likes to look every thing up.)