$200 for a $70 Item Isn’t Much of a Discount.

$200 for a $70 Item Isn’t Much of a Discount. By Charlie Mathers Assistant Professor of Mathematics Northampton Community College

Let’s do some Math • Take out a sheet of scrap paper and a pen. • Work out the following Multiple Choice arithmetic problems and write the letter that corresponds to your answer in the space on the Answer Sheet. • NO CALCULATORS!

98 x 4,053 = #1 • 68,694 • 39,791 • 397,194 • 4,151

#2 -99,091 + 464 = • 98,627 • -99,555 • -98,627 • -88,627

#3 0.67 x 98 = • 11.26 • 102.34 • 65.66 • 0.626

#4 4.08 ÷ 1.2 = • 4.896 • 1.02 • .34 • 3.4

#5 15% off of 384 = • 57.6 • 326.4 • 3.26 • 374.8

#6 a) b) c) d)

#7 a) b) c) d)

#8 a) b) c) d)

#9 Suppose that you were one of 98 people who participated in a group purchase of lottery tickets. Upon winning, you’re given $4,053. What would the total prize have to have been if that was the correct distribution of funds? • $68,694 • $39,791 • $397,194 • $4,151

#10 Imagine you’re sitting at a company meeting where the CEO is presenting their profits during these difficult economic times (that are not all Obama’s fault, by the way). He reports that two quarters ago, our profits were -$99,091 and last quarter, was only $464 better. What were our profits last quarter? • $98,627 • -$99,555 • -$98,627 • -$88,627

#11 Suppose you are considering purchasing some stock (“shares” of stock represent partial ownership in the company). The stock that interests you the most is currently $0.67 per share. How much would 98 shares of the stock cost? • $11.26 • $102.34 • $65.66 • $0.626

#12 Suppose you are working in a hospital setting and you have 4.08 milliliters of GobbleDeGook (that’s the stuff that comes out of a person’s YouKnowWhat) and you need to reduce it by dividing it by a factor of 1.2 for some reason. • 4.896 milliliters. • 1.02 milliliters. • .34 milliliters. • 3.4 milliliters.

#13 Suppose that as an employee of Pretty Good Buy you get an employee discount of 15% off any purchase at the store. The new WiiBoxStationOrWhatever is $384. How much would you have to pay? • $57.6 • $326.4 • $3.26 • $374.8

#14 • Imagine you are on a team of people working on the installation of a new bridge. One angle involved in the process measured 11/24 of a degree. Later in the process, it is determined that an increase of 19/36 of a degree would be required. What is the total angular measurement? a) b) c) d)

#15 • Bruce Perlowin, one of the most successful Marijuana Dealers in American history, was trying to get 59 pounds of product through various California harbors. He was unsuccessful at one port where authorities confiscated 4 1/3 pounds. How much marijuana was successfully imported? a) b) c) d)

#16 • A recipe calls for 2/3 of a pound of Whateverthehell. But that’s for a serving of six. How much Whateverthehell would be needed for one serving? a) b) c) d)

Why did some people find these problems to be so easy?Are we all varying degrees of this guy?

Did anyone find the Word Problems easier than the straight computations? • My students do. • In fact, their most common response to those questions here is “duh”. • Originally surprising to me because of their typical aversion to word problems.

Let’s not forget, he would do terrible on the word problem parts.

Should students know how to do the actual exact computations? • I do think so. • But having a strong Number Sense is actually more important. • Some will argue that since computers and calculators do the work, none of this is necessary.

Actor Dennis Quaid and his wife would have something to say about that. Their newborn twins nearly died after being given 1,000 times the dosage of a blood thinner. How could that happen?

So while I use the above described approach to connect classroom math to real world experiences. • In fact, I show them that they’re already doing it with examples like: • If I have $70, do I have enough to buy the pants for $39.99 and the shirt for $29.99. They say “of course, you have 70 bucks”. You didn’t do 9+9=18 carry the 1…. • The skill must be developed and used in their careers afterwards.

A Different Perspective • Discussing this with a Dean at my college, she indicated “maybe this stuff needs to covered in our developmental courses”. • A logical conclusion, of course. • But our expectations need to be reasonable. • My kid’s Kindergarten Teacher “covers” Drawing, but that doesn’t make what he brought home last week a Picasso.

Some Data • At the end of last semester, I gave a quiz very similar to the first half of these questions to several other Instructor’s class. • PreAlgebra (two sections) 50% and 59% • Trigonometry 82% • Calculus 87% • It should be noted that the PreAlgebra students just went through a semester covering this stuff!

In Practice • Little multiple choice quizzes such as these helps me to refocus students attention on the “big picture”. • Especially important with courses like Introductory Statistics, where getting them focused on the big picture is a big part of the course. • Where rounding error causes numbers to differ without being “wrong”.

One More Word Problem • A bear’s age, y, (in months) can be estimated from the equation y = 5.5 + .2x, where x represents it’s weight (in pounds). Suppose a bear was estimated to be 6.5 years old. How much did the bear weigh? (Feel free to use a calculator for this one.)

Did you get 5? • (at least at some point?) • I don’t know about you, but living up in the Poconos, I have seen my share of bears. And at least the ones I’ve seen, weigh a heck of a lot more than 5 pounds! • If you did get 5 though, you are understanding the algebra correctly, you just missed the conversion of the 6.5 years to 78 months. • This is kind of the point. Getting students to see that an answer doesn’t make sense.

$200 for a $70 Item Isn’t Much of a Discount.