Monday, June 4, 2012

PerCent Challenges From Middle School to SATs

Never too late in the school year to review percents, right? Well, even if you don't agree, here goes... 

First a problem similar to the one I posted on Twitter the other day.

Middle School Level?

The cost of a meal including a 10% tip was $13.75. What was the tip, in dollars?
Ans: $1.25

SAT-type (Higher level of difficulty)

The cost of a meal is $M. With an x% tip included,  the bill came to $T. Which of the following is an expression for x in terms of M and T? (A) T/M (B) (T-M)/M (C) 100T/M (D) 100(T-M)/M (E) (T-M)/(100M)
Ans: D

Thoughts and Questions...

What % of your middle school students could handle the first question? For that matter, what % of your secondary students would solve it?

Can you predict which of your students would be able to solve the first question mentally or with some quick trial-and-error (ok, G-T-R), using their calculators. I chose 10% to make this possible. Do you get upset when students do this? Should you?

What do you predict would be the difficulties your algebra students might confront in the 2nd problem?

Is it easy to eliminate some of the answer choices and to make an educated guess from the rest?
(NOTE: I composed the question and the answer choices and I know some of you could improve upon my efforts!)

NOTE: The 2nd question is representative of the harder problems on the SATs and there are many of these in my new Challenge Math Problem/Quiz Book mentioned below.

If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar. 175 problems divided into 35 quizzes with answers at back. Suitable for SAT I, Math I/II Subject Tests, Math Contest practice and Daily/Weekly Problems of the Day. Includes multiple choice, case I/II/III type and constructed response items. Price is $9.95. Secured pdf will be emailed when purchase is verified. DON'T FORGET TO SEND ME AN EMAIL (dmarain "at gmail dot com") FIRST SO THAT I CAN SEND THE ATTACHMENT!