I teach very capable math students who are usually taking some form of calculus. However, their high level of math proficiency does not make them immune to making careless errors on SAT math questions. Careless math mistakes can be very costly. For example, on the January 2013 SAT one error reduced a student’s overall math score by -30 points and two errors reduced a student’s overall math score by – 50 points.
One of my top math students recently missed the following Level 3 problem:
At a certain local supermarket, Rhea paid $6.40 for 4 pounds of watermelons and 2 pounds of pears, while Morgan paid $8.80 for 4 pounds of watermelons and 4 pounds of pears. At these rates, what is the cost, in dollars of 3 pounds of pears?
My student correctly calculated that a pound of pears costs $1.20. So with the clock ticking away, he answered (A) and moved on the next question. Take another look at the question. The question asked students for the cost, in dollars, for “3 pounds of pears.” The correct answer is therefore $3.60 or (C). My student made a very common mistake. He calculated the unit cost and then failed to remember how many units the question asked for. Note that the always-clever College Board test writers provided an answer for students who calculated the cost of 1 pound of pears.
Careless errors are surprisingly common. I have had students calculate X when the question called for 2X and calculate the area of a geometric figure when the question called for the perimeter of the figure. In order to eliminate this type of careless error I teach my students to underline or circle what the question is specifically asking for. So for this question a meticulous math student would circle or underline “3 pounds of pears.”