The Hardest ISEE Math Problem
STUMPERS Volume 2: Inches away.
In this series of posts, we will explore some of our practice questions that have stumped a remarkable number of students. We hope to highlight some common mistakes and how to avoid them on the official test.
If you were ever a child, you surely remember the sheer joy of working through a challenging measurement-based word problem.
Alright, maybe that was just us. In any case, our second installment of Stumpers looks at the math question that stymied more than 90 percent of our test-takers. And yes, it’s a delightful word problem.
Before we discuss it, let’s see how you do on the question, from one of our Middle Level Quantitative Reasoning sections:
A piece of foam insulation is cut into a rectangular shape to fit an old doorway that is 7 feet high, 3 feet wide, and 8 inches deep. What is the volume of the foam insulation required to completely fill the space of the doorway?
A) 14 ft³
B) 21 ft³
C) 100 ft³
D) 168 ft³
Did you answer D? If so, you’re wrong, but you’re not alone. Nearly 75 percent of the sixth and seventh graders who answered this question bit on 168 ft3. The correct answer is actually A) 14 ft3, the answer chosen by a mere 9.5 percent of test-takers.
Why this question is so hard
First off, a brief explanation of the correct answer—this should give us some insight into why students miss this question so often.
If you selected answer D, you probably arrived at that answer by simply multiplying the numbers in the question: 7 x 3 x 8 = 168. Go back and read the question closely, though, and you’ll see that the test-writers have switched things up in the middle. While the first two measurements (height and width) are described in feet, the third (depth) is described in inches.
It’s therefore necessary to convert the 8 inches into feet: 8 in ÷ 12 in = ⅔ feet. So we end up with 7 x 3 x ⅔ = 14.
Is this a trick question? No, but it’s a tricky question. And it’s the reading comprehension aspect of the question that apparently caught most students off guard.
This particular type of problem requires a thorough parsing of the entire question. If you’ve read the first installment of our Stumpers series (find it here), you may recognize this “READ EVERY WORD!!” refrain. Carelessness costs.
Take-aways: How to avoid this mistake
As mentioned above, the most critical strategy for success on these word problems is to read every piece of the question, and to re-read when necessary. This is especially important on questions like this one, which seems like a straightforward, one-step multiplication problem. There won’t be many cut-and-dry arithmetic problems on the Quantitative Reasoning section, so if the question seems too simple, you could very well be overlooking something.
To compound this, good test-writers create answer choices that correlate with common mistakes. Even if the answer you calculated shows up in the options, that doesn’t mean it’s correct.
That leads into a final pointer for the ISEE and standardized tests in general: think like a test writer.
Most of the time—and, yes, there may be the rare exception—the ISEE’s test writers will write story problems that could and do happen in the real world. If something in a question sounds utterly ridiculous, it could very well be that you’re reading the question wrong.
Look back at the question, and you’ll see it references the dimensions of a door frame. How many eight-foot-deep door frames have you come across? With the possible exception of Swiss bank vaults, probably not many.
Remember, the Quantitative Reasoning section requires reasoning, logic, and a good deal of care. Be sure your child has these skill-arrows in his or her test-taking quiver before the official exam.
