Tutoring For All Ages

Here’s today’s medium-level SAT Question of the Day (note that if you saw it on the SSAT/ISEE, it would be a Hard question):

In the figure above, the large rectangle is divided into six identical small squares. If the perimeter of the large rectangle is 30, what is the perimeter of one of the small squares?

A) 5
B) 8
C) 9
D) 10
E) 12

How do you solve this problem in the quickest way possible?

Here’s how the College Board thinks you should solve it. That’s the “right” way to do it: use the ratio of length to width to set up an equation using the overall perimeter. And assuming you don’t make a careless algebra error, that will get you to the right answer. For some students, it may even be the fastest way to get to the right answer.

But not every student is going to see this way immediately. If you’re one of them, consider another way: working backwards, sometimes called guess-and-check. Start with the middle answer choice and assume it’s the perimeter of a square. Figure out what each side of the rectangle then has to be, and see if that matches the given perimeter of the whole rectangle. If it does, you have your answer. If not, you should be able to tell whether you need the perimeter to be bigger or smaller, so you can figure out which answer choice to try next.

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We hear a lot of reasons for why students don’t like to write down their intermediate steps on standardized tests. Sure, it may not be necessary to show your work in the same detail as when you’re graded on that work, but you should think twice before leaving your test booklet blank. Our most commonly-heard excuse is:

Habit. It’s just what I’ve always done.

Now, sometimes this is just another way of saying, I’ve never been allowed to do it. Students taking statewide standardized tests aren’t always allowed to write in their test booklets. That’s because some schools re-use their test booklets from year to year, and erasing is time-consuming and can be damaging to the paper. (Whether or not we think that’s a good policy is a subject for another post.) So when students go from using separate scratch paper to having no separate scratch paper at all, they often just think they’re not supposed to write anything down.

If this sounds familiar to you, know that the ACT, AP, ISEE, SAT, and SSAT exams all expect that you’ll be using your test booklet as scratch paper. Part of your test fee is paying for that test booklet, which will be thrown away after you take the test. So, write away!

But for those students who are just in the habit of doing all their work in their head, consider the adage: “If you always do what you’ve always done, you’ll always get what you’ve always gotten.”

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Students often think that just because nobody will be checking their work on a standardized test, that means they won’t be punished for leaving the test booklet free of scratch work. To that end, we’re continuing our series on the most common reasons that students fail to “show their work” on standardized test day:

Pride. I should be able to go without.

We see this a lot from students who are taking a test that they expect to get a high score on, and it’s also a favorite excuse from people who like to get to an answer fast.

Unfortunately, standardized tests don’t care about your ego or your impatience. You don’t get bonus points for turning in a blank test booklet, or for turning it in early. If you missed a negative sign, no one but you is going to know that you made a simple, careless error. Careless errors get the same score as errors of knowledge or understanding.

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Today’s SAT Question of the Day is a double-blank sentence completion:

Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole.

The play, which features —— mix of comedy, pathos, and music, was correctly described by one honest critic as a ——.

A) a seamless . . debacle
B) an ungainly . . hodgepodge
C) an unfortunate . . masterpiece
D) an inappropriate . . success
E) a harmonious . . failure

It’s a question that, in some ways, hinges on one word: honest. A theater critic would have no reason not to be honest if they were reviewing a good play. So it’s likely that it was a bad play, so we should look for answer choices that reflect that.

However, even if you missed that clue word, you could still figure out the right answer from the other clue words (play, mix, correctly, and critic). (more…)

When it comes to homework and in-school tests, the vast majority of our students don’t have to be reminded to show their work (at least, not more than once or twice). Getting credit in school isn’t usually about getting the right answer; it’s about demonstrating that you know how to get the right answer.

But when it comes to standardized tests, many of the same students, who painstakingly write out every line of algebra or underline every important line in their history textbook, won’t touch pencil to paper except to fill in a bubble. We’ve yet to see a student who can get away with doing it on every question of a test — it inevitably leads to careless mistakes.

And yet, sometimes a student, despite just having seen the results of those careless mistakes, continues to leave a blank workspace again and again while working through practice problems.

Why does this happen? There are likely many reasons, but we’ll address a few of the more likely causes in a series of posts, starting with:

Time. If I write out my work, I won’t be able to finish the whole test.

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