Imagine this: you are standing in line at the concession stand at the movies, and you only have $20 to spend on snacks. You look at the menu and see that a medium popcorn costs $7.10, a soft drink costs $5.25, and a pack of candy costs $4.95, and you need to figure out whether your $20 will cover all three items plus an eight percent sales tax. Would you:
a) Frantically pull up the calculator on your phone, add the prices of the three items together, then multiply by 1.08 to determine the total including sales tax.All three methods will yield the same result (yes, you can afford to snack away), but it’s likely that in a real life scenario, you almost certainly would have defaulted to option C. Why? It’s because you intuitively understand that finding the exact price isn’t entirely relevant to your problem. It doesn’t matter whether the total is $19.00 or $18.68 -- you just want to know if it will be less than $20, so coming up with a rounded answer is quicker and more efficient for your purpose. The same logic can be applied to many SAT questions, especially those on the test’s No-Calculator section: since most questions are multiple choice, students don’t necessarily have to find the exact answer; solving for something close to the correct answer is often good enough to answer the question without spending extra time on unimportant details.
Example 1:
Joaquin wants to order a felt table pad to cover the surface of a circular table. He measures the distance around the outer edge of the table and determines the table’s circumference is 10π feet. If the felt costs $2.00 per square foot, approximately how much will Joaquin need to spend to completely cover the surface of the table with the felt pad?
This question includes a couple of indicators that students likely shouldn’t be concerned about calculating an exact answer. Firstly, the question asks students “approximately, how much money will Joaquin need to spend?”; since the answer will be approximate, any calculations can likely also be approximated. Additionally, the four answer choices are fairly disparate, meaning that it’s unlikely that students would come up with an approximate answer that is close to more than one of these options. Regardless of strategy, students first must identify what information is known (the price of felt per square foot and the circumference of the table), what they need to find out (the cost to cover the table with felt), and how to use the known information to solve for what they are trying to find (use the known circumference to solve for the area of the table top and multiply by the cost of the felt per square foot). Whether students choose to round or use the exact numbers, the steps will be the same; the difference is in the ease of the calculations within those steps.
Ultimately, the question required students to round their answer regardless of which method they used, but calculating 3(25) and 2(75) by hand is much quicker and easier than calculating 3.14(25) and 2(78.5398) by hand.
As we can see in the next example, this strategy can also apply to more straightforward algebra problems where rounding might not seem as obvious an approach.
Example 2:
An important thing to remember when dealing with the SAT’s No-Calculator Math section is that it is not designed to simply test students on their ability to perform calculations but rather to test them on their understanding of mathematical principles or concepts. In fact, if students find themselves dealing with numbers that leave them wishing they could pull out their calculators, it’s usually a good sign that there might be an easier way to find the correct answer. Oftentimes, this means taking a more outside-the-box approach than what students might try on a math test in school.