The following example of how to understand and solve a math problem on a standardized test such as the SAT or ACT is provided by John Accardi of Academic Testing Advantage in Boulder Colorado.

When preparing for the ACTs and SATs, there is no substitute for knowing the math.  This is especially true for the ACT. You are expected to remember the math you learned in your early high school courses.  The SAT focuses a little differently on more critical reasoning skills.  (The SAT doesn’t even expect you to remember the formula for the area of a square.) The SAT tests your ability to "think out of the box," be clever and insightful, see patterns and creatively solve problems.  You can prepare for the math portions of these tests accordingly.  Examine the following SAT example.

This problem is often presented in a variety of forms.  Six nails are nailed into a board as vertices of a six-sided figure like this:

You are asked to determine how many rubber bands you need to connect every possible pair of nails, without repetition (no two rubber bands on the same pair of nails) or without missing any pairs of nails.  There are a number of approaches.  Some students will randomly start drawing lines connecting the pairs they see, hoping to get them all.  Here is a solution to this random approach:

Can you tell if the above solution is correct?  You might not be able to quickly determine this because of the random approach to drawing the connections.  (There is one missing; see if you can find it.)

Now take a look at the start of a solution that indicates a more systematic approach.

The first thing to notice about this more organized approach is that the connections are drawn in a systematic way (they’re numbered in the figure), starting with all connections from a single nail (the one labeled with the circled number 5).  In other words, from that nail, connections are made to other nails in a clockwise direction (these connections are labeled 1-5).  Once all the connections from this first nail are drawn, the student noted the number of connections from that first starting nail (labeled with the circled 5).  Next, the student moved clockwise to the next nail (labeled with a circled 4) and repeated the procedure, drawing connections to the other nails in a clockwise direction (those labeled 6-9).  Again, a number was noted next to that second starting nail (the circled 4).  The student continued with the third nail, etc., until all the connections are made as shown below.

With this systematic approach it is easy to get all the connections and not miss any.  Writing the circled number next to each nail provides a self-check.   Notice how the circled numbers decrease by one each time.  This not only gives confidence in the correct approach as you solve the problem, but, once you see the pattern, you don't have to draw all the remaining connections.  Adding the circled numbers gives the final answer. 15 rubber bands are required.

There are many problems like this that put a premium on your ability to come up with an insightful, systematic approach.  The rigor of the approach often determines if you get the correct answer.

It is important to understand the underlying purpose of the questions on these standardized tests.  Such an understanding helps you can formulate effective strategies and approaches.

This is an example of the test taking strategies you will learn at Academic Testing Advantage.