Blog #41 – HOW CERTAIN PARTS OF A PROBLEM MAY HELP IN SOLVING IT

When teaching in the classroom or tutoring students to prepare for taking multiple choice tests or other kinds of tests, students need to learn that many times the problem can assist in acquiring the solution. To illustrate my point, look at the following problems.

Example 1: 2972 x 4563 = ___.
(A) 1,348,754 (B) 1,358,392 (C) 1,389,210 (D) 1,356,236 (E) 1,410,628

Multiplying the numbers would be tedious if you are not allowed the use of a calculator. However, if you look at the answer choices, all have a different units digit. When solving 2972 x 4563, notice that the product of the units digits is 6. Since the only answer choice with 6 in the units digit is (D), then that is the answer.

Example 2: Mercury metal is poured into a graduated cylinder that holds exactly 22.5 mL. The mercury used to fill the cylinder weighs 306.0 grams. Use the information given to calculate the density of mercury. ___ grams/mL.

Although this is a middle school problem, many students have a tendency of skipping it because they do not know what density is. In this type of problem, looking at how the answer must be written, is a clue as to how to solve the problem. In the fraction ¾, the bar means “divided by”. Thus, since the answer blank requires that it be grams/mL, to solve this, divide 306.0 grams by 22.5 mL. These are just a few of the types of strategies that students can learn to facilitate their work on mathematics tests.

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