# Common Math and Science Problem-Solving Mistakes

Often, students of math and science who actually understand the concepts involved in solving a problem will nevertheless fail to solve it correctly. This is usually caused by using an incorrect problem-solving technique. Students who follow a structured, methodical approach to solving problems will perform better on homework assignments and tests alike.

1. Solving the wrong problem

Many students don't take the time to read the question carefully and as a result solve a different problem than the one asked for. A student should analyze the problem statement and identify precisely what is wanted for an answer, and what information is given.

2. Failing to pay attention to units

In science, every number has a unit associated with it. Mathematical formulas are only valid if consistent units are used for all variables. Sometimes it will be necessary to convert units for the answer and/or the input variables. In the absence of directions on what units are wanted for the answer, assume Standard International (SI) units for all variables.

3. Losing track of details

There are many examples of this mistake including sign errors, dropping terms, miscopying variables or exponents, dividing by zero, and using other invalid operations. Often, these errors are caused by hurrying.

4. Incorrectly rounding the answer

Scientific measurements have a precision associated with them. This is expressed as the number of significant digits. For example, a measurement stated as 2.54 cm has three significant digits -- meaning the actual number is closer to 2.54 than it is to 2.55 or 2.53. When solving problems, in order to provide consistent precision, it is required to express the answer with the same number of significant digits as the numbers you are given. Using too many or too few significant digits in the answer misstates the precision with which the answer is known.

5. Applying a rule when it does not apply

Most math rules apply to all equations. However, there are exceptions. For example, it can be incorrect to divide by something that is zero, take the square root of a negative number, or subtract apples from oranges. In physics, an equation may only apply in a certain set of circumstances. For example, the equation F = mg gives the force of gravity near the earth's surface. If you attempt to use this equation to describe a system in orbit around the sun, it will not work. Use the rule that applies to the given situation.

In summary, read the question carefully; understand what is given and what is asked for; use consistent units; take the time to be careful with details; and round the answer appropriately. Do not apply a rule where it does not apply. If you do these things, you will tend to get the right answer every time. Reading a problem statement carefully, understanding what is known and what is unknown, and applying the appropriate rules carefully will yield the best results. In addition, trying to avoid the following common mistakes will pay dividends.

1. Solving the wrong problem

Many students don't take the time to read the question carefully and as a result solve a different problem than the one asked for. A student should analyze the problem statement and identify precisely what is wanted for an answer, and what information is given.

2. Failing to pay attention to units

In science, every number has a unit associated with it. Mathematical formulas are only valid if consistent units are used for all variables. Sometimes it will be necessary to convert units for the answer and/or the input variables. In the absence of directions on what units are wanted for the answer, assume Standard International (SI) units for all variables.

3. Losing track of details

There are many examples of this mistake including sign errors, dropping terms, miscopying variables or exponents, dividing by zero, and using other invalid operations. Often, these errors are caused by hurrying.

4. Incorrectly rounding the answer

Scientific measurements have a precision associated with them. This is expressed as the number of significant digits. For example, a measurement stated as 2.54 cm has three significant digits -- meaning the actual number is closer to 2.54 than it is to 2.55 or 2.53. When solving problems, in order to provide consistent precision, it is required to express the answer with the same number of significant digits as the numbers you are given. Using too many or too few significant digits in the answer misstates the precision with which the answer is known.

5. Applying a rule when it does not apply

Most math rules apply to all equations. However, there are exceptions. For example, it can be incorrect to divide by something that is zero, take the square root of a negative number, or subtract apples from oranges. In physics, an equation may only apply in a certain set of circumstances. For example, the equation F = mg gives the force of gravity near the earth's surface. If you attempt to use this equation to describe a system in orbit around the sun, it will not work. Use the rule that applies to the given situation.

In summary, read the question carefully; understand what is given and what is asked for; use consistent units; take the time to be careful with details; and round the answer appropriately. Do not apply a rule where it does not apply. If you do these things, you will tend to get the right answer every time. Reading a problem statement carefully, understanding what is known and what is unknown, and applying the appropriate rules carefully will yield the best results. In addition, trying to avoid the following common mistakes will pay dividends.