# Conquering the Enemy: 7 Ways to Wipe Out Careless Math Errors on Tests by Ian Pulizzotto

Careless errors are an enemy to high grades in mathematics. On math tests, countless students fail instead of passing, or earn a C or D instead of an A or B, just because of careless errors. Many students also wonder if their answers are right. Here are 7 ways for you to conquer this enemy.

2) Pay attention to details such as parentheses and negative signs and learn to recognize and avoid the common, tempting algebra errors. Errors with negative signs and parentheses are extremely common, and assuming that (x+y)^2 is always the same as x^2 + y^2 is an especially tempting error (this can be seen as an error just from using x=1 and y=1).

Paying attention to these details and avoiding the tempting errors will put you ahead of the game.

3) A basic technique of checking your solution to an algebra equation is to plug in your value of the variable and verify that the equation is true.

This basic idea can be extended to other situations. For example, if you solve a system of 2 equations and 2 variables, plug in your values for the variables and verify that both equations become true. If you are given two ordered pairs (points) and find an equation of a line through them, plug in the points and verify that both points make your equation true. If you solve a word problem, verify that the values you obtained for the quantities in the problem meet all the conditions stated in the problem.

4) Don't miss the correct answer by one step! Make sure to read the question again and do what is actually asked for. For example, a common technique of solving a word problem is to define a variable, but keep in mind that the answer to the word problem is not always just the value of that variable.

5) Read problems, especially word problems, carefully. Watch out for key words and phrases like "not", "sometimes", "always", "never", "except", "at least", etc. Also be on the alert for changes of units, which sometimes occur in geometry and measurement problems.

6) Make sure the size of your answer is reasonable. For example, this can help you catch common calculation errors such as misplacing the decimal point. This is because misplacing by even one decimal place usually makes the answer unreasonably large or small.

Let's say you were multiplying 0.75 times 0.32. Clearly the answer is less than 0.32 and also more than half of 0.2 (which is 0.1), so you can see that answers like 0.024 and 2.4 are clearly wrong. The correct answer is 0.24.

7) Consider more than one way to solve the problem and make sure to get the same answer each time.

For example, if a store offers 20% discount on a backpack normally costing $50, you can calculate the sale price by taking 20% of $50 to get $10, and then subtracting $10 from $50 to get $40. You can also calculate the sale price by subtracting 20% from 100% to get 80%, and then taking 80% of $50 to get $40 once again. Therefore, you can increase your confidence that the sale price is really $40.

Yes, analyzing your answers does require some extra work, but with practice you can do this extra work efficiently. Doing so will give you one more reason to celebrate when that test paper comes back. 1) Never turn in a test early without first analyzing your answers. The loss from careless errors far exceeds the gain from being the first student to turn in the test.

2) Pay attention to details such as parentheses and negative signs and learn to recognize and avoid the common, tempting algebra errors. Errors with negative signs and parentheses are extremely common, and assuming that (x+y)^2 is always the same as x^2 + y^2 is an especially tempting error (this can be seen as an error just from using x=1 and y=1).

Paying attention to these details and avoiding the tempting errors will put you ahead of the game.

3) A basic technique of checking your solution to an algebra equation is to plug in your value of the variable and verify that the equation is true.

This basic idea can be extended to other situations. For example, if you solve a system of 2 equations and 2 variables, plug in your values for the variables and verify that both equations become true. If you are given two ordered pairs (points) and find an equation of a line through them, plug in the points and verify that both points make your equation true. If you solve a word problem, verify that the values you obtained for the quantities in the problem meet all the conditions stated in the problem.

4) Don't miss the correct answer by one step! Make sure to read the question again and do what is actually asked for. For example, a common technique of solving a word problem is to define a variable, but keep in mind that the answer to the word problem is not always just the value of that variable.

5) Read problems, especially word problems, carefully. Watch out for key words and phrases like "not", "sometimes", "always", "never", "except", "at least", etc. Also be on the alert for changes of units, which sometimes occur in geometry and measurement problems.

6) Make sure the size of your answer is reasonable. For example, this can help you catch common calculation errors such as misplacing the decimal point. This is because misplacing by even one decimal place usually makes the answer unreasonably large or small.

Let's say you were multiplying 0.75 times 0.32. Clearly the answer is less than 0.32 and also more than half of 0.2 (which is 0.1), so you can see that answers like 0.024 and 2.4 are clearly wrong. The correct answer is 0.24.

7) Consider more than one way to solve the problem and make sure to get the same answer each time.

For example, if a store offers 20% discount on a backpack normally costing $50, you can calculate the sale price by taking 20% of $50 to get $10, and then subtracting $10 from $50 to get $40. You can also calculate the sale price by subtracting 20% from 100% to get 80%, and then taking 80% of $50 to get $40 once again. Therefore, you can increase your confidence that the sale price is really $40.

Yes, analyzing your answers does require some extra work, but with practice you can do this extra work efficiently. Doing so will give you one more reason to celebrate when that test paper comes back. 1) Never turn in a test early without first analyzing your answers. The loss from careless errors far exceeds the gain from being the first student to turn in the test.