Whenever I start teaching any math class, I start out with what should be really simple algebra problems, or maybe even problems that aren’t considered algebra. I ask my student or students to divide 3822 by 14 without using a calculator. In an algebra class of 30 people, around 18 to 20 will get the problem correct. This means that the average grade of the class would be failing if this was a quiz that was made up of only one problem. I then ask everyone in the class to stand up. Then I ask everyone who got the problem right to sit down. Finally, I ask anyone who did not check their answer to sit down. In the end, everyone is sitting down.

*Next, I’ll ask my algebra class to do another similar division problem with the catch that they must check their answers when they’re finished with multiplication. The logic behind this is that if you have something like 15 divided by 3 and you get an answer of 4, then multiplying 4 times 3 will give you 12 and show you that you have the wrong answer. Out of a class of 30 people, usually no one will get the problem wrong the second time around.*

The point of this exercise is to show how important it is to check your answers when you’re working on algebra problems, as well as problems from other math classes. If you have an equation you’re supposed to solve like 2x + 7 = 15, and you get an answer of x = 4, then you should check it by plugging x into the equation. You’ll get 2(4) + 7 which you know to be 8 + 7 = 15, so you know you have the answer. The key here is to be able to tell the difference between “an answer” and “the answer” to algebra problems.

A popular way to use this method is when you’re learning how to subtract integers and you want to know if you’ve got the right answer.

So whenever you’re taking notes in class, you should always be concerned with learning how to check your answers to algebra problems. In the division example, which many people would suggest is just basic arithmetic, checking your answer raised the letter grade of the class from an F to an A for a difference of about 30 to 35 percent. If this can help an entire class raise their grade on an arithmetic problem, then it’s pretty clear how it can help you with algebra concepts that you are recently learning.