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Explorations in Core Math - Grade 6: Online Textbook Help10 chapters | 118 lessons

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After reading this lesson, solving problems in your head will be easier, and you'll be able to answer your teacher or friends quickly and easily. Learn the technique that will help you quickly solve problems in your head.

As you start getting better at your math and you learn more and more math skills, you'll start doing more and more one-step problems. **One-step problems** are math problems that use only one operation to solve them. On paper, one-step problems will look something like this:

Sometimes, your teacher won't give you a piece of paper with problems on it. Instead, your teacher may simply use words to ask you the same problems. She might say something like this:

'I am thinking of a number that when you subtract 8 from it, you'll get 15. What is this number?'

If your teacher happens to ask you the problem verbally (with words), then you'll need to solve the problem using mental math. You perform **mental math** when you use your brain to solve problems. This means you use your brain to do all the work instead of writing your work down. The only thing that you'll write down, if anything, is the answer.

When using mental math to solve your one-step problems, you can use a technique that involves using the opposite operation. If you look at the one-step example problems above, you'll see that you have the number you are looking for written down as a letter, and then you see a number being added to or subtracted from this number. To find your answer using mental math and this technique, you'll use the opposite operation to combine the two numbers that you see. Addition is the opposite operation to subtraction. If you see subtraction, you'll use addition to solve the problem. If you see addition, then you'll use subtraction to solve the problem.

For example, you can solve the problem that your teacher just gave ('I am thinking of a number that when you subtract 8 from it, you'll get 15. What is this number?') by adding the 8 to the 15. Because 8 + 15 is equal to 23, your answer is 23.

Whenever you do mental math, though, you'll want to make sure that you always check your work. You can do this in your head, too. So, for the problem we were working on, you can check by subtracting the 8 from the 23 and seeing if it actually equals 15. Let's see: 23 - 8 = 15. Yes, that's right. So, 23 is a correct answer.

Let's try a couple more.

Your teacher now asks another problem:

'I am thinking of a number that equals 7 when you add 3 to it. What is this number?'

Using mental math and the technique you just learned, you look at the operation that is currently in the problem. It is addition. So, you'll use the opposite operation: subtraction. You go ahead and subtract the 3 from the 7 in your head. You get 7 - 3 = 4. Is this correct? You check this answer in your head too. You ask yourself, 'Does 4 plus 3 equal 7?' Yes it does! So 4 is the correct answer.

Your teacher asks still another question:

'I am thinking of another number now. This time, the number equals 5 when 2 is subtracted from it. What is this number?'

Again, you use the technique of using the opposite operation. The operation that is in the problem is subtraction, so you'll use addition. You go ahead and add the 2 to the 5 in your head. You get 7. Is this correct? Checking, you ask yourself, 'Does 7 minus 2 equal 5? Yes, it does! So 7 is the correct answer.

Hooray! You answered all the problems correctly!

Now, let's review a bit.

**One-step problems** are math problems that only need one operation to solve them. You may be asked to use mental math to solve these problems. **Mental math** involves using your brain to solve problems. To solve one-step problems using mental math, you can use the technique where you use the opposite operation to help you find your answer.

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Explorations in Core Math - Grade 6: Online Textbook Help10 chapters | 118 lessons

- Estimating With Whole Numbers
- Estimating Sums, Products and Divisors of Whole Numbers
- Performing Long Division with Large Numbers: Steps and Examples 9:12
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- The Commutative Property: Definition and Examples 3:53
- The Associative Property: Definition and Examples 4:28
- Distributive Property: Definition, Use & Examples 6:20
- Using Mental Math to Solve One-Step Problems: Lesson for Kids
- Go to Explorations in Core Math Grade 6 - Chapter 1: Operations & Properties

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