Lesson Plan - Get It!
You have probably seen some pretty crazy things that are NOT numbers in the math you've learned thus far, but have you ever seen a trapped number like this: |-3|? Why do you think there are bars around that negative three? Is it in number jail? Did it do something wrong? Can positive numbers be trapped, too? If you're baffled by that little number cage, then you're absolutely in the right place!
Can you think of some opposites?
Opposites are things that are completely different, or contrary to one another.
Go ahead and make a quick list of 9-10 opposites you can think of. Here is a quick example to get you started: Hot and Cold.
Now, what about opposites in math? You may have never thought about math or numbers having opposites, but let's give it a try.
What is the opposite of a negative number?
How about the opposite of –2?
And the opposite of –1000?
Did you say the opposite of negative is positive? It's the correct response! If you used reason and said the opposite of negative is positive, then does the same apply to a negative number? Is the opposite of a negative number a positive number? Let's find out.
The focus of this lesson is on something called "absolute value," and you will see shortly just how finding the opposite of a negative number ties right in. You see, absolute value is how far a number is from 0 on a number line. It looks like two vertical bars around a number, just like this:
EX: |-5 | = 5
The absolute value of –5 is 5, because it is 5 spaces away from 0 on the number line. Hopefully, you see you got the OPPOSITE of –5 when you took the absolute value.
This example teaches us an important lesson: The absolute value of a number will always be the positive version of that same number. Why is that? Because you cannot be a negative distance from 0 on a number line! Here are a few more examples:
|10| = 10
|-7| = 7
|-101| = 101
As you can see, it does not matter if you are asked to find the absolute value of a positive number or a negative number, your answer will always be the positive version of that number.
And, guess what? We actually don't even NEED a number line to find the absolute value! We KNOW that absolute value represents the distance a number is from 0 on a number line, and we also know we don't have to have a number line to count it. Instead, just remember:
The absolute value of any positive or negative number is just the positive version of that number!
Easy enough? Let's put this idea into practice and have you try a few on your own in the Got It? section!