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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Allison Petrovic*

Allison has experience teaching high school and college mathematics and has a master's degree in mathematics education.

In English, an interval is a period of time between events. In math, intervals are numbers that are between two other numbers. But what exactly is included and how can we use math symbols to show that? In this lesson, we'll learn what intervals are and how they can be written.

Did you hear that? The weather forecaster just said there is going to be a snowstorm with at least 3 but less than 8 inches of snow! So, what are the different amounts of snow that we could expect based on those numbers? Well, go get your snow shovel ready and then let's find out.

An **interval** is a range of numbers between two given numbers and includes all of the real numbers between those two numbers. As you may recall, **real numbers** are pretty much any number you can think of: 3.56, 171, âˆš5, -0.157, Ï€, etc. When the forecaster said that there would be at least 3 but less than 8 inches of snow, he described the amount of snow in an interval!

Intervals can be written using inequalities, a number line, or in interval notation! There are also special ways to indicate whether the two given numbers, known as endpoints, are included in the interval.

The math **inequalities** are the symbols that stand for less than, less than or equal to, greater than, and greater than or equal to. Like these. Find the picture to recall what each of these symbols are!

Let's break our weather forecast down and write the interval using inequalities:

The first part is that it will snow at least 3 inches. That means that the amount of snow, which we will represent with the variable *x* since it's unknown, will be at least equal to 3 but could be greater than 3. The second part of our interval is that the amount of snow, *x*, will be less than 8 inches.

Find the image that shows this inequality. We read this image like this: 3 is less than or equal to *x*, which is less than 8. So, this interval is including the endpoint 3 (because it's equal to), but not including the endpoint 8. So *x* is any real number from 3 all the way to the last real number before 8.

To show an interval on a number line, you first draw two circles at the two endpoints of the interval. So, we will draw circles at 3 and 8. Now, draw a line to connect the two circles! The last step is to color in the circles *only* if the endpoint is included in the interval.

As we just found out in our inequalities example, the weatherman did say that it could snow 3 inches. The 3 is included, so color in that circle. However, as we saw before, the weatherman said that it would snow less than 8 inches. So 8 is not included; don't color in that circle. Find a picture to show how to write this interval using a number line.

With interval notation, parentheses and brackets are used to indicate whether or not each endpoint is included. A bracket is used to indicate that an endpoint of an interval is included in the range. A parenthesis is to indicate the endpoint is not included.

First, write the two endpoints, separated by a comma! Then, next to each endpoint, indicate whether the end is included or not by writing either a bracket or a parenthesis. We've determined that the 3 is included in the interval, while 8 is not. So, the 3 will have a bracket while the 8 will have a parenthesis. Take a look at this image. You can see how all of this has played out:

[3,8)

Let's briefly review what we've learned. We learned that an **interval** is a range of numbers that include all the real numbers between those two interval endpoints. We also learned that **real numbers** are pretty much any number you can think of. You can indicate an interval using **inequalities**, which are the symbols that stand for less than, less than or equal to, greater than, and greater than or equal to; the number line, or interval notation.

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Math for Kids23 chapters | 325 lessons

{{courseNav.course.topics.length}} chapters | {{courseNav.course.mDynamicIntFields.lessonCount}} lessons | {{course.flashcardSetCount}} flashcard set{{course.flashcardSetCoun > 1 ? 's' : ''}}

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