*Contributor: Erika Wargo. Lesson ID: 12700*

Books have plots, and cemeteries have plots. Do numbers have plots, too? It doesn't sound rational, but number lines and coordinate grids let you plot rational numbers to help visualize their values!

categories

subject

Math

learning style

Kinesthetic, Visual

personality style

Beaver

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

A number that can be written as a fraction or a ratio is called a rational number. Unfortunately, 5 out of 3 people have problems with fractions! (Think about it!)

Rational numbers are numbers that can be written as fractions or ratios.

*Rational numbers* are integers, positive and negative fractions, mixed numbers, and decimals that terminate. *Integers* are positive numbers, negative numbers, and zero. Rational numbers can be plotted on a number line and coordinate grid to help you understand the value of the number based on its location.

A number line goes on forever in both directions, which is shown by the arrows pointing to the right and left.

Before you practice plotting rational numbers, respond to the following questions as you watch a video about rational numbers on a number line. Write a response in your math journal:

- Define the following in your own words: natural numbers, whole numbers, integers, and rational numbers.
- As you move to the left of 0 on a number line, what happens to the value of the number?
- As you move to the right of 0 on a number line, what happens to the value of the number?
- How do you decide where to plot a fraction on a number line?

Discuss the questions above with a parent or teacher after you watch *Rational number on a number line *from Smart School Online:

On a number line, the positive integers lie to the right of 0 and the negative integers lie to the left of 0. If the rational number is not an integer, determine if you want to write it as a fraction or decimal.

If a rational number is not an integer:

- Determine which two integers the number falls between. If the fraction is proper, or less than 1, then it lies between 0 and 1. If the fraction is improper, which is equal to or greater than 1, convert it to a mixed number.
- Determine where between the two integers it should be placed.
- Graph it on the number line.

**Example** Plot ^{2}⁄_{4} and 1¾ on the number line:

Since ^{2}⁄_{4} is a proper fraction, it falls in between 0 and 1.

1^{3}⁄_{4} is a mixed numer and lies between the whole numbers 1 and 2.

The denominator is 4, so the section between each whole number is divided into 4 parts.

^{3}⁄_{4} is the second mark after 0. 1¾ is the third mark after 1.

Rational numbers can also be plotted on a coordinate grid using *ordered pairs*. Ordered pairs name one specific location on the coordinate grid. Ordered pairs are written as (x, y) and the order is important. The first coordinate, x, represents the point’s location from 0 on the x-axis. The second coordinate, y, represents the point’s location from 0 on the y-axis. Coordinate grids are made up of a horizontal and vertical number line. Coordinate grids are useful in maps and finding the distance between two points.

**Example** Plot the following ordered pairs on the coordinate grid:

A (-3, 1)

B (5, -2)

C (4, 0)

When plotting ordered pairs, start at the origin (0, 0) where the horizontal and vertical number lines meet.

- First, find the x-coordinate by moving to the left or right of 0.
- Then, find the y-coordinate by moving up or down.

A (-3, 1): The x value is negative, so move to the left of zero 3 units. The y value is positive, so move up from that point 1 unit.

B (5, -2): The x value is positive five, so move right five units. The y value is negative, so move down from that point 2 units.

C (4, 0): The x value is positive, so move to the right of zero 4 units. The y value is zero, so do not move up or down.

In your math journal, write a response to the following:

- How can you tell if an integer is positive or negative?
- Explain how to plot a fraction on a number line.

In the *Got It?* section, you will practice plotting rational numbers on a number line and coordinate grid.

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