6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line.

Number Lines Number lines are a great way to be able to visually see the relationship between different numbers. You just finished learning more about rational numbers and now you will get a chance to work with rational numbers in the context of number lines. As you are working your way through this lesson, think about these two questions: Number lines are a great way to be able to visually see the relationship between different numbers. You just finished learning more about rational numbers and now you will get a chance to work with rational numbers in the context of number lines. As you are working your way through this lesson, think about these two questions:

In order to place numbers on a number line, we first have to know how to set up a number line. In order to place numbers on a number line, we first have to know how to set up a number line. The number line above is very basic and allows us to plot rational numbers anywhere from -6 to 6. The vertical lines above each number are called tick marks or hash marks. The number line above is very basic and allows us to plot rational numbers anywhere from -6 to 6. The vertical lines above each number are called tick marks or hash marks. Notice that as you go LEFT on the number line, the numbers get smaller. As you go RIGHT, the numbers get larger. Notice that as you go LEFT on the number line, the numbers get smaller. As you go RIGHT, the numbers get larger.

Plotting Numbers on a Number Line Now that we have reviewed what a number line is and what purpose they serve, let's start placing rational numbers on a number line. Now that we have reviewed what a number line is and what purpose they serve, let's start placing rational numbers on a number line. 1. If you were given a set of numbers {-2, 6, 3, -5} and told to graph them on a number line, here is what it would look like. 1. If you were given a set of numbers {-2, 6, 3, -5} and told to graph them on a number line, here is what it would look like.

We simply take each rational number and put a dot on the number line where the number occurs.

OBSERVATION: Did you notice that the numbers in the set were NOT listed in order from least to greatest or greatest to least? Not a big deal you probably say, but always remember that numbers get smaller as you move Left on the number line and larger as you move Right. When we plotted the numbers, it makes it really easy to see which number from the set is the biggest and which number is the smallest. This will become very important in the near future...

If you were given a set of numbers { } and told to graph them on a number line, here is what it would look like.

Notice again that we simply took each rational number and put a dot where it occurs on the number line. Did you also notice again that the set was not written in order? When we plot the numbers on the number line, however, we now have a visual way to easily compare numbers in this set. The number that is farthest left ( ) is the smallest number in this set while the 2 is farthest to the right and is therefore the largest number in this set.

You Try! In your math JOURNAL, copy down the number line below and plot the numbers in the given set (designated by the { }). {-1, 0.5, 0, 2.5, -0.5}

What to do when the tick marks aren't there! Three things you will want to consider: 1) What is the range of the numbers in the set? 2) Where does zero fit? 3) Do you need to convert any numbers?

1) What is the range of the numbers in the set? Given the set {-40, -10, 20, 50} should I use the number line below? Given the set {-40, -10, 20, 50} should I use the number line below? Absolutely Not!!! The numbers in your set wouldn't even come close to fitting between -2 and 2.

You would want to create a number line that looked closer to this for the numbers: {-40, -10, 20, 50}

2) Where does zero fit? Always remember that you can place zero anywhere you want on your number line (or not at all in some cases). If you had to plot the set {-1, 3, 6, 10), you would notice that the only negative number you need to plot is -1 while you will have to go all the way to positive 10. You could make your number line look like this:

3) Do you need to convert any numbers? If you had to plot the numbers { }, where would you begin? Looking at your set you have rational numbers in the forms of a basic integer (-1), a proper Fraction (1/2), A mixed decimal (-1.5), and an improper fraction(3/2).

It's probably best in this situation to find a common format for the numbers and choose the increments on the number line accordingly. In this case, since I only have 1 decimal I would probably keep it in fractions and use increments of 1/2. Convert all numbers to halves. { }

All that is left is to select an appropriate number line.

Identify the rational numbers that belong in the empty squares. Now, you try!

The same principle works for vertical number lines ~ like sea level, for example.

Also for temperature!

And Altitude!

Now, let’s practice!