6.NS.6c

Find and position integers Find and position integers and other rational numbers and other rational numbers on a horizontal or vertical on a horizontal or vertical

number line.number line.

Number Lines

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

In order to place numbers on a number In order to place numbers on a number line, we first have to know how to set up line, we first have to know how to set up a number line.a number line.

The number line above is very basic and The number line above is very basic and allows us to plot rational numbers allows us to plot rational numbers anywhere from -6 to 6. The vertical lines anywhere from -6 to 6. The vertical lines above each number are called tick marks above each number are called tick marks or hash marks.or hash marks.

Notice that as you go LEFT on the Notice that as you go LEFT on the number line, the numbers get smaller. As number line, the numbers get smaller. As you go RIGHT, the numbers get larger.you go RIGHT, the numbers get larger.

Plotting Numbers on a Number Line

Now that we have reviewed what a Now that we have reviewed what a number line is and what purpose they number line is and what purpose they serve, let's start placing rational serve, let's start placing rational numbers on a number line.numbers on a number line.

1.1. If you were given a set of numbers {- If you were given a set of numbers {-2, 6, 3, -5} and told to graph them on a 2, 6, 3, -5} and told to graph them on a number line, here is what it would look number line, here is what it would look like.like.

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

OBSERVATION: OBSERVATION: Did you notice that the Did you notice that the numbers in the set were NOT listed in order numbers in the set were NOT listed in order from least to greatest or greatest to least? from least to greatest or greatest to least? Not a big deal you probably say, but always Not a big deal you probably say, but always remember that numbers get remember that numbers get smallersmaller as you as you move move LeftLeft on the number line and on the number line and largerlarger as as you move you move RightRight. When we plotted the . When we plotted the numbers, it makes it really easy to see numbers, it makes it really easy to see which number from the set is the biggest which number from the set is the biggest and which number is the smallest. This will and which number is the smallest. This will become very important in the near future... 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 Notice again that we simply took each rational number and put a dot where it occurs on the number and put a dot where it occurs on the number line.number line.

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

You Try!In your math In your math JOURNALJOURNAL, copy down the , copy down the

number line below and plot the number line below and plot the numbers in the given set (designated numbers in the given set (designated by the { }). 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: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 Given the set {-40, -10, 20, 50}{-40, -10, 20, 50} should I use the number line below?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 Always remember that you can place zero anywhere you want on your number line anywhere you want on your number line (or not at all in some cases). If you had to (or not at all in some cases). If you had to plot the set {-1, 3, 6, 10), you would plot the set {-1, 3, 6, 10), you would notice that the only negative number you notice that the only negative number you need to plot is -1 while you will have to need to plot is -1 while you will have to go all the way to positive 10. You could go all the way to positive 10. You could make your number line look like this:make your number line look like this:

  

3) Do you need to convert any numbers?

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

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

0.1 0.3 0.5 0.8 0.9

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

Also for temperature!

And Altitude!

Now, let’s practice!