Plotting Whole Numbers
The Real Number Line
We can visualize all the numbers in the real number set with the real number line. Starting at the origin (or at the number zero), the line expands indefinitely in either direction. We determine the locations of different numbers on the line with labeled tick marks.
![The Number Line [(-5),5]](/assets/images/number_line/plotting/real_number_line.svg)
No matter what you think the biggest number is, you can always add 1 to it and turn it into an even larger value; thus, numbers (and the number line) go on forever, and into infinity (∞). To represent the never-ending nature of numbers, we put arrows at the end of each side of the number line to remind us that numbers (and it) go on forever in either direction.
Units
Units are how we describe and measure specific quantities. What are we: counting, measuring, or comparing? The answers to any of these questions should be the same as the units used on the number line which is used to illustrate the quantity.
![Tick Marks: The Number Line [0,20]](/assets/images/number_line/plotting/tick_marks.svg)
Units on the real number line are equal to the distances between subsequent integers; or, the space between 0 and 1. In order for the number line to make sense, all units need to be the same size.
Plotting Coordinates
To indicate the location of a particular number on the real number line, we plot its coordinate. To do this, place a heavy dot on the number's location on the number line as indicated by the tick marks.
For example, to plot the coordinate of the number 2 on the number line, place a dot on the line over the tick labelled with the number 2.
Scaling
Scaling is the art of moving, expanding, shrinking, and labeling the number line in such a manner that it effectively illustrates all the data we wish to show.
![Scaling: The Number Line [0,100]](/assets/images/number_line/plotting/scaling.svg)
Note that the units can be shrunk, or expanded to allow for more or less detail. We don't have to mark every unit with a tick mark, and every tick mark doesn't need a label to make a detailed number line.
Example 1
- Plot the coordinate of the number 5 on the number line below:
![The Number Line [0,10]](/assets/images/number_line/plotting/ex1.svg)
Solution:
Example 2
- A local pet store owner wants help visualizing the number of animals he has in his store. To help him, plot each coordinate and label it with the name of the animal.
Puppies: 4
Cats: 8
Rabbits: 3
Guinea Pigs: 5
Parakeets: 6
Lizards: 1
Solution:
Checkpoint 1
- Count the number of dots in the picture below, then plot the number on the number line:
Click for solutions...Checkpoint 2
- Count the number of squares in the picture below, then plot the number on the number line:
Click for solutions...Checkpoint 3
- Count the number of triangles in the picture below, then plot the number on the number line:
Click for solutions...Plotting Sets
Sets
A set describes the groupings of numbers, or quantities. To graph a set on the number line, plot each element (or member of the set) on the number line one after the other.
Example 3
- Graph each of the following sets on the real number line:
a. A = {2,3,6,7}
b. B = {0,3,6,9}
c. C = {1,3,7,8}
d. D = {2,5,9,10}
Solution:
a.
b.
c.
d.
Checkpoint 4
- Write down the set illustrated in each of the following number lines:
a.
b.
c.
d.
Exercises
Exercise Set 1
- Write the whole number plotted on each number line:
1-1.)
1-2.)
1-3.)
1-4.)
1-5.)
Exercise Set 2
- Plot the following numbers on the number line:
2-1.) a. 4, b. 8, c. 9, d. 10
2-2.) a. 1, b. 5, c. 6, d. 7
2-3.) a. 0, b. 3, c. 4, d. 9
Click for solutions...Exercise 3
- Plot the following sets on the real number line:
3-1.) A = {0,2,4,6,8,10}
3-2.) B = {1,3,5,7,9}
3-3.) C = {1,4,5,9}
3-4.) D = {0,1,7,8}
3-5.) E = {4,5,6}
Click for solutions...Exercise Set 4
- Write the number graphed on each number line:
Note: As we plot larger numbers, we need larger plots in which to fit them. Another useful trick is to cut off the ends of the number line and only focus on surrounding values when graphing.
4-1.)
4-2.)
4-3.)
4-4.)
4-5.)
4-6.)
4-7.)
4-8.)
4-9.)
4-10.)
Exercise Set 5
- Plot the following numbers on the real number line:
5-1.) 50
5-2.) 12
5-3.) 42
5-4.) 39
5-5.) 88
5-6.) 21
5-7.) 13
5-8.) 74
5-9.) 97
5-10.) 3
Click for solutions...Exercise Set 6
- A classmate has 2 CUTE gerbils. Last night, they both escaped their cage and nibbled on her homework. She still has a piece of the original assignment, and she wants you to help her complete the rest.
- Complete each number line by filling in the missing values:
6-1.)
6-2.)
6-3.)
6-4.)
Exercise Set 7
- Use the number line provided to find the answer to each question:
a. If B=1 and D=3, what is A?
b. If A=4 and E=8, what is C?
c. If A=-13 andE=-9, what is C?
d. If A=-4 and C=-2, what is E?
e. If B=-2 and E=1, what is D?
Exercise Set 8 - Car Dealership
A local car dealership wants a graph that illustrates the number of cars they've sold based on their color. Plot and label each quantity of car sales (by color):
black: 8
red: 4
green: 1
blue: 3
gray: 10
white: 6
- Extra Credit: Identify a trend for the cars that are selling.
Click for solutions...Exercise Set 9 - Long Jump Competition
- A track & field team would like your help visualizing the data from the long jump competition at the last meet. Plot each jump on the number line (which is in feet) and label each coordinate with the name of the athlete.
Christopher: 17 ft.
Fahim: 16 ft.
David: 13 ft.
Adam: 21 ft.
Omar: 20 ft.
Felix: 19 ft.
- Extra Credit: Highlight any athletes doing well or poorly based on their performance.
Click for solutions...Exercise Set 10 - Garden Produce
- A local neighbor has a garden, and she would like a graph to better visualize the number of each type of vegetable the garden produced this season. Use the number line below to graph the number of vegetables. Label each plot with the name of the vegetable.
Corn: 13
Carrots: 8
Cabbage: 4
Lettuce: 5
Tomatoes: 10
Green Beans: 19
Click for solutions...Exercise Set 11 - Local Archery Club
- The coach for the local archery club would like your help visualizing the performance of one of her star athletes.
Note: The number line can also be rotated to the up/down position to show vertical data.
- To key-in on his vertical performance, she has him line up and shoot 5 arrows at the target. Then, she recorded the number of centimeters above or below the bullseye each arrow landed. Graph each point on the number line.
a. 2 cm
b. 4 cm
c. -1 cm
d. 0 cm
e. 1 cm
- Extra Credit: Give the archer a tip to help him do better based on his performance.
Click for solutions...