Activity VI - 1 Variables and Coordinate Graphs

Unit VI – Patterns & Variables Names:

Part I: Jumping Jack Experiment

The following experiment is a test of endurance. The experiment requires four people:

  • A jumper to do the jumping jacks
  • A timer to keep track of the time
  • A counter to count the jumping jacks
  • A recorder to write down the number of jumping jacks

As a group decide who will do each task.

Fill in the following table to record the total number of jumping jacks after every 10 seconds, up to a total of 2 minutes (120 seconds).

Time in seconds / 0 / 10 / 20 / 30 / 40 / 50 / 60 / 70 / 80 / 90 / 100 / 110 / 120
Total Number of Jumping
Jacks

Here’s how to do the experiment:

When the timer says “go,” the jumper begins doing jumping jacks. The counter counts the jumping jacks out loud. Every 10 seconds, the time says “time” and the recorder records the total number of jumping jacks the jumper has done so far. Repeat the experiment four times so that everyone has a turn at each of the four tasks.

How did your jumping jack rate (the number of jumping jacks per second) change as the time passed? How is this shown in your table?

Part II: Making a Graph

In the jumping jack experiment, the number of jumping jacks and the times are variables. A variable is a quantity that changes or varies.

Steps to follow when making a coordinate graph:

Step 1Selecttwo variables.

For example, for the experiment in Part I, the two variables are time and number of jumping jacks.

Activity VI - 1 Variables and Coordinate Graphs

Unit VI – Patterns & VariablesNames:

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Step 2Select an axis to represent each variable.
If time is one of the variables, you should usually put it on the x-axis (the horizontal axis). This helps you see the “story” that occurs over time as you read the graph from left to right. So, in a
graph of the jumping jack data, time would go on the x –axis and the number of jumping jacks would go on the y-axis.

y

Number of jumping

jacks

x

Time (in seconds)

Many times, you can determine which variable to assign to which axis by thinking about how the two variables are related. Does one variable depend on the other? If so, put the dependent variable on the y-axis and the independent variable on the x-axis. The number of jumping jacks depends on time. Jumping jacks goes on the dependent or y-axis and time goes on the independent or x-axis.

Step 3Select a scale for each axis.

For each axis, you want to determine the largest and smallest values you want to show on your graph and how you want to space the scale marks.

For your jumping jack data, the values for time are between 0 and 120 seconds, so for this graph, you could label the x-axis from 0 to 120. Since you collected data every 10 seconds, you could place marks at 10-second intervals.

The scale for the y-axis (number of jumping jacks) depends on the number of jumping jacks your group actually did. For example, if you did 97 jumping jacks you could label your scale from 0 to 100. It would be very messy if you put a mark for every single jumping jack. Put a mark for every 10 jumping jacks.

Activity VI - 1 Variables and Coordinate Graphs


Unit VI – Patterns & Variables Names:

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Step 4Plot the Data Points

For example, suppose that at 60 seconds, you had done 65 jumping jacks. To plot this information, start at 60 on the x-axis (time) and follow a line straight up. On the y-axis (number of jumping jacks) start at 65 and follow a line straight across. Make a point where the two lines intersect. This point indicates that in 60 seconds, you did 65 jumping jacks.


  1. Make a graph of your jumping jack data.
  1. What does your graph show about jumping jack rate as time passes? (Another way to say this is, “What does your graph show about the relationship between the number of jumping jacks and time?”)
  1. Is the relationship you found between the number of jumping jacks and time easier to see in the table or the graph? Explain your answer.