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Compare Representation Portfolio

Use the worksheet to record your answers to the Compare Representation Portfolio activity. When you are finished, save your worksheet with your answers and submit it for a portfolio grade.
Your family decides to take a long road trip for the summer. You will be riding in the car while it moves at a fairly constant rate to reach your destination.
Question 1
Which quantity in this situation is the independent variable? Which quantity is the dependant variable? Describe how you know which is which in this situation.
Question2
What do you think is a reasonable speed for the car to travel for most of the trip? remember to include units of measurements in your answer. Why did you pick this number?
Question 3
Fill out the table below that shows the amount of time that has passed and how far you have traveled from 0-8 hours. Make sure to label the quantities on the top row of the table. Pay attention to which side each quantity should go on.
Question 4
Use the table to plot the points on the graph. Label the axes with the correct quantities and use an appropriate scale for the gridlines.
Question 5
Write an equation using the variables x and y that relates the distance to the time. Label the variables to show what they stand for in the equation. Be careful of which variable you use for the independent and dependent quantities.
Question 6
Use the table, graph, or equation to predict how far the car would travel if it drove for 10 hours instead of 8. Which representation (table, graph, or equation) did you use? Why did you choose this method?

1 answer

Compare Representation Portfolio

Question 1

  • Independent Variable: Time \(t\) (in hours)
  • Dependent Variable: Distance \(d\) (in miles)
  • Explanation: The independent variable is the quantity you control or change (in this case, time spent driving). The dependent variable is what you measure or observe in response to the independent variable (here, the distance traveled depends on how long the car has been driving).

Question 2

  • Reasonable Speed: 60 miles per hour (mph)
  • Explanation: I chose 60 mph as a reasonable speed because it is a common speed limit on highways in the U.S., making it a practical estimate for a long road trip.

Question 3

| Time (hours) | Distance (miles) | |--------------|------------------| | 0 | 0 | | 1 | 60 | | 2 | 120 | | 3 | 180 | | 4 | 240 | | 5 | 300 | | 6 | 360 | | 7 | 420 | | 8 | 480 |

Question 4

  • Graph:
    • X-axis: Time (hours)
    • Y-axis: Distance (miles)

Use appropriate scales, for example:

  • X-axis: 0 to 10 hours (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
  • Y-axis: 0 to 500 miles (0, 60, 120, 180, 240, 300, 360, 420, 480)

Plot the points from the table and connect them to form a line.

Question 5

  • Equation: \(d = 60t\)
  • Explanation of Variables:
    • \(d\): distance traveled in miles (dependent variable)
    • \(t\): time spent traveling in hours (independent variable)

Question 6

  • Prediction for 10 hours: Distance = \(d = 60 \times 10 = 600\) miles
  • Representation Used: I used the equation \(d = 60t\) for my prediction, as it provides a direct relationship between time and distance, making calculations straightforward.

Make sure to save this worksheet and submit it for your portfolio grade!