Using Graphs As A Visual Representation Of Rate Situations

Using Graphs As A Visual Representation Of Rate Situations

Racing

Opening

Racing

Use the Race and Graph interactive to set up the following race and see which racer wins.

Choose the street racetrack. Set the track distance to 500 m. Set up the cars with the following speeds:

Orange car: 70 m/s

Yellow car: 85 m/s

Green car: 100 m/s

  • What do you notice about the race and its graph? Discuss your observations with a partner.
  • Which racer won the race?

INTERACTIVE: Race and Graph

Who Is Faster?

Opening

Who Is Faster?

The green car traveled faster than the yellow car in the race from Task 1.

  • Where can you see this information on the racetrack?
  • Where can you see this information on the graph?

INTERACTIVE: Race and Graph

Hint:

  • The green car traveled the fastest. It reached the end of the track first, and its graph is the steepest line.
  • The orange car traveled the slowest. It reached the end of the track last, and its graph is not as steep as the other two lines.
  • The point at which each racer's graph intersects the 1-second line shows that racer's speed per second.

Math Mission

Opening

Analyze a graph to compare the speeds of three racers.

Twice as Fast

Work Time

Twice as Fast

Now create a new race by changing the speed, distance, and time.

Decide on the track you want and the distance of the track. Then set up the race so that Racer 1 goes twice as fast as Racer 2 and Racer 2 goes twice as fast as Racer 3.

  • Sketch a graph to predict what the graph of the race will look like, then start the race.
  • Compare your graph with the race graph in the interactive.
  • Explain your thinking in setting up the race and your prediction as compared with the results.

INTERACTIVE: Race and Graph

Hint:

What scale will you use for the axes?

Prepare a Presentation

Work Time

Prepare a Presentation

  • Explain how the speed and the graph of the racers are related. Use your work to support your explanation.

Challenge Problem

Set up a race that shows the following situation.

  • The graph of the orange racer is the steepest line.
  • The graph of the green racer is not as steep as the other two lines.
  • The graph of the blue racer is exactly in between the other two lines.

INTERACTIVE: Race and Graph

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes as your classmates make presentations about the relationship between the speed and the graph of their racers.

Hint:

As your classmates present, ask questions such as:

  • What does a point on the graph represent?
  • Explain how this line on the graph represents this racer’s race.
  • Which racer won the race? How is this shown on the graph?
  • What is the independent variable in this situation?
  • How did you choose the scale for your axis?

Understanding Graphs

Formative Assessment

Summary of the Math: Understanding Graphs

Read and discuss.

  • A situation can be represented by a graph.
  • Each point on a graph represents a pair of values. In the race graph, each point represents the time and the distance that the racer traveled in that amount of time.
  • Time is usually plotted on the horizontal axis. The farther right a point is from the origin, the more time has passed from the start.
  • Distance is usually plotted on the vertical axis. The higher up a point is from the origin, the farther the racer has traveled from the start.
  • A graph of a constant speed is a straight line.
  • Steeper lines show faster speeds.

Hint:

Check your understanding.

  • What does a point on the graph represent?
  • What does a straight line on the graph mean?
  • What does the steepness of a line mean?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

One thing I learned about representing rates on a graph is …