Using Rate To Determine Speed & Distance

Using Rate To Determine Speed & Distance

Jason Running

Opening

Jason Running

Watch the video and think about the following questions.

  • What two quantities in this video can be measured?
  • How does the double number line track the relationship between the quantities?

VIDEO: Jason Running

Math Mission

Opening

Explain how to use Jason’s speed to find how long it takes him to go any distance.

Jason’s Running Speed

Work Time

Jason’s Running Speed

Jason runs at a constant speed of 5 meters per second.

  • How much time does it take Jason to run 240 meters?
  • How many meters can Jason run in 55 seconds?
  • Include the following in your answers:
    • An estimate of what you think the answers might be
    • The quantities involved in the problem
    • A diagram, table, double number line, or other representation that shows why your solution makes sense
    • Your equations, your work, and your solutions
    • Two complete sentences that answer the questions

Hint:

Multiply the rate 5 meters per second by the amount of time to find the distance traveled. For example, to find the distance traveled in 20 seconds, multiply 5 meters per second by 20 seconds:

20 seconds • 5 meters/second = 100 meters

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation about your method for solving the problem.

  • Explain what you did differently to find the time compared with finding the distance.
  • Use your work to support your explanation.

Challenge Problem

At the 1996 Olympics, Michael Duane Johnson set world records for the 200-meter and 400-meter races. He ran the 200-meter race in 19.32 seconds and the 400-meter race in 43.49 seconds.

  • Calculate his speed for each race using a rate.
  • In which race did he have the fastest speed? Justify your thinking.

Make Connections

Performance Task

Ways of Thinking: Make Connections

  • Take notes during the class discussion about how to solve for both distance and time.
  • Answer questions about the methods you used to solve the problem.

Hint:

As your classmates present, ask questions such as:

  • Where do you see the rate 5 meters per second in your methods? Where do you see the answer?
  • What operation did you use and why?
  • Can you explain your solution in terms of the unit: what are the units of the rate, and how did the seconds cancel out?

Distance Equals Rate Times Time

Work Time

Distance Equals Rate Times Time

Emma walked 3 miles in 60 minutes.

  • What was her walking speed in terms of a rate?
  • If she walks 4.5 miles at the same rate, how long will she walk?
  • If she walks for 15 minutes at the same rate, how far will she walk?
  • Make a double number line to show the relationships between the numbers.

Hint:

  • What are the quantities in the situation?
  • How can you find the walking speed in terms of a rate?
  • Did you use the expression d =rt to help you solve for time or distance?

Understanding Speed

Formative Assessment

Summary of the Math: Understanding Speed

Summarize the mathematics of speed and how speed relates to rate.

Hint:

Check your summary:

  • Does your summary explain what speed means, and does it give an example?
  • Does your summary include the term rate ?
  • Does your summary show the relationship among speed, distance, and time in three different ways?

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.

Something I learned about speed that really helps me solve problems is …