Algebraic Reasoning

Algebraic Reasoning

Flying Backward

Speed

Opening

Speed

Look at the two diagrams. Think about the relationship between airspeed, wind speed, and ground speed.

Math Mission

Opening

Explore relationships between air speed, wind speed, and time of flight.

Expression for Distance

Work Time

Expression for Distance

Complete the table.

  • From the information in the table, determine whether each plane is flying forward, flying backward, or hovering.
  • Then choose one plane that falls into each of these categories, and write an equation that represents distance traveled. Let t = time in hours.
  • Describe the coefficient of t when a plane is flying forward, flying backward, or hovering.

HANDOUT: Forward, Backward, or Hovering

Hint:

  • Remember: In the expression 3 x , 3 is the coefficient ofx .
  • Think about whether the wind and the plane are going in the same or opposite direction.
  • If you know a plane is flying 500 miles per hour, how do you represent the miles it has flown in t hours?

Amelia Earhart

Work Time

Amelia Earhart

Amelia Earhart was the first woman in history to fly solo from North America to Europe. On May 20, 1932, she flew from Newfoundland to Ireland—a distance of 2,020 miles. It took her nearly 15 hours to make the trip. The average speed for a Lockheed Vega—the plane that Amelia flew—is 155 miles per hour (mph).

View this video footage of Amelia Earhart before her flight around the world.

  • How does the average speed of a Lockheed Vega compare to Amelia’s average speed?
  • What factor(s) might have affected her average speed?

VIDEO: Amelia Earhart

Hint:

Write an equation to help you find Amelia’s average speed.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about the expressions and equations your classmates wrote and their strategies for solving the problems.

Hint:

As your classmates present, ask questions such as:

  • Explain the difference in your equation when you had a headwind versus a tailwind.
  • How did you decide whether to add or subtract the values for airspeed and wind speed?
  • Can you explain why 800 t represents the distance in miles, wheret represents time in hours?
  • Can you write an inequality that would represent Amelia’s actual time versus her theoretical time?

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 wonder about expressions and equations is …