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Course: High School Math with NAO
Linear Equations: Distance, Rate, Time

  • 9-12 grade
  • Intermediate

Lesson Description:

In this lesson, students will need to build a function by observing the relationship between two quantities and then evaluate that function in order to meet a constraint.  The lesson also exposes students to the time-distance-velocity equation.
 


 

Standards Covered

CCSS.MATH.CONTENT.HSF.BF.A.

Build a function that models a relationship between two quantities.

CCSS.MATH.CONTENT.HSF.IF.A

Understand the concept of a function and use function notation.

CCSS.MATH.CONTENT.HSF.IF.B

Interpret functions that arise in applications in terms of the context.

CCSS.MATH.CONTENT.HSF.IF.C

Analyze functions using different representations.

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Lesson Modules


Teaching Tips:

Set up two robots as in the picture below.



To demonstrate the distance formula ( v=d/t) further, use the simulator, which is set up as the figure below.
It shows two robots facing a goal post.  The first robot, the “runner”, starts on the left side and is trying to reach the goal post by running as fast as it can.  The second robot, the “tackler”, is trying to prevent the first robot from reaching the goal post.  In order to do this, the tackler robot must estimate the speed of the runner robot and then run at a speed such that it arrives at the goal post just as the runner is also arriving.  The runner must be careful, run too fast and they go past the goal (too hard to stop once you pick up speed!), run too slow and the runner will reach the goal post.



Speed estimation is done by letting the runner start running and measure the speed.  The first checkpoint is used to measure the robot’s speed. After the runner reaches that checkpoint the students use the estimated speed to predict when the robot will arrive at the goal post.

 

You are the coach of your high school football team.  You explain to your players that estimating another player’s speed is very important. For example, a successful tackle requires one player to intercept another. As the coach, you want to make sure that your players are the ones doing the tackling, rather than being tackled.  To help his players understand the role speed plays in successful tackles, he uses his helpers—the NAO robots! 

The speed of the robot can be estimated using the formula v=d/t where v is the speed, d is the distance traveled, and t is the time it takes to travel the distance.
 


Teaching Tips:

Act 1:
 
This activity allows the students to practice the partial problem, i.e., simply estimating the speed of the runner.  They make an observation and have to solve the distance/time/speed equation in order to estimate the speed.  Knowing the speed, they can then estimate the arrival time to the goal post and compare their answer to the result of the simulation.
 
The simulator is set up as in Teacher Modeling module - it starts when the student presses the “Start” button. The tackler will remain stopped but the runner will begin moving towards the goal post and the clock starts ticking. Once the runner arrives at the checkpoint, the simulation stops and the student can now calculate the runner’s speed. The goal of this activity is for the student to use the estimated speed to predict when the robot will arrive at the goalpost. They can type the estimate in the text box. The simulation continues and once the robot arrives at the goal post the student can compare his/her estimate to the time it took. There will be a question underneath that asks the student if his/her estimate was correct and if not, why not.
 

Act 1:
 
This activity allows you to practice the partial problem, i.e., simply estimating the speed of the runner. Observe and solve the distance/time/speed equation in order to estimate the speed.  Knowing the speed, you can then estimate the arrival time to the goal post and compare their answer to the result of the simulation.
 

Directions: Use the simulator that is set up as in the Teacher Modeling module.

  1.  Press the “Start” button. The tackler will remain stopped but the runner will begin moving towards the goal post and the clock starts ticking.
  2. Once the runner arrives at the checkpoint, the simulation stops and you can now calculate the runner’s speed. The goal of this activity is to use the calculated speed to predict when the runner robot will arrive at the goalpost.


  3. Type your estimated time of arrival to the goalpost.

  4. Observe the simulation continues and once the runner robot arrives at the goalpost you can compare your estimate to the time it took.
  5. Was your estimate correct and if not, why not?





Simulator:



 


Teaching Tips:

Act 2:
The simulator is set up similar to Activity 1 but the distance between the two robots and the impact point will vary as will the speed of the runner robot.  In addition, the student now must take into account a simple constraint – both robots should arrive at the goal post for a successful tackle.  To do this, the game requires the student to specify the speed of the tackle so they can tackle the runner.

For every trial, the distance of the tackler to the goal post will be different and so will the speed of the runner robot. Upon pressing the 'Start' button, the runner robot will begin traveling towards the goalpost. When they cross the first checkpoint, the simulation will stop and the student will then need to specify the speed at which the “tackle” robot must travel to stop the runner. After the student types (or moves a slider), they click on the 'Continue' button and the simulation continues. If the speed was correct, one robot will intercept the other, otherwise, the runner robot will score. This will happen five times and the student gets a point for every successful tackle.
 

Use the simulator that is set up similar to the Student Activity module but the distance between the two robots and the impact point will vary as will the speed of the runner robot.  In addition, you now must take into account a simple constraint – both robots should arrive at the goal post for a successful tackle.  To do this, the game requires you specifying the speed of the tackle so the tackler can tackle the runner.

Direction:

  1. Press the 'Start' button, the runner robot will begin traveling towards the goalpost.
  2. Observe that when the runner robot crosses the first checkpoint, the simulation will stop.
  3. Specify the speed at which the “tackle” robot must travel to stop the runner.
  4. Click on the 'Continue' button and the simulation continues. If the speed was correct, one robot will intercept the other, otherwise, the runner robot will score.
  5. Repeat the step 1 through 4, five times and you will get a point for every successful tackle.




[speed of tackler robot] = _________________
 


Teaching Tips:

Close: (5 mins) Students write a brief explanation of how the use of the estimated speed predicts when a tackle will occur.

Write a brief explanation of how the use of the estimated speed predicts when a tackle will occur.