a1tD0000003mAP7IAM

Course: High School Math with NAO
Inverse Trigonometric Functions

  • 9-12 grade
  • Intermediate

Lesson Description:

Students find the slope of a line that the soccer ball travels on so NAO robot can score the goal. This lesson enhances skills on using inverse trigonometry functions to find the angles. 


 

Standards Covered

CCSS.MATH.CONTENT.HSF.TF.B.7

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*

CCSS.MATH.CONTENT.HSG.SRT.C.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP4

Model with mathematics.

CCSS.MATH.PRACTICE.MP5

Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6

Attend to precision.

image description

Lesson Modules


Teaching Tips:

Explain what RoboCup is to your students so they can be curious about the robot playing soccer. Show the video in the class view section. After watching the video move on the poll question. Have students write down their ideas and share the word cloud result in order to have a short discussion of the consensus. 

Have you played soccer? There are many soccer players and fans all over the world, including NAO. NAO is an amazing soccer player and you will see NAO play today.

Robot Soccer World Cup (RoboCup) is an annual international robotics competition. Your teacher will show a piece of the RoboCup match.

User-added image

What do you wonder? What information do you need to figure out the angle of the kicking line to score the goal?


Teaching Tips:

You can turn on/off specific information such as coordinate of Nao, coordinate of the ball, goal line, xy-axis, angle on the simulation. 

Imagine you are the coach of the NAO soccer team. You have to give the right instructions to make as many goals as possible. A goal is scored when the whole ball passes over the goal line, between the goalposts, and under the crossbar. See the animation below to become familiar with the soccer field.

Your NAO robot will attempt a goal, and you need to give the right angles so NAO can kick the ball to score a goal. Use the information below to figure out the angle and answer the following question. 

Visualize the line that the ball travels on for NAO to score a goal.


User-added image

 

Directions: Follow the directions below. Use a pencil/paper to sketch your work if that helps.

  1. Imagine where you want the ball to go.
  2. Move the slope slider to match the kicking line you want the ball to travel on.
  3. Place a point at which the goal line and the kicking line meet. 
  4. Draw a right triangle with the kicking line, horizontal and vertical lines.
  5. Measure the side lengths
  6. Use the inverse sine/cosine/tangent to calculate the angle.





Write your estimate of the angle of that line in the box below. ​
 ​


Teaching Tips:

Have students run the simulation individually/ by group. 

Pick a few students or each group to run the physical robot. The groups can compete as game playing. At the end of the game, you can give an award to the wining team. 

Find the angle of the line on which the ball travels to attempt the goal for NAO! Type the slope in the box the hit the [GO] button!



 


Teaching Tips:

Have students reflect on what they learned today individually.

Reflect on what you've learned, and write down what you know about each concept below.

 

Inverse trigonometric functions
  • 1. not at all
  • 2. kind of got it
  • 3. understand
  • 4. pretty good
  • 5. totally got it

Explain when you use an inverse trig. functions.