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Course: High School Math with NAO
Special Angles on Unit Circle

  • 9-12 grade
  • Intermediate

Lesson Description:

By playing the game introduced in this lesson, students should answer Nao robot's challenge on the circle by using the special angles. 


 

Standards Covered

CCSS.MATH.CONTENT.HSF.TF.A.3

(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π - x in terms of their values for x, where x is any real number.

CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP3

Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP5

Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6

Attend to precision.

CCSS.MATH.PRACTICE.MP7

Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8

Look for and express regularity in repeated reasoning.

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Lesson Modules


Teaching Tips:

1. Show the video to the class.
2. Have the students answer the question
3. Share the poll results and facilitate a quick discuss (less than 5 minutes)

Watch the video and answer the question below.




What strategies can you use to remember the numbers on the circle above?


Teaching Tips:

Many students have a hard time to deal with this topic. Encourage students that there can be many other ways that work for them and it is their job to explore to find the strategy that works for them. 

One tip, as introduced by the video, is to apply the special right triangles on top of the unit circle and use the figures they already know to answer any questions around the unit circle. 

At the end of this module, have students present the strategies and discuss the pros. and cons. of each strategy, then give some time for the students to practice the special angles on the unit circle.

1. Review the right triangle with special angles. 


2. Explore the special right triangles on the unit circle.




3. Pick one strategy that you think works for you the best and create a way to remember the special angles by using the special right triangles. 

Explain what strategy you will use to remember the special angles on the unit circle. 


Teaching Tips:

Classroom setting: 

Have a circle on the floor with the radius of 1 meter. Tape the special angles on the floor from the center. At each special angle point, place cards (Print out NAO Marks). The cards will be used to communicate the location of the student with Nao. 

Place Nao robot at the center of the circle. Nao is giving a direction for the student to follow.

Nao robot will lead a game that you will be able to practice and test your knowledge about the special angles on the unit circle. 

Follow your teacher's instruction and NAO's direction as well. Make sure you keep quiet when NAO speaks and listens to you or your classmate. 


Teaching Tips:

Have students answer the questions. You have access to the data from the dashboard.

You've learned the special angles on the unit circle and developed your strategy to remember the key values. Check how much you understand the concept.

Special angles on the unit circle
  • 1. not at all
  • 2. kind of got it
  • 3. understand
  • 4. pretty good
  • 5. totally got it


Explain your strategy and how you use the strategy to remember the key values.


Use of special right triangles for special angles on the unit circle
  • 1. not at all
  • 2. kind of got it
  • 3. understand
  • 4. pretty good
  • 5. totally got it


How can you use the special right triangles to create the angles on the unit circle?