a1tD0000003mBF0IAM

Course: High School Math with NAO
Introduction to Radians

  • 9-12 grade
  • Intermediate

Lesson Description:

This lesson introduces the radian measure and the game in this lesson helps students to practice the sense of radians vs. degrees. 


 

Standards Covered

CCSS.MATH.CONTENT.HSF.TF.A.1

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

CCSS.MATH.CONTENT.HSF.TF.A.2

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP5

Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6

Attend to precision.

image description

Lesson Modules


Teaching Tips:

1. Have students answer the question on the positive/negative angles.
2. Share the results and verify the answers.

  • question 1 answer is positive
  • question 2 answer is negative.


Answer the questions below:

Does the video show positive angles or negative angels?
  • positive
  • negative


 

Does the video show positive angles or negative angels?
  • positive
  • negative


Teaching Tips:

Have student explore the definition of 1-radian measure and reason why we need to use radian measure other than the degree measure. 

Question 1 answer: 3.14... or {latexinline{\pi}latexinline}
Question 2 answer: rational numbers
Question 3 answer: The degree system only can measure the rational numbers. We also need to be able to measure the irrational measure of angles. 

Share the students' answers and facilitate the discussion around the norms. If there is a misconception among the students, correct it and focus on the definition of 1 radian measure.

Play with the interactive tool below.

Move the slider and observe how the radian measure works on the circle.






How many radians do you need to place them on the circle to complete the half circle (180 degrees)? Type your answer using only one word.

Complete the sentence by choosing one from the options. "The numbers we use for the degree measure is _______."
  • integers
  • rational numbers
  • irrational numbers
  • real numbers

We already know how to use the degree to measure angles. Why do we need another system for the angle measurement? Type your answer in a sentence.


Teaching Tips:

Create a circle in the middle of the classroom or outdoors where all the students can sit on the circle and a quiet environment.

Have students sit on the circle and place Nao robot at the center of the circle. 

Nao robot needs to hear student's answer clearly to verify the answer so have students quiet and follow the directions of the robot.

Run this Choregrephe file for this activity.

Following is the activity details:

NAO tells, “Now, we see what radian measures look like and I want you to tell me if it’s true or false.” NAO rotates and points out one student, saying “Can you please raise your hand? So guys, from here” and NAO turns a certain degree, saying “To here. Raise your hand please and answer my question.” “This angle is about 2.5 radians. Is it true or false?

NAO rotates and points out one student, saying “Can you please raise your hand? So guys, from here” and NAO turns a certain degree, saying “To here. Raise your hand please and answer my question.” “This angle is about 4 radians. Is it true or false?

NAO rotates and points out one student, saying “Can you please raise your hand? So guys, from here” and NAO turns a certain degree, saying “To here. Raise your hand please and answer my question.” “This angle is about 6.3 radians. Is it true or false?

NAO rotates and points out one student, saying “Can you please raise your hand? So guys, from here” and NAO turns a certain degree, saying “To here. Raise your hand please and answer my question.” “This angle is about 3 radians. Is it true or false? 

Sit on the circle. Make sure all of you are evenly distributed on the circle. 

Follow NAO's instruction for this activity. 

When Nao robot asks a question, she needs to hear your or your peer's answer clearly to verify the answer. Make sure everyone is quiet and follow the robot's direction. 


Teaching Tips:

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

Mark how much you understand each concept. Your response won't be graded. Be honest so your teacher can plan better the next lesson.

I understand the concept of radian measure of an angle
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

Explain how you calculate one-radian measure on the unit circle. Type your answer in a sentence.

I understand how to convert between degree and radian 
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

Explain how you convert degree to radian, and radian to a degree.