a1tD0000003mM5jIAE

Sine and Cosine Graphs (BB 8)

  • 9-12 grade

Lesson Description:

Students write a sinusoidal equation that the BB-8 (the Sphero robot) to follow so it can avoid the gun fires from the bad guys. This lesson helps amplitude, frequency, and vertical translation of graph of a sinusoidal function.


 

Standards Covered

CCSS.MATH.CONTENT.HSF.BF.A.1

Write a function that describes a relationship between two quantities.*

CCSS.MATH.CONTENT.HSF.IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

CCSS.MATH.CONTENT.HSF.TF.B.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*

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.MP7

Look for and make use of structure.

image description

Lesson Modules


Teaching Tips:

Show the student the video of BB-8 running zigzag and have students write their answer to the given question. Share the word cloud results with them and have a quick discussion about the common answers. 

While picking up the words from the poll results, select the words that are related to this lesson.

To recall, the learning goal of this lesson is 

1. to compare and contrast sine and cosine curves
2. to understand the amplitude
3. to compare and contrast period and frequency
4. to understand vertical/horizontal translations



 

Experts say you should not run in a straight line when fleeing from an attacker who is shooting. Generally, a zig-zag pattern is recommended as the BB-8 did. Read the question below and type your answer. 

Type your answer using only ONE word.



What information does BB-8 need in order to run away in a zig-zag pattern?


Teaching Tips:

Have students play with the interactive tools. Help them to focus on the different shapes of sine and cosine graphs. This activity helps students to see how the variables, a, b, and c change the graph.

Give the students some time to discuss with the group before answer the questions. 

Change the amplitude (a), period (b), and the vertical translation (c) by using the slides. 

See how each coefficient affects the graph. 

If you don't see a curve, click on the background picture. 

Pay attention to the equation while you are changing the coefficient a, b, and c. 






 Discuss with your team members to answer the following questions. 

What is the difference between sine and cosine graphs? Type your answer in a sentence.

How does the coefficient a change the graph? Type your answer in a sentence.

How does the coefficient b change the graph? Type your answer in a sentence.

How does the coefficient c change the graph? Type your answer in a sentence.


Teaching Tips:

Have students play the simulation. This activity helps students to calculate the coordinate of the vertex so BB-8 can go to the right position to be picked up by the x-fighter. 



Teaching Tips:

Give students a quiet individual time to answer the questions to reflect on what they've learned from this lesson. Share the self-reported scores with the class and have an open discussion of what went well and what could've done differently. You have access to the students' responses in your dashboard. 

 

Note that this lesson is mentioning only the frequency. If the students are ready, then introduce the period vs. frequency. 

 

 

Check your knowledge on each concept. 

I understand the concept of sine and cosine graphs.
  • Not at all
  • Kind of got it
  • Understand
  • Pretty good
  • Totally got it

Explain the similarity and the difference between sine and cosine graphs.

 

I understand the concept of amplitude
  • Not at all
  • Kind of got it
  • Understand
  • Pretty good
  • Totally got it

Explain how the coefficient 'a' changes the amplitude.

 

I understand the concept of frequency/period.
  • Not at all
  • Kind of got it
  • Understand
  • Pretty good
  • Totally got it

Explain how the coefficient 'b' changes the period and the frequency.

 

I understand the concept of vertical translate
  • Not at all
  • Kind of got it
  • Understand
  • Pretty good
  • Totally got it

What did you change in the equation to translate the graph vertically?