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Course: High School Math with NAO
Introduction to Functions

  • 8-12 grade
  • Intermediate

Lesson Description:

This lesson introduces the concept of functions and the application to Nao robot's dance sequence. 


 

Standards Covered

CCSS.MATH.CONTENT.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

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

Determine an explicit expression, a recursive process, or steps for calculation from a context.

CCSS.MATH.CONTENT.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

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.IF.C.7.A

Graph linear and quadratic functions and show intercepts, maxima, and minima.

CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2

Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP2

Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3

Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP4

Model with mathematics.

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:

Show NAO's dance!

Charge NAO robot the night before.

Use this file to run the live demo for class.

Place Nao in front or in the middle of the classroom so every student can see it.

NAO will ask how many motions you want him to repeat. Say a number between 1 and 10 clearly to NAO. Nao will do a sequence of motions. Once the dance is finished, try with different numbers.

First, try only with one, then two, and three. Students will notice the pattern of the dance motions.

Ask students what would be the next movement of Nao if you ask 4 times repeat.

Help students to see the patterns and repeat the demo as needed. 

 

Have students estimate and answer the question. 

Download the Choregraphe file to your computer and open it in Choregraphe program. 

Follow NAO's instruction and observe NAO's dance.

  1. How many poses did NAO do for one cycle of the dance?
  2. How many poses did NAO do for two cycles of the dance?
  3. How about 3 times?
  4. What would NAO do if you ask 10 times?
  5. Think for a moment and answer the following question.

 

 

 



If 50 taps are given to Nao, how many motions will NAO have for his dance? Estimate the number based on your observation.



How can you find the patterns and express them? Type your answer only in ONE word.


Teaching Tips:

Students might use the following strategies:

  • using pictures
  • using tables
  • using equations
  • using graphs

The goal of this lesson is 

1) to introduce a function as the relations of input and output

2) to use variables 

3) to write an equation to express the relations and 4)apply the function to a complex problem-solving.

4) apply the function to a complex problem-solving.


Monitor students while they are developing the patterns and mark who is working on what strategy. We suggest at the end of this Explore module, you have students present what they did and why. Make connections among the different strategies and emphasize using variables and equations are useful for the case when we deal with big numbers where we cannot really draw what's going on.


Show the class how to use the Math Tool before the students use it. You can show how to create a table, how to graph points/equations, etc. 

How can you find the number of motions if 50 taps given to Nao? Follow the directions below:

  1. Model Nao's dance with 4 taps and 5 taps. How many join movements will Nao make in 4 taps and 5 taps?
  2. Make some observations about the movement that could help you describe a larger number of taps.
  3. Describe a method for finding the total number of joint movement for 50 taps without modeling it.
  4. Write a rule that could be used to determine the number of joint movement needed for any taps. Explain how your rule relates to the visual representation of the movement.


Feel free to use the tools you have. You can create a table to visualize the patterns or a graph or anything that you feel comfortable with. Keep in mind that you want to find the patterns of NAO's motion in this dance.



Teaching Tips:

Call on the students/team that you checked while they were working.


Make sure you have the sequence of strategies to share with the class that helps students to realize why a certain way is more beneficial. 


When each strategy is presented, ask questions, why they choose that way and how they used the strategy to solve the challenge. 


Discuss with the class about cons/pros of each strategy. 

Share what you figured out with your team members. 




Which strategy do you think is the most efficient to represent the pattern? Type your answer in only in ONE word.
 

Which strategy do you think is the most effective way to find NAO's poses when NAO is repeating 50 times of cycle?  Explain why.
 


Teaching Tips:

Give students a quiet time to answer the questions individually. 

Share students' understanding and have a quick discussion with the class to review the learning experience.

You have access to the students answers on the dashboard.

Check your knowledge below. Mark how much you understand each concept. Be honest! This will NOT be your grades. Your feedback will be used for the next lessons. 


Take some individual time and answer the following questions. 


I understand the concept of use variables
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

Explain what variables you used to express what.

I understand how to use an equation to apply for any number of taps
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

Explain how you wrote your equation and why that works for any number of taps

I understand different equations can express the same thing
  • Not at all
  • Not really
  • Kind of understood
  • Pretty much understood
  • Totally got it

What other equations did you see that actually give the same answer? Why do they give the same answer?