Course: High School Math with NAO
Systems of Linear and Quadratic Equation

Teaching Tips:

Act 1: Teacher Modeling

Follow the steps below:

1. Sets up a chalk grid on the floor (make sure 10 cm represent 1 unit on the grid).
2. Places the robot at the origin (0,0).
3. Start the program on the robot and the robot announces the function it will ‘walk to’.  
4. Then call out a number (which would be the ‘x’) and the robot moves to the x, y location that corresponds to a specific function by walking as many feet as x, then turns 90 degrees to the left or right and walks the number of feet represented by a function of (x).
5. A marker is placed at that location.
6. The robot is put back at (0,0).

Repeat step 1 through 6 as needed, placing a mark on the floor each time.
Discusses that the line that goes through the markers describes the function originally announced by the robot. Also, discuss how charting a function works, but ‘walking’ along the x-axis an amount equal to the ‘x’ component of the equation and then ‘walks’ along the y-axis an amount equal to ‘y’ which is also the function of x, i.e., f(x).  This can repeat as needed by having the robot ‘walk’ a different function which is done by saying ‘Pick another function’ and the robot will then announce the new function and repeat the process.
 

Teaching Tips:

Act 2: Student Activity
This is the same activity as the one demonstrated in the previous module, but students can do it with the robot simulator.  The students can type the numbers instead of speaking them out. There has to be a button that places the robot at the origin and the scene is viewed from above so the relationship between the robot’s walk and the coordinates on the x-y plan are obvious.
 
The students can type a number and click on a move button. The robot will then move forward as many units as the number of taps, then turn 90 degrees facing the target point and then move forward until it reaches the target point. A virtual marker is left at that point.  Question to students “Can you determine the function represented by the markers?”
 

Teaching Tips:

Act 3: Student Activity
 
The screen has an overlay of the US with major cities tagged with a marker that includes their (x, y) coordinates. Various routes crisscross the country and go through the various cities, in addition, each route tagged with a label that describes a mathematical function that describes the route.  There are multiple routes and hence multiple functions, some linear and some quadratic. Each function represents a route.  The goal is for the student to come up with the travel schedule to go through particular cities (tour) where the concerts will be being held. Each travel leg consists of three pieces of information (route, x_1, x_2) and the tour consists of a series of travel legs.  Effectively, the students are asked to visually interpret functions and their coordinates and boundaries. They also need to have the ability to switch among multiple functions.
 

 
The screen will pose a tour, i.e.:  Portland, Nashville, Houston.
The students then have to fill in the legs that will visit these cities, in this case:
Portland à Kansas City:  y=0.026x2, (-14, 5.1) à (0, 0)
Kansas City à Nashville: y = -0.7x, (0, 0) à (4, -2.8)
…
 
Some of the coordinates of cities that lay on route intersections are missing. The students would then have to identify the coordinates first and then provide the routes.  For example, the coordinates of KC, NASH, NY and LA would not be provided on the map.
 
Students could create their own tour schedule. However, you have to visit at least 5 cities to break even your production company's investment. 
 

Teaching Tips:

Close: (5 mins)
Students will share with the class the routes they developed.  This will lead to a discussion of how there may be multiple solutions to a problem and how a point can belong to multiple functions.