Course: High School Math with NAO
Graphing a Linear Equation

Teaching Tips:

As part of the ‘Hook’, the robot can be used to walk around making ‘whacking’ movements, as part of the ‘attraction’
 
Act 1: (15 mins) Teacher Modeling
Select a linear equation and construct a table of values and demonstrate how these values, when plotted on an x-y chart go through a unique line.
 
Demonstrate how given a line on the x-y notation and one of the variables the other variable can be solved.
 
Specific examples:    
Equation: y = 2x + 1
 

 
Corresponding Graph

 
 
 
 
Equation: y = -0.5x + 5
 

 
Corresponding Graph

 
 

Teaching Tips:

Act 2: (15 mins) Student Activity
The students are given a linear function and its equivalent line in a graph. This activity involves the system coming up with a set of values for x and asking the students to compute the value for y that solves the equation. A corresponding marker is placed on the line.
 
Example:
Function:  

y = 0.5x + 2 
 
x = 0,    y =  _____  (Ans = 2)
x = 1,    y =  _____  (Ans = 2.5)
x = 2,    y =  _____  (Ans = 3)
x = 3,    y =  _____  (Ans = 4.5)
x = 8,    y =  _____  (Ans = 6)
x = 10,   y =  _____  (Ans = 7)

Teaching Tips:

Act 3: (15 mins) Student Activity
The students are given a linear function and its equivalent line in a graph. This activity involves the system coming up with a set of values for y and asking the students to compute the value for x that solves the equation. A corresponding marker is placed on the line.
 
Example:
Function:  y = -0.5x + 1
 
y= 1,    x = ________   (Ans = 0)
y= 0,    x = ________   (Ans = 2)
y= -1,   x = ________   (Ans = 4)
y= -2,   x = ________   (Ans = 6)
y= -3,   x = ________   (Ans = 8)
y= 3,    x = ________   (Ans = -4) (Challenge)
 

Teaching Tips:

Act 4: (15 mins) Student Activity
The students are given a linear function and its equivalent line in a graph. This activity involves the system coming up with a set of values for x or y and asking the students to compute the value of the other variable that solves the equation. A corresponding marker is placed on the line.
 
Example:
Function:  y = 1.5x - 1
 
x= 1,    y = ________   (Ans = 0.5)
y= 1,    x = ________   (Ans = 0)
x= -2,   y = ________   (Ans = 4)
y= 5,   x = ________    (Ans = 4)
x= 0,   y = ________    (Ans = 1)
y= 3.5, x = ________   (Ans = 3)
 

Teaching Tips:

Act 5: (20 mins)Student Activity
This activity is a version of the Whack-a-Mole game. The simulator environment shows a 10x10 grid with a clear marking of an x- and y-axis and an origin. The rest of the grid looks like grass.
 

 
The students are told that the robot has a “mole pop-up location predictor” that conveys the location at which the mole will pop up.   Moles can come up in any location but because the robot will take some time to reach the location, the student must guide the robot before the mole actually pops-up, based on information given to them by the robot.  During the activity, the goal is for the student to guide the robot so it whacks the mole before it pops down based on the given information. There is a time limit on this and if the student makes a mistake or takes too long, the mole will escape. Students are given a chance to whack up to 10 moles and points are given each time a student whacks a mole.
 
There are three variations of the game, as follows:

1. In the first variation, the robot offers the student a function and the x coordinate of the upcoming pop-up.  The student must solve for the y and the robot will move to the (x,y) coordinate in order to whack the upcoming mole.
2. In the second variation, the robot offers the student a function and the y coordinate of the upcoming pop-up.  The student must solve for the y and the robot will move to the (x,y) coordinate in order to whack the upcoming mole.
3. In the third variation, the robot offers the student two functions and the mole will pop-up at the intersections of these functions.  The student must determine the location at which the lines intersect and the robot will move to the (x,y) coordinate in order to whack the upcoming mole.

In all cases, once the student provides the answer, the robot will move along the x-axis and then the y-axis, and then perform a ‘whack’ movement.  If it happens to be on top of the mole pop-up location the student gains a point otherwise the mole escapes.
 
The following illustration shows the steps involved in gameplay in the 1^st variation.
 

 
 

Teaching Tips: