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NetLogo Models Library: 
If you download the NetLogo application, this model is included. (You can also run this model in your browser, but we don't recommend it; details here.) 
In this activity students can explore functions. Each student controls one point in the function. The activity supports several different kinds of exploration, with open ended possibilities for learning.
Students can try to make their points match an equation or description supplied by a teacher or student, or they can try to find an equation that best fits where their points are. The class should be encouraged to find unique or interesting equations that fit the criteria, to enforce the ideas of equivalence and simplification.
When students log in they are assigned a character in the coordinate system. Students control the character, which is merely a point placed in the coordinate system. The teacher can send instructions to students.
Teachers can challenge students to follow a rule like, "move until your y value equals your x value". Students can explore the space, pushing the boundaries of this rule, the point (1,1) works, but so does (1,1) and (0.5, 0.5).
Then students can explore alternate ways to phrase the rule, the function y = x defines this space, but so does y = 3 * x  2 * x.
Teachers can test students' functions, by graphing them over the class' set of points. You can use any valid NetLogo code to define the function in terms of y = f(x). You can also define inequalities in terms of x. See the How To Use It section for examples.
To run the activity press the GO button. To start the activity over with the same group of students stop the GO button by pressing it again, press the SETUP button, and press GO again. To run the activity with a new group of students press the RESET button in the Control Center.
Buttons: SETUP  clears the grid, if you have moved the xmaximum and minimum sliders the grid will automatically resize and redraw. GO  starts the activity so students can move their characters around the grid. ENTEREQUATION  prompts you to enter an equation to graph in the form y = f(x), where any valid NetLogo code can be used in the function defining y, for example: "y = x" or "y = 2 * pi * sin x". You can also define inequalities in terms of x for example: "y >= 3 * x + 1". You can use any math operations supported by NetLogo and you should use correct NetLogo syntax. So instead of 2x you should enter 2 * x. CLEARLASTEQUATION  removes the last equation graphed from the list and erases it from the grid
Sliders: YMAXIMUM, YMINIMUM, XMAXIMUM, XMINIMUM  define the bounds of the grid the students work in. Note that this is different than the size of the world, this allows you to use different size spaces without the world growing too large. You could also increase the size of the world to get a higher resolution.
Monitors: MOUSE POSITION  reports the position of the mouse in the grid.
Switches: GRID?  toggles the grid lines on and off REVEALLEGEND?  toggles the legend of equations in the lower right hand corner
Students' Equations: Students can send equations to the teacher, they appear in the STUDENTEQUATION monitor. The teacher can browse through them using the "<" and ">" buttons. GRAPHSTUDENTEQUATION  graphs the equation displayed in the STUDENTEQUATION monitor EDITSTUDENTEQUATION  allows the teacher to change the student equation, either to correct the syntax or to give feedback to the student. The edits are sent to the student.
Linear Regression: If LINEARREGRESSION? is on all other equations will be erased and a line will be interpreted, using the students as points. The SLOPE, YINTERCEPT, and COEFFICIENT OF CORRELATION are calculated and displayed in the corresponding monitors.
Send a Rule: The teacher can also send a rule for students to follow by clicking the SETRULE button and entering the "verbal" rule. The current rule is displayed in the RULE monitor.
Client Interface: Buttons: Move your character around the grid by pressing the UP, DOWN, LEFT, and RIGHT buttons which move you STEPSIZE in the specified direction. CHANGE APPEARANCE  changes the way the characters looks in the view
Monitors: RULE  the rule set by the teacher. YOU ARE A:  a word description of your character LOCATED AT:  your coordinates in the grid
Input Boxes: MYEQUATION  enter your equation to turn into the teacher here
Turn the LINEARREGRESSION? switch to on, to see the linear regression of your set of points.
The legend can be turned on and off in the bottom right hand corner of the interface.
The bounds of the grid are controlled by the corresponding sliders. (They are distinct from the maximum and minimum world coordinates; the grid coordinate system does not depend on the patch grid coordinates.)
Ask the students to follow a verbal rule like "make your y coordinate match your x coordinate". Then ask students to come up with an equation that fits the rule. Graph the different equations. Ask students to stretch the bounds of any given equation to come up with unique solutions.
Adjust the range sliders so the center of the world is not in the center of the view and graph the same equations.
Students' equations are not checked for syntax errors until the teacher attempts to graph them. Change the code for handling student equations so that it automatically lets students know if what they have submitted does not compile.
This model uses the runresult primitive to approximate the y value for each x value, thus, functions can use any valid NetLogo code in the function defining y.
If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.
For the model itself:
Please cite the NetLogo software as:
Copyright 1999 Uri Wilensky and Walter Stroup.
This work is licensed under the Creative Commons AttributionNonCommercialShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/byncsa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.
Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.
This activity and associated models and materials were created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORKBASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs)  grant numbers REC #9814682 and REC0126227.
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