Shannon Coombs

For Dr. Thompson's Functions 1

Inequality Lesson Logic

To do this activity you will need

• Graphing Calculator (retail) or Graphing Calculator Player (free) from PacificTech.
• A clear overhead transparency sheet
• Scotch tape
• Transparency marker (erasable)

Let’s Begin!

• Type |x³ - 5y² + xy - 3y| into Graphing Calculator (DO NOT press enter)
• Select Graph>Density Plot (i.e., in the Graph menu, select Density Plot
• Press Enter (or click Graph)

Step	Action	Reason
1.	Discuss with students that the expression at the page's top is simply a calculation rule. It says what to do with values of x and y once they are given. You might give them several values of each for them to calculate.	You don't want students to think that you expect them to solve anything nor that you expect them to "know what x and y are".
2.	Tell them to click anywhere on the graph (but not on an axis). Explain that where they clicked indicates a point in the coordinate plane, and that GC tells them the point's x-coordinate, its y-coordinate, and the value of the expression after substituting those values of x and y into it. Have them click several places so that they can see that this is indeed how it works.	This familiarizes them with the program's interface and builds confidence that this complicated formula can be evaluated easily for whatever values of x and y they choose.
3.	Ask students to use their markers to indicate 5 points on the screen that have coordinates that make the expression have a value less than 6.	This is to allow the students to play with the program with a goal in mind.
4.	Ask the students to find 100 points on the screen that have coordinates that make the expression have a value less than 6	This makes the students try to look critically at where the values are that make the expression less than 6. They will need to try to think of the general “region” of where those coordinates are
5.	Ask the students to use their markers to indicate 5 points on the screen that have coordinates that make the expression have a value less than 3	This should have the students re-practice finding values. Only this time they are hopefully looking already at where these points are, and what a pattern might be
6.	Ask the students to find 100 points on the screen that have coordinates that make the expression have a value less than 3	Again, to make the students analyze the nature of where the values are that satisfy this request.
7.	Ask the students to find ALL of the points on the screen that have coordinates that make the expression have a value less than or equal to 3.	This will allow the students to look very closely at where the values are that work and to look at the contour lines to help them make a “boundary” line that divides the graph into regions that work, and regions that don’t work.
8.	Have the students test their conjecture by graphing x^3 - 5y^2 + xy - 3y < 3	To allow them to see if they were correct. =)
9.	Perhaps repeat this one more time with another value, maybe > 4 or something, just to see if they can do it better/faster/more effectively.