What follows is a reprise of our discussion in class. It ends with a table giving the first few steps of the activity in which you engaged. The aim of this assigmnent is that you recreate the logic of that activity, so that you not only recreate the activity itself, but also create a justification of it that makes sense to you. NOTE: The expression used here differs from the one we used in class. This is to highlight the logic of the activity instead of focusing you on replicating the activity.
Students often have a very hard time understanding inequalities and their solution sets. They often approach inequalities as if the idea is unrelated to everything they have done. This activity suggests one way to approach the idea of inequality so that what is conventionally proposed as an outoftheblue procedure instead emerges as a natural response to very sensible questions.
For them to understand the idea of inequalities and their solution sets, they must have a particular understanding of equations and variables.
How students understand equations is either the biggest obstacle or the biggest aid to their coherent understanding of inequalities.
3x^{2}+2x7 = 4

3x^{2}+2x7 < 4


UNDERSTANDING OF EQUATIONS THAT POSES AN OBSTACLE 
IF students think of this equation as "the answer" being a number that hides behind the letter "x", and that his or her responsibility is to figure out what that number is, THEN

AS A RESULT they will likely think of " 3x^{2}+2x7 < 4" in a number of confusing ways:




UNDERSTANDING OF EQUATIONS THAT IS SUPPORTIVE 
IF students think of this equation as an open sentence, a statement that is neither true nor false by itself, and becomes true or false as you replace x with various values, then

AS A RESULT they will likely think of this statement more coherently:

The following activity can be used to introduce students to the idea of inequalities. It begins with inequalities in two variables rather than inequalities in one variable. This is because the added complexity actually increases the level of interest students feel.
Tape the clear overhead transparency to your computer's screen.
Be sure to remind students of the meaning you already established for equations (see prior comments), the implied question, and what a solution set is.
Click on the graph to get a GC file for this activity,
OR
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 xcoordinate, its ycoordinate, 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. 
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4.  (You complete the rest of this table)  
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