A Basic Activity
The most basic of the ideas for teaching graphing inequalities is to let students figure out the basics of how graphing works. Due to this, write a simple linear equation on the board, such as y = x + 5. Have a student come up to the board and graph and equation.
Then change the equal sign to a “<" sign. Ask students to come up with ordered pairs that would satisfy the inequality, such as (2, 1) or (0, 0). Plot at least fifteen of these ordered pairs on the graph and then ask students if they can find a pattern as to which area contains all of the ordered pairs that satisfy the inequality. Students should realize that all of the ordered pairs are beneath the graphed line. Color in this area, and explain that this is how you would graph y < x + 5. Ask students to predict what the graph of y > x + 5 would look like.
At the end of this instruction, students should realize that to graph an inequality, the first step is to graph the associated equation by substituting in an equal sign for the inequality sign. The second step is to shade in the area above the graphed line if the inequality sign is “>,” and the area below the graphed line if the inequality sign is “<."
Hand out one index card to each student, with each index card containing an inequality. Challenge students to find pairs of index cards that contain perpendicular inequalities. For example, the student with the index card containing the inequality y < x - 3 would pair off with the student who has the index card containing the inequality y < 7 - x because the associated equations of these two inequalities are perpendicular.
As students find the pair of inequalities, they should work in their pairs to graph the two inequalities and shade appropriately. Ask students to predict, based on their graphs, where the ordered pairs are that would solve for both inequalities. Students can then check their prediction by finding some ordered pairs that would solve for both, and seeing which section of the graph they fall in. (They should all be in the overlap of the two shaded areas.)
Which Inequalities Make a…
In this activity, students use their knowledge of inequalities to make simple pictures. They will need to be familiar with basic geometric terms to complete some parts of this activity. For example, challenge students to make a triangle using overlapping inequalities. To do this, they will need to find three equations that overlap in a way that a triangle forms in the center. They can then try out different combinations of inequality signs in each of the equations to figure out which one lends itself to a solution of a shaded in triangle. Other options include a stripe, a diamond or a parallelogram.
These ideas for teaching inequalities will help teachers engage students in the learning process, as well as give students hands-on experience in working with the mathematical forms.