How To Teach Math - Solution Sets for Inequalities

A1.2.3 Find solution sets for linear inequalities when possible numbers are given for the variable

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Topic Discussion

The first time I read this standard I felt it did not merit inclusion on its own. However, as I considered it further, I realized it is a vital part for most students understanding of inequalities. I have found students often have a poor understanding of what the solution of an inequality is. From a teaching standpoint this topic is pretty simple. But it is very important to utilize it to prepare for solving inequalities algebraically.

The Concept

Students often struggle with remembering which symbol means greater than and which means less than. I have heard different ways that students can help students to memorize which is which. Some say the mouth of the arrow eats the larger number. For me it has always seemed pretty logical. The small end goes with the small number and the large end goes with the large number. Whatever the case it becomes a memory thing for students.

Once it is clear the students understand the symbols then it becomes a matter of showing students how to check each solution. This is not a difficult concept, but it is very, very important they understand that each number has a truth value. Either it makes the inequality true or it makes the inequality false. It is very important for students to view inequalities in this manor. It not only helps in understanding basic algebraic inequalities, it will become invaluable when help students study linear inequalities later in the year.

The Bridge

As I alluded to above this can be used very effectively to introduce algebraic and linear inequalities. The way I like to do this is to give students inequalities and then have them check 10 to 15 points. I then have them plot the true points in one color and the false in another. Eventually the students will begin to see the pattern. This is a very good activity to be done in cooperative groups. It can also be done by giving the students a range and asking them to find 5 true and 5 false points. This gives the students more sense of ownership in the problem and can lead to them developing their own way to solve the problem.