Common Core Standards: Math
8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
It's no secret that sixth graders everywhere throw crazy math parties. We're talking huge, school-wide blowouts, complete with pocket calculators, prime number recitations, and, of course, pi-eating contests. Oh…you didn't know about these shindigs? Shoot, maybe it was a secret.
In any case, the noble equation often comes up at these parties, and the sixth-grade partygoers discuss and raise their glasses (of apple juice) to toast such a useful mathematical statement. But what about the lonely, forgotten inequality? Shouldn't he have his moment of glory?
Yeah. We think so, too.
If your students don't attend these mathematical jamborees (and even if they do), they should know that inequalities are mathematical statements just like equations, but they represent an unequal (inequal?) relationship as opposed to an equal one. That's no surprise, as they've been working with symbols like > and < since elementary school.
But what happens when we start throwing variables into the mix? Students should recognize that inequalities like x < c or x > c represent a lower or upper limit for the variable as opposed to one specific value. That means these inequalities have an infinite number of solutions as opposed to just one.
You know what might help with understanding this? The number line. And good thing, too, because students will have to represent these inequalities on the number line. Make sure to be as strict as those inequalities about drawing open circles on those boundary values.
Once students can write and represent these types of equations, they should apply them to real-world scenarios to represent boundaries and constraints. Of course, that means recognizing when a situation requires a boundary or constraint as opposed to one specific value.
Basically, students should interpret a real-world problem, write a very simple strict inequality to describe it, and represent that inequality on the number line.
They should also toast inequalities at fancy sixth-grade math parties, but that's a different situation altogether.
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