3 Tips to Teach Solving and Graphing Inequalities

Solving and graphing inequalities notes with pencil

After teaching solving and graphing inequalities for a few years, I noticed my middle school math students kept making the same mistakes. I immediately started teaching inequalities different, and deliberately had some conversations with my students which made all the difference.

Now, I call them conversations, because the key is to not just tell them how to do it. The key is to lead the conversations with thoughtful questions. Here are three conversation topics that are essential for teaching inequalities in math.

Essential Conversations while Teaching Inequalities

1) There is a difference between x > 7 and x > 8. Graph both solutions on the same graph. Then have the conversation why they are not the same. Have students give examples of numbers that are included in x > 7, but not x > 8.

2) Start a conversation about x < 7 and 7 > x. Some ideas to direct the conversation: think of three numbers that are less than 7 and think of three numbers that 7 is greater than. Do your solutions work for both inequalities? Why? Have the students graph both, and notice that they are the same. Have students practice changing from the variable on the right, to the variable on the left. Though both are correct and mean the same thing, it is standard to have the variable written on the left-side of the inequality.

3) Understanding inequality graphs on a number line. There is a more effective way to teaching graphing than saying that the inequality points to the way the arrow should be drawn. When teaching this way, students often do not understand why. Also, if the students do not happen to flip a solution such as 7 > x so that the variable is on the left, their arrow will be incorrect. You could teach students to test a point such as 0. If 0 works, then point the arrow towards 0. If 0 does not work, then point the arrow away from. However, make sure that you are explaining that the arrow represents every single solution to the inequality. I often say that since it is impossible to write out every solution, the arrow visually shows every solution.

Having these conversations with your students definitely takes more time teaching. However, my experience is that they will retain solving and graphing inequalities better and you will spend less time reviewing.

Guided notes are a great way to keep your thinking and conversations on track while teaching. Here are some solving inequalities guided notes that may help you while teaching. Click on the image below to take a look at the notes.


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Solving and graphing inequalities guided notes with pencil




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