This is an exploratory lesson for inequalities and absolute value. It involves questioning and students demonstrating their understanding with a visual. I find it difficult to script my question writing because I take cues from my students, but hopefully, this will be a good place to start. You will be tempted to show your students a number line like below. Don’t do this. They will probably use this because they’ve seen it before but don’t limit them. You will be surprised with the visual representations that your students will come up with.

This is a 3 lesson series that build upon the last. Inequalities is the first lesson in the series.

x+4<5 What numbers make this statement true? Create a visual representation to show all of the solutions your group finds.

What are some ideas about you have that would help us solve this problem? Try them out and see if you get a solution similar to your visual representation from before.

Discuss successes and failures as a group and what we could learn from them.

-2x > 6 What numbers make this statement true? Create a visual representation to show all of the solutions your group finds.

Solve this one with the same method you used before or another method you hear about when we discussed. Was this process the same or different? Why do you think it was this way?

-3x+2 ≤ -4 What numbers make this statement true? Can we use the same procedure as before? Create a visual representation to show all of the solutions your group finds.

Solve this one with the same method you used before or another method you hear about when we discussed. Was this process the same or different? Why do you think it was this way?

What is a rule that seems to work for all of these? Discuss at your table, everyone has something to add.

Compound Inequalities

-5<x<4 How might this problem be the same and different from the ones before? What numbers make this statement true? Create a visual representation to show all of the solutions your group finds.

What ideas do you have for solving this? We will share our ideas and discuss.

-9 ≤ 2x + 3 < 5 What numbers make this statement true? Can we use the same procedure as before? Create a visual representation to show all of the solutions your group finds.

Try to solve this based on our discussion. What are some thoughts you have about this type of problem?

6 > -2x +4 ≥ -12 What numbers make this statement true? Create a visual representation to show all of the solutions your group finds.

Solve this one with the same method you used before or another method you hear about when we discussed. Was this process the same or different? Why do you think it was this way?

What is a rule that seems to work for all of these? Discuss at your table, everyone has something to add.

5x ≥ 15 or 2x+3 < -13 How would you solve this? Think and discuss with your table and try to find a solution. You can use any method that works.

I would at the end talk about AND and OR symbols and have the students write down what they feel like is important for notes.

The next lesson will explore Absolute Value.