SWBAT solve two variable inequalities by constructing an appropriate boundary line and shading a half plane.

See how to use test points to determine how to determine the solution to a two-variable inequality.

10 minutes

**Note**: The impetus behind this lesson is the students lack of understanding during the previous lesson. This lesson was added after reflecting on students' progress. It may not be necessary to teach this lesson.

We start this lesson by investigating the ticket out from the previous day:

*What pairs of numbers satisfy this statement: The sum of two numbers is less than 10. Create an inequality in two variables and graph the solution set.*

We first revisit the understanding that there are an infinite number of solutions to this question. Those solutions lie all over the coordinate axes. However, there is a boundary between where the statement is true or false.

Ask students to think about solutions to the following statement:

**The sum of two numbers is equal to 10**.

I ask my students to write down as many pairs as they can think of by themselves. I then have them turn and talk with a neighbor to try to extend their list. We compiled many of the answers on the board so that students could see the relationship between the variables (all sum to 10). We then graphed the coordinates and discussed the type of line that could be drawn (dotted or solid) and why.

Finally, I ask students to work with their partners to determine some numbers that made the statement "**the sum of two numbers is less than 10"** true.

In class, students came up with a variety of solutions. Through a "popcorn" style share out (calling on students at random) we created a list and plotted to results. Students could then see that if they wanted to represent all of the solutions the graph could be shaded downwards.

I then ask students to choose a point that is in the unshaded are and test it in the inequality. Showing that that point does not work reinforces why that part of the graph is not shaded.

20 minutes

Because we fell short on time in the previous lesson, I had students work with their partner to begin with questions a-f on solving_two_variable_inequalities_investigation.

After today's Open, they now had a more solid understanding of how to determine a boundary line before trying to shade the graph. As students work with their partners, I confer with various students. Most of my questions centered around understanding of why certain coordinates were in the solution and others were not. I want students to explain that coordinates in the shaded solution make the inequality true, while the others did not (MP3).

10 minutes

This very simple closure will give some good feedback on what students are understanding and what they are still unsure of. The question to the class was as follows:

**Write down on a half sheet of paper:**

**(1) One thing that you feel you learned as a result of today's class.**

**(2) One thing you are still confused about as a result of today's class.**

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