# Writing, Graphing, and Solving Inequalities (lesson)

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Lesson guidelines below. For the actual lesson, see attached file below or click the link at the bottom.

Part 1: Give the students 5 minutes to complete part 1.  Encourage them to write down any and all answers they think could work.

Part 2:  Without giving any direct instruction, ask the students to use the number lines provided to show all the answers they thought of or could think of from part 1 on the number line below.  Choose a few students at random to show how they represented all the possible answers and make sure other students can understand the thinking.  Ask a few probing questions, such as, “Could it also be ___?”  “What about a number in between 4 and 5?”

Part 3:  Begin by asking the students “How many answers are there to each of these problems?”  “Do you think we could represent the answer with an equation, such as x = 3?”  “Why or why not?”  After the class agrees that there is a whole group of possible answers, direct their attention to the reading at the top of page 2.  Ask the class if they recall seeing these symbols in elementary school and what they might mean. Then allow them to work alone or with a partner to write in inequality for each of the 4 scenarios.

Part 4:  Direct the students’ attention to the box on the right of part 4.  Go over the math conventions for noting if a point is or is not included  and discuss the concept of a “boundary” point by asking them, for each of the scenarios, what was the largest or smallest number it could have been.  Ask the students to try to represent scenario 1 using the correct notation and check the work as a class.  Finally, have them graph the other 3 scenarios and choose students at random to present their solutions.

Part 5:  Allow the students 5-10 minutes to try to complete the chart on their own, explaining that they need all three representations for each row.  The second row may pose a challenge and is there to help them be aware that not all inequalities are single.  After most students are finished, have them work in a group of 4 and use roundtable to share (begin with 1 member of the group and go in a circle, having each student share their work on each problem).  While they are sharing, circulate to see how well they are understanding and provide additional explicit instruction and practice, if necessary.

Part 6:  End class by having the students try to summarize or explain what in inequality is by comparing it with an equation.

Click to access Inequalities.pdf