Getting Started 
Misconception/Error The student does not understand how to graph a linear inequality (or line) in the coordinate plane. 
Examples of Student Work at this Level The student incorrectly graphs the boundary line and does not show the graph of the halfplane that represents the solution region.
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Questions Eliciting Thinking What is the slope of the boundary line of the inequality you are trying to graph? Is the slope positive or negative?
What is the yintercept of the boundary line of the inequality you are trying to graph?
Did you graph the boundary line using the correct slope andÂ yintercept?
Is there more to the graph of an inequality than just the boundary line? 
Instructional Implications Review graphing lines written in slope intercept form and the role of the boundary line in graphing the solution region of an inequality. Demonstrate for the student how to use the yintercept and the slope to graph a line. Emphasize that solutions of a linear equation are points on aÂ line, but all possible solutions of an inequality lie in a halfplane separated by a boundary line. Guide the student to understand the relationship between the inequality symbol and whether or not points on the boundary line are solutions of the inequality. Provide instruction on conventions for graphing boundary lines (i.e., drawing solid versus dashed lines). Provide additional examples of strict (< or >) and nonstrict (Â or ) inequalities for the student to graph. Emphasize the relationship between the shaded part of the graph and the solutions of the inequality.
Provide additional opportunities to graph inequalities. After each graph is completed, ask the student to identify a point on the graph that is a solution of the inequality and a point that is not. Then ask the student to justify his or her choices by determining whether or not the points satisfy the inequality. 
Moving Forward 
Misconception/Error The student does not shade or incorrectly shades the halfplane that represents the solution region. 
Examples of Student Work at this Level The student:
 Correctly graphs the boundary but does not shade the halfplane that represents the solution region.
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 Correctly uses a testpoint to determine which halfplane contains the solutions but misinterprets the results and shades the wrong region.
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Questions Eliciting Thinking Did you graph all solutions to the inequality or just the boundary line?
How is graphing the solutions to an inequality different from graphing a line?
How did you determine which halfplane contains the solutions of the inequality? 
Instructional Implications Review the method of testing a point to determine the region of the plane in which solutions are found. Emphasize the relationship between the shaded part of the graph and the solutions of the inequality. Review the logic used when testing a point to determine the solution region.
Provide additional opportunities to graph both strict (< or >) and nonstrict (Â or ) inequalities written in both slopeintercept and standard form. Caution the student not to rely on the direction of the inequality symbol to determine the region to shade (e.g., concluding that the less than symbol indicates to shade below the line) as this is only true on special cases. 
Almost There 
Misconception/Error The student makes a minor graphing error. 
Examples of Student Work at this Level The student:
 Does not draw arrows at each end of the boundary line.
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 Uses a solid line instead of a dashed line when graphing the strict (< or >) inequality.
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 Graphs the line as if the slope were Â instead of , but all other boundary line details are correct.
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Questions Eliciting Thinking Did you graph a line or a segment? What notation is used to indicate the boundary is a line rather than a segment?
What is the relationship between the inequality and the type of line you draw? Why is the boundary line for an inequality sometimes solid and sometimes dashed?
You made a mistake when graphing your boundary line. Can you find your mistake? 
Instructional Implications Provide feedback to the student concerning any errors made. If needed, review the conventions for graphing boundary lines (i.e., drawing solid versus dashed lines). Be sure the student understands points on the boundary line of nonstrict (=or=) inequalities are contained in the solution region, but points on the boundary line of strict (< or >) inequalities are excluded from the solution region.
Provide additional examples of both strict (< or >) and nonstrict (Â or ) inequalities for the student to graph written in both slopeintercept and standard form. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student correctly graphs the Â the inequality using a dashed boundary line and shades the halfplane below it.
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Questions Eliciting Thinking Why did you show the boundary line as a dashed line? What does the dashed line signify? What would a solid line signify?
How did you determine which halfplane contains the solutions of the inequality?
What does the shading indicate about the solutions of the inequality? 
Instructional Implications Challenge the student to graph a system of linear inequalities and to describe the portion of the plane that represents solutions ofÂ the system. 