# 5. Solve system problems with graphs (A)

teaches Common Core State Standards CCSS.Math.Content.8.EE.C.8a http://corestandards.org/Math/Content/8/EE/C/8/a
teaches Common Core State Standards CCSS.Math.Content.8.EE.C.8b http://corestandards.org/Math/Content/8/EE/C/8/b
teaches Common Core State Standards CCSS.Math.Content.8.EE.C.8c http://corestandards.org/Math/Content/8/EE/C/8/c
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1

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Lesson objective: Apply graphs to solve systems of equations with a real-world context.

This lesson provides an opportunity for students to apply their knowledge and understanding of graphs and systems of equations to a real-life situation. Students are asked to construct a graph to show which hikers meet on a trail given different clues.

Key Concept students will use:

• A point of interesection represents a solution to a system of equations.

Skills students will use:

• Construct a graph of a linear function (Unit 7).
• Interpret points on the graph representing a real-world situation (Unit 6).
• Understand a solution to a system as an ordered pair where two conditions are true at the same time.

Students engage in Mathematical Practice 1 (make sense of problems and persevere in solving them) as they make sense of multiple relationships in a problem and the connection between the relationships. Students will use a graph to represent the relationships and interpret features such as intersection points and parallel lines in the context of a real-world situation.

Key vocabulary:

• intersection
• parallel
• slope
• y-intercept

Special materials needed:

• graph paper or graphing technology
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