A2.A.1.9 Solve systems of equations containing one linear equation and one quadratic equation using tools that may include graphing calculators or other appropriate technology.
In a Nutshell
Students will use previous knowledge of linear systems learned in Algebra 1 to understand systems containing one linear and one quadratic equation. They will use technology or mathematical methods to find the intersection of the two equations and interpret those as no solution, one solution or two solutions as appropriate. Finally, they will be able to test the solution within the context of the problem.
Student Actions
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Teacher Actions
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Students will generalize and extend their knowledge of systems to include systems containing one linear and one quadratic equation with the use of technology or other mathematical methods. Students will generate methods for solving these systems based on their previous knowledge of linear systems.
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Students will develop accurate and appropriate procedural fluency for finding the solution to systems containing one linear and one quadratic equation as the intersection between the two.
- Students will develop strategies for problem solving and verify their answer and will question the reasonableness of this solution within context by testing their coordinate point within the original problem.
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Elicit and gather evidence of student understanding of systems of equations containing one quadratic and one linear equation by assigning tasks that allow students to use various methods, including technology, to describe and/or solve the system.
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Facilitate meaningful math discourse by allowing time for students to compare and contrast the characteristics and results of a system of linear equations and the system of one linear and one quadratic.
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Use models and representations to make connections from the mathematical ideas about a system of equations learned in Algebra 1 to a system containing one linear and one quadratic equation.
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Design ways to elicit and assess students’ ability to test their solution against the original problem.
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Key Understandings
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Misconceptions
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Understand the solution to a system of equations containing one linear and one quadratic equation as the point(s) of intersection.
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Understand that a lack of intersection in a system of equations containing one linear and one quadratic equation means there is no solution.
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Extend methods learned in Algebra 1 for solving systems of equations to include one linear and one quadratic equation.
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Use technology to graph a system and be able to find the point(s) of intersection by manipulating the device’s window dimensions if necessary.
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Procedural:
Conceptual:
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Students forget the solution to a system of equations is the point or points of intersection and only provide a single number as their answer.
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Students do not understand systems of equations with a linear and quadratic functions can have three distinct types solutions: no solution, one solution or two solutions.
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Students do not know how to interpret the solution of a system of equations when there is no intersection.
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OKMath Framework Introduction
Algebra 2 Grade Introduction
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