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A1-A-1-3

Page history last edited by Tashe Harris 6 years, 1 month ago

A1.A.1.3 Analyze and solve real-world and mathematical problems involving systems of linear equations with a maximum of two variables by graphing (may include graphing calculator or other appropriate technology), substitution, and elimination. Interpret the solutions in the original context.


In a Nutshell

Students will solve systems of linear equations with at most two equations and two variables. Students will use graphing, substitution, and elimination as possible ways to solve the systems of linear equations. Students may incorporate  technology when appropriate to solve the systems of linear equations.

Student Actions


Teacher Actions

  • Students will develop accurate and appropriate procedural fluency by graphing systems of linear equations to find the ordered pair solution (x,y) or use the substitution or elimination method to solve for the solution of linear equations.

  • Students will develop strategies for problem solving, beginning with examining a wide variety of models (verbal descriptions, sketches, graphs, algebraic expressions) to develop multiple strategies to solve for the solutions of linear equations and use technology to verify their answers in context of the problem.

  • Students will develop mathematical reasoning by examining various models of situations which involve systems, choosing appropriate methods to solve them, and correctly interpreting their solutions in the context of the problem, including no solution and infinitely many solutions.

     

  • Pose purposeful questions, asking  students to relate problems to real-world situations using systems of equations and to explain their reasoning as they solve these problems.

  • Work with students as they use and connect mathematical representations including models of many kinds (verbal descriptions, sketches, graphs and algebraic equations) using these models to gain understanding of the meanings of their solutions in context.

  • Build procedural fluency from conceptual understanding, helping students to understand that the solution of a system is a pair of solutions where both conditions are met (i.e. when x, then y) in a variety of algebraic and real-world situations

Key Understandings

Misconceptions

  • Students will use many models of systems systems of equations, including coordinate graphing, and understand:

      • The solution of a system is a coordinate (x, y).

      • Parallel lines will result in no solution.

      • Equations which result in the same graphed line will have infinitely many solutions.

  • The use of graphing utilities can help students observe how two variables are graphed in two lines in order to find the solutions, x,y.

  • Students will understand the relationship of systems of equations to real-world situations, especially that the solution is a situation in which two values coincide.

  • Ex:  Company A charges a setup fee of $25 plus $5 for each t-shirt.  Company B charges no setup fee, but the cost is $10 per shirt.  How many shirts must you order for the cost to be the same from both companies?  What will the cost be?
  • Students will solve for a variable and may interpret y instead of x as the first coordinate of the system instead of using the proper order, (x,y).  Also, they may misidentify x and y in terms of the context of the problem.

  • Students may forget to multiply by the correct number to make equivalent terms while using elimination.

  • Students incorrectly isolate a variable before substituting or substitute incorrectly (often omitting the distributive property) when using the substitution method.

  • Students may graph the two lines incorrectly and will, therefore,  not successfully find the correct solution of the system.

  • Students may incorrectly translate a verbal model to an algebraic equation.

  • Students stop working after finding the first variable and do not find a complete solution.

OKMath Framework Introduction

Algebra 1 Introduction

 

 

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