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# A2-A-1-8

last edited by 5 years, 1 month ago

A2.A.1.8 Represent real-world or mathematical problems using systems of linear equations with a maximum of three variables and solve using various methods that may include substitution, elimination, and graphing (may include graphing calculators or other appropriate technology).

In a Nutshell

Students will represent and solve mathematical problems by using systems of equations.  Students may use a variety of methods to solve systems of equations. They will understand systems of equations with three variables can be represented within a three dimensional coordinate space.  They will be able to identify how many solutions, if any, a systems of equations has and determine what those solutions look like within a coordinate space.

## Teacher Actions

• Students will develop a conceptual understanding of when and how to use systems of equations to represent a real-world problem.  They will be able to contextualize their mathematics in terms of a real-world situation, identify the unknown quantities, and translate it into a system of equations.

• Students will generalize and  develop strategies to solve systems of three linear equations.  These will include substitution, elimination. graphing and/or methods using technology.

• Students will develop the ability to communicate their mathematics and will interpret the solution within a system of three equations with three variables as having:

• one solution when all planes meet at a single point.

• no solution when the planes do not have any points in common.

• infinitely many solutions when the planes intersect at a line or they are all the same plane.

• Support productive struggle as students make the connection between systems with two variables and systems with three variables. Anticipate where the students might struggle when setting up and solving systems of equations and be prepared to support this productive struggle by asking scaffolding questions without stepping in to do the work for them.

• Facilitate meaningful mathematical discourse as students make three dimensional drawings or use other visual supports (such as technology) to explain and justify no solution, one solution, or infinitely many solutions within a system of three equations.

## Misconceptions

• Analyze real world problems and translate them to systems of up to three equations.
• Solve systems of up to three linear equations by substitution, elimination or graphing.
• Use technology to visually find the solution to systems of equations.
• Understand that three equations in a system of equations implies a three dimensional solution with a coordinate point of three real numbers as a possible solution.
• Recognize systems of three equations that have no solution or infinite number of solutions.

Procedural:

• When using the substitution method to solve equations, students will solve for one equation and substitute it back into the equation they solved for.

• Students will forget to put all equations in standard form when using elimination and incorrectly add the terms.

• Students will graph the equations incorrectly when using pencil and  paper and miss the point of intersection.

• Students have difficulty finding any errors in their algebraic path when the solution does not fit the original problem.

Conceptual:

• Students will improperly write the solution of a systems of three equations as a single real number, or a coordinate point with only two real numbers.

• Students have difficulty translating real world problems into algebraic systems of equations.

OKMath Framework Introduction