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Solving Linear Equations/Systems of Linear Equations - Algebraically and/or Graphically

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Solving Linear Equations/Systems of Linear Equations - Algebraically and/or Graphically

Grade Levels

10th Grade, 11th Grade, 12th Grade, 7th Grade, 8th Grade, 9th Grade

Course, Subject

Algebra I, Algebra II
Related Academic Standards
CC.2.1.HS.F.3 CC.2.1.HS.F.3
Apply quantitative reasoning to choose and Interpret units and scales in formulas, graphs and data displays.
CC.2.1.HS.F.4 CC.2.1.HS.F.4
Use units as a way to understand problems and to guide the solution of multi-step problems.
CC.2.2.HS.C.2 CC.2.2.HS.C.2
Graph and analyze functions and use their properties to make connections between the different representations.
CC.2.2.HS.C.3 CC.2.2.HS.C.3
Write functions or sequences that model relationships between two quantities.
CC.2.2.HS.C.5 CC.2.2.HS.C.5
Construct and compare linear, quadratic and exponential models to solve problems.
Expand
  • Big Ideas
    Bivariate data can be modeled with mathematical functions that approximate the data well and help us make predictions based on the data.
    Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
    Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Patterns exhibit relationships that can be extended, described, and generalized.
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
  • Concepts
    Algebraic properties, processes and representations
    Analysis of one and two variable (univariate and bivariate) data
    Exponential functions and equations
    Functions and multiple representations
    Linear relationships: Equation and inequalities in one and two variables
    Linear system of equations and inequalities
    Polynomial functions and equations
    Quadratic functions and equations
  • Competencies
    Extend algebraic properties and processes to quadratic, exponential, and polynomial expressions and equations and to matrices, and apply them to solve real world problems.
    Represent a polynomial function in multiple ways, including tab les , graphs, equations, and contextual situations, and make connections among representations; relate the solution of the associated polynomial equation to each representation.
    Represent a quadratic function in multiple ways, including tab les , graphs, equations, and contextual situations, and make connections among representations; relate the solution of the associated quadratic equation to each representation.
    Represent exponential functions in multiple ways, including tab les , graphs, equations, and contextual situations, and make connections among representations; relate the growth/decay rate of the associated exponential equation to each representation.
    Represent functions (linear and non-linear) in multiple ways, including tables, algebraic rules, graphs, and contextual situations and make connections among these representations. Choose the appropriate functional representation to model a real world situation and solve problems relating to that situation.
    Write, solve, and interpret systems of two linear equations and inequalities using graphing and algebraic techniques.

Rationale

  • How would you correlate the solution of a linear equation to its graphical representation?
  • How would you use graphical and/or algebraic techniques to solve a system of equations and how would you interpret the solutions of that system?

Description

The student will use algebraic and graphical representations to solve linear equations and systems of linear equations.

Students will need to have access to a computer.  Students will use the Function Analyzer (see below) to understand the concept of intersection.  The Function Analyzer is a tool that is not difficult to learn.

The photo shows the intersection of several highways.  Students will understand how the concept of intersection is related to solving linear equations.

Content Provider

The Concord Consortium:  http://www.concord.org/

Resource

See the link below for the interactive resource.  After creating a free account, you will have access to all ITSI-SU Math and Science interactive resource and lessons.

http://itsisu.portal.concord.org/activities/26.jnlp?teacher_mode=true

 

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