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Movement with Functions

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Movement with Functions

Grade Levels

10th Grade, 11th Grade, 12th Grade, 6th Grade, 7th Grade, 8th Grade, 9th Grade

Course, Subject

Related Academic Standards
CC.2.2.HS.C.1 CC.2.2.HS.C.1
Use the concept and notation of functions to interpret and apply them in terms of their context.
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.
CC.2.4.HS.B.3 CC.2.4.HS.B.3
Analyze linear models to make interpretations based on the data.
A1.1.2.2.1 A1.1.2.2.1
Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).
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  • 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 and processes
    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
    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.
    Use algebraic properties and processes in mathematical situations and apply them to solve real world problems.
    Write, solve, and interpret systems of two linear equations and inequalities using graphing and algebraic techniques.
    Write, solve, graph, and interpret linear equations and inequalities to model relationships between quantities.

Description

These investigations use movement to reinforce the concepts of linear functions and systems of equations. Multiple representations are used throughout, along with tools such as motion detectors and remote-controlled cars. Students explore how position, speed, and varying motion are reflected in graphs, tables, and algebraic equations.

Web-based Resource

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Movement with Functions

Content Provider

Illuminations

 

Illuminations is a project designed by the National Council of Teachers of Mathematics (NCTM) and supported by the Verizon Foundation.  Illuminations works to serve you by increasing access to quality standards-based resources for teaching and learning mathematics, including interactive tools for students and instructional support for teachers.

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