LEARN NC

K–12 teaching and learning · from the UNC School of Education

Exploring linear functions: Representational relationships

http://standards.nctm.org/document/eexamples/chap7/7.5/

A lesson plan for Grades 9–12 Introductory Mathematics, Integrated Mathematics 1, Algebra 1, Integrated Mathematics 2, Pre-Calculus, Technical Mathematics 2, Advanced Functions and Modeling, Algebra 2, and Integrated Mathematics 4

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
9–12
Subjects
mathematics (algebra, applied mathematics)
Provider
National Council of Teachers of Mathematics

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Creative Commons License

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Technology allows the linking of multiple representations of mathematical situations and the exploration of the relationships that emerge. This example presents a series of explorations based on two linked representations of linear functions.

E-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

North Carolina Curriculum Alignment

Mathematics (2004)

Grades 9–12 — Advanced Functions and Modeling

  • Goal 1: Data Analysis and Probability - The learner will analyze data and apply probability concepts to solve problems.
    • Objective 1.01: Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, and logarithmic functions of bivariate data to solve problems.
      • Interpret the constants, coefficients, and bases in the context of the data.
      • Check models for goodness-of-fit; use the most appropriate model to draw conclusions and make predictions.

Grades 9–12 — Algebra 1

  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.01: Use linear functions or inequalities to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret constants and coefficients in the context of the problem.

Grades 9–12 — Algebra 2

  • Goal 2: Algebra - The learner will use relations and functions to solve problems.
    • Objective 2.04: Create and use best-fit mathematical models of linear, exponential, and quadratic functions to solve problems involving sets of data.
      • Interpret the constants, coefficients, and bases in the context of the data.
      • Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

Grades 9–12 — Integrated Mathematics 1

  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.01: Use linear functions or inequalities to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret the constants and coefficients in the context of the problem.

Grades 9–12 — Integrated Mathematics 2

  • Goal 3: Data Analysis and Probability - The learner will collect, organize, and interpret data to solve problems.
    • Objective 3.02: Create and use, for sets of data, calculator-generated models of linear, exponential, and quadratic functions to solve problems.
      • Interpret the constants, coefficients, and bases in the context of the data.
      • Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

Grades 9–12 — Integrated Mathematics 4

  • Goal 3: Data Analysis and Probability - The learner will analyze data to solve problems.
    • Objective 3.02: Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions of bivariate data to solve problems.
      • Interpret the constants, coefficients, and bases in the context of the data.
      • Check models for goodness-of-fit; use the most appropriate model to draw conclusions or make predictions.

    Grades 9–12 — Introductory Mathematics

    • Goal 4: Algebra - The learner will understand and use linear relations and functions.
      • Objective 4.01: Develop an understanding of function.
        • Translate among verbal, tabular, graphic, and algebraic representations of functions.
        • Identify relations and functions as linear or nonlinear.
        • Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.
        • Interpret and compare properties of linear functions from tables, graphs, or equations.

    Grades 9–12 — Pre-Calculus

    • Goal 2: Algebra - The learner will use relations and functions to solve problems.
      • Objective 2.03: For sets of data, create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions.
        • Interpret the constants, coefficients, and bases in the context of the data.
        • Check models for goodness-of-fit; use the most appropriate model to draw conclusions or make predictions.

    Grades 9–12 — Technical Mathematics 2

    • Goal 2: Algebra - The learner will use relations and functions to solve problems.
      • Objective 2.03: Create, interpret, and analyze best-fit models of linear, exponential, and quadratic functions to solve problems.
        • Interpret the constants, coefficients, and bases in the context of the data.
        • Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.