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

Learning about rate of change in linear functions using interactive graphs: Constant cost per minute

http://standards.nctm.org/document/eexamples/chap6/6.2/

A lesson plan for Grades 6–8 Mathematics

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
6–8
Subjects
mathematics (algebra, arithmetic)
Provider
National Council of Teachers of Mathematics

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Creative Commons License

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In this two-part example, users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). In this first part, Constant Cost per Minute, the cost per minute for phone use remains constant over time. In the second part, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls.

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)

Grade 6

  • Goal 4: Data Analysis and Probability - The learner will understand and determine probabilities.
    • Objective 4.03: Conduct experiments involving simple and compound events.
  • Goal 5: Algebra - The learner will demonstrate an understanding of simple algebraic expressions.
    • Objective 5.04: Use graphs, tables, and symbols to model and solve problems involving rates of change and ratios.

Grade 7

  • Goal 5: Algebra - The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.
    • Objective 5.03: Use and evaluate algebraic expressions, linear equations or inequalities to solve problems.
    • Objective 5.04: Develop fluency in the use of formulas to solve problems.

Grade 8

  • Goal 5: Algebra - The learner will understand and use linear relations and functions.
    • Objective 5.01: 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.
    • Objective 5.02: Write an equation of a linear relationship given: two points, the slope and one point on the line, or the slope and y-intercept.
    • Objective 5.03: Solve problems using linear equations and inequalities; justify symbolically and graphically.