LEARN NC

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

Taking its toll

http://illuminations.nctm.org/LessonDetail.aspx?ID=L571

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, applied mathematics, probability, statistics)
Provider
National Council of Teachers of Mathematics

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Students compare the price of a toll to the distance traveled, investigate data numerically and graphically to determine the per-mile charge, and predict the cost if a new tollbooth were added along the route. Illuminations provides an activity sheet, an overhead transparency, links to important web resources, and instructions necessary for completing this lesson. After explaining the concept of toll roads, the teacher guides students in the process of collecting data and creating scatterplots with the information found in their research. Once students have gathered data and made their graph, they analyze the results and participate in a follow-up discussion about the activity.

Students will:

  • Determine slope given two ordered pairs.
  • Determine a line of best fit based on given data.
  • Determine the average cost per mile for passenger vehicles.
  • Model, analyze, and make predictions for adding a new toll plaza.

NCTM Standards and Expectations covered in this lesson include:

  • Identifying functions as linear or nonlinear and contrasting their properties from tables, graphs, or equations.
  • Exploring relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.
  • Using graphs to analyze the nature of changes in quantities in linear relationships.
  • Making conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.

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.
    • Objective 4.04: Determine and compare experimental and theoretical probabilities for 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 4: Data Analysis and Probability - The learner will understand and use graphs and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including box plots and histograms) to solve problems.
    • Objective 4.05: Solve problems involving two or more sets of data using appropriate statistical measures.
  • Goal 5: Algebra - The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.
    • Objective 5.01: Identify, analyze, and create linear relations, sequences, and functions using symbols, graphs, tables, diagrams, and written descriptions.
    • Objective 5.02: Translate among different representations of algebraic expressions, equations and inequalities.
    • 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 4: Data Analysis and Probability - The learner will understand and use graphs and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including scatterplots) to solve problems.
    • Objective 4.02: Approximate a line of best fit for a given scatterplot; explain the meaning of the line as it relates to the problem and make predictions.
  • 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 5.03: Solve problems using linear equations and inequalities; justify symbolically and graphically.