LEARN NC

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

Space Shuttle O-ring failure

Students will use a TI82 or TI83 calculator to construct a scatterplot, find the equation of the least-squares regression line for a set of data, find the coefficient of determination, and make predictions by using the line.

A lesson plan for grades 9–12 Mathematics

By Brenda Goforth

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Learning outcomes

Students will:

  • produce scatterplots
  • recognize positive or negative association and linear patterns
  • use r2 to describe how much variation in one variable can be accounted for by a straight-line relationship with another variable.

Teacher planning

Time required for lesson

1 hour

Technology resources

  • TI82 or TI83 graphing calculator
  • Overhead projector LCD display unit for graphing calculator (Optional, but very helpful)

Pre-activities

Students should be familiar with entering data into lists and producing scatterplots.

Activities

  1. Students will enter O-ring data using temperature as the X-values in L1 and the brittleness coefficient as the Y-values in L2. (see Data attachment)
  2. Students will find the equation of the regression line and the value of r2. (see RegEq attachment) The teacher might want to simplify the discussion of r2 for non-statistics classes.
  3. Students will use statplot to plot temperature vs brittleness. (see Plot attachment)
  4. Students will fit regression line to points in scatterplot.
  5. Students will predict brittleness coefficient at 31ºF.

Assessment

Students will answer questions based on the scatterplot, coefficient of determination, and regression line. (see Questions attachment)

Supplemental information

Tests on shuttle O-rings have determined that when the brittleness coefficient reaches 0.035, an O-ring breaks. The forcasted low temperature for the morning of Challenger’s launch was 31 degrees Fahrenheit. The launch team after reviewing the data made the decision to proceed with the launch.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 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.

Grade 9–12 — Advanced Placement Statistics

  • Goal 4: Algebra - The learner will analyze bivariate data to solve problems.
    • Objective 4.01: Analyze bivariate data.
      • Recognize and analyze correlation and linearity.
      • Determine the least squares regression line.
      • Create residual plots and identify outliers and influential points to analyze data.
      • Use logarithmic and power transformations to analyze data.

Grade 9–12 — Discrete Mathematics

  • Goal 2: Data Analysis and Probability - The learner will analyze data and apply probability concepts to solve problems.
    • Objective 2.01: Describe data to solve problems.
      • Apply and compare methods of data collection.
      • Apply statistical principles and methods in sample surveys.
      • Determine measures of central tendency and spread.
      • Recognize, define, and use the normal distribution curve.
      • Interpret graphical displays of data.
      • Compare distributions of data.

Grade 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.

    Grade 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.

    Grade 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.