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5.7: Problem Solving Strategies: Use a Linear Model

Difficulty Level: At Grade Created by: CK-12

Learning Objectives

At the end of this lesson, students will be able to:

  • Read and understand given problem situations.
  • Develop and apply the strategy: Use a Linear Model.
  • Plan and compare alternative approaches to solving problems.
  • Solve real-world problems using selected strategies as part of a plan.

Vocabulary

Terms introduced in this lesson:

linear modeling

Teaching Strategies and Tips

In Example 1:

  • The problem combines a question from geometry with a solution from algebra.
  • Assume a linear association exists between circumference and diameter, which is plausible given the scatterplot.
  • Allow students to pick their own points to find the line of best fit. Compare regression models as a class.
  • As a class, compute one interpolation and one extrapolation. Compare with the results obtained from the line of best fit.
  • All models will contain some error due to measurement. Convince students that the \begin{align*}y-\end{align*}intercept should be \begin{align*}0\end{align*} in any model: a circle of zero diameter has no circumference.

Observe in the scatterplot in Example 2 that the data are not linear.

  • Assume that the data do not change drastically between the known data points.
  • Interpolation or extrapolation methods will give better estimates than the line of best fit.

Error Troubleshooting

General Tip: Before performing a linear regression on a data set, have students always check the scatterplot first for approximately linear data.

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CK.MAT.ENG.TE.1.Algebra-I.5.7