# 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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Activities
Answer Key
Answers
(48 more)
Assessment
circumference
CK.MAT.ENG.TE.1.Algebra-I.5
Common Misconceptions
Concept Check and Troubleshooting
dependent variable
diameter
Differentiated Instruction
Enrichment
extrapolate
family of lines
finding equations for lines
Inquiry Process
interpolate
line of best fit
linear equations
linear functions
linear regression
measurement error
negative reciprocal
outliers
Pacing
Parallel Lines
perpendicular lines
point slope form
point-slope form
Problem Sets
Problem Solving
Quizzes
reciprocal
scatter plot
Science Inquiry
slope
slope formula
slope-intercept form
Solution Key
Solutions
standard form
Survey
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
Testing
Tests
vertical shift
Worksheets
x-intercept
y-intercept

Subjects:

Date Created:

Feb 22, 2012
Last Modified:

Aug 22, 2014
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