Pre-Calculus Lesson Plan – Math lab: Old Faithful’s Eruptions

Purpose:

This lesson will focus on the formation of a linear equation using the slope-intercept method or the point-slope method. After some guided practice and written homework, the students will model data on Old Faithful’s eruptions and the interval between the eruptions. Excel will be used during this portion of the lesson to perform some of the tedious calculations.

Unit:

This lesson is part of a unit on relations, functions, and graphs. Chapter 1, in particular, discusses linear relations and functions.

Objectives:

· The students will write linear equations using slope-intercept form.

· The students will write linear equations using point-slope form.

· The students will apply the writing of linear equations to the formation of such an equation from real data.

Standards:

7.A.4b, 8.B.4b, 8.D.4, 10.A.4a, 10.B.4

Materials:

Textbook, paper & pencil, overhead/chalkboard, small whiteboards & dry erase markers, Excel, lab copies of “Modeling Old Fatihful’s Eruptions”, overhead transparencies of example outcomes

Activities:

Note-taking, guided practice, individual practice, math lab

Procedures:

Day one:

1. Introduction of lesson

2. Discuss slope-intercept form and how to use it to write a linear equation when given the slope of a line and a point it will go through. Do some guided practice on the whiteboards.

3. Discuss point-slope form and how to use it to write a linear equation when given the slope of a line and a point it will go through. Do some guided practice on the whiteboards.

4. Discuss how to use the above forms to write a linear equation when given two points that the line will go through. Do some guided practice on the whiteboards.

5. Use the cost function example in the text to discuss variable cost vs. fixed cost.

6. Individual practice: #2-4, 17, 20, 21, 23, 28, 31, 33, 35 pages 40-41

Day two:

1. Introduce the lab, “Modeling Old Faithful’s Eruptions,” by discussing the opening paragraphs about geysers and their eruptions.

2. Discuss the purpose of the lab:

· Model the data on Old Faithful’s eruptions and the interval between the eruptions

· Compare the paper and pencil model with the model found using Excel and with the model used by Yellowstone Park to predict eruptions

· Describe what it means to have a “best-fitting” model

3. Briefly, discuss the nine steps/questions of the lab.

4. Use Excel to show how to find the “sum of the squares of the differences” of the actual y-values and the y-values generated by the three models (paper-and-pencil model, the model used by Yellowstone Park to predict the eruptions of Old Faithful, and the linear regression model generated by Excel).

5. Use Excel to show how to produce a scatter plot of the given data that includes the computer trend line. The graph should include a title, subtitles, the computer trend line, and its equation.

6. Assign: #1-9 of the lab handout, the Excel chart and graph, and a summary paragraph which includes an explanation of what it means to have a “best-fitting” model and how Excel helped with the otherwise paper-and-pencil calculations.

The Excel chart headings should be as follows:

G

x-values

y-values

y-values of paper-and-pencil equation

Square of the differences

(C2-B2)^2

y-values of Park equation

Square of the differences

(E2-B2)^2

y-values of Computer equation

Square of the differences

(G2-B2)^2

Assessment/Evaluation:

· Guided practice

· Written homework (individual practice)

· Lab questions, Excel chart, Excel graph, summary paragraph

· Quiz and test over material at a later date