TEMPLATE FOR LESSON PLANNING

Name(s): Peter Jeon

Title of lesson: Best Fit Lines

Length of lesson: 2 class periods

Source of the lesson:

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TEKS addressed:

= ; (A.1) Foundations for functions. The student understands that a function represents a dependence of one quantity= on another and can be described in a variety of ways.

&= nbsp; (D) represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities;

&= nbsp; (E) interpret and make decisions, predictions, and critical judgments from functional relationships.

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&= nbsp; (A.2) Foundations for functions. The student uses the properties and attributes of functions.

&= nbsp; (D) collect and organize data, make and interpret scatterplots (including recognizing positive, negative= , or no correlation for data approximating linear situations), and model, predic= t, and make decisions and critical judgments in problem situations.

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I. = Overview

In this l= esson, students will collect data and plot them out. However, not all data collected fo= llow a function properly. So the nex= t best alternative would be to find the best fit to make predictions of where the function may go.

II. Performance or learner outcomes

&= nbsp; Students will be able to:

- Predict a best fit line from a set of data points.

- Devise a formula using the best fit line

- Utilize technology to calculate a regression=

III. Resources, materials and supplies needed

= ; Graphing Calculator (TI-83)

IV. Supplementary materials, handouts. (Also address any safety issues

Concerning equipment used)

V. Safety Considerations. (may be N/A)

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Five-E Organization

Teacher Does = Probing Questions &nbs= p; Student Does =

Engage:=

Present the students with a scatterplot of data. The data should be pr= etty straight-forward with a data set that follows a linear function perfectly= .

Is there a pattern to this data set?

What are the intercepts of this data if it were a line?

What is the = function that this data set follows?

Hopefully th= ere should be no misconceptions in this section since the students should be = able to figure out where the graph goes. The trouble may come when it comes to finding the correlating function.

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Explore:

Have the students look up data online and create a table and plot them onto a graph. Since this is= a lesson on oil and it’s supply, it would = be optimal to look up the stats of oil supply in the = US by year.

More than li= kely, a nice function can’t be made to fit these data points, so it would be best to have students construct a line that represents a good representat= ion of the stat plot.

Can a functi= on be made from this set of data that fits all the data points?

What is the = function behind your best fit line?

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When will th= e oil supply reach zero?

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Why do you t= hink this “best fit” line is necessary?

Since the st= udents are to construct a best fit line without the aid of anything other than t= heir mere intuition, different answers will be made. But, these answers should be in = the same general area. It would= be best to use the same data set for the classroom.

Explain:

Like what an average does to represent a single entity, a regression = is used to give a general idea of a trend, given some information to start o= ff with. Regressions are by no= means completely accurate. The st= rength of a regression is represented by the correlation coefficient, which rang= es from -1 to 1.

Why do we ha= ve regressions?

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What does a = strong regression look like?

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Are all regr= essions restricted to linear functions?

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Does having = a best fit line mean we know what will happen to future data values?<= /i>

Regressions = are a simple representation of what the data currently looks like, and may give= the students some insight of what may happen later on. It is a strong predictor of what= is to come, but not completely true. The strength of a correlation coefficient is highest at 1 which represents perfection (which is usually not possible). In the extension, students will = realize that there are more regressions out there that may be better representati= ves of the data.

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Extend / El= aborate:

Regressions can be performed on a TI graphing calculator. Using the stat function on the calculator, the students can record data points on a table and plot them onto a graph. A good feature of using the calculator is that there are many other types of regressions to choose from. The correlation coefficient is also given when finding the strength of the regression.

Is there a b= etter regression to represent the data set that you currently have?

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What is a st= rong correlation coefficient value?

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A good corre= lation coefficient may vary from student to student, but keep in mind that it is= 0 that represents no correlation and -1 that represents a correlation, but = in the opposing direction.

Evaluation:

1. What = is a best fit line (regression)?

2. What = is a correlation coefficient?

3. Suppo= se the supply of oil in a certain country was represented by f(x). In what year will the oil supply r= un out?

4. Why d= o we have regressions?