E 3 Research Program

Tom C. Clark HS Northside ISD

•Studied the behavior of flame speed in a controlled environment

•Studied the numerical analysis of the data, in order to create regression functions that can be used to model the data and predict values

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•Pre Test

•Introduce Engineering as a student and as a profession

*Talk about the E 3 Program and how it impacted my teaching , thinking, and perceptions about engineering

*Introduce the Research Assignment, present the experiment, analysis and talk about real world impact (gas turbine industry)

PARENT FUNCTION NOTES AND REVIEW

•Introduce various graphs (parent functions) and discuss the different functions they represent

•Work backwards and recognize the graph from given functions to build base knowledge of various functions

•Discuss the Domain and Range of the parent functions by analyzing the graphs

•Students will be able to recognize name, equation, graph and state the domain and range for various parent functions

LINEAR DATA ANALYSIS

•Introduce an actual data set from the flame speed analysis to plot and analyze

•Explain the different ways to model the data, and discuss which functions would produce that type of data arrangement

y = 282.61x + 0.5683

R2 = 0.9997

0

1

2

3

4

5

6

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

Series1

Linear (Series1)

LINEAR DATA ANALYSIS

•Calculate a Regression for the data and find a “best fit” function, discuss accuracy of the regression

•Discuss the Domain/Range of real world data, discuss the intercepts of the graph, discuss possible predictions

y = 282.61x + 0.5683

R2 = 0.9997

0

1

2

3

4

5

6

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

Series1

Linear (Series1)

NON LINEAR DATA ANALYSIS

•Introduce another (non linear) data set from the flame speed analysis to plot and analyze

•Explain the differences between the two sets of data

y = 144.82x + 0.3008

R2 = 0.9916

0

0.5

1

1.5

2

2.5

3

3.5

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Series1

Linear (Series1)

NON LINEAR DATA ANALYSIS

•Calculate a Linear Regression for the data and find a “best fit” function

•Discuss the problems with applying the Linear Regression and possible solutions to any problems

•Calculate a NON LINEAR Regression to better fit the data, discuss accuracy of the regression

y = 144.82x + 0.3008

R2 = 0.9916

0

0.5

1

1.5

2

2.5

3

3.5

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Series1

Linear (Series1)

STUDENT EXPERIMENT SETUP

•Students will set up their own experiment similar to the flame speed analysis, analyzing the growth of a balloon as it is being “blown up”

•Document the change of the RADIUS of a balloon as a function of TIME

•Students will record their balloons being “expanded” at various rates (different groups)

•Students will set up a meter stick and stopwatch in order to document the data (time, radius length)

STUDENT DATA COLLECTION

•Students will use their recorded video to analyze (frame by frame) the change of the radius of the balloon through the use of video editing software

•Document the change of the RADIUS by referring to their set up meter stick (center of balloon and how far it has expanded)

•Document the change in TIME by noting the change of time in each frame from the stopwatch

•Students will set up a graph to plot the data

STUDENT DATA ANALYSIS

•Students will set up their data in a graph in order to document the possible parent functions that could “fit” the graph

•Students will use their calculators to calculate a regression to best fit their data

•Students will present their findings for their data (with a graph and a best fit equation

•Students will discuss the parent function of their regression analysis and explain why they think it works for their data

CONCLUSION AND POST TEST

•Give students chance to discuss their different findings for different rates of change of the radius of the balloon

•Discuss what their findings mean in terms of the speed of the flame with respect to the change of the radius of the balloon

•Talk about Real World applications

•Where does the engineer fit in all this?

•POST TEST

ALGEBRA II / PRE CALCULUS

•Function Relationships

•Function Recognition

•Domain and Range

•Linear Functions

•Non Linear Functions

Thank You!

•NSF

•Texas A&M University

•E 3 Program and Directors

•Dr. Eric Petersen

•Will Lowry

•Turbo Lab Researchers

•E 3 Program Participants