Georgia Performance Standards(As Listed on the Ga DOE Website)

Mathematics Course:____8th Math ____Math 1(9th)__X__Math 2(10th)

Title of Lesson Losing Your Marbles

Unit 2 Performance Task 2 __X__Exploration ____Direct Instruction ____Culminating Task

Georgia Performance Standards(as listed on the Ga DOE website) Reviews standards 1.MA1A1 Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques. 2.MA1A3 Students will solve simple equations. 3.MA2A5. Students will explore inverses of functions. Introduces standards MA2A1 Students will explore exponential functions.

b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior. c. Graph functions as transformations of f(x) = ax. d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

Essential Question(s) 1.How do you determine which regression model is the “best fit” for a set of data?

Resources 1.Losing Your Marbles – Warm Up 2.Losing Your Marbles – Worksheet 3.Losing Your Marbles – Ticket Out the Door(Culminating Activity) Supplies 1. c- clamp 2 rulers (at least one clear one) 3. paper clip 4. cup basket 5. marbles 6. poster sheet 7. markers 8. graphing calculator – TI 84+ Timing Outline

Bellringer – 5 minutes

Lab Worksheet /Data Collection/Technology(TI 84+) - 60 minutes

Ticket Out the Door – 15 minutes Losing your Marbles Bellringer

Complete the table Graph Name of Function Function Table of Values X values Y f(x) = values -3 -2 -1 3 0 -5

X values Y values -2 0 f(x) = (x-3)³ - 2 3 -1 6 62 Losing Your Marbles – Lab Worksheet

Member Name LEADER responsible for keeping the group on task/asks questions EQUIPMENT responsible for getting and setting up equipment MEASURER responsible for taking accurate readings RECORDER responsible correctly recording all data PRESENTATION responsible for creating the group poster

PROCEDURE You will be conducting two experiments and recording all information on poster board.. In EXPERIMENT 1, you will determine how varying forces (adding marbles) affects the bend in your cantilever. In EXPERIMENT 2, you will be keeping the number of marbles constant, varying the length of the cantilever, and recording bend For each experiment: (Include these things on your poster!) 1. Find and record 8 measurements and complete the table.

2. Make a scatterplot of the collected data.

3. Using the graphing calculator find the possible equations for best fit lines and their related R2 value. Determine the most appropriate model between linear, quadratic, cubic, and quartic. You may write the equations with decimals rounded to the 3rd decimal place.

4. Describe the domain and range of your function.

a. Include a graph of your data that contains the best fit line.

QUESTIONS: (Turn in one completed copy of this sheet per group)

EXPERIMENT 1 You will determine how varying forces (adding marbles) affects the bend in your cantilever. Be sure to keep your cantilever the same length in this experiment. Record your data in the table below.

Trial Number of Marbles Bend(nearest tenth of a cm.) 1 2 3 4 5 6 7 8

Make a scatterplot using collected data.

Enter data into the graphing calculator and complete the following table. Regression Equation R2 Linear Quadratic Cubic Quartic

Questions 1. Using the R² values which is the best model ______and the corresponding regression equation. ______Now graph your regression equation on the same grid as the scatterplot. 2. Using complete sentences explain your choice of regression equation.

3. Using your model predict how much bend would exist for … 50 marbles ______1,000 marbles ______

EXPERIMENT 2 You will be keeping the number of marbles constant, varying the length of the cantilever, and recording bend. It is up to your group to decide how these experiments will be performed. Use cm to the nearest tenth to measure bend. Record your data in the table below.

Trial Length of the Cantilever Bend(nearest tenth of a cm.) 1 2 3 4 5 6 7 8

Enter data into the graphing calculator and complete the following table. Regression Equation R2 Linear Quadratic Cubic Quartic

Questions 1. Using the R² values the equation of best fit is______and the corresponding regression equation is______Now graph your regression equation on the same grid as the scatterplot above. 2. Using complete sentences explain your choice of regression equation.

3. Using your model predict how much bend would exist for … 16 in cantilever ______50 in cantilever ______Ticket Out the Door Statistics

Lowndes County, GA Population and Components of Change

Components of Change Inter- Total national Net % Population Immigra- Domestic Date Population Change Change Births Deaths tion Migration 2000 92,115 0.7 643 - - - - 2001 92,527 0.4 412 1,766 857 123 -546 2002 94,272 1.9 1,745 1,369 667 -72 1,184 2003 95,047 0.8 775 1,455 744 -372 553 2004 96,953 2.0 1,906 1,617 737 250 874 2005 98,504 1.6 1,551 1,532 700 44 766 2006 100,482 2.0 1,978 1,719 728 157 883 2007 101,715 1.2 1,233 1,805 771 19 200 2008 104,684 2.9 2,969 1,798 789 69 1,878 2009 106,814 2.0 2,130 1,832 795 46 1,061 Source: U.S. Bureau of Census Site: http://recenter.tamu.edu/data/popc/pc13185.htm

Use the above chart and a graphing calculator to complete the following.

1. Enter the data using the STAT key: use List 1 (L1) for the year and List 2 (L2) for the population. (HINT: use the number 0 for year 2000, the number 1 for year 2001, the number 2 for year 2002, and so on.)

2. Graph the data in a scatter plot using the STAT PLOT key.

3. What type of function best fits the regression of the data?

4. What is the regression equation that best fits the data?

5. Graph your regression equation on the scatter plot of data.

6. Use your regression equation to predict the population of Lowndes County in year 2010. Adapted from Accelerated Math 2 ,Unit 2 Performance Task 2,from the Georgia Dept of Education website, Futures Channel and credits to Becky Martin .