How+long+is+Kobe+Bryant's+Forearm?

=How Long is Kobe Bryant's Forearm? =

INTRODUCTION:
The purpose of this lesson is to help students understand how linear regression can be used to make predictions with their own collected data.

**TEACHER CANDIDATE**: Courtney Hansen, Trenna Seidel, Stacey Smith, Chloe’ Davis

**DATE & TIME**: March 8th at 11:00 AM

**SCHOOLDISTRICT & COOPERATINGTEACHERS**: Any school district and any teacher

**GRADE LEVEL & SUBJECT**: High School: Mathematics 3 or Algebra 2


 * LEARNING TARGETS: **
 * Students extend their use of statistics as they graph bivariate data and analyze the graph to make predictions. (EALR M3.4)
 * Students use linear functions to analyze relationships, represent and model problems, and answer questions. (EALR M1.3)

Net Standard
 * **1.** || **Creativity and Innovation** ||
 * || **Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students:** ||
 * || || a. || apply existing knowledge to generate new ideas, products, or processes. ||
 * b. || create original works as a means of personal or group expression. ||
 * c. || use models and simulations to explore complex systems and issues. ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">d. || <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">identify trends and forecast possibilities. || ||

<span style="font-family: Georgia,serif;">Students will be able to:
 * <span style="font-family: Georgia,serif;">LEARNER OUTCOMES: **
 * <span style="font-family: Georgia,serif;">Collect and graph bivariate data
 * <span style="font-family: Georgia,serif;">Create own best fit line
 * <span style="font-family: Georgia,serif;">Use a linear regression line to make predictions

<span style="font-family: 'Calibri','sans-serif'; font-size: 15px;">In this project students will be learning how to gather measurements and input them into a list onto the calculator. From this list they create a graph and learn about linear regression. They will then learn how to create a line of best fit and how to analyze the graph using this. Finally they will use their graph to estimate multiple basketball stars shoe size. The lesson includes the net standards through the above items. The students already know how to graph equations when one is given, but the students apply new knowledge by learning how to graph something by using a list. The students are working in groups to create and original work by creating a graph. Then, the line of best fit will allow the students to determine if some of the listed items are outliers, which would cover the explore complex systems. Finally, the students will use the results from their activity to predict different basketball stars shoe size, which would satisfy the last part of the standard. As for the learner outcomes, this lesson is all about how to use a calculator to solve an interested question. The students need the calculator to create the list, graph, and line of best fit. Without these, the students cannot not analyze the information and make a decisive conclusion. Therefore the learning objectives cannot be reached without the use of the technology and the net standards.


 * <span style="font-family: Georgia,serif;">ASSESSMENT STRATEGIES: **
 * <span style="font-family: Georgia,serif;">Formative: Verbal assessment of progress throughout class time as well as completion of worksheet
 * <span style="font-family: Georgia,serif;">Summative: By having the students answer the reflective questions on the worksheet we will be able to see how well the students understand the basic concepts of linear regression and best fit lines, and how these concepts can be used to make future predictions.

<span style="font-family: Georgia,serif;">**GROUPING OF STUDENTS FOR INSTRUCTION**: groups of 4-5 students


 * <span style="font-family: Georgia,serif;">INSTRUCTIONAL MATERIALS, EQUIPMENT, AND TECHNOLOGY NEEDED: **
 * <span style="font-family: Georgia,serif;">TI 83 + calculator
 * <span style="font-family: Georgia,serif;">Doc cam
 * <span style="font-family: Georgia,serif;">Ruler
 * <span style="font-family: Georgia,serif;">Worksheet


 * <span style="font-family: Georgia,serif;">PRIOR KNOWLEDGE AND SKILLS: **
 * <span style="font-family: Georgia,serif;">Basic understanding of how to deal with variables
 * <span style="font-family: Georgia,serif;">Basic calculator/graphing use
 * <span style="font-family: Georgia,serif;">Know slope

<span style="font-family: Georgia,serif;">Prerequisite Vocabulary: <span style="font-family: Georgia,serif;">Learned Vocabulary:
 * <span style="font-family: Georgia,serif;">VOCABULARY: **
 * <span style="font-family: Georgia,serif;">Linear – a straight line
 * <span style="font-family: Georgia,serif;">Quantitative variable- a variable that can be measured with a numerical value
 * <span style="font-family: Georgia,serif;">Qualitative variable- a variable that is categorical that cannot be given a numerical value
 * <span style="font-family: Georgia,serif;">Outliers – a point that lies an abnormal distance from the line of best fit
 * <span style="font-family: Georgia,serif;">Regression Line/ Best Fit Line- the approximate curve that best fits a set of data points. Regression line can also be used to make predictions
 * <span style="font-family: Georgia,serif;">Linear Regression- the measure of a relationship between two or more quantitative variables that can be represented by a regression line


 * <span style="font-family: Georgia,serif;">LEARNING EXPERIENCES: **

<span style="font-family: Georgia,serif;">1. Anticipatory Set: Show students a video of Kobe Bryant playing basketball. <span style="font-family: Georgia,serif;">[] <span style="font-family: Georgia,serif;">2. We will discuss with the class the following: <span style="font-family: Georgia,serif;">3. Explain the general outline of the worksheet and student expectations.
 * <span style="font-family: Georgia,serif;">How long do you think Kobe Bryant's forearm might be?
 * <span style="font-family: Georgia,serif;">The prior knowledge and vocabulary:
 * <span style="font-family: Georgia,serif;">quantitative/qualitative variables using examples
 * <span style="font-family: Georgia,serif;">picking out linear functions using pictures of different functions
 * <span style="font-family: Georgia,serif;">What are some ways we might be able to predict the length of Kobe Bryant's forearm? What could you use to compare to get a prediction for his forearm length?

<span style="font-family: Georgia,serif;">4. Break students up into groups of 4-5 students and gather materials: ruler, calculator, and activity worksheet. <span style="font-family: Georgia,serif;"> <span style="font-family: Georgia,serif;">5. Students follow instructions on worksheet while teachers walk around oberserving and helping during activity (questions 1-3 only). NOTE: Girls will have to subtract 2 shoe sizes from their shoe size. <span style="font-family: Georgia,serif;">6. After completing question 3 on the worksheet, have someone from each group write their group's data on the board. <span style="font-family: Georgia,serif;">7. Gather students as a whole class and use direct instruction to explain how to use calculators to enter the entire class data, find the linear regression, graph best fit line, and make predictions. <span style="font-family: Georgia,serif;">8. Now that you have a graph, make conclusions and ask concluding questions: <span style="font-family: Georgia,serif;">9. Have students finish the rest of the worksheet in their groups. Any questions they have not answered can be finished as homework. <span style="font-family: Georgia,serif;">
 * <span style="font-family: Georgia,serif;">Calculator instructions to be done under a document camera for class to view as they follow along:
 * <span style="font-family: Georgia,serif;">Gathering Data: Press the STAT button. Press 1 to edit. Put shoe sizes in L1 and Forearm length in L2. Do not include your estimate for Kobe Bryant.
 * <span style="font-family: Georgia,serif;">turn on your stat plot for Plot 1 (by following 2nd, then y= buttons). Observe that the shoe sizes lie along th x-axis and forearm length along the y-axis. You may need to adjust the window to see all of the points.
 * <span style="font-family: Georgia,serif;">Hit the STAT button. Go over to CALC. Press 4 for LinReg ax+b. Then press VARS, go over to Y-VARS, press 1 for Function, press 1 again for Y1. Press enter. This will give you the numbers for a and b in the equation y=ax+b and plug those numbers into Y1.
 * <span style="font-family: Georgia,serif;">Using the line of best fit, what is your prediction for Kobe Bryant's forearm length?
 * <span style="font-family: Georgia,serif;">Are there any outliers? If so, what makes these points outliers?
 * <span style="font-family: Georgia,serif;">Can you also give a prediction for Shaq's forearm length knowing his show size is 23?

**<span style="font-family: Georgia,serif;">EXTENSIONS: **
====<span style="font-family: 'georgia','serif'; font-size: 10pt;">One thing that could be done after this lesson in order to help make sure students really understand linear regression would be to let the students work in their groups used in this lesson to investigate their own question. This would be a larger project that would take more time and research. For example, the students would first find an interesting question to investigate. Then, they would find another quantitative variable that may be an independent variable to the dependent variable that they decide to investigate. If given a longer amount of time, say a week or even two, the students could then delegate roles in the group, gather data from classmates or even other peers at the school, and make visual presentations that would be given to the class. This would allow students to find out what it takes in order to find usable data to make a linear regression. ====

====<span style="font-family: 'georgia','serif'; font-size: 10pt;">Finally, the students would learn a final lesson on how some things may seem like they make a linear regression, but are actually not a correlation. Through their research projects, they may encounter data that does not have a strong correlation. This would allow this lesson to be taught during the research. ====

<span style="font-family: 'georgia','serif'; font-size: 10pt; line-height: normal; margin: 0in 0in 10pt;">At the end of all of these lessons, students will have made their own connections with interesting and relevant data to making and using linear regressions.

<span style="font-family: Georgia,serif;">**TEACHING REFLECTIONS:**
====<span style="font-family: Georgia,serif; font-size: 13px; line-height: 19px;">The anticipatory set seemed to be very effective. Students were engaged in the Kobe Bryant video and were left with a sense of excitement. The class participation was very high and students were able to make testable predictions before the lesson. ====

<span style="font-family: Georgia,serif;">During the lesson, students followed the instructions well and worked cooperatively. With teacher guidance, the transitions between group work and direct instruction went smoothly. Students successfully collected and graphed their data.

<span style="font-family: Georgia,serif;">After the lesson, students were able to make conclusions regarding the class data through the worksheet and class discussion. Also, they were able to make predictions about other data based off of the class made linear regression. One thing that the teacher could do next time would be to better relate the vocabulary to the lesson during the concluding discussion.