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 Using Scatter Plots to Predict the Future
 Subject:Math Grade Level: 10-12 Description: In this unit, students learn to graph scatter plots. Scatter plots help us identify patterns, trends, and relationships for two quantitative variables. The stiudents explore the interaction between these two variables to reach meaningful conclusions about their predictability for future events. How it Works: The relationship between variables is the driving force behind the mastery of statistics research. Students explore questions between two variables such as: is the shoe size of a man related to his height? Is horsepower in a vehicle related to its gas mileage? Does how long children remain at the lunch table help predict how much they eat? Final Project/Product: A statistical research document predicting the quantity of cell phone users in the United States by the year 2015. The presentation should include scatter plots, and/or bar graphs, and pie charts or any other visual aid to help explain the results (a PowerPoint presentation is an acceptable alternative). Teachers are encouraged to create their own questions. Overall Value: The student develop the ability to recognize relationships between two seemingly unrelated variables. The lessons provide the tools necessary to explore the conjecture and reach valid conclusions. They have the opportunity to use a graphing calculator, and use the Internet to research data and take a practice test. English Language Learners: There are vocabulary/key words before each lesson. The lessons use visual aids such as transparencies, overhead graphing calculator, and LCD projector. In addition, questions should explore relationships that are meaningful to language learners. For example, does bilingualism help me to be a better student? Does educational level predict future earnings? Before collecting data, students should be encouraged to create their own survey questions and practice speaking skills by asking the questions to members of the school community. Tips for the Teacher: Try to explore questions regarding variables that are meaningful to teenagers and/or ELL students. In addition, document all the projects by taking pictures, which can be used as visual diary of the class progress and can be displayed on a bulletin board or website.
 Students understand and become mathematically confident by communicating and reasoning mathematically, by applying math in real world settings, and by solving problems through the study of statistics and data analysis. Grade: 9-12 Subject: Math As listeners and readers, students collect data, facts, and ideas; discover relationships, concepts, and generalizations; and use knowledge generated from oral, written, and electronically produced texts. As speakers and writers, they use oral and written language to acquire, interpret, apply, and transmit information. Grade: 9-12 Subject: Math As listeners and readers, students analyze experiences, ideas, information, and issues presented by others using a variety of established criteria. As speakers and writers, they present, in oral and written language and from a variety of perspectives, their opinions and judgments on experiences, ideas, information, and issues. Grade: 9-12 Subject: English Language Arts Students listen, speak, read, and write in English for critical analysis and evaluation. Students learning English as a second language use English to express their opinions and judgments on experiences, messages, ideas, information, and issues from a variety of perspectives. They develop and use skills and strategies appropriate to their level of English proficiency to reflect on and analyze experiences, messages, ideas, information, and issues presented by others using a variety of established criteria. Grade: 9-12 Subject: ESL

 Day 1: What is a scatter plot graph?

 Day 2: What is the correlation coefficient?

 Day 3: How do we find the line of best fit for a set of data?
 Objectives Students will state the properties of the best fit line or trend line. Students will use the properties of the best fit line to find its equation. Students will use the graphing calculator to find the equation of the best fit line. Materials Graphing calculators, overhead graphing calculator Overhead projector, LCD projector Transparency of graphing calculator Computer(s) with Internet access, printer Keywords Horsepower, advertised, ratings, gas mileage Procedure 1 Get data - Advertised horsepower ratings and expected gas mileage for several 2001 vehicles. (see website below) a. Enter data in the graphing calculator. b. Create a scatter plot. c. Predict the correlation coefficient. d. Use the calculator to find the actual correlation coefficient. Pearson’s media, data and analysis http://media.pearsoncmg.com/aw/aw_deveaux_introstats_2/datasets/stat2dv_data.html Procedure 2 Additional questions a. Describe the direction, form, and strength of the plot. b. Write a few sentences telling what the plot says about fuel economy. Procedure 3 Find the equation of best fit line. a. Use the algebraic method. b. The line of best fit is one of many lines that can be used to model the relationship between horsepower and gas mileage. c. Find the mean of both variables (x, y) d. Select a coordinate from the data (x2, y2). Use the formula (y – y2) = m (x – x2) where m is the slope. Procedure 4 Get the best fit line using a graphing calculator. a. Compare the two results. b. Why do we get two different lines? Is one equation better that the other? Explain. The possibility that both equations are exactly the same is remote. However, we should pay attention at their similarities. Both processes are attempting to approximate the best possible line (equation) to represent the relationship. c. We should try to repeat the process with other coordinates to try to provide alternatives equations to the same relationship. d. The students can try to input these new equations into the calculator to compare with the one provider by the calculator. mathbits http://mathbits.com/MathBits/TISection/Statistics1/LineFit.htm Extension Visit Pearson’s website – Find the best fit line for exercise 19, chapter 7. Fast food is often considered unhealthy because much of it is high in both fat and calories. But are the two related? Here are the fat (in grams) and calories contents of several brands of burgers. Analyze the association between fat and calories. (Hint: Use a scatter plot, coefficient of correlation and the equation of the line of best fit.)

 Day 4: How can we use the line of best fit to predict unknown values?

 Day 5: In Class Project
 Objectives Students will be able to design their own experiment. Students will be able to collect the data needed to prove or disprove their hypothesis. Materials Graphing Calculator, overhead calculator Overhead projector, LCD projector Computers, printer Keywords Typos, extrapolating, interpolating, label, hypothesis Procedure 1 Hypothesis: Is there a relationship between the height of a person and his/hers arm span? a. How do you suppose we can prove this hypothesis? Allow for the students to come up with a plan. Encourage their answers in the direction of collecting data to support the hypothesis. b. How do you suppose we can collect data? Should we divide the class into groups and then place all data together or should each group work with their own data? Procedure 2 Ask the students to go around the school (if it is allowed) and ask volunteers to provide their measurements. a. When the data is collected encouraged the students to use all the available data together. b. Procedure 3 Place all data in a properly labelled table (on the board) so that everyone has access to it (maybe a transparency). a. Discuss the possibility of transferring incorrect data (typos) into the table. How would incorrect data affect my hypothesis? b. Allow the student to answer the following question by themselves: What is the equation of the best fit line? What is the correlation coefficient? What conclusions can you extrapolated from your results? (Calculators should be available.) Assessment Evaluating the final work.

Miguel Pineda

pineda3247@hotmail.com

Newcomers High School
28-01 41 Avenue
Long Island City, NY 11101

Miguel Pineda has been a mathematics teacher since 1991. He has worked in Queens, NY at Far Rockaway High School and at Newcomers High School in Long Island City. He graduated from Queens College in 1990 with a degree in computer science. He obtained his master’s degree in math education from City College, NY in 1994. His teaching experience ranges from 9th grade to college-level statistics.

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