8.4.1Ma


 * Grade: 8 Unit: 4 Week: 1 **
 * Content: Scatter Plots and Association **
 * Dates: 2/4-2/8 **


 * Theme Essential Question **** : **
 * How do we use scatter plots to create predictions of real world data by analyzing relationships or associations, between two quantities considering outliers and clusters? **


 * Essential Questions: **
 * How can you construct and interpret scatter plots? **


 * Standards **
 * ** 8. SP.1 ** Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.


 * Objectives **
 * The student will construct scatter plots from either a word problem or a table.
 * The student will describe patterns in two-variable data including trends, clusters, outliers and association.
 * The student will interpret scatter plots by making conclusions and/or conjectures.

In this unit, students will be required to use a great deal of their work from the Function Unit. It is important that time is spent helping students make the connections between the units. It is an excellent time to __reflect__ on the Common Core foundation of depth of understanding and students’ ability to apply and extend their learning.
 * Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team **

@http://www.azed.gov/wp-content/uploads/PDF/MathGr8.pdf Building on the study of statistics using univariate data in Grades 6 and 7, students are now ready to study bivariate (using two variables) data. Students will extend their description and understanding of variation to the graphical displays of bivariate data. Scatter plots are the most common form of displaying bivariate data in Grade 8. Provide scatter plots and have students practice informally finding the //line of best fit//. Students should create and interpret scatter plots, focusing on outliers, positive or negative association, linearity or curvature. By changing the data slightly, students can have a rich discussion about the effects of the change on the graph. Have students use a graphing calculator to determine a linear regression and discuss how this relates to the graph. Students should informally draw a line of best fit for a scatter plot and informally measure the strength of fit. Discussion should include “What does it mean to be above the line; below the line?” The study of the line of best fit ties directly to the algebraic study of slope and intercept. Students should interpret the slope and intercept of the line of best fit in the context of the data. Then students can make predictions based on the line of best fit.
 * Background Information **
 * Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials. **
 * (Taken from [|Ohio Dept of Education Mathematics Model Curriculum 6-28-2011] ) **

Teacher Note: The degree of difficulty varies. It is recommended that you or your inclusion teacher, if applicable, review and rate the activities. The websites are displayed at the teacher lesson level. You will need to extract the information needed by the students. @http://illuminations.nctm.org/LessonDetail.aspx?id=L298 Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students work to construct scatter plots, interpret data points and trends, and investigate the notion of line of best fit. @http://illuminations.nctm.org/LessonDetail.aspx?id=L646 The consideration of cord length is very important in a bungee jump—too short, and the jumper doesn’t get much of a thrill; too long, and //ouch//! In this lesson, students model a bungee jump using a Barbie® doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions. ||  || @http://www.pbs.org/teachers/connect/resources/4442/preview/ Students will explore the relationship between the amount of weight that can be supported by a spaghetti bridge, the thickness of the bridge, and the length of the bridge to determine the algebraic equation that best represents that pattern modeled by the three variables. @http://www.pbs.org/teachers/connect/resources/4384/preview/ Students will apply their knowledge of scatter plots to discover the correlation between heartbeats per minute before and after aerobic exercise. This lesson calls for an aerobic instruction to talk about the heart. It is recommended that the PE teacher be substituted for this guest speaker. @http://www.education.ucsb.edu/ucsbpt3/afield/teacher_projects/jimsfinal/Jimstudent.htm Students measure each other’s height and wingspan and then create a scatter plot of the data. They then determine whether Leonardo da Vinci’s proportion theories are valid. Students then develop a clothing business whose sizes are determined by the plot results. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L673 In this activity, students plot the data from two teams during the 2004‑05 NBA season. They will be dealing with the effects of outliers.
 * Assessment **
 * Product **
 * Divide the students into groups to explore, conduct the research, and/or solve problems. They are to prepare a presentation using the best means possible to bring a new level of understanding to the class on the concept of scatter plot and interpretation/prediction. During this lesson, students should start to explore and discuss their assigned topic with their group members.
 * Exploring Linear Data:
 * || * Barbie Bungee
 * Stressed to the Breaking Point
 * In a heartbeat
 * DaVinci: Body Proportion Theories
 * Impact of a Superstar


 * Key Questions **
 * What does a trend in data mean?
 * What are the different associations (correlations), and how do they influence the analysis of the scatter plot?


 * Observable Student Behaviors **
 * Given a verbal description, word problem and/or a table of bivariate measurement data, the student can create a scatter plot.
 * The student can interpret a scatter plot by investigating the patterns of association (correlations), clustering, and outliers.

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * **Mathematical Practices **

Bivariate data, scatter plot, cluster, outlier, association (correlation)
 * Vocabulary **

Unit 6.1 p. 145-148 @http://illustrativemathematics.org/illustrations/41 (SP.1)The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
 * Suggested Activities ** [see Legend to highlight MCO and HYS]
 * Houghton Mifflin OnCore Mathematics Middle School Grade 8
 * ABC Mastering the Common Core in Mathematics, Chapter 8 p. 110-111
 * Gizmo Lessons
 * 8.SP.1
 * Scatter Plots - Activity A
 * Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line.
 * Solving Using Trend Lines
 * Examine the scatter plots for a data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best ‑ fit line.
 * __ Teaching the Common Core Math Standards with Hands-On Activities __ by Judith Muschla
 * 8.SP.1 p. 237
 * JBHM 8th GP3 p. 220-221 and p. 236-338
 * Glencoe Algebra 1- p.298-303
 * Highly Recommended:


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Algebra’scool: Unit C Module 9

Suggested:
 * Homework **
 * ** @http://www.kutasoftware.com/free.html ** to print assignments on variety of topics
 * See appropriate Glencoe, OnCore, JBHM, and ABC materials


 * Terminology for Teachers **

** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice | ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback | ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers  || Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * ** Multicultural Concepts **


 * Resources **


 * Professional Texts **


 * Literary Texts **

// **Informational Texts** // @http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htm
 * See New York Common Core Aligned Task (other resources)


 * Art, Music, and Media **


 * Manipulatives **
 * http://nlvm.usu.edu/ National Library of Virtual Manipulatives
 * Graphing calculators


 * Games **


 * Videos **
 * Discovery Learning @http://www.discoveryeducation.com/

This activity explains how to collect and graph data and discusses the difference between correlation and causation.
 * SMART Board Lessons, Promethean Lessons **
 * Smartboard Resource Website Smartboard lesson search engine8. SP.1 Reasoning: Correlation and Causation


 * Websites **
 * @http://illustrativemathematics.org/standards/k8 PARCC Online (released items)
 * http://www.khanacademy.org Online tutorials
 * @http://www.tli.net/ TLI Quiz Builder


 * Other Activities, etc. **

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