General Information
Subject(s): Mathematics
Grade Level(s): 8, 9, 10, 11, 12
Suggested Technology:
Graphing Calculators, Computer for Presenter, Computers for Students, Internet Connection, Microsoft Office, GeoGebra Free Software (
Download the Free GeoGebra Software)
Instructional Time:
1 Hour(s) 30 Minute(s)
Resource supports reading in content area:Yes
Freely Available: Yes
Keywords: scatter plot, correlation, correlation coefficient, linear regression, bivariate data, line of best fit
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Lesson Content

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to predict an outcome utilizing the correlation coefficients to write a linear equation for a line of best fit.
Students will be able to use one of three technology tools to compare and contrast previous predictions given a positive correlation between the number of weeks a song is on the top ten charts and the number of videos for its official music videos.

Prior Knowledge: What prior knowledge should students have for this lesson?
MAFS.8.SP.1.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope, and intercept.
 Students know how to find the equation of a line.
 Students know how to find slope by at least two methods.
MAFS. 912.SID.2.6 Represent data on two quantitative variable on a scatterplot and describe how the variables are related.
 Students know how to graph and plot points.
 Students understand correlations and linear relationships.
 Students understand vocabulary associated with the topic: scatter plot, correlation, correlation coefficients, linear regression,bivariate data, and line of best fit.

Guiding Questions: What are the guiding questions for this lesson?
 What are the determining factors for correlations?
 What components would influence a scatterplot to have a weak or strong correlation?
 Does a line of best fit pass through every point on the graph? Why or Why not?

Teaching Phase: How will the teacher present the concept or skill to students?
 The teacher will provide the students with a formative assessment at the start of class. Ask the following questions to guide an open discussion during the formative assessment activity:
What are the determining factors for correlations?
Answer: An independent and dependent variable with either increasing and/or decreasing values.
What components would influence a scatter plot to have a weak or strong correlation?
Answer: If the independent variable does not influence the dependent variable strongly, then there will be a weaker correlation. If the independent variable does influence the dependent variable strongly, then there will be a stronger correlation.
Can we draw a line through the graph to represent the data?
Answer: Yes
What would this look like?
Answer: The line would go through the middle of all the data points to best represent the information.
What do we call this line?
Answer: Line of best fit.
 Misconception: A student might suggest to connect all the points on the graph. Redirect by asking: Why would we not want to connect all the points? (If a student does not make this connection, you may want to ask this anyway).
Answer: We would have a series of line segments rather than a line of best fit. We want a line that best represents the data.
 Ask them to calculate the slope.
Answers will vary among groups. Discuss ways to write an equation for the line of best fit with your students.
 Note: To create an environment where students are constructing viable arguments and critiquing the reasoning of others, be sure to follow up each question by asking other students if they agree and extending them to explain further (MP 3)
 Begin the instruction with a bellwork activity to find slope with two methods only given two points. Displaying the slope formula for the students can be helpful if you do not require that it is memorized. Students will work in groups and check for understanding with their peers.Walk to and from each group and listen for misconceptions. Redirect students who are offtopic. Ask guiding questions when you discover student errors.
Example: If a student is using rise over run and counting horizontally before vertically, redirect by asking these questions: "I see you are counted horizontally first, (turn to another group member) what approach did you take?" Further the questioning, by asking which approach do they agree with and why. This will encourage group conversation by constructing viable arguments.
 Show the YouTube video (Dancing Statistics). Prevideo ask students to write down familiar vocabulary words they see during the video. Postvideo discuss the words the students wrote down.
 Discuss correlations with your students. Suggested examples:
The amount of soda you drink on an average day and the number of cavities you have.
The amount of time spent practicing basketball, and the number of games you win.
 Ask the following questions to guide an open discussion:
What are the determining factors for correlations?
Answer: An independent and dependent variable with either increasing and/or decreasing values.
What components would influence a scatter plot to have a weak or strong correlation?
Answer: If the independent variable does not influence the dependent variable strongly, then there will be a weaker correlation. If the independent variable does influence the dependent variable strongly, then there will be a stronger correlation.
 Ask each pair or group of students to sketch a variety of scatter plots representing data with positive, negative, and no correlations. Students need to come up with at least 8 coordinate points to plot for each graph. Provide them with graph paper, a pencil, and a ruler. Have each group focus on their graph with the positive correlation.
 Allow students to complete the formative assessment activity. Collect this activity and check for understanding by any of the following:
Display the answer key on the board and allow students to check their answers. Clarify any misconceptions.
 Grade the assessment on your own via the answer key to check for understanding. Determine what concepts need to be retaught or redirected.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
 During the guidedpractice activity, visit with each group of students. Ask guiding questions, redirect any misconceptions, offer verbal praise, and feedback. Encourage topicrelated peer conversation.
 *Note: To create an environment where students are constructing viable arguments and critiquing the reasoning of others, be sure to follow up each question by asking other students if they agree and extending them to explain further (MP 3.)
 Choose which technology you would like your class to explore. There are guiding worksheets for each type of program or tool.
 a) Excel
 b) GeoGebra
 c) Graphing Calculators
 Each student will need the technology steps guide for the chosen technology, Interpret and Predict! Guided Practice, and the data sheet.
 The first page of the guided practice does not require the use of technology. Students will need graph paper and pencils to complete this page. Students will plot their data and draw a line of best fit. Students will also create the equation for the line of best fit by utilizing a method for finding equations of lines.
 This information will be compared with the technology component on the next page.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students can access the following links for additional help:
YouTube Line of Best Fit
Math is Fun Correlations
Khan Academy Line of Best Fit
Each student needs an Extend The Data page. Depending on the length of your class time and the timing in which students complete their guided practice, this can be an inclass or outofclass assignment.
Information can accessed at:
YouTube
Billboard
Students will collect their own data for the current month and year. They will use this information and create a scatter plot, line of best fit, and an equation for the the line of best fit using any of technology options.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
To follow up after the extension activity (independent practice) and as an exit slip, ask students how this compared to the original data from June of 2014.
Ask the question, "Are there similar trends to the original data for June of 2014? Why or why not? How does the equation for both lines of best fit compare?"

Summative Assessment
 Before beginning the summative assessment, discuss the independent practice and exit slip from the day before with the students. Clarify any misconceptions and check for understanding.
 Collect the summative assessment and grade via the answer key.
Summative Assessment
Key Summative Assessment

Formative Assessment
Students will take a formative assessment (see attachment) to provide the teacher with information regarding their present level of understanding prior to the lesson.
Collect the formative assessment and check for understanding by any of the following:
 Display the answer key on the board and allow students to check their answers. Clarify any misconceptions.
 Grade the assessment on your own via the answer key to check for understanding. Determine what concepts need to be retaught or redirected.
 Assess through questioning (above).
Formative Assessment
Key Formative Assessment

Feedback to Students
Teacher will be able to visit each group of students and provide constructive criticism or positive feedback. The students will use this verbal feedback to adjust any misconceptions in the students' thinking.
Assessment
 Feedback to Students:
Teacher will be able to visit each group of students and provide constructive criticism or positive feedback. The students will use this verbal feedback to adjust any misconceptions in the students' thinking.
 Summative Assessment:
1. Before beginning the summative assessment, discuss the independent practice and exit slip from the day before with the students. Clarify any misconceptions and check for understanding.
2. Collect the summative assessment and grade via the answer key.
Summative Assessment
Key Summative Assessment
Accommodations & Recommendations
Accommodations:
 Graphic representation to clarify written directions, text, or vocabulary.
 Highlight, italicize, bold, or circle key words on charts, written directions or tasks, and personal copies provided to students.
 Give incremental feedback during multistep tasks.
 Help manage behavior and time on task by using verbal and nonverbal prompts.
 Allow extra time for written responses.
Extensions:
Have students pair up. Each pair will be asked to collect bivariate data from the class that will represent a correlation. The students will need to graph the information, find the line of best fit, and its equation.Ask the question, "Is this a representation of causation with correlation? Explain."

Suggested Technology: Graphing Calculators, Computer for Presenter, Computers for Students, Internet Connection, Microsoft Office, GeoGebra Free Software
Special Materials Needed:
Graph paper
Rulers
Pencils
YouTube
Computers
One of the following programs or tools: Graphing calculators, Microsoft Excel 2010, or GeoGebra
Additional Information/Instructions
By Author/Submitter
The following Standard for Mathematical Practice will likely be utilized within this lesson:
MAFS.K12.MP.3.1  Construct viable arguments and critique the reasoning of others. (Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.)
Source and Access Information
Name of Author/Source: Anonymously Submitted
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.