Linear Correlation

Objectives

In this lesson, students will learn what correlation means. Students will:

· categorize two variables as having a specific type of correlation.

· give their own examples of variables having a given correlation.

Essential Questions

· How can we determine if two variables correlate linearly?

· How can we use data to make predictions about the future?

Vocabulary

· Correlation: A measure of the relationship between two variables.

· Continuous: The representation of data for which no individual values other than a range between intervals can be established. Continuous data is usually associated with physical measurements such as growth.

· Discrete: The representation of data for which one-to-one correspondence is established between individual points of data and the medium of representation.

· Patterns: Regularities in situations such as those in nature, events, shapes, designs, and sets of numbers.

· Scatter plot: A graph of plotted points that show the relationship between two sets of data.

· Slope: The rate of change of the ordinate with respect to the abscissa; the ratio of the change in the vertical dimension to the corresponding change in the horizontal dimension.

Duration

60–90 minutes/1–2 class periods [IS.1 - All Students]

Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.

Materials

· four 8-foot ropes marked off with tape at each foot

· Correlation Notes (M-A1-6-1_Correlation Notes and KEY.doc)

· Example Scatter Plots (M-A1-6-1_Example Scatter Plots.doc)

· Human Scatter Plot Cards (M-A1-6-1_Human Scatter Plot Cards.doc) [IS.2 - All Students]

· Lesson 1 Exit Ticket (M-A1-6-1_Lesson 1 Exit Ticket and KEY.doc)

Related Unit and Lesson Plans

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

· https://www.purplemath.com/modules/scattreg2.htm

· http://dictionary.reference.com/browse/correlation (for definition of correlation)

Formative Assessment

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· Teacher observations during group activities must include an evaluation of students’ ability to generalize the data trends in the scatter plots. Specific words that students use to describe the trends and how accurately those words describe them are indicators of engagement and understanding.

· Lesson 1 Exit Ticket evaluates understanding of correspondence between characteristics of a scatter plot and familiar examples of real-world data.

Suggested Instructional Supports

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Active Engagement, Explicit Instruction

W:	Students will know where they are headed after the introductory statement. They will know that this lesson is about patterns and how two variables are related to one another. They will be evaluated throughout the lesson when they are actively participating in the human scatter plot.
H:	Students should be hooked right from the start. Students like to see real-world applications and the first two questions would hold students’ interest until they see the connection.
E:	Students will be actively involved by creating a human scatter plot. They will be given different situations in which they have to determine what type of correlation exists between the two variables.
R:	Students will be given time to reflect throughout the lesson. They will work as a group to determine correlation and if they are wrong, they will need to revise their thinking before moving on to other problems.
E:	Students will express their understanding during the human scatter plot activity. They will then work individually on the exit ticket and will be given time to evaluate their own work.
T:	This lesson is tailored to all students, especially the visual and kinesthetic. The visual learners will see the lesson goals initially in the correlation notes and then the kinesthetic learners will see the lesson goals when they partake in the human scatter plot.
O:	This lesson begins with an attention getter and then teacher-led instruction. It smoothly transitions to a whole-class activity that will then lead them to their individual exit ticket.

IS.1 - All Students

Consider pre-teaching the concepts critical to this lesson, including the use of hands-on materials. Throughout the lesson, based on the results of formative assessment, consider the pacing of the lesson to be flexible based on the needs of the students. Also consider reteaching and/or review both during and after the lesson as necessary.

IS.2 - All Students

Consider showing students sample of scatter plots and review how they are read and used. Show real world examples of how they are used.

IS.3 - All Students

Consider having students write about what they see in the scatter plots.

Instructional Procedures

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“Do you think your age determines the number of words in your vocabulary? Do you think your shoe size determines your weight? These questions lead to a concept called correlation. Today we are going to look at some data to determine how two variables relate to one another.”

Hand out the Correlation Notes (M-A1-6-1_Correlation Notes and KEY.doc). Before writing down a definition, discuss what the words correlate or correlation sound like. Hopefully students hear the relate or relation.

“Look at the scatter plots on your notes. What do you see?” Students might say “patterns” or “clusters” or “lines of dots.” [IS.3 - All Students]“There are many types of correlation, but we are going to focus on linear correlation. Does anyone want to guess at what two ways variables could correlate linearly?” Give students some time to think. If they aren’t sharing any ideas, ask them to compare the first scatter plot with the second. Now they will probably say the first one is decreasing and the second one is increasing. “What type of slope does the first plot have? (negative) “What about the second scatter plot?” (positive)

Finish filling in the names of the correlations. “A good rule of thumb is that if you can draw a line through the graph and the dots go in the same direction, then the variables correlate linearly. But take a look at the fourth graph. We could graph a horizontal line through the points. However, a horizontal line has a slope of 0, therefore the relationship is constant.”

“Consider this question: Do we connect the dots on a scatter plot? Why or why not?”

Students should be lead to discover that the dots are not connected because the data are not continuous; the points represent discrete data points. A trend line is the line that models a continuous relationship between the points.

Part 1

Next, students are going to categorize different scatter plots as negative, positive, no correlation, or nonlinear correlation. Show students the Example Scatter Plots (M-A1-6-1_Example Scatter Plots.doc). Let students think about each one and then ask for a volunteer to give his/her answer and explain why that scatter plot has that type of correlation.

Part 2

Split the class in half. Go to a large space such as the hallway, cafeteria, gym, or outside. Place the four 8-foot ropes (two per group) on the ground to represent the x- and y-axes. Each group will stand at the origin of their axes. Read a card from the Human Scatter Plot Cards (M-A1-6-1_Human Scatter Plot Cards.doc). Each group must decide how the two variables correlate and then create a scatter plot to represent that correlation. The options will be negative, positive, no correlation, or nonlinear correlation. The first group with the correct scatter plot gets a point. Go through as many as time allows, leaving time for an exit ticket activity afterwards.

Part 3

Hand out the Lesson 1 Exit Ticket (M-A1-6-1_Lesson 1 Exit Ticket and KEY.doc) to evaluate whether students understand the concepts.

Linear Correlation

Lesson Plan