
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 determine if two variables have a linear relationship by analyzing the correlation coefficient.
Students will distinguish between a situation where correlation does not imply causation and one where it does.
Students will determine the correlation between the performance of a person's heart rate and the amount of time spent exercising using the technology tool GeoGebra.

Prior Knowledge: What prior knowledge should students have for this lesson?
MAFS. 912.SID.2.6 Represent data on two quantitative variable on a scatterplot and describe how the variables are related.
 Students understand correlations and linear relationships.
 Students understand vocabulary associated with the topic: scatter plot, correlation, correlation coefficients, and linear regression.

Guiding Questions: What are the guiding questions for this lesson?
Is there a relationship between a person's heart rate and the amount of time spent exercising?

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. The teacher may want to copy the assessment on different color paper to make it easier to assign groups for the GeoGebra activity. Have students write complete sentences to support or refute the given statements.
 The teacher will provide the hook for the realworld application of the need to investigate data for correlation. Ask students: How many of you would like to learn how to interpret data among two things that you think might be related to solve real life problems? Or to interpret that data to create opportunities to market products or services? Today, we will investigate how mathematicians determine whether two variables are related.
 The teacher will introduce the topic under investigation for the lesson. Does the amount of weekly exercise affect your working and/or recovery heart rate? In order to determine if they are related, we will use the statistical measurement Correlation Coefficient.
 The teacher will use the PowerPoint on the correlation coefficient to provide the general steps used to analyze the correlation between two variables.
 The teacher will provide time for students to revisit their formative assessment worksheet to add to or delete their statements.
 The teacher will assign groups (or use the suggestions for colorcoded formative assessment sheets in assigning groups as stated in step 1) and then introduce the GeoGebra tool.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
Students will use the GeoGebra tutorial to graph the Heart Rate data that is available in the attachments section of this lesson plan. It is advised that the data already be uploaded in a folder on their computers.
The attached tutorial will walk each group through the steps to calculate the correlation. Students should generate at least 2 correlations by examining
 the weekly exercise time verses working heart rate,
 the weekly exercise time verses recovery heart rate.
Working heart rate refers to the heart rate during vigorous exercising for 3 minutes and the recovery heart rate refers to the 5 minutes of rest from the vigorous exercise.
Students should generate a response to these questions: (Suggested Guided Practice Responses are attached.)
 Is there a correlation between the hours of exercise and working heart rate? Explain your response.
 Is there a correlation between the hours of exercise and recovery heart rate? Explain your response.
 What are at least 2 questions your group can generate from this data that may require further research?

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
The teacher will play the video Spurious Correlations (3 minutes) by YouTube user Tyler Vigen to look for more examples of how correlation does not imply causation.
Student will consider an excerpt from one article discussing correlation and causation. Students will review and read the article to look for evidence to support or refute the statistical statements given at the beginning of the lesson. The teacher will ask or put these prereading questions on the board to guide students as they read. The prereading questions should be a part of the ending discussion.
 How is correlation different from causation?
 What is one example of correlation and one example of causation from the article?
 Can correlation be used to infer or imply a causal relationship?

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
After students have collected evidence for all statements on the formative assessment, have them share and compare their findings in small groups of 3 or 4 people. The teacher will engage the class in a discussion of the content and how their initial thoughts about each statement were challenged or confirmed. The teacher will poll everyone's final responses and reveal a sample template that shows the sample responses to each statement.

Summative Assessment
The Final Thoughts column of the formative assessment and a quiz will be used as the summative assessment for the lesson. Part of the formative assessment will purposely be left blank until the end of the lesson after the class discussion is completed.

Formative Assessment
Students will take the attached formative assessment to provide the teacher with information regarding their present level of understanding prior to the lesson. Note that formative assessment attachment can be copied in different colors that will easily form groups.
Students will update this formative assessment throughout the lesson as their ideas are supported or refuted. The teacher will ask students to review the statements carefully and decide whether they agree or disagree with each one.
As students learn more (through the lesson, through reading, and through analyzing the data), the teacher will ask them to collect evidence that supports or refutes each statement. After students have collected evidence for all statements, have them share and compare their findings in small groups of 3 or 4 people. The teacher will engage the class in a discussion of the content and how their initial thoughts about each statement were challenged or confirmed.

Feedback to Students
The teacher can use an electronic polling tools such as responders, clickers, or a text messaging polling tool such as Poll Everywhere to collect the general agree or disagree responses to the initial formative assessment. This same tool can be used at the end of the lesson to see if the class overall responses stayed the same or changed. The teacher will visit each group of students and provide constructive criticism or positive feedback. Students will also provide peertopeer feedback in their small groups as they discuss their evidence with each other. The students will use this verbal feedback to adjust any misconceptions in their thinking and reflect those adjustments in their written final thoughts.