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 gather data and use the data to generate a linear model using graphing technology, estimate and calculate the correlation coefficient, and compare the effects of changes to the data on the equation and the r value.
Students will interpret the correlation coefficient of a linear fit.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know slope and the y-intercept.
Students should know how to graph a linear function and plot points provided in a data set.
Students should know the difference between a linear model and a nonlinear model.
Students should know how to use graphing technology to generate the equation for the line of best fit and calculate the correlation coefficient
Students should be able to collect data.
Guiding Questions: What are the guiding questions for this lesson?
Do taller students also have a larger hand size? Is hand size a good predictor of height? Is the relationship between hand size and height different between males and females?
Teaching Phase: How will the teacher present the concept or skill to students?
As the students enter the room, the teacher will collect the shoe size and height from the first ten (10) students that enter the room. The information may be entered into a T-table on the board. The teacher will plot the information on the board using the x-axis for shoe size and y-axis for student height (in inches). The teacher may decide to have the students graph the points independently as he or she models it on the board. The teacher will model for the students how to fit a linear function to a scatter plot that suggests a linear association. If the students plotted the data points individually, the teacher might have them predict the line of best by sketching the line on their graph paper before he or she models the process for them. The teacher will gauge student's understanding by asking the following questions.
1. After plotting the students' height and shoe size, does the scatter plot suggest a linear association?
2. If our data suggests a linear association, will the line of best fit be useful in predicting other students' measurements?
3. Just by looking at the scatter plot, is there a strong linear association in the data, in other words a high value for the correlation coefficient (r), or is there a weak linear association, a low value for r? Have the students predict the correlation coefficient.
The teacher will generate the equation for the line of best fit by using graphing technology (e.g., TI-84 calculator or GeoGebra) and then graph the equation on the board. The teacher should also use the graphing technology to find the correlation coefficient for the equation. The teacher should have the students compare the r value given by the calculator with the value the students predicted. If needed, the teacher can provide examples of data with different strengths of correlations to deepen student understanding of the r value.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The teacher will instruct the class to measure their own hand size (i.e., measured from the base of their palm to the tip of their middle finger in cm). The teacher will ask approximately twenty (20) students to record their hand size and height on the board. (Be sure to not include the data of 5 students in the class.) The students should record their hand size (in cm) as the x-coordinate and their height (in cm) as the y-coordinate. The teacher should have the students graph the data points at their desk.
The students will answer the following questions when they are finished plotting the data points:
- Does the scatter plot suggest a linear association? Answer: yes
- If your data does suggest a linear association, find the equation of the line of best fit using the TI-84 calculator. What is the equation of your line? Sample answer is provide (see attached)
- Will you be able to predict the height of a person given their hand size? Answer: yes
- What is the correlation coefficient? Answers vary
- Does the correlation coefficient suggest a strong or weak linear association? Answers vary
The teacher will walk around the room helping students plot and label their axes correctly on their graph papers, plot their points, and use their TI-84 calculators correctly.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Have the students add the data of the 5 remaining students in the class. The students should answer the following questions.
- Is a linear model appropriate for the additional data? If not, what was the predicted hand size for these students?
- What is your new equation for the line of best fit?
- What is the new correlation coefficient?
- How does your correlation coefficient compare to the previous value? What does this mean?
- Will you be able to approximate a person's height given the new equation more accurately than before?
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will ask the students to come up with other examples of linear relationships in real-world data.
The teacher will ask the student to explain the effect an outlier (e.g., Shaquile O'Neal, whose shoe size and height can be found on various sports websites), would have on the line of best fit. Would it stay the same or would it change? Will the slope, y-intercept or both change? Will the correlation coefficient be affected? Without using a calculator, have the students discuss possible equations for the line of best fit and possible values for the correlation coefficient.
After the lesson is complete, in a class discussion, ask the students: How much effect does an outlier have on a line of best fit? How do we make sure that a linear model is good predictor of the data?
The teacher may decide to have the students separate the data by gender and compare the equations and correlation coefficient for each. Is there a stronger correlation between height and hand size for boys or girls, or is it the same?
The teacher may ask the students to add several outliers as discussed in the Closure section of this lesson plan to generate a new line of best fit and to calculate a new correlation coefficient. Have the students explain/justify the change in both the line of best fit and the r value.
Have students answer the following questions as a Warm Up in order to assess their readiness for this lesson.
- What is the correlation coefficient?
Possible solution: The correlation coefficient measures the strength and the direction of a linear relationship between two variables.
- Make a scatter plot of the following data. Which type of association does the data represent?
(- 5, 4), (0, 0), (5, -3), (1, 1), (8, 7), (9, 5), (4, 7), (11, 15), (-1, -4) (14, 2)
Answer: Positive association
- First predict and then use your calculator to find the correlation coefficient of the previous data.
Answer: Predictions will vary. r = 0.46 for the data in Question 1.
- How would the correlation coefficient change if we were to change the last point from (14, 2) to (14, 7)? (Do not use your calculator.)
Answer: The correlation coefficient would increase.
- Use your calculator to check your response to Question 4. Compare the correlation coefficients for the line of best fit for the data set in Question 2 and the new data set in Question 4. Explain/Justify the change in the r value.
Possible solution: From the scatter plot, the last point (14, 2) appears to be the farther from the line of best fit than the other points. This can be confirmed by looking at the residual plot. (The graphing software can be used to graph the residual plot.) By moving this point closer to the line of best fit, the correlation between the data and the prediction line becomes stronger and the r value increases.
Feedback to Students
When students are gathering their data, provide feedback regarding the strategy they are using and the accuracy of their measurements. The measurements should be in centimeter (cm) for this lesson.
As the teacher monitors the students during the Independent Practice activity, provide feedback as needed regarding appropriate scales, the use of graphing technology, and their understanding of the correlation coefficient.
The teacher should allow the students to compare predictions throughout the lesson. The students can provide feedback regarding these predictions.