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 calculate and plot residuals and interpret the meaning of residuals.
Prior Knowledge: What prior knowledge should students have for this lesson?
- Students can calculate and use a least squares regression equation.
- Students can calculate and interpret a correlation coefficient.
Guiding Questions: What are the guiding questions for this lesson?
What is the relationship between the number of rows a fan is from the field and the price of their ticket?
Teaching Phase: How will the teacher present the concept or skill to students?
I Do: The teaching phase will take place while the students progress to the Guided practice activity. The teacher will guide the students with key questioning throughout the process that will help on the understanding of the lesson.
Use the Residual PowerPoint presentation that will help to guide through the teaching phase. The PowerPoint presentation contain the goals for the lesson. After the introduction, the teacher will talk about the key words for the lesson. It will go over what is a residual and why we would use it, and why and how to create the residual plot. It shows the meaning of the results of the residual plot (non-pattern or patterns).
The teacher will go over 2 examples step by step on how to find the residuals and build a residual plot.
Suggested Questions throughout the PowerPoint:
- Slide 2 – Introduction: What kinds of mistakes do you think we have in math?
- Slide 3 – Key Terms: After reading this introduction, in your own words, what does residual mean to you? Give me an example of residual. What could residual mean in a math class?
- Slide 4 – Residual - Suggested Questions: What would be the observed data? And what would be the predicted data? (Clues: Think about the actual data and the regression line which one is observed and predicted). Why do you think the sum and the mean of the residual equal zero (0)? (Show next slide and check how the total of the residual and the mean equal zero).
- Slide 6 – Residual Analysis in Regression: What does it mean to be appropriate to the data?
- Slide 7 and 8 – Residual Plot: More details will come on how to build a Residual Plot later in the lesson.
- Slide 13 – Step 1 - Each click will show a value on the table starting from the y-value going down then on the residual column given the residual amount. Students can try to calculate the value before the teacher shows the value.
- Slide 16 – Step 1 (Example 2) - Each click will show a value on the table starting from the y-value going down then on the residual column given the residual amount. Students can try to calculate the value before the teacher shows the value.
Notes are included in the PowerPoint as well. Make sure to explain to your students that the residual plot is a scatterplot with x as the independent variable and y as the residual.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
I Do/We Do: As students come in to the class they will receive the Residuals Lesson Worksheet. Students will work in pairs to complete the worksheet. After completion, the teacher will discuss the answers with the students.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
You Do: The students will receive The "Orlando City Residual" worksheet. The posing question for the lesson is "What is the relationship between the number of rows a fan is from the field and the price of their ticket?" Students will work using the Kagan Strategy "RallyCoach" (Partners take turns, one solving a problem while the other coaches. Then partners switch roles.)
The teacher should monitor team progress and address any misconceptions. When students are finished working, discuss the answers as a class.
Discuss again how a residual is the amount of error between a piece of data and the regression equation's predicted value. (We would like there to be as little error as possible.) The amount of error determines if that particular regression equation is a good fit for the data.
A residual plot is a visual to help determines if the regression equation is the best fit for the data. If there is not a mathematical pattern to the residual plot, then that regression equation is the best fit (or as good as we can get it to be)
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Have the students answer the following questions as an exit ticket:
- What do the residual plots tell us about how well the model fits the data?
Answer: Residual plots tell is whether that particular regression model is appropriate for the data.
- What is a residual?
Answer: It's the amount of error between a data point and its predicted value.
After completing the activity the groups will turn in their activity. Teacher will assess their performance based on the Rubric.
If time allows, students will take an Exit Ticket: (last 10 minutes)
- A group discussion will be used to close the lesson, and students' notes of the discussion will be collected.
- What do the residuals tell us about how well the model fits the data?
- Could analyzing the residuals help us justify our model in conjunction with using the correlation coefficient?
- Do you think residuals are more or less important than the correlation coefficient? What do you think the residuals will look like if the data are not linear?
Students will be asked questions during discussion that they will be answering verbally and/or using SmartBoard or whiteboards. Questions like:
- What do you notice when you compare the actual y-values and the predicted y-values from the model?
Expected Answer: Sometimes the predicted value and actual value are not the same
- After plotting points, what shape does the scatterplot suggest? What does a point falling below or above the line of best-fit mean?
Expected Answer: Plots can represent many shapes but to look for linear correlations. If the point is below the estimate of line of best fit, the point is less than the predicted value (a residual that is negative), and if it is above, the point is above the predicted value (a residual that is positive).
- What does it mean if the residuals are randomly dispersed about the x-axis? Or the residuals follow a pattern?
Expected Answer: No pattern indicates that a linear model provides a decent fit to the data. Plots that have a pattern (such as U-shaped and inverted U, all points above or below), suggesting fitting a better linear model or even a non-linear model.
Feedback to Students
- Student to Student
- Teacher to Student
- Students will check and compared their results during the learning process.
Accommodations & Recommendations
Students with special needs may receive guided notes (copies of the PowerPoint) that helps the to fill the blank with key words instead of coping the notes. Provide a graphic Organizer with the steps on how to find a residual and how to produce a Residual Plot.
On the teaching phase, the teacher could share the points plotted on the table so they can calculate the residual more easily.
Students may search online the price of the tickets not from the half way line but also form other positions in the stadium such as behind the goals, corners and investigate the correlation and the new residual comparing the price versus the seat of the whole stadium.
As an extension activity teacher may also let students use graphing calculators and/or GeoGebra. Students would compare and contrast the work that they did by hand versus the results that they get from the graphing calculator and or Geogebra.
Suggested Technology: Document Camera, Graphing Calculators, Computer for Presenter, Computers for Students, Internet Connection, Interactive Whiteboard, LCD Projector, Assistive Technology, Adobe Acrobat Reader, Microsoft Office, GeoGebra Free Software
Students may search on the Internet what are the best seats in a soccer game if they do not have a knowledge or experience watching a live soccer game. That could also been a reading/research assignment where students could share their findings with the class.
Applicable Math Practices:
Source and Access Information
Name of Author/Source: Renato Freitas
District/Organization of Contributor(s): Lee
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.