General Information
Subject(s): Mathematics
Grade Level(s): 9
Suggested Technology:
Graphing Calculators, Computer for Presenter, Internet Connection, Basic Calculators, LCD Projector, Scientific Calculator
Instructional Time:
40 Minute(s)
Keywords: Residual, scatter plot, regression equation, bivariate data
Sorry! This resource requires special permission and only certain users have access to it at this time.
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 define a residual.
 Students will be able to find residuals given a set of points and their regression equation.
 Students will be able to interpret what a positive or negative residual means.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be familiar with:
 creating a scatter plot,
 finding the line of best fit,
 finding and understanding linear regression equations.

Guiding Questions: What are the guiding questions for this lesson?
 Why are some regression equations better than others?
 How can we determine how well a line fits the data?

Teaching Phase: How will the teacher present the concept or skill to students?
Teachers can use the PowerPoint to teach the lesson or familiarize themselves with how to find residuals and then teach it to their students. Teachers can also use previously acquired data from a scatter plot activity, and after finding the linear regression equation actually find the residuals of that same set of data. Teachers can use the following format in order to implement the lesson:
 Pass out the warmup activity to the students (this should activate prior knowledge). Students can quickly graph their scatter plots as a way to review and recall. The teacher can also suggest that students draw what they think a line of best fit is. However the linear regression equation provided should be given to them.
 The teacher can then go over the warmup (this has been embedded in the PowerPoint).
 Continue with the new lesson on finding residuals in the PowerPoint.
 Students can work along with the teacher, using the warm up problem as a step by step to finding the residuals. (This has been embedded in the PowerPoint as for the teaching phase). Formative assessment questions and expected answers have also been embedded into the PowerPoint presentation.
 Once the teacher has modeled how to find the residual using the warm up example, the teacher can move onto the guided practice. (This also has been embedded into the PowerPoint.)

Guided Practice: What activities or exercises will the students complete with teacher guidance?
Teachers can continue to use the PowerPoint in order to do a guided activity with the students. Formative assessment questions have been embedded at the bottom of the slides.
 The teacher can give the students the guided practice problem titled "Now you try" located in the PowerPoint.
 The teacher can, after students have tried the problem, go over the problem with the students, answering questions in order to clarify any errors students may have made.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Once the guided practice portion is complete, students can move onto the independent practice portion.
Teachers can either:
 Send students home with the independent practice portion and use the closure assignment within the class to close out the lesson.
 Or teachers can allow students to complete the independent lesson within the class and discuss problem number 5 as a way of closing the lesson and send the closure assignment home.
The activity provided is a worksheet on finding the residual values. The questions are mixed. It has graphs with the equation as well as the table of values with the linear regression equations given.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Teachers should ask students two questions to answer in writing as an exit ticket:
 What is a residual and how is it calculated?
The distance between the y value of the point plotted and y value on the the line of regression; the difference between the actual y value and the predicted y value as determined by the line of regression.
 What might residuals tell about a line of regression?
This hasn't been discussed so students are asked to come up with their own ideas. There is no correct answer at this time. This will help the teacher focus and plan for upcoming residual plot lesson that typically would be the next lesson.

Summative Assessment
A short closure assignment is attached that can be used at the end of class or as a homework assignment, depending on time needed for lesson. It checks students' understanding of how to find residuals given a table or graph.

Formative Assessment
 The attached warmup activity reviews graphing scatter plots and finding a regression equation.
 Also, throughout the PowerPoint teaching presentation, there are different questions in the comment section that teachers can utilize in order to formatively assess for student comprehension.

Feedback to Students
Feedback will be done through both formative as well as summative assessment.
 When students respond to those formative questions throughout the PowerPoint they will be given feedback on whether they are proceeding correctly.
 After the summative assessment exit ticket students will receive corrective feedback.
Accommodations & Recommendations
Accommodations:
 Give fewer problems to those students who need those accommodations.
 Provide the scatter plots and line of regression for the students who need accommodations, as this lesson is not for plotting points but rather finding the residuals.
 For those students who may need reinforcement, the teacher should stand ready to prescribe the provided link that reinforces the lesson.
 Also, prior to the lesson, the teacher can also give those learners who are ahead some of the extension activities.
 The teachers can differentiate the PowerPoint presentation.
 Those students who comprehend how to find the residual can work ahead and begin to do the independent practice assignment.
 Teachers can also have students find a line of best fit themselves and utilizing that equation find residual values and compare the two while working with those who still need assistance.
 Groups can be created by giving students a quicker warm up activity either utilizing the provided warm up activity or if the teacher prefers to utilize another formative assessment they can. Then allow students who can to work ahead without holding them back and the teacher can work with the groups of students who need more assistance.
Extensions:
Extensions relate this resource to other topics, realworld applications, other subjects, other contexts, other lessons. Extensions for this lesson could be for students to create a residual plot of any of the given graphs (they can either do this by hand, on geogebra, or any online source that will assist in creating residual plots. Remember that all residual equations have already been included throughout the lesson, power points and lesson keys. If technology is not available the equations have already been provided.) Students can also compare a line of best fit they've created utilizing y=mx+b, and find residual values utilizing those and compare it to the actual linear regression equation residual values they've found. This can lead to students finding the Sum of Squared errors.

Suggested Technology: Graphing Calculators, Computer for Presenter, Internet Connection, Basic Calculators, LCD Projector, Scientific Calculator
Special Materials Needed:
Students will need the attached handouts.
Further Recommendations:
Links to videos that may further assist or serve as reinforcement: https://learnzillion.com/student/lessons/3175
Additional Information/Instructions
By Author/Submitter
Math Practices:
MAFS.K12.MP.2: Reason abstractly and quantitatively.
MAFS.K12.MP.4: Model with mathematics.
MAFS.K12.MP.7: Look for and make use of structure.
MAFS.K12.MP.8: Look for and express regularity in repeated reasoning.
Source and Access Information
Contributed by:
Gina Harris
Name of Author/Source: Gina Harris
District/Organization of Contributor(s): MiamiDade
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.