Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 71144
Slope and y-Intercept of a Statistical Model
After activating prior knowledge and presentation of new skills, students will be collecting and evaluating data to interpret the line of best fit and yintercept in order to develop an equation in point-slope form to represent the data.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Internet Connection, Basic Calculators, LCD Projector,
Adobe Flash Player, GeoGebra Free Software
(Download the Free GeoGebra Software)
Instructional Time: 4 Hour(s)
Freely Available: Yes
Keywords: Graph, Line of Best Fit, Correlation, Slope (rate of change), Y-Intercept (constant term), SlopeIntercept Form
Instructional Design Framework(s): Direct Instruction
Resource Collection: FCR-STEMLearn Algebra
ATTACHMENTS
Check Your Understanding Assessment.pdf
Discussion Questions Slope and y intercept.docx
Summative Assessment on Interpreting Slope.pdf
What is the Relationship Assessment.pdf
Warm up Activity.pdf
Warm Up Activity Answer Key.pdf
What is the Relationship Answer Key.pdf
Shoe Size and Height Relationship Group Project.pdf
Summative on Interpreting Slope Answer Sheet.pdf
Shoe Size and Height Relationship Group Project Teacher Copy.pdf
Check Your Understanding Answer Key.pdf
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 and interpret the rate of change (slope) of a linear model.
identify and interpret the constant term (y-intercept ) in terms of the data set.
use the correlation coefficient to determine whether a linear function models a data set.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be able to:
1. plot coordinate points.
page 1 of 3 2. find the slope of a line between two points.
3. write the equation of a line between two points.
4. to find the y-intercept of a linear equation.
Guiding Questions: What are the guiding questions for this lesson?
1. What does the rate of change (slope) of the line represent in terms of the data set?
2. What does the constant term (y-intercept) represent in terms of the data set?
3. What is the significance of the correlation coefficient?
4. What is the relationship between the correlation coefficient and the line of best fit?
Teaching Phase: How will the teacher present the concept or skill to students?
First the teacher will administer the Warm-up Activity to activate prior knowledge. Students will:
Plot data points
Draw line of best fit
Discuss the significance of the line of best fit
In order to show students a visual representation of the material, a white board could be used to draw graphs, lines of best fit, etc. A better alternative would be to
use computer software and a projector to demonstrate concepts as they are being discussed.
During the discussion phase, ask students to recall the definition for the line of best fit. Elicit volunteers to explain how they drew their lines of best fit in the warm-up.
Ask students what is the purpose of finding the line of best fit. Expect answers such as, "Describe the trend of the line," or "Use it to predict values that are not actual
data points." Lead students to the definition, "The line that passes most closely through several coordinates, minimizing the distances between the line and the actual
points. It does not have to pass through the points." Have students record the definition on their graphs.
Next the teacher will introduce the topics of correlation, slope, y-intercept, and the point/slope formula as it applies to statistical data. The teacher will reference the
discussion questions to explore the topics.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
During the Teaching Phase, students will be discussing the following questions from the discussion questions:
1. Does the amount of time spent studying have an effect on the grade received on a test?
2. What is the pattern?
3. What do you think a negative correlation would be?
4. What about no correlation?
5. Can a prediction be made about the amount of time spent studying and the grade received on the test?
6. Students will calculate the slope and the y-intercept after discussion on how they are calculated.
7. Is the y-intercept valid? Based on what we know about the time spent studying and the grade on the test, does this constant term make sense for our data?
Students will be asked to make predictions with the slope intercept formula.
During the team projects, the teacher will take an active roll in assisting students with completing the tasks successfully.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students will complete two assignments.
First, students will complete the group assignment "Shoes Size and Height Relationship." Students will:
Collect data on shoes sizes and height.
Plot all student data on a scatterplot.
Draw the line of best fit.
Discuss correlation.
Calculate slope and discuss.
Discuss trend line.
Calculate y-intercept and discuss.
Create point-slope formula.
Make predictions.
The teacher will then administer the summative assessment; see the summative assessment section.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will review the solutions to the summative assessment with the class and have students correct their mistakes.
Summative Assessment
Administer the attached Summative Assessment. Students will complete the following task:
Plot the given data on a scatterplot.
Draw a line of best fit.
Explain correlation.
Calculate and explain slope.
Calculate and explain the y-intercept.
Create a point slope formula.
Make a prediction.
Formative Assessment
There will be two formative assessments given at the end of the first and second days.
Day 1 -"What is the Relationship?" Students will be given three different statistical graphs. Using the graphs, students will:
Determine if the variables are correlated. Label the correlation as positive, negative, or does not exist.
Draw an oval around the data points if there is a correlation.
page 2 of 3 Draw a line through the data from end to end.
Define "line of best fit."
Day 2 - "Check Your Understanding"
Students will be given a graph that plots the money a babysitter earned for each babysitting job. Using the scatter plot provided, students will:
sketch a line of best fit.
solve for the slope and y-intercept of the line of best fit.
analyze and interpret the slope and y-intercept as it relates to the problem.
find the equation of the line of best fit and understand that it represents the average value of data.
The teacher will circulate around the room and check for understanding. The teacher will ask students to explain their reasoning. After each assessment, the teacher
will lead a question and answer session, having students explain the answers to each question.
The teacher will demonstrate drawing the line of best fit using a graphing program and a projector, and then have students compare it to the lines they drew.
Feedback to Students
During questioning, the teacher can correct any misconceptions right away for all students. Some common misconceptions are:
Students may draw a piecewise function, connecting all of the dots on the scatterplot rather than drawing a straight line for the line of best fit.
Students may not understand that the line of best fit represents an average.
Students may not understand that the slope represents a rate of change.
Students may not understand that every position on the line of best fit represents an x and y relationship.
Just because a point is on the best fit line does not mean that it is actually a data point.
While students are completing the team project, the teacher will circulate around the room to ask questions and assist students with questions they may have.
Formative assessments will be discussed.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: ESE students will:
be paired with higher level students during group activity
be given extra time to complete assignments and assessments
be permitted to ask questions for clarification during assessments
ELL students will:
be be grouped with bilingual students during group project
be permitted to ask questions for clarification during assessments
Extensions: "What is the Relationship" assessment - if graphing calculators are available, students could calculate the line of best fit and then compare it with the
line they drew.
Suggested Technology: Computer for Presenter, Internet Connection, Basic Calculators, LCD Projector, Adobe Flash Player, GeoGebra Free Software
Further Recommendations: Desmos offers a great online calculator for displaying scatterpoint graphs and line of best fit as well as other functions.
GeoGebra is also an alternative, as it will draw the line of best fit, derive the slope-intercept formula based on the data and line of best fit, and calculate other statistical
information if needed.
SOURCE AND ACCESS INFORMATION
Contributed by: Tina Gilligan
Name of Author/Source: Tina Gilligan
District/Organization of Contributor(s): Volusia
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.S-ID.3.7:
Description
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. ★
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