Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 71168
Line of Best Fit
This lesson provides students with opportunities to examine the slope and y-intercept of a line of best fit using scatterplots. Students will gain a
deeper conceptual understanding of slope and y-intercept based on real world data. Students will graph scatterplots and draw a line of best fit.
Then, students will use the line to interpret the slope and y-intercept with regard to the data. Students will also make predictions using the graph
and the equation of the data.
Subject(s): Mathematics
Grade Level(s): 7, 8, 9, 10, 11, 12
Intended Audience: Educators
Suggested Technology: Document Camera, Graphing
Calculators, Computer for Presenter, Internet
Connection, Basic Calculators, LCD Projector, Microsoft
Office, GeoGebra Free Software (Download the Free
GeoGebra Software)
Instructional Time: 1 Hour(s) 20 Minute(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: linear models, statistics, slope, rate of change, data
Resource Collection: FCR-STEMLearn Algebra
ATTACHMENTS
Line of Best Fit Lesson Plan.docx
Student Discovery and Exploration Spaghetti Models.docx
Teacher Discovery and Exploration Spaghetti Models.docx
Line of Best Fit Guided Practice.docx
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 use line of best fit to make predictions.
Students will analyze a line of best fit to interpret the slope and y-intercept.
Students will use the slope and y-intercept to write an equation for a line of best fit.
Students will use the equation for a line of best fit to make predictions.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be able to:
Identify the slope and y-intercept given a table, graph or equation.
Graph a linear equation in slope-intercept form.
Write a linear equation in slope-intercept form.
Use a point and the slope to write an equation in point-slope form.
Use the point-slope form of an equation to rewrite the equation in slope intercept form.
Construct a scatterplot.
page 1 of 4 Recognize whether a graph shows a positive, negative or no correlation.
Guiding Questions: What are the guiding questions for this lesson?
What does the slope of a line tell us about the relationship between two variables?
What does the y-intercept for a line of best fit represent?
How can we use a line of best fit to make predictions?
Teaching Phase: How will the teacher present the concept or skill to students?
The teacher will begin class with the Discovery and Exploration Activity that is attached. Students will determine if there is a relationship between fat grams and the
total calories in fast food. Students will be paired in groups of two.
Display the instructions for the students and distribute graph paper and a strand of spaghetti to each pair of students.
1. Given a data set, students will create a scatterplot using graph paper and pencil. Students should include a title for the graph and label all axes.
2. Students will position a piece of spaghetti so that the plotted points are as close to the spaghetti as possible. This will accurately reflect the line of best fit for the
data set.
3. Students will find two points that lie on their line of best fit that most accurately reflect the data. Students may choose different points.
4. Students will calculate the slope of their two points, rounding to the nearest hundredths place.
5. Students will use the slope and choose a point from the data. They will then use point-slope form to find the equation of the line in slope intercept-form. Some
students may choose to use a point and the slope to find the y-intercept and then rewrite the equation in slope-intercept form.
6. Students will compare their equation with other groups and answer the following questions.
Did you obtain similar results?
Is there a correlation between fat grams and number of calories? If so, what is the correlation?
What does the slope of your line represent in terms of the relationship between fat grams and calories?
(Each student's results should be similar. The students should also state the positive correlation and mention that the slope is representative of the fact that as fat
grams increase, calories also increase)
When students are finished comparing, ask students the following questions:
What general shape did your scatterplots make? (In general, the data points were linear and showed a positive correlation.)
Is there a constant rate of change? (No.)
How do you know? (Calculating different pairs of points would produce different slopes.)
How did you determine one slope that best described the data? (Answers will vary but students should mention that they chose points based on how closely they fell
to the spaghetti line of best fit.)
What is the independent variable? Dependent variable? How do you know? (Fat grams and calories, respectively. The number of calories in a sandwich depends on
the number of fat grams.)
Use the graph and the equation to make a prediction about how many calories sandwiches with 7 and 40 fat grams would have. (Answers will vary. Ask students to
share their answers. Write them on the board discuss as a class whether or not the answers are reasonable.)
Explain to students that different people may choose different points and arrive at different equations. All of these equations are correct, but in order to arrive at the
best answer a graphing calculator would be a better tool.
The student and teacher instructions are attached. The teacher attachment includes a graph of what student models should look like, as well as slope and equation
calculations. The attachments also include extension activities using TI graphing calculators to determine the line of best fit. Students have essentially covered every
objective in the lesson with this activity.
Teacher Discovery and Exploration Activity with Answer Key
Guided Practice: What activities or exercises will the students complete with teacher guidance?
During guided practice the teacher will introduce new vocabulary and have students copy the definitions into their notes. Next, they will display Example One in the
Guided Practice attachment. Students will use the data in the examples to create a scatterplot. The teacher will then instruct students to use a straight edge to draw a
line of best fit. The class will choose two points to calculate the slope and use point-slope form to write an equation for the line of best fit in slope-intercept form.
Students may also choose to use the slope and a point to find the y-intercept and then rewrite the equation in slope intercept form. This will be a teacher led follow up
to the discovery and exploration activity. At this point, students have covered the objectives of the lesson. However, new vocabulary (interpolation and extrapolation) is
introduced during this guided practice. The guided practice shows an example of each, as well as an example involving a negative correlation in which the y-intercept
is more meaningful with respect to the data. The real world examples include a connection to Biology (giraffe growth), gasoline prices and the relationship between
the temperature and an airplane's altitude.
Guided practice attachment with answers: Line of Best Fit Guided Practice
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
During independent practice, students will take out their individual whiteboards and dry erase markers to complete the attached practice problems.
See the Formative Assessment box for the Independent Practice Problems.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will assign a project. Students will be told to collect their own data for two related variables and compare the relationship. They must have at least 20
pairs of numbers. Students may use a almanac, newspaper, magazine, the internet or conduct a survey of people they know to collect the data.
Once the data has been collected, students will graph the data and draw a line of best fit. Students will then calculate the slope and write an equation for the line of
best fit.
Students will then write a paragraph about what they found that describes the relationship between the two variables.
The teacher will give students the following suggestions and ask the class to add to the list. However, students may choose whatever they wish, provided that the two
variables show a correlation.
Height vs. shoe size
Highway vs. city mileage
page 2 of 4 Points scored vs. time on court
Hits vs. times at bat
Sunlight exposure vs. plant growth
Student instructions and rubric are attached.
Project for Line of Best Fit
Rubric for Line of Best Fit Project.docx
Summative Assessment
The attached Summative Assessment will test students ability to analyze a line of best fit and interpret the slope and y-intercept. Students will use the slope and yintercept to write an equation for a line of best fit and will use the graph to make predictions about the data.
The assessment will be distributed at the end of class and each student will complete the assessment independently. The answer key is also attached.
Line of Best Fit Summative
Line of Best Fit Summative Answer Key
Formative Assessment
Individual whiteboards may be used to answer the formative assessment questions. After the gradual release problem, during guided practice, students will be given
the attached problems to complete on their whiteboards.
Students will copy a table and create a scatterplot. Then students will draw a line of best fit and write an equation for the line. Students will interpret the slope and yintercept and make inferences about the data based on the graph and equation.
After completing each problem on their own, students will compare their answers to others at their table group and justify their answers to each other. The teacher
will walk around the room observing student work to determine understanding and adjust instruction as needed. The teacher also will use this time to provide one on
one instruction to students that need help while other students compare their answers.
Finally, the teacher will ask students to share their answers with the rest of the class. If the students demonstrate a clear understanding of the material, the teacher
will move on to the summative evaluation for students to complete on their own. If the students are struggling, more practice problems will be required.
Formative Assessment: Line of Best Fit Independent Practice
Feedback to Students
As students work, the teacher will circulate around the room to ensure that the students are creating their scatterplots correctly. During the Discovery and Exploration
Activity, teachers may need to guide students who are unsure of where to place their line of best fit. Students may also need to be reminded of the slope formula. The
teacher should also circulate during whiteboard practice in order to assist students with corrections and misconceptions as they work practice problems on
whiteboards. Students may need to be reminded to label their graphs. Students may also need to be led by guided questions to help them to interpret the slope and yintercept.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students with special needs may benefit from the following accommodations:
During the discovery activity, ensure that students are able to construct the scatterplot and provide assistance when needed.
Repeat and clarify instructions as the lesson progresses.
Insert vocabulary meaning into the lesson whenever important vocabulary is used.
During whiteboard practice ask ESE students a question and tell them that they have a moment to discuss it with their table groups. Return and ask the question
again.
Allow for additional response time.
Use graphic organizers.
Extensions:
Students may complete the Texas Instruments activity Lines, Models, CBR - Let's Tie Them Together for a calculator exploration.
Students may use Geogebra to plot the scatterplots and find the equation for the linear regression.
Suggested Technology: Document Camera, Graphing Calculators, Computer for Presenter, Internet Connection, Basic Calculators, LCD Projector, Microsoft Office,
GeoGebra Free Software
Special Materials Needed:
Teacher computer and presentation system
Student attachment for Discovery and Exploration (see the Teaching Phase box)
Graphing calculators (optional)
Pencil and graph paper
Spaghetti
Attachment for Guided Practice (see Guided Practice box)
Straight edge
Attachment for Independent Practice
White board and dry erase markers
Further Recommendations:
page 3 of 4 Be sure to allow time for class discussion. Use a document camera to display student work and open up discussion in the class. You will probably find many similarities
and differences among student's scatterplots that can be discussed.
Additional Information/Instructions
By Author/Submitter
This lesson covers the following mathematical practice:
MAFS.K12.MP.1.1: Make sense of problems and persevere in solving them.
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
MAFS.K12.MP.3.1: Construct viable arguments and critique the reasoning of others.
MAFS.K12.MP.4.1: Model with mathematics.
MAFS.K12.MP.5.1: Use appropriate tools strategically.
MAFS.K12.MP.6.1: Attend to precision.
MAFS.K12.MP.7.1: Look for and make use of structure
SOURCE AND ACCESS INFORMATION
Contributed by: Angela Ciresi
Name of Author/Source: Angela Ciresi
District/Organization of Contributor(s): Pinellas
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. ★
page 4 of 4