Lesson Title: 8.SP.A.2 Lesson Line of Best Fit
Date: _____________ Teacher(s): ____________________
Course: Common Core Mathematics 8
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For
scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by
judging the closeness of the data points to the line.
MP3:
MP4:
MP5:
MP7:
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Look for and make use of structure.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
The creation of a bivariate measurement data situation
will help students access previous knowledge of
associations and give students an opportunity to write a
new situation of interest to them.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
Students will share their individual work and the teacher
will lead a class discussion about the various situations.
(Look for evidence of MP7.)
 Which situations were alike?
 Which situations were different?
 What did you notice about positive associations?
 What did you notice about negative associations?
Students can also complete the graphic organizer to
summarize understanding of linear models and
associations.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
Note: Depending on length of the class period, this lesson may take two class periods to complete.
1. Warm-Up: Ask students to describe a bivariate measurement situation in which there is either a positive or
negative association (they will write their situation on a piece of colored paper). Students should use their
knowledge from the previous lesson on associations of bivariate measurement data. Students can share their
situation with a partner and ask the partner to determine if the association is positive or negative. Students will
post their situations on one chalkboard and organize them by positive/negative associations. (Look for evidence
of MP3.)
2. Construction and Investigation: Share the objective for the lesson and tell students they will be creating scatter
plots and constructing linear models to fit the data.
 The teacher will lead a group investigation into finding an equation of a line of best fit for a set of data.
Let the class vote on which of the four situations they would like to investigate first.
 Students will create a scatter plot of the data by plotting points onto an appropriately labeled coordinate
grid. The teacher can guide students who are struggling to create the scatter plot. (Look for evidence of
MP4 and MP6.)
 The teacher will lead a group discussion about finding a line to fit the data. Some questions to ask are:
Is this a positive or negative association? Is this a linear situation? Will a line fit all of these points?
Why or why not? Students will then be given a piece of spaghetti and asked to tape the spaghetti onto
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: 8.SP.A.2 Lesson Line of Best Fit
Course: Common Core Mathematics 8
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
their scatter plot in the place that seems like a “good line” for the data. (Look for evidence of MP3.)
 The teacher will then guide students in finding an equation for their line by choosing two points from the
line. Students can use any of the methods they have previously learned for determining this equation.
(Look for evidence of MP4.)
 Once all students have an equation for a line, ask them to write their equations up on the chalkboard.
The class should vote on the equation they think is best.
3. Technology Investigation: Students will use Transformation Graphing on their graphing calculators to
determine a line of best fit for their data set. Students will choose a slope and y-intercept and adjust until they
have a line they think is appropriate. Use the Transformation Graphing resource sheet to guide students through
the process. (Note: Choose an x-value for the discussion questions that appropriately fits the current data set).
Have students compare this equation to their previous vote and discuss the benefits and drawbacks to using each
method. (Look for evidence of MP5.) A few notes about using the graphing calculator:
 To enter data: Go to STAT, choose EDIT, and enter values in the columns.
 To clear data from a list: Scroll up to the very top of the list, press CLEAR, then begin entering data.
 To graph a scatter plot: Go to 2nd, Y=, turn on one of the scatter plots, press GRAPH, then ZOOM
9:ZoomStat.
4. Individual Choice: Students can then choose one of the three situations that were not discussed in class to create
a scatter plot and find an equation for a line of best fit using whichever method they prefer. Students can post
their work around the classroom when they are finished. (Look for evidence of MP4.)
5. Lesson Closure: The teacher should lead a class discussion about the differences between the various situations.
This discussion could lead to a conversation about the meanings of the slopes and y-intercepts of students’
equations.
6. Organizing Results: Students can complete a graphic organizer to summarize their understanding of the
equation of a line of best fit, methods for finding the equation, benefits and drawbacks of the methods, and
differences among equations for various situations. This can be done on the computer or on paper if copies are
made.
Optional Extension Activity: Students will calculate an equation for a line of best fit using linear regression on the
graphing calculator. (Look for evidence of MP5.)
 Explain to students how the calculator uses the data to find a line that fits the data. Guide students through
using the calculator steps to determine the equation.
 Ask students to discuss the benefits and drawbacks of using linear regression as opposed to the other
methods.
 Discuss which equation is a better fit, using the same discussion questions from the Transformation
Graphing resource sheet.
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
Students need to be able to recognize positive and negative linear associations, construct scatter plots and linear
equations to model data sets, and determine an equation of a line of best fit. Evidence of success will be measured
through student participation, successful completion of scatter plots, linear models, and appropriate completion of
the graphic organizers.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Key vocabulary: scatter plot, bivariate measurement data, association/correlation, linear model, rate of change/slope
Common mistakes and misconceptions: Students may attempt to create a line by “connecting the dots”. Students
need to understand that all lines are straight and they will need to pick a line to fit as many dots as possible.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: 8.SP.A.2 Lesson Line of Best Fit
Course: Common Core Mathematics 8
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Connections: This lesson should come after students have learned to graph scatter plots and prior to using the
equation of a line of best fit. Students will use a more formal approach to determining the “best fit” in Algebra I
when learning about residuals.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Data sets
Spaghetti
Individual choice investigation sheets
Graph paper
Markers, colored pencils, rulers
Graphing calculators, computers
Transformative graphing resource sheets
Graphic organizers/Inspiration resource sheet
Homework sheets
Depending on time, students may either complete graphic
organizer as homework or complete an attached resource
sheet about associations and equations of lines.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
What concepts do students have a strong understanding of?
What concepts/skills do students need additional support/reinforcement?
The follow-up lesson will be focused on a variety of data sets and prediction questions-can students apply their
understanding to various situations?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.