Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 71433
Scatter Plots at Arm's Reach
This lesson is an introductory lesson to scatter plots and line of best fit (trend lines). Students will be using m&m's to represent different
associations in scatter plots, and measure each other's height and arm span to create their own bivariate data to analyze. Students will be
describing the association of the data, patterns of the data, informally draw a line of best fit (trend line), write the equation of the trend line,
interpret the slope and y-intercept, and make predictions.
Subject(s): Mathematics
Grade Level(s): 8
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Internet Connection, LCD Projector
Instructional Time: 2 Hour(s) 30 Minute(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: Scatter Plots, Line of Best Fit, Slope, Y-Intercept, Making Predictions
Resource Collection: FCR-STEMLearn Algebra
ATTACHMENTS
Scatter_Plots_at_Arm_Reach.pptx
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:
Display bivariate data on a scatter plot
Describe the association of a scatter plot and its linear association
Identify outliers and clusters in a scatter plot
Informally plot the line of best fit (trend line)
Assess a trend line by judging the closeness of the points
Write an equation for a trend line
Interpret the slope and y-intercept of the trend line
Use the trend line to make predictions and solve problems involving bivariate data
Prior Knowledge: What prior knowledge should students have for this lesson?
Prior to the lesson, students should be able to:
Plot points on a coordinate plane
Find the slope of a line
Understand the difference between positive and negative slope
Identify the y-intercept of a line
Write the equation of a line
Evaluate equations given an input value
page 1 of 4 Guiding Questions: What are the guiding questions for this lesson?
How do you represent data on a scatter plot?
- Create an x-axis and y-axis, and plot your data as ordered pairs.
How can you describe the data on a scatter plot?
- Using terms such as, positive, negative, linear, nonlinear, clusters, and outliers.
How can you informally graph a line of best fit, or trend line on a scatter plot?
- Use a straightedge to draw a straight line that has about the same number of points above and below the line.
How can a trend line describe the relationship between two sets of data?
- The equation of the line can describe the relationship between the independent variable (x) and dependent variable (y), by interpreting the slope and the yintercept.
How can a trend line be used to make predictions?
- By looking at a trend line, you can make a prediction based on an estimate of where the line crosses for the given value; or to get a more accurate prediction, you
can substitute the given value for either y or x (depending on which is given), and solve for the second variable.
Teaching Phase: How will the teacher present the concept or skill to students?
Phase 1: Warm up/Introduction
(Slide 2) As students walk into the classroom, the warm up will be displayed on the PowerPoint. Students will have 10 minutes to complete the warm up.
After the 10 minutes, the teacher will go over the answers to the warm up and discuss the responses; reviewing any concepts that should be prior knowledge
(plotting points on a coordinate plane, finding slope of a line, positive and negative slope, identifying the y-intercept, writing the equation of a line, and evaluating
equations given an input value).
(Slide 3) After introducing the lesson and having the students write down the title, the teacher will introduce the vocabulary words. The students will write down the
vocabulary words in their notebooks under the heading "Vocabulary". The words will be defined later in the lesson.
Scatter Plot
Association
Cluster
Outlier
Line of Best Fit
The class will discuss the responses to the questions and how they arrived to their responses.
Phase 2: Instruction
(Slide 4) The teacher will first define a scatter plot and say, "A scatter plot is a graph with plotted points to show a relationship between two sets of data." The
students will write down the definition of a scatter plot and draw an example.
"Scatter plots have an independent and dependent variable. Who can tell me which variable (x or y) represents the independent and depended variable?" The
teacher will call on a student to answer and have the students label the dependent and independent variable on their scatter plot.
(Slide 5) The teacher will then explain that scatter plots have different types of associations, and have the students write down the definition of association. The
teacher will explain that association is similar to slope and say, "Recall the different types of slope we have learned: positive, negative, no slope, and undefined.
Association is very similar to slope." Four different students will come up to the board to draw an example of positive slope, negative slope, no slope, and undefined
slope. While the students are doing this, the teacher will begin to pass out a bag of m&m's to every pair of students.
"With your partner, draw three blank scatter plots (no points yet) on a sheet of paper and label them Positive Association, Negative Association, and No Association.
Use the m&m's to show what you think these different types of associations look like". The teacher will walk around the classroom to observe the students.
After two minutes, the class will discuss the associations as the teacher asks different students to describe what positive, negative and no association look like.
"Now draw two more blank scatter plots and label them Linear Association and Nonlinear Association. Again, use your m&m's to show what you think those types of
associations look like."
(Slide 6) Students will share what their scatter plots looked like and then the teacher will show them the slide with the different types of associations. The students
will write down the different associations and draw examples of each one.
(Slide 7) "Just as with any data set, in a scatter plot there may appear to be an outlier or multiple outliers. These outliers will be farther away from the trend line
than all of the other points. Draw an example of a scatter plot that would appear to have an outlier."
"In a scatter plot, there may also be a cluster, which is a collection of data points that are close together." The students will draw a scatter plot with a cluster.
(Slide 8)The teacher will show three different scatter plots and have the students, in pairs, identify each scatter plot as having positive, negative, or no association,
whether the association is strong or weak, and identify if the scatter plot has an outlier.
(Slide 9) The teacher will say, "With a scatter plot, a line of best fit can be drawn to describe the relationship, or trend between two data sets. In future math
courses, you will learn how to precisely determine a line of best fit, but in this class we will informally plot the line of best fit and call it a trend line. When you draw
your trend line, approximately the same amount of points should be above and below the line." Students will write the definition of line of best fit draw an example
of a trend line.
(Slide 10) "To describe the relationship between the two sets of data, you can use the equation of your trend line. Let's recall the different steps to writing the
equation of a line." The teacher will give the students about two minutes to write down the steps of how to write the equation of a line.
(Slide 11) The class will do a sample problem together and write determine the equation of the line.
"Now that we have the equation, we can use the equation to describe the relationship between the two data sets by interpreting the slope and the y-intercept.
Remember that slope is the change in y, over the change in x. Write this down in your notebooks. In the example we just completed, what would the slope
represent?" The class will discuss what the slope represents for the sample problem. "Remember that the y-intercept is the value of y, when x=0. What would the
y-intercept represent in our example?" The class will discuss what the y-intercept represents.
(Slide 12) "The trend line and equation of the trend line allows us to also make predictions based on the data. This is simply done by reading the problem, deciding
if the value given is your x or y value, and then plugging it in and solving for the other variable. You can estimate based on your trend line, but the accurate solution
is found using the equation." The class will then predict the number of As for period 6 as asked in the sample problem, and discuss the process.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
(Slide 13) Students will be grouped into pairs and each pair will be given a measuring tape
Each student will measure the other student's height and arm span (in inches), and write it down on a sheet of paper.
After all of the groups have finished measuring, the teacher will have each student share their measurements. The teacher will write the measurements on the
board in a function table and the students will write the table in their notebooks as well (x: height, y: arm span).
(Slide 14) The students will plot the points on a scatter plot while the teacher creates one on the board.
page 2 of 4 The teacher will ask the students to write down the association of the scatter plot and if there appears to be any outliers or clusters. There will be a discussion
about the correct response.
Next, the teacher will ask the students to use a straightedge to draw a trend line that could be used to represent the data. (Remind the students that there should
be approximately the same amount of points above and below the line.) Two students will come up to the board and share what their lines looked like.
The students will then write the equation of their trend line as the teacher walks around to ensure that the students are doing their work correctly.
(Slide 15) The teacher will present the following questions and the students will write them down and answer them in their notebooks:
What is the independent variable and dependent variable for this data?
What does the slope of the trend line represent?
What does the y-intercept of the trend line represent?
Predict the arm span of a basketball player who is 7'4". Show your work.
The class will discuss the responses to the questions and how they arrived to their responses.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Using the given data set, students will answer the following questions.
Use graph paper to create a scatter plot for the data.
Describe the association of your scatter plot.
Draw a trend line for the scatter plot.
Write the equation of the line for your trend line.
What does the slope represent?
What does the y-intercept represent?
Predict the number of ice creams sold in a month where there are 12 sunny days.
Class will discuss their answers, and students will then complete the summative assessment individually.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher will refer back to the vocabulary slide and have a whole class discussion, engaging the students in the purpose of the lesson. The discussion will include
the following questions:
What did you learn about each of these vocabulary words that were introduced to you today?
What are the benefits of using a scatter plot to represent data?
How does a trend line help you better analyze the data?
When do you think you can use a scatter in the real-world setting?
Summative Assessment
Students will complete the attached worksheet individually. The worksheet will assess all of the objectives with open-ended questions. Summative Assessment-Dreaming of Math.docx
Formative Assessment
The teacher will assess students' prior knowledge with a warm up at the beginning of the class.
After the scatter plot has been introduced, the teacher will ask the students to recall the four different types of slope (positive, negative, zero, and undefined) and
have students come up to the board to show what those types of slope look like.
Before explaining the different types of associations, the teacher will have the students draw three blank scatter plots (no points) on a sheet of paper and label
them Positive Association, Negative Association, and No Association. They will use m&m's to show what they think the different types of associations look like.
Students will describe what the different associations look like. Then the teacher will ask them to add two more blank scatter plots and label them Linear
Association and Nonlinear Association. The students will again use the m&m's to show what they think those types of associations look like.
Once the teacher has explained how to identify linear or nonlinear associations, as well as outliers and clusters in a scatter plot, the teacher will show three
different scatter plots on a slide and in pairs, students will have to identify each scatter plot as having positive, negative, or no association, whether the association
is linear or nonlinear, and identify if the scatter plot has an outlier and/or cluster.
Before explaining to students how to write the equation of a line for the trend line, the teacher will have the students individually write down the steps of writing the
equation of a line in their notes.
After explaining how students can interpret the slope and the y-intercept, the teacher will give the students a sample problem that includes a scenario that can
described by a linear equation, and have the students interpret the slope and the y-intercept given what each variable represents.
During the guided practice, students will create and analyze a scatter plot for a given set of data with guidance from the teacher.
During the independent practice, students will create and analyze a scatter plot for a given set of data individually.
Feedback to Students
The teacher will go over the warm up with the students; providing feedback and correcting any misconceptions the students may have.
After describing what the different associations look like using the m&m's, the class will discuss what the associations look like and the teacher will show the slide of
what the different associations are; asking how many students were correct with the placement of their m&m's.
Students will share their responses with another pair, and the class will discuss what the correct responses were for each scatter plot.
The teacher will review the process of writing the equation of a line, using the line of best fit in the sample class scatter plot; having the students make corrections,
as needed, to the steps they wrote down.
Various students will share their interpretation of the slope and why intercept and discuss them with the class.
While the students work on the guided and independent practice, the teacher will walk around monitoring, and providing feedback to the students.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
When pairing students for the guided practice activity, the teacher will consider the students' level of proficiency in algebraic expressions and linear functions,
pairing weaker students with a stronger student.
The teacher will repeat instructions as needed to students individually.
The teacher will use large font on the PowerPoint.
The teacher will assist students with graphing a trend line if necessary.
page 3 of 4 Extra time will be allotted for the summative assessment if needed.
Extensions:
Students will research the internet and collect a set of data that has a positive or negative association.
Create a table of values.
Plot the values on a scatter plot as ordered pairs.
Write a sentence describing the association and any other patterns.
Draw a trend line.
Make a prediction based on the trend line. Justify your prediction with data from the table.
Suggested Technology: Computer for Presenter, Internet Connection, LCD Projector
Special Materials Needed:
Materials for the Teacher:
Computer with Microsoft PowerPoint
Projector
Materials for the Students:
Graph paper
Pencil
Measuring Tape
Ruler or Straight edge
M&M’s (about 30 for each pair)
Copies of “Dreaming of Math” Further Recommendations:
Teacher should have students pairs set up prior to the lesson.
The m&m's should be sorted into bags for students (unless using smaller bags).
Students may use calculators for this lesson.
Additional Information/Instructions
By Author/Submitter
This lesson is related to the following Mathematics Practice Standards:
MAFS.K12.MP.1.1 - Make sense of problems and persevere in solving them.
MAFS.K12.MP.1.4 - Model with mathematics.
MAFS.K12.MP.1.7 - Look for and make use of structure.
SOURCE AND ACCESS INFORMATION
Contributed by: Kelsey Ludvigsen
Name of Author/Source: Kelsey Garcia
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.8.SP.1.1:
MAFS.8.SP.1.2:
MAFS.8.SP.1.3:
Description
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two
quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and
nonlinear association.
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.
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the
slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning
that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
page 4 of 4