STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Author: Arra Chung, Overlea High School, Baltimore County Public School
Background Information
Subject:
Identify the course the unit will be
implemented in.
Grade Band:
Identify the appropriate grade band for
the lesson.
Duration:
Identify the time frame for the unit.
Overview:
Provide a concise summary of what
students will learn in the lesson. It
explains the unit’s focus, connection to
content, and real world connection.
Background Information:
Identify information or resources that
will help teachers understand and
facilitate the lesson.
STEM Specialist Connection:
Describe how a STEM Specialist may
be used to enhance the learning
experience. STEM Specialist may be
found at http://www.thestemnet.com/
Enduring Understanding:
Identify discrete facts or skills to focus on larger
concepts, principles, or processes. They are
transferable - applicable to new situations within
or beyond the subject.
Algebra 1
9-12
Two 90 minutes class periods
Students will engage in regression analysis to determine the relationship among
variables and predict the outcome of future events. Students will develop scatter plots,
describe correlations, create lines of best fit for data and interpret the slope and
intercept of a linear model in the context of the data. A STEM Specialist will be used
to engage students in a hands-on STEM learning experience that addresses how
regression analysis is used in the workplace.
Teachers should review determining slope, analyzing scatter plots, and writing an
equation using two points. Teachers will discuss with the class the three main types
of correlations – positive, negative, and no correlation. Teachers should also
familiarize themselves with what a strong and weak positive and negative correlation
look like in order to challenge students that are a bit more advanced.
It is important to note that the linear regression line is a statistical analysis of the
relationship of two variables.
The STEM Specialist will engage students in a hands-on learning experience that
demonstrates how mathematics can be used to predict future outcomes focusing on
scatterplots, linear regression, and lines of best fit.
Mathematics can be used to predict future outcomes.
Page 1 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Background Information
Essential Questions:
Identify several open-ended questions
to provoke inquiry about the core ideas
for the lesson. They are grade-level
appropriate questions that prompt
intellectual exploration of a topic.
Student Outcomes:
Identify the transferable knowledge and
skills that students should understand
and be able to do when the lesson is
completed. Outcomes must align with
but not limited to Maryland State
Curriculum and/or national standards.
1. How can scatter plots and lines of best fit be used to predict future outcomes?
2. How can scatter plots and lines of best fit be used to analyze data?
3. How can mathematical representations be used to communicate information
effectively?
Students will be able to:
 recognize a linear relationship displayed in a scatter plot.
 determine an equation for the line of best fit for a set of data points.
 interpret the slope and intercept of a linear model in the context of the data.
Audience:
☒Peers
☐Experts /
Practitioners
☒Teacher(s)
☒School
Community
☐Online
Community
☐Other______
Product, Process, Action,
Performance, etc.:
Identify what students will produce to
demonstrate that they have met the
challenge, learned content, and
employed 21st century skills.
Additionally, identify the audience to
which they will present what they have
produced.
Students will work in teams to develop posters in which they
develop scatter plots, draw line of best fits, and use regression
analysis to predict the outcome of a select event.
Standards Addressed in the Unit:
Identify the Maryland State Curriculum
Standards addressed in the unit.
Domain: Descriptive Statistics
Cluster: Summarize, represent, and interpret data on two categorical and
quantitative variables.
Standard: Represent data on two quantitative variables on a scatter-plot, and
describe how the variables are related.
Standard: Interpret the slope (rate of change) and the intercept (constant term)
of a linear model in the context of the data.
Page 2 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Background Information
Equipment:
 Computer (Internet access)
 Elmo Projector
 Chalkboard/White Board
People, Facilities:
STEM Specialist
Suggested Materials and Resources:
Identify materials needed to complete
the unit. This includes but is not limited
to websites, equipment, Power Points,
rubrics, worksheets, and answer keys.
Materials (rubrics, worksheets, Power Points, answer keys, etc.):
 Line of Best Fit PowerPoint
 Pictures of different types of correlations printed
 Right Salaries Handout
 The Right Salaries Answer Key
 Linear Regression Calculator Instructions
 Predicting Ravens Touchdown Handout
 Classwork Assignment
 Poster Rubric
 Newsprint or other large paper
 Markers or colored pencils
Page 3 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model
is not linear.
☒Engagement
☐Exploration
☐Explanation
☐Extension
☐Evaluation
Details
Materials:
1. Line of Best Fit PowerPoint (slides one-five)
2. Pictures of different types of correlations printed
3. One copy of the Right Salaries Handout for each student
4. The Right Salaries Answer Key
Preparation:
 PowerPoint slides one-five will be used for the engagement portion of
the lesson. Slides should be projected so that all students can see.
 Slide five displays the different types of correlations. Print out a
picture of each type of correlation (strong positive, moderate positive,
no correlation, moderate negative, strong negative and curvilinear
relationship) and post them around the classroom.
 Review the lesson ahead of time and be mindful that student results
will vary.
Facilitation of Learning Experience:
The purpose of this learning experience is to have students create and
analyze scatterplots, correlation, and lines of best fit.
1. Provide each student The Right Salaries Handout. Students will
guess the salary of each person and record their guesses on the data
table.
2. After a couple of minutes, provide the actual salary of each person.
Actual salaries may be found in the answer key and on PowerPoint
slide three. Students will record the actual salaries and create a
scatter plot of the data points using Guess the Salary as the x-axis
Standards for
Mathematical Practice
☐Make sense of problems
and persevere in solving
them.
☐Reason abstractly and
quantitatively.
☐Construct viable
arguments and critique
the reasoning of others.
☒Model with mathematics.
☐Use appropriate tools
strategically.
☐Attend to precision.
☒Look for and make use of
structure.
☐Look for and express
regularity in repeated
reasoning.
Page 4 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model
is not linear.
Details
Standards for
Mathematical Practice
and the Actual Salary as the y-axis.
3. Once all students have created their scatter plot, inform them that
there are different types scatter plots posted around the classroom.
Students will compare their scatter plot to those posted around the
room and place their scatter plot beneath the plot that looks similar to
theirs. Have students describe characteristics of their scatterplot
focusing on correlations.
4. Call on students to identify where they would draw a line of best fit for
each graph. Have each student draw lines of best fit by having
students using their pencil, a piece of string, or a spaghetti noodle as
a model to demonstrate what he or she believes is the correct line.
Call on students to justify the placement of their line of best fit.
Confirm correct answers and provide guidance as necessary.
5. Show students how to create a line of best fit using the points on the
graph by making sure there is approximately the same number of
points above and below the line (if possible – explain when a line of
best fit is unable to be created). Use PowerPoint slide six for
guidance.
6. Use the information on slide seven to walk students through how to
determine the slope and y-intercept of their line. Information from
slide seven may also be found here >>
http://www.mathworksheetsgo.com/sheets/algebra/linearequation/write-equation-from-2-points-worksheet.php.
7. Allow students time to determine the slope and y-intercept for their
line. Provide guidance as necessary.
Page 5 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model
is not linear.
Details
Standards for
Mathematical Practice
Transition:
Inform students that the type of data and equations they have been
reviewing can be used to make predictions.
☐Engagement
☒Exploration
☐Explanation
☐Extension
☐Evaluation
Materials:
1. Linear Regression Calculator Instructions
2. Predicting Ravens Touchdown
3. PowerPoint slides 9-12.
Preparation:
Prepare one copy of the Linear Regression Calculator Instructions and
Predicting Ravens Touchdown handout for each student.
Facilitation of Learning Experience:
☐Make sense of problems
and persevere in solving
them.
☐Reason abstractly and
quantitatively.
☐Construct viable
arguments and critique
the reasoning of others.
1. Ask the class how many touchdowns they think the Ravens will have
this year. Accept all answers.
☒Model with mathematics.
2. Project the Raven Touchdown Table (slide nine) and ask, based on
the data presented would you change your previous guess?
Randomly call on students and have them justify their answers.
☐Use appropriate tools
strategically.
3. Explain to the class that we are going to try to predict the number of
touchdowns the Ravens will score this session. Provide each student
with the Predicting Ravens Touchdown handout.
4. Students will create a scatter plot using the year and number of
touchdowns data and describe the correlation and create the line of
best fit.
☐Attend to precision.
☒Look for and make use of
structure.
☐Look for and express
regularity in repeated
Page 6 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model
is not linear.
Details
5. Inform the class that there are two methods for solving the line of best
fit.
Standards for
Mathematical Practice
reasoning.
6. The first method is just like writing equations using two points on a
line by hand. This method was reviewed during the engagement
portion of the lesson (slides 8-10).
7. The second method is using all the points on the graph so that a
more accurate equation can be found with the linear regression line
by using a calculator. Students may write down the calculator steps,
the steps can be projected to the front, or a handout with the
directions can be passed to each student (slide 11).
8. Students will be asked to analyze the slope and its meaning in the
context of the problem as well as make predictions.
9. Teachers can post on the board the number expected and the
number of actual touchdowns scored throughout the season. At the
end of the season see how accurate your prediction was and ask the
class why you did not pick the exact number of touchdowns.
Teachers should stress to the class that the line of best fit is used as
a prediction and will not produce an exact number.
Transition:
Review the answers on the Predicting the Ravens Touchdown handout.
Inform students that they will work independently to extend their knowledge
on linear regression.
Page 7 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model
is not linear.
☐Engagement
☐Exploration
☐Explanation
☒Extension
☐Evaluation
Details
Standards for
Mathematical Practice
Materials:
1. Classwork
2. PowerPoint slides 12.
☒Make sense of problems
and persevere in solving
them.
Preparation:
Prepare one copy of the classwork handout for each student. This
assignment may be completed for homework as well.
☐Reason abstractly and
quantitatively.
Facilitation of Learning Experience:
1. Provide each student with a copy of the classwork assignment to
work on independently.
☐Construct viable
arguments and critique
the reasoning of others.
☐Model with mathematics.
2. Monitor student progress and provide assistance as necessary.
Transition:
Inform students that they have learned about using linear regression to
predict future outcomes. Next class, they are going to engage in a learning
experience that demonstrates how lines of best fit, linear regression and
scatter plots are applied in the workplace. Students will meet with a STEM
Specialist to learn the real-world applications of their content knowledge.
☐Use appropriate tools
strategically.
☐Attend to precision.
☐Look for and make use of
structure.
☐Look for and express
regularity in repeated
reasoning.
Page 8 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model
is not linear.
☐Engagement
☒Exploration
☐Explanation
☐Extension
☐Evaluation
Details
Materials:
Technology needs of the STEM Specialist.
Preparation:
Contact the STEM Specialist in advance to review plans for the lesson and
explain his/her role. A description of the ability level of the students, as well
as some of the prior knowledge your students may have of scatterplots,
lines of best fit and linear regression may be helpful to the STEM Specialist
prior to the visitation. Prepare a list of questions to guide the learning
experience with the STEM Specialist or have students prepare some
questions in advance.
Facilitation of Learning Experience:
The STEM Specialist will engage students in a hands-on learning
experience that demonstrates how mathematics can be used to predict
future outcomes focusing on scatterplots, linear regression, and lines of best
fit.
Standards for
Mathematical Practice
☐Make sense of problems
and persevere in solving
them.
☒Reason abstractly and
quantitatively.
☐Construct viable
arguments and critique
the reasoning of others.
☐Model with mathematics.
☐Use appropriate tools
strategically.
☐Attend to precision.
☐Look for and make use of
Transition:
Inform students that they will use the information learned to develop a poster structure.
to predict the outcomes of selected events.
☐Look for and express
regularity in repeated
reasoning.
Page 9 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model
is not linear.
☐Engagement
☐Exploration
☐Explanation
☐Extension
☒Evaluation
Details
Materials:
 PowerPoint slide 13
 Poster Rubric
 Newsprint or other large paper
 Markers or colored pencils
Preparation:
 Students will need space to create their poster and to display it in the
classroom or hallway. Limit the amount of time that students have to
create the poster so the emphasis is placed on quality not quantity of
information. The instructor may want to project the required items of
the poster on a document camera or projector to remind students
what should be included on the poster.
 Students will need access to data via the internet or handouts.
Arrange for students to have access to computers with internet to
conduct research or provide students data that they can use.
Standards for
Mathematical Practice
☐Make sense of problems
and persevere in solving
them.
☒Reason abstractly and
quantitatively.
☐Construct viable
arguments and critique
the reasoning of others.
☒Model with mathematics.
☐Use appropriate tools
strategically.
☐Attend to precision.
Facilitation of Learning Experience:
1. Inform students that they will work in teams of three – four to create a
poster that predicts the outcome of certain events. Students can selfselect a topic or the teacher can provide students a list of topics to
choose from. Suggested topics include
 Number of accidents caused by texting
 Number of students who pass the Algebra 1 High School
Assessment in Baltimore County
 Obesity rates in Maryland
 Number of students who graduate from high school in
Maryland
☒Look for and make use of
structure.
☐Look for and express
regularity in repeated
reasoning.
Page 10 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Learning Experience
5E Component
Identify the 5E component
addressed for the learning
experience. The 5E model
is not linear.
Details
Standards for
Mathematical Practice
2. Project slide 13 and review poster components.
3. Provide each student with a copy of the rubric student teams will selfassess their poster before submitting for a grade.
Page 11 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Interventions/Enrichments
Identify interventions and enrichments for
diverse learners.
Supporting Information
Struggling Learners
 Create a graph with the x and y axis labeled.
 Provide students with the calculator notes as a guide on how to find the
line of regression.
 Instructors can create teams based upon ability, learning style, or other
appropriate criteria, so all students can equally contribute to the
development and creation of their poster.
 Specific deadlines for work completion would be important to establish
with the teams, so class time is effectively used.
 Provide access to computers with word-processing programs for students
to type their research and/or poster.
 Provide resources to define and/or pronounce difficult vocabulary.
 Break work into chunks for teams, so they are able to achieve small goals
and meet all expectations.
 Provide additional time for work completion or assign some parts of the
assignment for homework.
English Language Learners
 Strategies to help English Language Learners are similar to those listed
above.
 Provide resources to define and/or pronounce difficult vocabulary. A
native language dictionary may also be beneficial.
 Use visuals (pictures displayed on a document camera or PowerPoint
presentation), when appropriate.
 Read directions and documents aloud to students, when appropriate.
Gifted and Talented
 Provide students with the following questions to answer:
o How can anyone be certain on how accurate their equation is?
o Is there another mathematical formula to use to find the strength of the
linear regression equation?
 The instructor will foster independent thinking and collaboration between
the partners. No one student should take over the work for the
Page 12 of 23
STEM-Centric Unit
Predicting the Ravens’ Touchdowns
Supporting Information
partnership.
 Higher level thinking questions should be asked throughout the lesson
with the expectation of responses that are thoughtful and elaborate.
 Encourage students to develop discussion questions for the STEM
Specialist presentation.
Page 13 of 23
Name:
THE RIGHT INCOMES
Directions: Guess the average yearly income of each person. Your teacher will provide you
with their actual income. Create a scatter plot of the data points using Guess the Income as
the x-axis and the Actual Income as the y-axis. Answer the questions below.
Name
Guess the
Income
(millions)
Actual
Income
(millions)
The Right Income
Jay-Z
LeBron
James
Oprah
Winfrey
Angelina
Jolie
Eli
Manning
Britney
Spears
President
Obama
Actual Income (millions)
Lady
Gaga
Guess the Income (millions)
1. Identify the type of correlation your graph represents. Justify your answer.
2. Draw a line of best fit for the data.
3. Calculate the slope and y-intercept for the line of best fit. Show your work below.
THE RIGHT INCOME ANSWER KEY
Student answers will vary. 2012 salaries retrieved from paywizard.org.
Name
Guess the Income
(millions)
Actual Income (millions)
Lady Gaga
52
Jay-Z
40
LeBron James
19.7
Oprah Winfrey
315
Angelina Jolie
33
Eli Manning
Britney Spears
President Obama
1.75
58
2.65
1. Identify the type of correlation your graph represents. Justify your answer.
-
Answers may vary
2. Draw a line of best fit for the data.
3. Calculate the slope and y-intercept for the line of best fit. Show your work below.
Name:
Predicting Baltimore Ravens Touchdowns
Year
Number of
Touchdowns
2002
36
2003
41
2004
33
2005
25
2006
38
2007
27
2008
42
2009
47
2010
47
2011
41
2012
44
1. Create a scatterplot and draw the line of best fit for the Raven’s Touchdown data.
2. Determine the linear regression equation for the data.
3. What does the slope mean in the context of the problem?
4. Based on the linear regression equation, how many touchdowns should the Ravens
score in the 2013 season?
Predicting Baltimore Ravens Touchdowns KEY
Year
Number of
Touchdowns
2002
36
2003
41
2004
33
2005
25
2006
38
2007
27
2008
42
2009
47
2010
47
2011
41
2012
44
The Red line is your Line of Best Fit and the green line is the line connected based on the data
provided.
1. Create a scatterplot and draw the line of best fit for the Raven’s Touchdown data.
2. Determine the linear regression equation for the data.
Y = 1.18x – 2333.64
3. What does the slope mean in the context of the problem?
Slope is 1.18 – Each year the Ravens score an additional 1.18 touchdown
4. Based on the linear regression equation, how many touchdowns should the Ravens
score in the 2013 season?
Y = 1.18 (2013) – 2333.64
Y = 41.7
About 41.7 touchdowns should be scored in 2013
Name:
Classwork
Problem 1:
Fast Food and Calories
Fat (g)
0
9
13
21
30
36
42
Calories
0
30
72
100
164
166
208
1. Using a calculator, find the slope and explain it meaning in the context of the problem.
2. If a burger has 40 grams of fat, how many calories will it have?
Problem 2:
Height
(in)
67
70
73.5
75
78
Shoe
Size
8.5
9.5
11
12
13
3. Using a calculator, determine the equation of linear regression.
4. If a person is 82in in height, what is his/her shoe size?
5. If a person has a 10.5 shoe size, how tall would he/she be?
Name:
Classwork KEY
Problem 1:
Fast Food and Calories
Fat (g)
0
9
13
21
30
36
42
Calories
0
30
72
100
164
166
208
1. Using a calculator, find the slope and explain it meaning in the context of the problem.
Slope is 4.62 – For each gram of fat there are 4.62 calories
2. If a burger has 40 grams of fat, how many calories will it have?
Y = 4.62x +14.64
Y = 4.62(40) +14.64
Y = 199.44 calories
Problem 2:
Height
(in)
67
70
73.5
75
78
Shoe
Size
8.5
9.5
11
12
13
3. Using a calculator, determine the equation of linear regression.
Y = 0.42x – 19.93
4. If a person is 82in in height, what is his/her shoe size?
Y = 0.42 (82) – 19.93
Y = 14.51
Size 14 and a half
5. If a person has a 10.5 shoe size, how tall would he/she be?
10.5 = 0.42x – 19.93
30.43 = 0.42x
Add 19.93 to both sides
72.45 = x
Divide both sides by 0.42
72.5 inches
Name:
Linear Regression Poster Rubric
Earned Assessment
1
Points
Title
Question
Data
Graph
2
3
There is no title
A weak title is
provided
Title clearly states
the meaning of the
problem
There is no
question
A vague questions is
asked
An in-depth
question is asked
with clear details
There is no data
Data is provided
without any clear
organization
Data is clearly
organized and
provided easy for
anyone to read
There is no graph
Line of Best
Fit
The line of best fit
is not calculated by
hand or by
calculator
Prediction
There is no
prediction made
Teacher Comments:
A graph is provided,
however there are
no labels and/or a
line of best fit is not
(or incorrectly)
drawn
The line of best is
written down(or
incorrectly
calculated) without
the proper steps
A prediction is
calculated (or
incorrectly
calculated) with
little or no
explanation
A graph is provided
with all the proper
labels and a line of
best is correctly
drawn
The line of best fit
is neatly written
displaying the
proper steps in
order
A clear prediction
is calculated with a
brief analysis.
Self
Teacher