Mathematics Education Students and Faculty
Wake Forest University
North Carolina Council of Teachers of Mathematics Annual Meeting
Greensboro, NC
October 28, 2010
Wall Street Tycoon ‐ Brian Smith
Big League Salary ‐ Lauren Redman and Phil Brame
Eggcellent! ‐ Heidi Arnold and Cayce Poindexter
The Math of the Miners ‐ Chloe Johnson and Jacob Perry
Hurricane Havoc ‐ Jill Klinepeter and Lauren Schnepper
Questions or Comments
Dr. Leah McCoy: [email protected]
NCCTM 2010
1
Math in the News
NCCTM 2010
Wall Street Tycoon
Brian Smith
Wake Forest University
Introduction: Stock prices appear in the newspaper and scroll across the bottoms of our
television screens every day. Occasionally they make front page headlines, and other days they
are just a bunch of numbers printed on a page. In either case, almost all students have had some
type of exposure to the stock market. This activity will help students not only learn how to apply
and calculate percent change, but also make sense of numbers they will seefor the rest of their
lives. This activity is presented in two different forms. The first option is meant to take up one,
45-minute class period and the other is a series of 5 to 10 minute warm-ups over the course of six
school days.
Course: Algebra I.
Materials: Worksheet, document camera, dice, coins and computers/newspapers.
NCTM Standards: Algebra, Communication, Connections, Representation, Problem Solving
NCSCOS: Algebra 1 – 1.02 Use formulas and algebraic expressions, including iterative and
recursive forms, to model and solve problems
21st Century Skills: Financial, economic, business and entrepreneurial literacy. Communication
and Collaboration. Life and Career Skills
Objectives:
1. Students will be able to apply percent increases/decreases given a starting value and a percent.
2. Students will be able to find percent increases/decreases.
Activities:
 One day option
o As a weekend homework assignment, have students bring in a stock price from a
newspaper or the internet
 Students will need to bring in the company name, stock symbol and stock
price
 Encourage students to bring an entire section of the newspaper to class
 Have some stocks prepared in case students do not do this
 Show students Google Finance and how they can look up stock prices
there
o Using the attached worksheet, simulate a week’s worth of stock activity in the
following manner
 Split groups up into groups of 3 or 4
Math in the News
NCCTM 2010


Each group will be assigned a real-life stock with Monday’s actual closing
price
 Students will roll the dice
 For each day, each group will roll a die and flip a coin to see whether the
number they rolled will be an increase or decrease (heads increase, tails
decrease)
 The stock will increase or decrease the number rolled on the die
 Check that the previous day’s calculations are correct before you flip the
coin for each group
 Repeat this process for the entire week.
 Calculate their percent change for the entire week
o Each group will present their results for the week for a grade orally and in writing
(in order to receive credit, you must share at least some part of your group’s data)
One week option
o Same weekend homework assignment from one week option
o Split students up into groups to decide which stock in which they are going to
invest
o Once each group has decided on their stock, let each group know that part of their
homework for the next night is to look up the percent change for their stock for
Monday on the internet or in a newspaper
 Have the whole group find the stock which will be a good check to see if
the students’ are finding the correct numbers
 Just in case, know all of the groups stocks and have the percent’s ready
each morning
o Every morning, starting with Tuesday, have the groups find yesterday’s closing
price as a warm-up
 Each group must turn in a short write-up of how their stock did the
previous day and the new price of the stock
 Since each group has three or four people, a different student should do
the write up each day
 Provide an example for the students on Tuesday using a stock of your
choice
o On the following Monday morning, have the students bring in their stock’s
percent change from Friday
 In addition to finding Friday’s closing price, have the student’s calculate
their stock’s percent change for the week
 Show an example of this with your stock
o Once the students have done this, have each group present their stock’s
performance from last week
 Have the groups explain each day before giving a summary for the week
o After the presentations, have the class vote on what stock they would invest in,
based on last week’s performance
Assessment: Daily write-ups on the group’s stock and final presentation. Make sure that
students do not simply read chart out loud but provide reasons for their findings and make sense
of their calculations.
Math in the News
NCCTM 2010
Wall Street Tycoon
Day of the week
Stock Value
Yesterday
Percent Change from
Yesterday
Final Price for the
Day
Monday’s Price
Friday’s Price
Percent Change for
the week
Monday
Tuesday
Wednesday
Thursday
Friday
Change for the week
Math in the News
NCCTM 2010
Wall Street Tycoon
Example: Merck (MRK)
Day of the week
Stock Value
Yesterday
Percent Change from
Yesterday
Final Price for the
Day
Monday
N/A
N/A
36.52
Tuesday
36.52
+3%
37.62
Wednesday
37.62
-2%
36.87
Thursday
36.87
+1%
37.24
Friday
37.24
+6%
39.47
Monday’s Price
Friday’s Price
Percent Change for
the week
36.52
39.47
8.1%
Change for the week
Math in the News
NCCTM 2010
Wall Street Tycoon
Example: Merck (MRK) Daily Reports
Tuesday: Merck’s stock rose by three percent on Tuesday from 36.52 per share to 37.62 per
share.
Wednesday: On Wednesday, Merck’s stock fell by two percent from 37.62 a share to 36.87 a
share.
Thursday: Merck edged forward one percent moving from 36 dollars and 87 cents a share to 37
dollars and 24 cents a share.
Friday: Merck had a huge trading day on Friday jumping 6 percent from 37.24 per share to
39.47 per share.
Weekly Summary: Merck had a very successful week on Wall Street as its shareholders earned
8.1 percent. The value of its shares rose from 36 dollars and 52 cents a share to 39 dollars and 47
cents a share.
Math in the News
NCCTM 2010
Big League Salary
Lauren Redman and Phil Brame
Wake Forest University
Introduction: Every year, professional athletes’ salaries increase and every year these
increases bring up conversations about salary caps and in Major League Baseball.
Recently, USA Today created a website that contains information about each Major
League team, its team payroll, and the salaries of the 25 highest paid players for the
last 22 years.
Materials: Computers with Internet Access and Excel (or Graphing Calculators),
Worksheet
Objective: To apply models of best fit to real-world data.
NCSCOS: Algebra II: 2.04 Create and use best-fit mathematical models of linear,
exponential, and quadratic functions to solve problems involving sets of data.
NCTM Standards: Problem Solving, Communication, Multiple Representations
21st Century Skills: Core Subject, Critical Thinking, Communication, Collaboration,
Technology Skills, Life and Career Skills
Activities:
Provide background on data and introduce worksheet.
Have students work in small groups stopping to discuss conclusions from each part with
the entire class.
*Most of the data is provided in tables on the worksheet for convenience and time
considerations. If more time and computers are available, the worksheet without data
filled in can be used and students can find the data themselves using this website:
http://content.usatoday.com/sports/baseball/salaries/default.aspx.
Part I: Students analyze data from a graph displaying the most expensive player’s
salary since 1990 and make predictions about the most expensive player’s salary in
2020 as the beginning step in using trendlines without actually finding the line of best fit.
They will also compare the “cost per home run” of the four Yankee players with the most
homeruns this season. This comparison can be used as part of the justification in Part
IV.
Math in the News
NCCTM 2010
Part II: Similar to Part I, but this time students will predict the most expensive team
payroll in 2015; students will then construct a scatter plot from a table of data containing
the most expensive team payroll since 1990 using Excel or graphing calculators if
computers with Excel are not available. From the scatter plot, students will choose a line
of best fit and use it to check their previous prediction.
Part III: Students construct another scatter plot comparing total payroll to wins in 2010,
describe the relationship, and then make a conclusion related to the data.
Part IV: Culmination of the previous three parts where students use results from the
other parts to justify why the MLB should or should not institute a salary cap. Groups
should construct their arguments to briefly present to the class. All members should be
encouraged to participate in the presentation since the group’s argument should include
at least one point for each person to explain.
*Additional information for Part IV: MLB has 9 different World Series champions
for the last 10 seasons including this season. The teams that made the playoffs
this year ranked 1st, 4th, 10th, 11th, 15th, 19th, 21st, and 27th in total payroll.
Assessment:
Groups will turn in their worksheets and each group will present, to the class, its final
conclusion of whether a salary cap should be imposed on the league.
Big League Salary
Name: _____________________________
Part I: Most Expensive Individual Player Salary
$35,000,000
$30,000,000
$25,000,000
$20,000,000
$15,000,000
$10,000,000
$5,000,000
$0
1990
1995
2000
2005
2010
1. In which 5 year period did the salary of the highest paid player increase the most? _______________________
_________________________________________________________________________________________
2. How much do you think the salary of the most expensive player in 2020 will be? ________________________
_________________________________________________________________________________________
3. In 2010, Alex Rodriguez was the highest paid player in baseball with a salary of $33 million. Use the statistics
at http://espn.go.com/mlb/team/stats/batting/_/name/nyy/seasontype/2/new-york-yankees to determine the
“cost” of each of his homeruns in the 2010 season. ________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
4. Compare Rodriguez’s cost per home run to 3 of his Yankee teammates: Robinson Cano, Mark Teixeira, and
Nick Swisher using the Statistics from ESPN.com and the USA Today Salary Database: http://
content.usatoday.com/sports/baseball/salaries/teamdetail.aspx?year=2010&team=9&loc=interstitialskip
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
1
Part II: Most/Least Expensive Team Payroll
$250,000,000
$200,000,000
Most
Expensive
Team
$150,000,000
Least
Expensive
Team
$100,000,000
$50,000,000
$0
1990
1995
2000
2005
2010
5. In 1995, the most expensive team cost about four times as much as the least expensive team. Use the graph
to determine the ratio of the most and least expensive teams in 2010. ________________________________
_______________________________________________________________________________________
6. If the current pattern continues, estimate the cost of the most expensive team in baseball for the 2015 season.
Justify your answer. ______________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
7. Use the data to the right to construct a scatter plot in Excel of the most expensive team in baseball. Find the line of best fit and use it to check your guess
from #6. Is a linear model realistic for predicting team payroll?
Explain. _________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
2
Year
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Total Payroll
$23,873,745
$33,632,500
$44,352,002
$45,747,666
$44,785,334
$49,791,500
$52,189,370
$59,148,877
$70,408,134
$88,130,709
$92,938,260
$112,287,143
$125,928,583
$152,749,814
$184,193,950
$208,306,817
$194,663,079
$189,639,045
$209,081,577
$201,449,189
$206,333,389
Part III: Team Payroll vs. Wins in 2010
Team
NYY
BOS
CHC
PHI
NYM
DET
CHW
LAA
SF
MIN
LAD
STL
HOU
SEA
ATL
COL
BAL
MIL
TAM
CIN
KC
TOR
WAS
CLE
ARI
FLA
TEX
OAK
SD
PIT
Payroll
$206,333,389
$162,447,333
$146,609,000
$141,928,379
$134,422,942
$122,864,928
$105,530,000
$104,963,866
$98,641,333
$97,599,166
$95,358,016
$93,540,751
$92,355,500
$86,510,000
$84,423,666
$84,227,000
$81,612,500
$81,108,278
$71,923,471
$71,761,542
$71,405,210
$62,234,000
$61,400,000
$61,203,966
$60,718,166
$57,034,719
$55,250,544
$51,654,900
$37,799,300
$34,943,000
Wins
95
89
75
97
79
81
88
80
92
94
80
86
76
61
91
83
66
77
96
91
67
85
69
69
65
80
90
81
90
57
8. Using the data to the left and Excel, construct a scatter plot comparing a team’s payroll to its wins. Sketch below.
9. Describe the relationship between wins and payroll in your scatterplot. _________________________________________________
_____________________________________________________
_____________________________________________________
10. In this data set, several teams had a lower payroll and a high number of wins, or a higher payroll and a low number of wins. Name
at least two reasons why a team could outperform or underperform
its payroll. (Hint: Consider factors such as the age and health of
the team’s roster) ______________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Part IV: Conclusions
Unlike other professional sports leagues, Major League Baseball does not have a salary cap, which limits the
amount of money a single team can spend on player salaries. Use the data from Parts I, II, and III to explain why
baseball would or would not benefit from a salary cap.
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
3
Big League Salary
Name: _____________________________
Part I: Most Expensive Individual Player Salary
$35,000,000
$30,000,000
$25,000,000
$20,000,000
$15,000,000
$10,000,000
$5,000,000
$0
1990
1995
2000
2005
2010
Plot on the graph the most expensive player’s salary from 1990 to 2010.
1. In which 5 year period did the salary of the highest paid player increase the most? ______________________
_________________________________________________________________________________________
2. How much do you think the salary of the most expensive player in 2020 will be? ________________________
_________________________________________________________________________________________
3. In 2010, Alex Rodriguez was the highest paid player in baseball with a salary of $33 million. Use the statistics
at http://espn.go.com/mlb/team/stats/batting/_/name/nyy/seasontype/2/new-york-yankees to determine the
“cost” of each of his homeruns in the 2010 season. ________________________________________________
_________________________________________________________________________________________
4. Compare Rodriguez’s cost per home run to 3 of his Yankee teammates: Robinson Cano, Mark Teixeira, and
Nick Swisher using the Statistics from ESPN.com and the USA Today Salary Database: http://
content.usatoday.com/sports/baseball/salaries/teamdetail.aspx?year=2010&team=9&loc=interstitialskip
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
_________________________________________________________________________________________
1
Part II: Most/Least Expensive Team Payroll
$250,000,000
$200,000,000
Most
Expensive
Team
$150,000,000
Least
Expensive
Team
$100,000,000
$50,000,000
$0
1990
1995
2000
2005
2010
Plot on the graph the most and least expensive team payrolls since 1990.
5. As you can see, in 1995, the most expensive team cost about four times as much as the least expensive team,
determine the ratio of the most and least expensive teams in 2010. ________________________________
6. If the current pattern continues, estimate the cost of the most expensive team in baseball for the 2015 season.
Justify your answer. ______________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
7. Fill in the table to the right with the most expensive team payroll since 1990 and
construct a scatter plot in Excel. Find the line of best fit and use it to check your
guess from #6. Is a linear model realistic for predicting team payroll?
Explain. _________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
2
Year
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Total Payroll
Part III: Team Payroll vs. Wins in 2010
Team
NYY
BOS
CHC
PHI
NYM
DET
CHW
LAA
SF
MIN
LAD
STL
HOU
SEA
ATL
COL
BAL
MIL
TAM
CIN
KC
TOR
WAS
CLE
ARI
FLA
TEX
OAK
SD
PIT
Payroll
Wins
95
89
75
97
79
81
88
80
92
94
80
86
76
61
91
83
66
77
96
91
67
85
69
69
65
80
90
81
90
57
8. Fill in the total payroll for each team in the table to the left and in
Excel, construct a scatter plot comparing a team’s payroll to its
wins. Sketch below.
9. Describe the relationship between wins and payroll in your scatterplot. _________________________________________________
_____________________________________________________
_____________________________________________________
10. In this data set, several teams had a lower payroll and a high number of wins, or a higher payroll and a low number of wins. Name
at least two reasons why a team could outperform or underperform
its payroll. (Hint: Consider factors such as the age and health of
the team’s roster) ______________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Part IV: Conclusions
Unlike other professional sports leagues, Major League Baseball does not have a salary cap, which limits the
amount of money a single team can spend on player salaries. Use the data from Parts I, II, and III to explain why
baseball would or would not benefit from a salary cap.
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
3
Big League Salary
Name: _____________________________
Part I: Most Expensive Individual Player Salary
$35,000,000
$30,000,000
$25,000,000
$20,000,000
$15,000,000
$10,000,000
$5,000,000
$0
1990
1995
2000
2005
2010
1. In which 5 year period did the salary of the highest paid player increase the most? __2000-2005____________
_________________________________________________________________________________________
2. How much do you think the salary of the most expensive player in 2020 will be? __~$50,000,000__________
_________________________________________________________________________________________
3. In 2010, Alex Rodriguez was the highest paid player in baseball with a salary of $33 million. Use the statistics
at http://espn.go.com/mlb/team/stats/batting/_/name/nyy/seasontype/2/new-york-yankees to determine the
“cost” of each of his homeruns in the 2010 season. __~$1,100,000 (30 homeruns)_______________________
_________________________________________________________________________________________
_________________________________________________________________________________________
4. Compare Rodriguez’s cost per home run to 3 of his Yankee teammates: Robinson Cano, Mark Teixeira, and
Nick Swisher using the Statistics from ESPN.com and the USA Today Salary Database: http://
content.usatoday.com/sports/baseball/salaries/teamdetail.aspx?year=2010&team=9&loc=interstitialskip
___Cano: 29 homeruns, $9,000,000 salary, ~$310,350/hr__________________________________________
___Teixeira: 33 homeruns, $20,625,000 salary, ~$625,000/hr_______________________________________
___Swisher: 29 homeruns, $6,850,000 salary, ~$236,210/hr________________________________________
1
Part II: Most/Least Expensive Team Payroll
$250,000,000
$200,000,000
Most
Expensive
Team
$150,000,000
Least
Expensive
Team
$100,000,000
$50,000,000
$0
1990
1995
2000
2005
2010
5. In 1995, the most expensive team cost about four times as much as the least expensive team. Use the graph
to determine the ratio of the most and least expensive teams in 2010. __~5:1_________________________
_______________________________________________________________________________________
6. If the current pattern continues, estimate the cost of the most expensive team in baseball for the 2015 season.
Justify your answer. __~$210,000,000________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
7. Use the data to the right to construct a scatter plot in Excel of the most expensive team in baseball. Find the line of best fit and use it to check your guess
from #6. Is a linear model realistic for predicting team payroll?
Explain. ___Linear: y = 10,773,875.86x - 21,433,959,782.19; R² = 0.93__________
___Exponential: y = 5.46571E-89e0.110784212x; R² = 0.95 _______________________
_________________________________________________________________
Most Expensive Team
$300,000,000
$250,000,000
$200,000,000
Most
Expensive
Team
$150,000,000
$100,000,000
$50,000,000
2
$0
1990
1995
2000
2005
2010
2015
Year
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Total Payroll
$23,873,745
$33,632,500
$44,352,002
$45,747,666
$44,785,334
$49,791,500
$52,189,370
$59,148,877
$70,408,134
$88,130,709
$92,938,260
$112,287,143
$125,928,583
$152,749,814
$184,193,950
$208,306,817
$194,663,079
$189,639,045
$209,081,577
$201,449,189
$206,333,389
Part III: Team Payroll vs. Wins in 2010
Team
NYY
BOS
CHC
PHI
NYM
DET
CHW
LAA
SF
MIN
LAD
STL
HOU
SEA
ATL
COL
BAL
MIL
TAM
CIN
KC
TOR
WAS
CLE
ARI
FLA
TEX
OAK
SD
PIT
Payroll
$206,333,389
$162,447,333
$146,609,000
$141,928,379
$134,422,942
$122,864,928
$105,530,000
$104,963,866
$98,641,333
$97,599,166
$95,358,016
$93,540,751
$92,355,500
$86,510,000
$84,423,666
$84,227,000
$81,612,500
$81,108,278
$71,923,471
$71,761,542
$71,405,210
$62,234,000
$61,400,000
$61,203,966
$60,718,166
$57,034,719
$55,250,544
$51,654,900
$37,799,300
$34,943,000
Wins
95
89
75
97
79
81
88
80
92
94
80
86
76
61
91
83
66
77
96
91
67
85
69
69
65
80
90
81
90
57
8. Using the data to the left and Excel, construct a scatter plot comparing a team’s payroll to its wins. Sketch below.
Payroll vs. Wins
100
95
90
85
80
75
70
65
60
55
$45,000,000
$95,000,000
$145,000,000
$195,000,000
9. Describe the relationship between wins and payroll in your scatterplot. __No correlation/slight positive_______________________
_____________________________________________________
_____________________________________________________
10. In this data set, several teams had a lower payroll and a high number of wins, or a higher payroll and a low number of wins. Name
at least two reasons why a team could outperform or underperform
its payroll. (Hint: Consider factors such as the age and health of
the team’s roster) ______________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
Part IV: Conclusions
Unlike other professional sports leagues, Major League Baseball does not have a salary cap, which limits the
amount of money a single team can spend on player salaries. Use the data from Parts I, II, and III to explain why
baseball would or would not benefit from a salary cap.
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
_____________________________________________________________________________________________
3
Math in the News
NCCTM 2010
Percent of Change
Heidi Arnold & Cayce Poindexter
Wake Forest University
Objectives:
 Calculate percent of change.
 Interpret graphical representation of data.
Standards:
 North Carolina Standard Course of Study (Algebra I):
o 1.02 Use formulas and algebraic expressions, including iterative and recursive forms, to
model and solve problems.
 NCTM Standards:
o Number and Operations, Date Analysis and Probability, and Algebra
st
 21 Century Skills:
o Core Subjects and 21st Century Themes: Global Awareness and Health Literacy
o Learning and Innovative Skills: Critical Thinking and Problem Solving
o Information, Media, and Technology Skills: Information Literacy and Media Literacy
o Life and Career Skills
Materials:
 Egg Recall Warm‐Up
 Reported Illnesses: Percent of Change In Class Activity
 Moe s Grocery Activity
Activities:
 Egg Recall Warm‐Up
o Reviews their knowledge of percentages
o Introduce them into the egg recall
o Includes collected data from internet resources about
 Julian Date 001 is January 1st and 365 is December 31st
 Amount of eggs recalled
 Number of states with recalled egg producing farms
 Interesting facts about the recall that could be shared are included below.
 Reported Illnesses: Percent of Change
o Students practice estimating and calculating percent of change
o Students explore what it means to have 100% increase
o Includes an algebraic and graphical representation of percent of change
o Requires students to give written explanations of their answers
Math in the News
NCCTM 2010
Assessments:
 Moe s Grocery
o Combines percent increase and decrease
o Incorporates a real world situation where students have to use their knowledge of
percent of change to calculate prices at a grocery store
 Calculate percent of change between sale items
 Make financial decisions resulting in the best savings
 Discover another meaning for buy one get one free
o Teachers could also use a grocery circular from a local grocery store to make activity
more authentic
Interesting Facts about the Egg Recall:
 Much of the investigation so far has been centered on restaurants in California, Colorado,
Minnesota and North Carolina. They are not necessarily breakfast places ‐‐ it's possible some got
sick from eating a salad dressing that had a raw egg in it, or eating soup with an undercooked
egg dropped in, Braden said. In North Carolina, a cluster of about 80 illnesses in April were
linked to meringue‐containing chocolate pie and banana pudding served at a Durham barbecue
restaurant, health officials said.
o http://www.huffingtonpost.com/2010/08/19/wright‐county‐egg‐recall‐2010‐
salmonella_n_684995.html
 Wright County Egg, a Galt, Iowa egg company has issued a voluntary 2010 egg recall on thirteen
brands of their eggs due to an incident that was reported concerning salmonella poisoning. (The
interesting fact is that the egg recalls were voluntary by the egg companies and not mandated
by the FDA).
o http://www.huliq.com/10017/salmonella‐poisoning‐leads‐2010‐egg‐recall
 Shell eggs are by far the most common source of Salmonella Enteritidis illness in the U.S. Of the
47 billion shell eggs Americans eat as table eggs each year, the USDA estimates that 2.3 million
are contaminated with this salmonella strain.
o http://www.webmd.com/food‐recipes/food‐poisoning/news/20100819/egg‐recall‐
expands‐cdc‐expects‐more‐illnesses
Additional Resources:
 Venn Diagram
o Students are asked to find parts of data
o Ways of contamination
 Rodents
 Contaminated Hens
 Tainted Feed
o Symptoms of Salmonella
 Cramps
 Fever
 Vomiting
 Introduces parts of wholes which leads to percentages
Name:____________________________ Date:_______ Period:____
Egg Recall Warm Up
Solve these Algebra problems to learn more about the egg
recall of the summer of 2010.
1. A Julian Date is the date that is expressed as a number. The Julian date on egg cartons refers
to the date that the eggs were packed. The Julian Date 001 corresponds to January 1st and
365 corresponds to December 31st.
If the egg recall dates are 136 through 225, what day and month did the recall start and end on?
How many days did the egg recall last?
What percentage of the year were eggs recalled?
2. According to the American Egg Board, hens lay approximately 5 eggs per week. Wright
County Egg and Hillandale Farms have almost 8 million hens combined. Assume the two egg
products have approximately 7.8 million hens combined. Between the two egg producers,
more than half a billion eggs were recalled. Assume that 501,000,000 eggs are recalled.
How many eggs will Wright County Egg and Hillandale Farms produce annually?
What percentage of the egg producers annual egg production was recalled?
http://www.msnbc.msn.com/id/38741401/ns/health‐food_safety
http://www.huffingtonpost.com/andrew‐gunther/food‐safety‐we‐need‐more‐_b_705969.html
http://www.seedsnc.org/YAWYE.htm#Answers
Name:____________________________ Date:_______ Period:____
3. Fourteen states sold eggs from Hillandale Farms, one of the egg producers affected by the re‐
call. What percentage of states did not have eggs recalled from Hillandale Farms?
4. If 1,854 illnesses were linked to the recalls between May and July, on average, how many ill‐
nesses occurred each day?
5. According to SEEDS (South Eastern Efforts Developing Sustainable Spaces, Inc.), the average
American eats 254 eggs each year.
How many eggs does the average American eat per month? (Round your answer to the nearest
whole number.)
How many eggs does the average American eat per week? (Round your answer to the nearest
whole number.)
http://www.msnbc.msn.com/id/38741401/ns/health‐food_safety
http://www.huffingtonpost.com/andrew‐gunther/food‐safety‐we‐need‐more‐_b_705969.html
http://www.seedsnc.org/YAWYE.htm#Answers
Solve these Algebra problems to learn more
about the egg recall of the summer of 2010.
ANSWER KEY
1. A Julian Date is the date that is expressed as a number. The Julian date on egg cartons refers
to the date that the eggs were packed. The Julian Date 001 corresponds to January 1st and
365 corresponds to December 31st.
If the egg recall dates are 136 through 225, what day and month did the recall start and end on?
It started on May 16th and ended on August 13th (May 15th and August 12th if they considered a
leap year)
How many days did the egg recall last?
It lasted 89 days
What percentage of the year were eggs recalled?
89/365 = 24.38% of the year
2. According to the American Egg Board, hens lay approximately 5 eggs per week. Wright
County Egg and Hillandale Farms have almost 8 million hens combined. Between the two egg
producers, more than half a billion eggs were recalled. Assume that 501,000,000 eggs are re‐
called.
How many eggs will Wright County Egg and Hillandale Farms produce annually?
2,028,000,000 eggs annually
What percentage of the egg producers annual egg production was recalled?
24.7%
http://www.msnbc.msn.com/id/38741401/ns/health‐food_safety
http://www.huffingtonpost.com/andrew‐gunther/food‐safety‐we‐need‐more‐_b_705969.html
http://www.seedsnc.org/YAWYE.htm#Answers
ANSWER KEY
3. Fourteen states sold eggs from Hillandale Farms, one of the egg producers affected by the re‐
call. What percentage of states did not have eggs recalled from Hillandale Farms?
(50‐14)/50 ≈ 72%
4. If 1,854 illnesses were linked to the recalls between May and July, on average, how many ill‐
nesses occurred each day?
1854 illnesses/92 days ≈ 20 illnesses/day
5. According to SEEDS (South Eastern Efforts Developing Sustainable Spaces, Inc.), the average
American eats 254 eggs each year.
How many eggs does the average American eat per month? (Round your answer to the nearest
whole number.)
254 eggs/12 months ≈ 21 eggs/month
How many eggs does the average American eat per week? (Round your answer to the nearest
whole number.)
254 eggs/52 weeks ≈ 5 eggs/week
http://www.msnbc.msn.com/id/38741401/ns/health‐food_safety
http://www.huffingtonpost.com/andrew‐gunther/food‐safety‐we‐need‐more‐_b_705969.html
http://www.seedsnc.org/YAWYE.htm#Answers
Reported Illnesses: Percent of Change
Name __________________________________
Use the graph to answer
the following questions.
You will have to
approximate the amount of
reported illnesses each
month.
1. Find the percent of change from the 1st week of June to the 4th week of June. Is it a percent of increase or
decrease?
2. Find the percent of change from the 3rd week of June to the 2nd week in July. Is it a percent of increase or
decrease?
3. Find the percent of change from the 1st week of the year to the week that has the most reported illnesses.
Is it a percent increase or decrease?
What do you notice about this percent of change? What does it mean?
4. Find two months that have a percent increase of approximately 100%. Explain what this means about the
relationship between the two months reported illnesses?
5. Explain what it means to have a percent of increase.
6. Explain what it means to have a percent of decrease.
http://www.cdc.gov/salmonella/enteritidis/index.html
Reported Illnesses: Percent of Change
Name __________________________________
ANSWER KEY
Use the graph to answer
the following questions.
You will have to
approximate the amount of
reported illnesses each
month.
1. Find the percent of change from the 1st week of June to the 4th week of June. Is it a percent of increase or
decrease?
(205‐135)/135 = 51.85% ≈ 52%
increase
2. Find the percent of change from the 3rd week of June to the 2nd week in July. Is it a percent of increase or
decrease?
(220‐155)/220 = 29.54% ≈ 30%
decrease
3. Find the percent of change from the 1st week of the year to the week that has the most reported illnesses.
Is it a percent increase or decrease?
(225‐48)/48 = 368.75% ≈ 368%
increase
What do you notice about this percent of change? Compare the reported illnesses for each week and
explain what this means?
The percent of increase was more than 100%. The original amount grew almost 4.5 times as much. The
bar for he week with the most reported is almost 4.5 times as high as the 1st week of the year.
4. Find two months that have a percent increase of approximately 100%. Explain what this means about the
relationship between the two months reported illnesses?
4th week in January
> 1st week in May: (100‐50)/50 = 100% (answers will vary)
The original amount doubled during this time. The bar for 1st week in May is twice as high as the bar for the
4th week in January.
5. Explain what it means to have a percent of increase.
The original amount increased by a percent of that original number.
6. Explain what it means to have a percent of decrease.
The original amount decreased by a percent of that original number.
http://www.cdc.gov/salmonella/enteritidis/index.html
Name:____________________________ Date:_______ Period:____
Use the grocery circular below to calculate the cost of
food for the following questions. Percentage of
change will be integral in your calculations. Round
answers to the nearest hundredth.
Was: $1.39
20% off of $3.45
$1.88
Sale Price: 99₵
Was: 79₵/lb.
2 for $1
10% off of $3.99
$1.99
99₵ Each
Sale Price: 59₵/lb.
$2.99/lb.
Name:____________________________ Date:_______ Period:____
1. Find the percentage change between the old price and the sale price of the eggs and
the bananas. Which percentage change is greater?
2. The bread and the cheese are on sale this week at Moe s Grocery. Find the price for
exact price for each item. What is the percentage of change for each item?
3. You have a coupon for 50 cents off of a jar of jam. What is the percentage of change
between the original price and the price you will pay per jar by using the coupon?
4. While you are shopping, the store manager of Moe s Grocery announces that milk is
now on sale for 1 dollar. Find the percentage of change between the original price and
the sales price.
Name:____________________________ Date:_______ Period:____
5. You decide to purchase 2 pounds of bananas, 3 mangoes, 2 cartons of eggs, 1 loaf of
bread, and 3 pounds of ham. Sales tax is 4.5%. How much is your total before and after
tax?
6. Jam is on sale, buy one get one free. What is rate of change between one jar of jam at
the original price and one jar of jam on sale?
Describe in other words what buy one get one free represents.
7. You decide to purchase one of each item (or 1 pound of each item if applicable) from
Moe s Grocery circular. A discount coupon offers $5 off or 20% off your total bill.
Which option will you choose and why?
Answer Key – Moe’s Grocery
1. Eggs‐ percentage decrease of 28.78%
Bananas– percentage decrease of 25.32%.
The eggs have a greater percentage change than the bananas
2. Bread = $2.76, percentage decrease of 20%
Cheese = $3.59, percentage decrease of 10%
3. Percentage decrease of 25.13%
= ($1.99 ‐ $1.49)/$1.99 because the amount of decrease in sales price is
given (50 cents)
4. Percentage decrease of 46.81%
5. Total before tax = $17.86
Total after tax = $18.66
6. Percentage decrease of 50%
You get each jar 50% off.
7. The total bill is $16.28. Using the $5 discount makes the total bill $11.28
and using the 25% coupon makes the bill $12.21. Therefore, using the $5
discount will result in greater savings. $5 = 30.71% decrease
25% off = 25% decrease
Name:_______________________________ Date:__________ Period:____
Solve the following Egg Recall problems using Venn Diagrams.
1. 5.5 billion eggs have been recalled due to salmonella that a food safety expert attributes
to rodents, contaminated hens, and tainted feed. 80 million eggs were recalled because ro‐
dents were discovered on the farms, 3 billion eggs were recalled because of contaminated
hens, and 2.42 billion eggs were recalled due to tainted feed. 4 million eggs were recalled
because of both rodents and contaminated hens, 1 million eggs were recalled because of
both contaminated hens and tainted feed, and 2 million eggs were recalled because both
rodents and tainted feed. If no eggs are recalled due to all three reasons, find the number of
eggs recalled for each reason.
http://www.msnbc.msn.com/id/38741401/ns/health‐food_safety
http://news.yahoo.com/s/ygreen/20100819/sc_ygreen/massiveeggrecallhowtocheckyourcartonforrecalledeggs
Name:_______________________________ Date:__________ Period:____
2. The massive egg recall that has caused hundreds of people to be sick is caused by
salmonella on egg shells. The symptoms of salmonella poisoning begin to take effect within
6 to 72 hours of ingesting a tainted egg. Assume that 300 people have the following
salmonella poisoning symptoms: fever, vomiting, and lower abdominal cramps. 160 people
had fevers, 160 vomited, and 110 had cramps. 50 people experienced both fevers and
cramps, and of those, 30 vomited as well. 50 people only had cramps and 80 people only
vomited. How many people only had fevers?
http://www.msnbc.msn.com/id/38741401/ns/health‐food_safety
http://news.yahoo.com/s/ygreen/20100819/sc_ygreen/massiveeggrecallhowtocheckyourcartonforrecalledeggs
Math in the News
NCCTM 2010
The Math of the Miners
Jacob Perry & Chloe Johnson
Wake Forest University
Introduction
The San José Mine cave‐in that trapped 33 miners almost a half mile underground, and the subsequent two‐month
rescue effort that brought all 33 safely to the surface, has been an event that has stunned and united the world.
Through a global collaboration effort, the final rescue operation was more efficient and brilliantly successful than
anyone could have predicted. In this project, students will analyze raw data from the timeline of the rescue effort in
order to examine and illustrate in mathematical terms the success of the operation.
NCTM Standards
Numbers and Operations; Data Analysis and Probability; Algebra; Measurement; Communication; Connections.
NCSCOS: Algebra I
Goal 3: The learner will collect, organize, and interpret data with matrices and linear models to solve problems.
21st Century Student Outcomes
Learning and Innovation; Information, Media, and Technology; Core Subjects.
Materials
Computer for students or pairs, Internet access, graphing calculator, or graph paper (based on resources), pencil,
worksheets, data sets.
Goals
Students will be able to examine data from an online source, and then analyze and graphically represent that data.
Activities






Begin with a discussion on the San José Mine event, how it was covered in the media, what the students heard
or read about in the news, etc.
Assign students to pairs. Have students look up timeline website online and another online news article about
the rescue. Students will write a short reflection imagining what being trapped in a mine would be like.
Students will be provided with data for the timeline of the rescue mission, broken into two different workable
sets (option for differentiation: have students find data online, or extract needed data from raw data).
They will analyze both data sets, create two scatterplots with their corresponding lines of best fit, and then
examine these lines and what they indicate in terms of the real life rescue. (Option for differentiation: provide
direct instruction, scaffold, or have students work without instruction when working with Excel or calculator.)
Options for Differentiation (move all from above to here together)
The group will then complete a full report of their research, consisting of graphs with lines of best fit, the
worksheet with questions, and a one‐page document explaining the results obtained. This document should
include a one‐paragraph explanation of what each scatterplot and line shows. Students should include their
answers to the worksheet, as well as a conjecture on possible factors that contributed to the rescue timeline
appearing as it does.
Math in the News
NCCTM 2010
Assessment
The full report for each group will be presented to the class, turned in and graded.
A possible add‐on activity: there were 33 miners, and the website has a link on each miner s name to a short biography.
Each student can pick one of the miners and write a letter from the point of view of that person to the surface about the
rescue mission. Data from the assignment can be incorporated into the letter, e.g. how long that individual s rescue
took.
Math in the News
NCCTM 2010
Name ___________________________________
The Math of the Miners
The rescue mission at the San Jose mine started at 10:22pm on Tuesday, October 12, 2010. The first miner,
Florencio Avalos, was pulled from 2,000 feet below the surface at 12:04 am on Wednesday, October 13. By
that time, 1 hour 42 minutes had passed.
The mission continued with Mario Sepulveda Espina, who was brought to the surface at 1:10 am. This was 1
hour 6 minutes after Florencio Avalos was rescued, and 2 hours 48 minutes after the mission began.
Warm-Up: Go to http://www.telegraph.co.uk/news/worldnews/southamerica/chile/8063049/Chile-mine-rescuetimeline.html which gives the rest of the timeline. Find another online news article about the mine rescue. Write a short
reflection about what you think being trapped in a mine and being rescued would be like.
1. Averages
 Find the average rescue time per miner over the whole mission.

Find the average rescue time per miner for the first half of the mission by only looking at the data for the
first 16 miners.

Now find the average rescue time per miner for the rest of the miners (17-33).
Compare these averages. What does this tell you about the rescue times over the whole mission?
2. Scatterplots
a) Using graph paper, a graphing calculator, Microsoft Excel or another computer graphing utility, create a
scatter plot using the data from the “Miner Number” column and the “Total Time Elapsed” column.
 What is the independent variable?

What is the dependent variable? What are the units?
Math in the News

NCCTM 2010
Write down your observations of the graph.
b) Next, create a scatter plot using the data from the “Miner Number” column and the “Time from last rescue”
column.
 What is the independent variable?

What is the dependent variable? What are the units?

Write down your observations of the graph, and compare with the “Total Time Graph.”
What can you say about the rescue times as the mission goes on? How do the rescue times change? Why might
this be the case?
3. Lines of best fit
For each of these scatter plots, construct the line of best fit. Record or display the equation of the line.
What does each line tell you about the rescue mission?
What do the y-intercept and slope represent for each line? What do they mean in terms of hours?
If there had been 40 miners, estimate how long the rescue mission would have taken, in hours and minutes.
Estimate how long the 40th rescue would take, in hours and minutes. Do these values make sense? Why or why
not?
Math in the News
NCCTM 2010
Do the same for 50 miners. Do both of these values make sense? Why or why not? What can you conclude
about the lines of best fit? (Optional: What other models might work better for the data?)
Math in the News
NCCTM 2010
Report
With your partner, write a one-page report of your research. Include your graphs with lines of best fit and
equations. Write one paragraph for each graph, analyzing what each scatterplot and line of best fit represent.
Explain how the coefficients in the formula for the line relate to the real-life rescue mission. Use your answers
to the worksheet to guide you. Also write a paragraph explaining why you think the data appears as it does.
What factors could have contributed?
Timeline for the San José Mine Rescue
Miner
Number
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Miner Name
Time of rescue
Start mission
Florencio Avalos
Mario Sepulveda Espina
Juan Illanes
Carlos Mamani
Jimmy Sanchez
Osman Isidro Araya
Jose Ojeda
Claudio Yanez
Mario Gomez
Alex Vega
Jorge Galleguillos
Edison Pena
Carlos Barrios
Victor Zamora
Victor Segovia
Daniel Herrera
Omar Reygadas
Esteban Rojas
Pablo Rojas
Dario Segovia
Johnny Barrios Rojas
Samuel Avalos
Carlos Bugueno
Jose Henriquez
Renan Avalos
Claudio Acuna
Franklin Lobos
Richard Villarroel
Juan Carlos Aguilar
Raul Bustos
Pedro Cortes
Ariel Ticona
Luis Urzua
10:22 PM
12:04 AM
1:10 AM
2:08 AM
3:09 AM
4:10 AM
5:34 AM
6:21 AM
7:02 AM
7:59 AM
8:52 AM
9:31 AM
10:11 AM
10:54 AM
11:30 AM
12:07 PM
12:49 PM
1:38 PM
2:49 PM
3:27 PM
3:59 PM
4:31 PM
5:04 PM
5:32 PM
5:59 PM
6:24 PM
6:51 PM
7:18 PM
7:44 PM
8:13 PM
8:37 PM
9:03 PM
9:33 PM
9:55 PM
Total
Time from last rescue
elapsed time
Hours (decimal)
0.00
0.00
1.70
1.70
1.10
2.80
0.97
3.77
1.02
4.78
1.02
5.80
1.40
7.20
0.78
7.98
0.68
8.67
0.95
9.62
0.88
10.50
0.65
11.15
0.67
11.82
0.72
12.53
0.60
13.13
0.62
13.75
0.70
14.45
0.82
15.27
1.18
16.45
0.63
17.08
0.53
17.62
0.53
18.15
0.55
18.70
0.47
19.17
0.45
19.62
0.42
20.03
0.45
20.48
0.45
20.93
0.43
21.37
0.48
21.85
0.40
22.25
0.43
22.68
0.50
23.18
0.37
23.55
Data retrieved on 10-19-10 from
http://www.telegraph.co.uk/news/worldnews/southamerica/chile/8063049/Chile-mine-rescue-timeline.html
Math in the News
NCCTM 2010
Making Sense of Hurricane Havoc
Jill Klinepeter and Lauren Schnepper
Wake Forest University
Objective: Students will be able to use hurricane data to construct best‐fit mathematical models. They will use these
models to solve problems and where appropriate, draw conclusions or make predictions.
Class: Algebra II
Standards:
NCSCOS Standards: 2.04 - Create and use best‐fit mathematical models of linear, exponential, and quadratic functions
to solve problems involving sets of data. 2.04b ‐ Check the model for goodness‐of‐fit and use the model, where
appropriate, to draw conclusions or make predictions.
NCTM Standards: Data Analysis and Probability Standard for Grades 9‐12 ‐ Formulate questions that can be addressed
with data and collect, organize, and display relevant data to answer them. Select and use appropriate statistical methods
to analyze data (for bivariate measurement data, be able to display a scatterplot, describe its shape, and determine
regression coefficients, regression equations, and correlation coefficients using technological tools).
21st Centruy Skills: Learning and Innovation Skills (Communication and Collaboration); Core Subject; Information, Media,
and Technology Skills
Introduction: Meteorologists use elementary data analysis and statistics in order to predict how many named storms
are to make landfall in a season. Using these basic statistical and data analysis methods, including linear modeling,
scientists can predict the number of named storms and their breakdown by intensity (i.e. the number of tropical storms,
hurricanes, and major hurricanes) using data from past occurrences. In this activity students will have the chance to play
the role of meteorologists, using different forms of graphs to display hurricane data and then using linear
modeling/best‐fit lines of the data to predict how many storms will make landfall in the U.S. Students will also use their
mastery of best‐fit lines to predict the number of hurricanes in a season based on the total number of storms, and to
predict the amount of damage in billions of dollars that results from hurricane seasons of certain sizes (number of
hurricanes).
Materials: Microsoft Office Excel, colored pencils, pencils, activity sheets
Instructional Activities:
Warm‐Up: The warm‐up is a review of displaying data using different forms of charts/graphs. Using Excel, students will
create a bar graph and a pie chart that accurately represent provided hurricane data from the hurricane seasons
between 2000 and 2006.
Whole Class Activity: (guided practice scaffolding for group work)
Math in the News




NCCTM 2010
Using Excel, students will make a scatterplot that represents the relationship between the number of hurricanes
that make landfall in the U.S. and the year.
Using the Excel tools, students will then find a best‐fit line for the data, finding the equation and R‐squared for
the data. Then using the linear model students will make predictions for future hurricane seasons.
They will then repeat the process for the data relating the number of tropical storms that make landfall in the
U.S. to the year.
Discussion: As a class, discuss if finding the best‐fit line for this type of data is an accurate way to predict the
number of hurricanes. Also, discuss which line fits best and using guided questions help students discover how it
is possible to measure goodness of fit (R‐squared).
Group Activity:
 In groups of 2‐3 students will organize given hurricane data into a table.
 Using excel students will find the scatterplots and best‐fit lines for the data.
 Based on the best‐fit lines for the data students will make predictions.
 Finally students will compare the goodness of fit based on the R‐squared numbers found using excel.
 Students will turn in completed group activity sheet.
Assessment: Students will be graded based on the completed group activity sheet. All members of the group will be
given the same grade based on a randomly chosen paper from someone in the group. The grade will be based on
accuracy of tables, graphs, and answers, as well as the quality of explanations.
Warm‐Up: Reviewing Graphs
1. Enter the information given into an Excel document.
Year
2000
2001
2002
2003
2004
2005
2006
Tropical Storms
7
6
8
9
6
13
5
Hurricanes
5
5
2
4
3
8
3
Major Hurricanes
3
4
2
3
6
7
2
2. Use the data to plot a bar graph. Sketch the result below.
14
12
10
8
Tropical Storms
Hurricanes
6
Major Hurricanes
4
2
0
2000 2001 2002 2003 2004 2005 2006
3. Now choose one year from the table and construct a pie chart for that data. Sketch your result below.
Year: _____
Tropical Storms
Hurricanes
Major Hurricanes
Whole Class Activity: Scatterplots & Best‐Fit Lines
Year
2000
2001
2002
2003
2004
2005
Tropical storms making landfall in U.S. Hurricanes making landfall in U.S.
2
0
2
0
7
1
1
2
3
5
2
5
1.
Using the year 2000 as year 0, fill in the missing column and plot the data in a table in Microsoft Excel.
2.
Plot the Year column as the independent variable (x‐axis) and the Hurricanes making landfall in U.S. column as the de‐
pendent variable (y‐axis). Sketch your results below.
5
3. Using excel, find the linear
trendline (best‐fit line). Choose to
display the equation and r‐
squared value on chart and write
below.
4
Equation:
3
R‐squared value:
2
4. If this trend continued, how
many hurricanes would you ex‐
pect to make landfall in the U.S. in
year 7 (year 2007)?
Hurricanes making landfall in U.S.
Number of Hurricanes
6
1
0
0
1
2
3
4
5
6
‐ What about year 20 (year 2020)?
Year
5. Would this be an appropriate conclusion to make? Why or why not?
6. Plot the Year column as the independent
variable (x‐axis) and the Tropical storms mak‐
ing landfall in U.S. column as the dependent
variable (y‐axis). Sketch your results below.
Equation:
R‐squared value:
8. How well does this line fit the data? How
can we tell if the line is a good‐fit?
8
Number of Tropical Storms
7. Using excel, find the linear trendline (best‐
fit line). Choose to display the equation and
r‐squared value on chart and write below.
Tropical storms making landfall in U.S.
7
6
5
4
3
2
1
0
0
1
2
3
Year
4
5
6
Group Activity: Using Models to Predict Hurricane Havoc
1. Using the following information fill in the table below:

In 2002, there were 12 total tropical storms, 4 of which were classified as hurricanes. The total damage to the U.S. was 2.6 billion dollars.

In 2003, there were 16 total tropical storms, 7 of which were classified as hurricanes. The total damage to the U.S. was 4.4 billion dollars.

In 2004, there were 15 total tropical storms, 9 of which were classified as hurricanes. The total damage to the U.S. was 50 billion dollars.

In 2005, there were 28 total tropical storms, 15 of which were classified as hurricanes. The total damage to the U.S. was 130 billion dollars.

In 2006, there were 10 total tropical storms, 5 of which were classified as hurricanes. The total damage to the U.S. was 0.5 billion dollars.

In 2007, there were 15 total tropical storms, 6 of which were classified as hurricanes. The total damage to the U.S. was 3 billion dollars.

In 2008, there were 16 total tropical storms, 8 of which were classified as hurricanes. The total damage to the U.S. was 47.5 billion dollars.

In 2009, there were 9 total tropical storms, 3 of which were classified as hurricanes. The total damage to the U.S. was 0.1 billion dollars.
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In 2010, there were 16 total tropical storms, 9 of which were classified as hurricanes. The total damage to the U.S. was 8 billion dollars.
Year
Total number
of storms
Number of
hurricanes
Total damage
(in billions)
2. Plot the Total number of hurricanes as the independent variable and the Total damage as the dependent variable. Sketch
your results below. Make sure to label your title and axis s appropriately.
3. Using excel, find the linear trendline (best‐fit
line).
Damage (Billions)
Equation:
140
R‐squared value:
5. Is this a reasonable prediction? Why or why
not?
Axis Title
4. If there were 20 hurricanes in a year, what
could you predict the total damage in billions
to be?
120
100
80
60
40
20
0
0
5
10
Axis Title
15
20
6. Plot the Total number of storms as the independent variable and the Number of hurricanes as the dependent variable.
Sketch your results below. Make sure to label your axis s appropriately.
7. Using excel, find the linear trendline
(best‐fit line).
Hurricanes
Equation:
R‐squared value:
16
8 If there were 21 total storms in a year,
what could you predict the number of
hurricanes to be?
14
10. Are these reasonable predictions?
Why or why not?
Axis Title
9. If there were 37 total storms in a year,
what could you predict the number of
hurricanes to be?
12
10
8
6
4
2
0
0
5
10
15
20
25
Axis Title
11. If you knew there were 26 total storms in a year, how much would you predict to be the total damage? Show your work.
(Hint: The answer will have two steps using both linear models)
12. Which of these best‐fit lines do you think would give a more accurate prediction? Why?
30
Making Sense of Hurricane Havoc
Teacher Answer Key
WARM‐UP
14
2005
12
10
8
Tropical Storms
6
Hurricanes
Tropical Storms
Major Hurricanes
Hurricanes
4
Major Hurricanes
2
0
2000 2001 2002 2003 2004 2005 2006
WHOLE‐CLASS ACTIVITY
1. Column should read 0, 1, 2, 3, 4, 5
2.
3.
Hurricanes making landfall in U.S.
Number of Hurricanes
6
y = 1.1714x ‐ 0.7619
R² = 0.8949
5
4
3
Hurricanes making
landfall in U.S.
2
Linear (Hurricanes
making landfall in U.S.)
1
0
0
2
4
6
Year
4. 7.4379
22.6661
5. Just because the year is getting bigger, the number of hurricanes isn t necessarily increasing as
well.
6.
7. D
8. The line is not a good‐fit. The r‐squared value needs to be close to 1 or ‐1 to be a good‐fit.
Making Sense of Hurricane Havoc
Teacher Answer Key
GROUP ACTIVITY
1.
4.
5.
2002
12
4
2.6
2003
16
7
4.4
2004
15
9
50
2005
28
15
130
2006
10
5
0.5
2007
15
6
3
2008
16
8
47.5
2009
9
3
0.1
2010
16
9
8
2.
3.
165.106 billion dollars
It is a reasonable prediction because the more hurricanes that occur in a season, the higher you
can expect the total damage to be.
6.
7.
Number of Hurricanes
Total number of storms and hurricanes
16
14
12
10
8
6
4
2
0
y = 0.6182x ‐ 2.0773
R² = 0.9051
Hurricanes
Linear (Hurricanes)
0
10
20
30
Total Number of Storms in a Year
8. 10.9049
9. 20.7961
10. This data shows that roughly half of the storms each year reach hurricane status which is a
reasonable prediction.
11. According to the second model, if there are 26 total storms in a year, you can predict that there
will be 13.9959 hurricanes. According to the first model, if there are 13.9959 hurricanes in a year,
you can predict the total damage to be 99.8054 billion dollars.
12. The second model will give a more accurate prediction because the r‐squared value is closer to 1.