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Water Bottle Unit
Teacher Background Information: Please see
teacher background information page at the end of
these lesson plans.
* There is a PowerPoint Presentation (PPT) to
accompany this lesson plan entitled “Water Bottles”.
Each slide has accompanying notes to help you
deliver background information to students. You
should review this PPT and use it whenever you see
that your students may need more information.
The Water Bottle Unit is divided into 3 sections
1. The U.S. Bottled Water Market
a. A Graphical Analysis
b. Trends and trend Lines
2. Packaging e-ratio
a. A Study of 0.5-Liter Plastic Water Bottles
b. 1 Liter-10 Wide; How Shape Influences
Packaging
An Efficient Packaging Study
3. The Global Bottled Water Market
a. Analyze Data Using Pie Charts
b. A Statistical Analysis of Data
Goals: To give students an understanding of the
waste generated through consuming bottled water.
To use Statistics, Linear Algebra, Functions and
Regression Models to analyze data in order to make
an environmental decision.
©2010 Beyond Benign – All Rights Reserved.
Content Area:
Statistics
Linear Algebra
Functions
Regression Models
Prerequisites:
Linear Algebra
Equations of a Line
Standards met:
Standards met:
NM-Num.9-12.1a
NM-Num.9-12.2a
NM-Num.9-12.3a,b
NM-Alg.9-12.1b,c,e,f
NM-Alg.9-12.2a,b,c,e
NM-Alg.9-12.3a,b.c
NM-Alg.9-12.4
NM-Data.9-12.1a,b,c,d,e
NM-Data.9-12.2a,b,c,e
NM-Prob.Pk-12.1,2,3,4
NM-Prob.Comm.Pk-12.1,2,3,4
NM-Prob.Conn.Pk-12.1,2,3
NM-Prob.Rep.Pk-12.1,3
Time required:
3 x 45-60 minute class
periods
Materials:
Protractor
Ruler
Calculator
Graphing Calculator
The U.S. Bottled Water Market
A Graphical Analysis
Name: ___________________________________Hour:____________________
The consumption of bottled water has been increasing across the globe. The increase in
bottled water production also leads to the increase in empty plastic water bottle waste.
These plastic bottles are sometimes recycled but more often end up in landfills or as
litter. In this problem you will graphically represent 8 years of U.S. Bottled Water
Market data using scatter graphs, trend and regression lines.
©2010 Beyond Benign – All Rights Reserved.
1.
Make a scatter graph. Use the nonsparkling sales volume data for the
years 2000 to 2007
a.
let 2000 = year 1, 2001 = year 2 etc.
b.
Use a straight edge to draw a trend line.
c.
Use a graphing calculator to find a line of
best fit (LinReg)
d.
Record Pearson’s Correlation
Coefficient:
r = __________
e.
and the equation;
N(x) = ______________________________
2.
Describe the trend over time for domestic non-sparkling bottled water sales
in the U.S. for the years 2000 to 2007.
3.
Based on the sales trend line, how many bottles of domestic nonsparkling water will be sold in the U.S. in the year 2008?
4.
This time use the equation of the LinReg line to predict how many
bottles of domestic non-sparkling water will be sold in the U.S. in the
year 2008.
N(9) = __________
5.
also find
What does N(13) represent?
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N(13) = __________
6. On the same graph make
a connected line graph of
the sales volume data for
a.) Domestic,
b.) Sparkling and
c.) Imports
in the U.S. for the years
2000 to 2007.
2000 = year 1 2001 =
year 2 etc.
7.
Describe the trends over time for domestic sparkling bottled water and
imported bottled water consumption in the U.S. for the years 2000 to
2007.
8.
Based on the sales trends, predict the number bottles of Domestic Sparkling
Bottled Water and Imported Bottled Water that will be consumed in the U.S. in
the year
2008?
9.
In which prediction are you the most confident? Why?
10.
Use a graphing calculator to find a regression line (LinReg) for each data set.
©2010 Beyond Benign – All Rights Reserved.
Domestic Sparkling Bottled Water:
____________________
S(x) =
Pearson Correlation Coefficient:
r = __________
Imported Bottled Water:
I(x) = ______________________
Pearson Correlation Coefficient:
r = __________
11.
Find:
S(9) = ______________
12.
What do the values S(9) and I(9) represent?
13.
Which prediction is more reliable? Why?
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I(9) = ________________
The U.S. Bottled Water Market
Trends and Trend Lines
Name: ________________________ Hour:_____
The consumption of bottled water has
been increasing across the globe. The
increase in bottled water production also
leads to the increase in empty plastic
water bottle waste. These plastic bottles
are sometimes recycled but more often
end up in landfills or as litter.
In this problem you will make a graph of
U.S. per capita water consumption over
time on the graph below. Label all axes.
Directions to find a trend line.
1. Plot 11 data points;
is the year # and the
per capita
x- coordinate
y-coordinate is gallons
2. With a ruler draw a trend line that you thinks best
fits the data.
3. From your trend line, select two points that can be
rounded to whole numbers.
(_____,____)
(_____,____)
4. Calculate the slope of the line containing these two
points.
m = ______
5. Visually estimate the ‘y-intercept’ then write the
equation of your trend line.
©2010 Beyond Benign – All Rights Reserved.
1.
Describe the ‘trend‘ illustrated by your trend line.
2.
Let’s compare the equation of your trend line to one computed by your
graphing calculator.
First enter the data into two Lists; L1 and L2 (Stat – Lists – Edit). Next go to the
LinReg (Stat – Calc- LinReg) program and record the equation of the line along
with Pearson’s Correlation Coefficient (the r value).
LinReg Equation: _________________________________
Pearson’s Correlation Coefficient: r = ________________
3.
Enter the linear regression equation into your graphing calculator.
How well does the calculator’s trend line fit the data? Does the r-value
support your conclusion? Explain.
4.
How well does your trend line equation compare with the calculator
trend line? Are they different? Explain.
5.
Now you will predict per capita bottled consumption for 2008. There are
three ways to predict.
a.
Extend your trend line and estimate y when x = 12
©2010 Beyond Benign – All Rights Reserved.
b.
2008 = year 12 of the study.
#5.
Your equation:
Evaluate your equation from question
y = _____ (12) + _____
y = ______
c.
LinReg equation: y = ______ (12) + _______
6.
To what degree do these three predictions for per capita bottled
consumption for 2008 differ?
a.
Start by calculating the percent that your answers to b and c differ from a.
Compare: a and b
Compare: a andc
Compare: b andc
b.
y = ______
a b

b
 0._______ ______%
ac

c
 0._______ ______%
bc

c
 0._______ ______%
Is one estimate
more reliable than the other? Which one do you think is the

most reliable? Explain.
©2010 Beyond Benign – All Rights Reserved.
The U.S. Bottled Water Market
A Graphical Analysis–Teacher
Answer Key
Name: ______________________________________ Hour:___________
The consumption of bottled water has been increasing across the globe. The increase in
bottled water production also leads to the increase in empty plastic water bottle waste.
These plastic bottles are sometimes recycled but more often end up in landfills or as
litter. In this problem you will graphically represent 8 years of U.S. Bottled Water
Market data using scatter graphs, trend and regression lines.
©2010 Beyond Benign – All Rights Reserved.
1.
Make a scatter graph. Use the
non- sparkling sales volume data for
the
years 2000 to 2007
a.
etc.
let 2000 = year 1, 2001 = year 2
b.
Use a straight edge to draw a
trend line.
c.
Use a graphing calculator to find a
line of
best fit (LinReg)
d.
Record Pearson’s Correlation
Coefficient:
r =
2000
2001 2002 2003 2004 2005 2006 2007 200
__0.996________
e.
and the equation;
N(x) = _576.2 X + 3743.3_______
2.
Describe the trend over time for domestic non-sparkling bottled water sales
in the U.S. for the years 2000 to 2007.
3.
Based on the sales trend line, how many bottles of domestic nonsparkling water will be sold in the U.S. in the year 2008?
About 8,900 Million Gallons
4.
This time use the equation of the LinReg line to predict how many
bottles of domestic non-sparkling water will be sold in the U.S. in the
year 2008.
N(9) = 8,928 Million Gallons also find
Gallons
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N(13) = 11,234 Million
5.
What does N(13) represent? N(13) represents the projected
numberof gallons of bottled water consumed in the U.S
U.S. Bottled Water Consumption 2000 to 2007
a.) Domestic,
b.) Sparkling and
c.) Imports
2000 = year 1 2001 =
year 2 etc.
Key
Domestic
Sparkling water
Imports
Number gallons of bottled water consumed in the U.S. ( x 1 million)
6. On the same graph make a connected
line graph of the sales volume data for:
Time : Year
7.
Describe the trends over time for domestic sparkling bottled water and
imported bottled water consumption in the U.S. for the years 2000 to 2007.
Both are trending upward over time. Sparkling sales are more steadily increasing. Imports
are up and down.
8.
Based on the sales trends, predict the number bottles of Domestic Sparkling Bottled
Water and Imported Bottled Water that will be consumed in the U.S. in the year 2008?
From my graph I predict that sparkling bottled water sales will be 205 million gallons in
2008 and that imports will increase to 225 million gallons.
9.
In which prediction are you the most confident? Why?
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I am most confident in the domestic sparkling trend prediction. The trend is steady but
erratic for imports.
10.
Use a graphing calculator to find a regression line (LinReg) for each data set.
Domestic Sparkling Bottled Water: S(x) = 8.88x + 126.6
Pearson Correlation Coefficient:
Imported Bottled Water:
r = 0.966
I(x) = 7.68x + 137.3
Pearson Correlation Coefficient:
11.
Find:
r = 0.5683
S(9) = 206.52
I(9) =
206.42
S(9) = 8.88 • (9) + 126.6
I(9) = 7.68(9) + 137.3
12.
What do the values S(9) and I(9) represent?
S(9) Represents predicted sales of Domestic sparkling water in 2008
I(9) Represents predicted sales of Imported bottled water in 2008
13.
Which prediction is more reliable? Why?
I have far more confidence in the projections in 2008 for domestic sparkling
water because the sales trend has been steady over time.
©2010 Beyond Benign – All Rights Reserved.
The U.S. Bottled Water Market
Trends and Trend Lines –
Teacher Answer Key
Name: ________________________
Hour:_____
The consumption of bottled water has
been increasing across the globe. The
increase in bottled water production also
leads to the increase in empty plastic
water bottle waste. These plastic bottles
are sometimes recycled but more often
end up in landfills or as litter.
In this problem you will make a graph of
U.S. per capita water consumption over
time on the graph below. Label all axes.
(12,30.5.5)
Directions to find a trend line.
1. Plot 11 data points; x- coordinate is the year # and
the y-coordinate is gallons per capita
2. With a ruler draw a trend line that you think best
fits the data.
(8,24)
3. From your trend line, select two points that can be
rounded to whole numbers.
(__4___,_17___) answers will vary
(__8___,_24___)
(4,17)
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4. Calculate the slope of the line containing these
two points. m = 1.75
5. Visually estimate the ‘y-intercept’ then write the
equation of your trend line.
y = 1.75x +
11
1.
Describe the ‘trend‘ illustrated by your trend line. Bottled water
consumption is increasing over time.
Answers will vary
2.
Let’s compare the equation of your trend line to one computed by your
graphing calculator.
First enter the data into two Lists; L1 and L2 (Stat – Lists – Edit). Next go to the
LinReg (Stat – Calc- LinReg) program and record the equation of the line along
with Pearson’s Correlation Coefficient (the r value).
LinReg Equation: ____y = 1.59x
+
11.06______________________
Pearson’s Correlation Coefficient: r = _0.9926_______________
3.
Enter the LinReg equation into your graphing calculator. How we does the
calculator’s trend line fit the data? Does the r-value support your
conclusion? Explain.
The LinReg equation fits the data very well. The r value was close to 1 and that
supports this conclusion.
4.
How well does the equation of your trend line compare with the calculator
trend line? Are they different? Explain.
They are very close; the y- intercepts are almost the same. The slopes are
1.75 1.59
1.59
1.59 and 1.75 about a 10% difference.

0.16
1.59
 10.06%

5.
Now you will predict per capita bottled consumption for 2008. There are
three ways to predict.
©2010 Beyond Benign – All Rights Reserved.
a.
Extend your trend line and estimate y when x = 12
b.
2008 = year 12 of the study.
Your equation:
35 Answers vary
Evaluate your equation from question #5.
y = 1.75 (12) + 11
y = 32
Answers will vary.
c.
LinReg equation: y = 1.59 x (12) + 11.06
6.
To what degree do these three predictions for per capita bottled
consumption for 2008 differ?
a.
Start by calculating the percent that your answers to b and c differ from a.
Answers for a and b will vary.
a = 35
b = 32
y = 30.14
c = 30.14
Compare: a and b
35  32 3

 0.09375  9.375%
32
32
Compare: a and c
35  30.14 4.86

 0.161  16.1%
30.14
30.14
Compare: b and c
32  30.14 1.86

 0.0617  6.17%
30.14
30.14


b.
Is one estimate
more reliable than the other? Which one do you think is the

most reliable? Explain.
Answers vary.
©2010 Beyond Benign – All Rights Reserved.
Packaging e-ratio
Goals: To…
Objectives: Students will…





Analyze the Packaging E-Ratio (PER)
For 19.9ox/0.5L bottled water found in
Local grocery stores.
Determine the distance the water travels from
Plant to distributor to store to home. (PDSH)
Prep:
 Make a class set of worksheets.
 prepare sets of 16.9oz/0.5L water bottles.
 Arrange for scales from the science
department.
Procedure:





Content Area:
Ratios and Percents,
Number sense,
Measuring, converting
within metrics and
between the metric and
U.S. measurements
Prerequisites:
Standards met:
L1.2.4
Time required: 1 class
period
Materials: (teams of 3)
set of bottles
scale
laptop (optional)
rulers
-e:
Make assignments or ask students to get into groups of three.
Hand out the student sheet.
Explain that today the students will be looking at the packaging ratios
in water bottles.
Explain to the students that a tool that is often used to analyze
packaging for the purpose of considering environmental impact and
yield is e-factor or
E-factor ≡ mass of waste ÷ mass of product.
For the purpose of this lesson the students could also think of it as Efactor = Mass of packaging / Mass of consumable product.
©2010 Beyond Benign – All Rights Reserved.
The Packaging E-Ratio
A Study of 0.5-Liter Plastic Water
Bottles
Name: ___________________
Class period:__________
Team Members: _______________________________________________
In this activity you will calculate the Packaging E-Ratio (PER) for
16.9oz/0.5L-bottled water.
(PEF) is the ratio of product waste to product consumed? Both are
measured in grams.
Step 1: Gather the following materials at your teamwork station.
a.)
b.)
c.)
One each of the different half-liter bottles
Scale
Laptop (optional)
Step 2: (Round off to the nearest tenth of a centimeter or gram)
a.
Measure the diameter (width) of each bottle
b.
Weigh and record bottles:
First: empty with caps/tops on
c.
Second: full with caps/tops on.
Calculate and record the information below
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Bottle
width
Brand
Size
Mass
(full)
Mass
(empty)
Mass
consumed
Product
E-Ratio
%
Waste
0.5L
0.5L
0.5L
0.5L
0.5L
0.5L
Answer the following questions:
1.
Which product has the lowest E-Ratio? __________________
2.
Which product has the highest E-Ratio? __________________
3.
Calculate the average weight of the two heaviest bottles.
( _________ +
4.
_______ grams/0.5L bottle
Calculate the average weight of the two heaviest bottles.
( _________ +
5.
_________ ) ÷ 2 =
_________ ) ÷ 2 =
_______ grams/0.5L bottle
In 2008 it is projected that bottled water sales in the US will reach
9.418 billion gallons*.
*
Source: Beverage Marketing Corporation
a.
How many half-liter bottles would this fill?
Fact: 1 gallon = 3.78 liters
9,418,000,000 gallons = ____________________ liters
9,418,000,000 gallons = ____________________ half-liter bottles
©2010 Beyond Benign – All Rights Reserved.
b.
Find the total weight of the number of empty plastic bottles
using the high average of _________ g /0.5 liter bottle.
Total weight in grams = # of 0.5L bottles
x
= _____________________
# of g /0.5L bottle
x ____________
= _____________________ grams
= __________________ kg
= __________________ metric tons
= __________________ U.S. tons
c.
Find the total weight of the number of empty plastic bottles
using the low average of _________ g /0.5 liter bottle.
Total weight in grams = # of 0.5L bottles
x
= ___________________
# of g /0.5L bottle
x _______________
= _____________________ grams
= __________________ kg
= __________________ metric tons
= __________________ u.s. tons
d. If every company used the lighter plastic bottle, how much would
the tonnage of wasted plastic be reduced?
_______________ u.s. tons
6. The average width of the plastic bottles used = __________.
(Measure each bottle then divide by the number of bottles measured)
©2010 Beyond Benign – All Rights Reserved.
a.
If lined up in a standing position, how many miles would the plastic
bottles stretch?
_______________________ miles
b.
If the circumference of the earth is 24,902 miles at the equator, how
many times could we ‘circumpolute’ (Circle with trash) the earth each
year with just plastic water bottles?
_____________ times
©2010 Beyond Benign – All Rights Reserved.
The Packaging E-Ratio
A Study of 0.5-Liter Plastic Water
BottlesTeacher Answer Key
Name: _________________
Class period:__________
Team Members: _______________________________________________
In this activity you will calculate the Packaging E-Ratio (PER) for
16.9oz/0.5L-bottled water.
(PEF) is the ratio of product waste to product consumed. Both are measured
in grams.
Step 1: Gather the following materials at your teamwork station.
a.)
b.)
c.)
One each of the different half-liter bottles
Scale
Laptop (optional)
Step 2: (Round off to the nearest tenth of a centimeter or gram)
a.
Measure the diameter (width) of each bottle
b.
Weigh and record bottles:
First: empty with caps/tops on
caps/tops on.
c.
Second: full with
Calculate and record the information below –
answers will vary depending on the brand of water used.
©2010 Beyond Benign – All Rights Reserved.
Bottle
width
Size
Mass
(full)
Mass
(empty)
Mass
consumed
Product
E-Ratio
%
Waste
Dasani
0.5L
571.6
17.7
553.9
0.032
3.1%
Primo
0.5L
582.3
28.5
553.8
0.051
4.9%
Fiji
0.5L
535.6
30.0
505.6
0.059
5.6%
Aquafina
0.5L
534.0
27.8
506.6
0.055
5.2%
Absopure
0.5L
526.0
15.7
510.3
0.031
3.0%
Kroger
0.5L
527.5
18.0
509.5
0.035
3.4%
Brand
Answer the following questions:
1.
Which product has the lowest E-Ratio? __Absopure_____________
2.
Which product has the highest E-Ratio? _Fiji_________________
3.
Calculate the average weight of the two heaviest bottles.
( __28.5____ +
4.
_29.25__ grams/0.5L bottle
Calculate the average weight of the two heaviest bottles.
( __15.7___ +
5.
__30___ ) ÷ 2 =
__16__ ) ÷ 2 =
__15.85_ grams/0.5L bottle
In 2008 it is projected that bottled water sales in the US will reach
9.418 billion gallons*.
*
Source: Beverage Marketing Corporation
a.
How many half-liter bottles would this fill?
Fact: 1 gallon = 3.78 liters
9,418,000,000 gallons = _18,836,000,000__ liters
9,418,000,000 gallons = _37,672,000,000_ half-liter bottles
©2010 Beyond Benign – All Rights Reserved.
b.
Find the total weight of the number of empty plastic bottles
using the high average of __29.25_ g /0.5 liter bottle.
Total weight in grams = # of 0.5L bottles
= __37,672,000,000___
= _1,102,094,360,000___ grams
= __1,102,000__ metric tons
c.
x
x ___29.25__
= __1,102,094,360___ kg
= ________1,215,000____ U.S. tons
Find the total weight of the number of empty plastic bottles
using the low average of __15.85__ g /0.5 liter bottle.
Total weight in grams = # of 0.5L bottles
x
= __37,672,000,000_____
= _59,710,120,000____ grams
= ___597,101.2___ metric tons
d.
# of g /0.5L bottle
# of g /0.5L bottle
x __15.85______
= _59,710,120____ kg
= ___658,200___ U.S. tons
If every company used the lighter plastic bottle, how much would the
tonnage of wasted plastic be reduced?
_556,800_______U.S. tons
6. The average width of the plastic bottles used = _3 inches___.
(measure each bottle then divide by the number of bottles measured)
©2010 Beyond Benign – All Rights Reserved.
a.
If lined up in a standing position, how many miles would the plastic
bottles stretch?
_1,783,712.1_ miles
b.
If the circumference of the earth is 24,902 miles at the equator, how
many times could we ‘circumpolute’ (Circle with trash) the earth each
year with just plastic water bottles?
____71.6______ times
©2010 Beyond Benign – All Rights Reserved.
One Liter - 10 Wide
How shape influences packaging
An Efficient Packaging Study
Name: __________________________ Hour:__________
Businesses want product containers that require the least materials and can be
shipped economically. If a container can be devised that requires less material then
resources are conserved and money is saved. Also by packaging the product more
efficiently, so that more can be shipped per truck or boatload, the company saves on
gas and fuel costs.
Challenge: Determine the dimensions of the 1liter container that has the least
surface area.
Assumptions: The container must be 10cm wide and have a volume of 1000ml =1L.
The base can either be a square, an equilateral triangle, a circle, or a hexagon.
Missing information: You need to find the height then the surface area of each object.
1. Square Base:
V=
H = _________
SA = _________
2. Isosceles Triangle Base:
V=
H = _________
SA = _________
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3. Circular Base (cylinder)
V =_________
H = _________
SA = _________
4. Hexagonal Base:
V=
H = _________
SA = _________
5.
Find the radius of the sphere that has a volume of 1000 ml. r = _________
Find the surface area of this sphere.
©2010 Beyond Benign – All Rights Reserved.
S.A. = _______
6.
Summarize your calculations below.
Base Shape
Square
Triangular
Circular
Hexagonal
Sphere
height
volume
surface area
7.
Conclusions: Which 1L package has the least surface area?
Pack a Pallet
Shipping a product can be very costly. Efficient packing leads to lower
transportation costs. In this section you will explore how to pack the square based
and the spherical shapes into a container that is 120cm by 100cm by 120cm.
Goal: Determine the maximum number of 1-liter containers that can be loaded
into one 124cm by 124cm by 250cm container
1. Square Base:
a.
How many 10cm by 10cm by 10cm containers fit on the bottom.
_____________ containers
2.
b.
How many rows are possible?
_____________ rows
c.
Total # of containers:
___________ 1L containers
Spheres:
a.
How many 12.4 cm diameter spheres fit on the bottom?.
_____________ containers
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3.
b.
How many rows are possible?
_____________ rows
c.
Total # of containers:
___________ 1L containers
Summarizing:
Surface Area:
Cube: ____________
Sphere: ___________
Containers per Shipping Unit:
Cube: ____________
Sphere: ___________
4.
Which shape is more efficient; the cube or the sphere?
5.
Are there other factors that need to be considered? Explain.
6.
Assume that the cubic shaped containers are shipped in cases; 24 to a
case. The cases are then arranged on a pallet that is 120cm by 100cm by
120 cm high. Only consider cases that are either 6 by 4 or the 8 by 3.
Design a stacking arrangement that will allow for the most cases to be
shipped per pallet.
a.
Make a sketch showing how the cases are arranged on the bottom row of
the pallet.
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b.
Find the following:
cases per layer: ___
c.
layers per pallet: ____ # of cases per Pallet: _____
Compare your results with others in class.
©2010 Beyond Benign – All Rights Reserved.
How shape influences packaging
an Efficient Packaging Study
Teacher Answer Key
Name: __________________________ Hour:__________
Businesses want product containers that require the least materials and can be
shipped economically. If a container can be devised that requires less material then
resources are conserved and money is saved. Also by packaging the product more
efficiently, so that more can be shipped per truck or boatload, the company saves on
gas and fuel costs.
Challenge: Determine the dimensions of the 1liter container that has the least
surface area.
Assumptions: The container must be 10cm wide and have a volume of 1000ml =1L.
The base can be either a square, an equilateral triangle, a circle, or a hexagon.
Missing information: You need to find the height then the surface area of each object.
1. Square Base:
V = 10 • 10 • h = 1000
H = __10cm___
SA = 600 cm 2_
2. Isosceles Triangle Base:
V = 20 cm
H = ___20 cm______
SA = __782.8 cm 2__
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3. Circular Base (cylinder)
V = ∏• 52 • H = 1000
H = 12.7324
SA = __557.08 cm2__
4. Hexagonal Base:
V=
H = __15.40 cm_______
SA = _591.9cm2_
5.
Find the radius of the sphere that has a volume of 1000 ml. r = _6.2 cm__
Find the surface area of this sphere.
6.
S.A. = _483.6 cm2__
Summarize your calculations below.
Base Shape
Square
Triangular
Circular
Hexagonal
Sphere
height
10 cm
20 cm
12.73 cm
15.40 cm
D=12.41 cm
volume
1000cm3
1000cm3
1000cm3
1000cm3
1000cm3
surface area
600 cm2
782.8 cm2 557.08cm2 591.9cm2
©2010 Beyond Benign – All Rights Reserved.
483.6 cm2
7.
Conclusions: Which 1L package has the least surface area?
The sphere requires the least packaging (483.6 cm2) the
cylinder is second needing 557 cm2 of packaging.
Pack a Pallet
Shipping a product can be very costly. Efficient packing leads to lower
transportation costs. In this section you will explore how to pack the square based
and the spherical shapes into a container that is 120cm by 100cm by 120cm.
Goal: Determine the maximum number of 1 liter containers that can be loaded
into one 124cm by 124cm by 250cm container
1. Square Base:
a.
2.
12 x 12
___144_______ containers
b.
How many rows are possible?
_____25________ rows
c.
Total # of containers:
____3600__ 1L containers
Spheres:
a.
3.
How many 10cm by 10cm by 10cm containers fit on the bottom.
How many 12.4 cm diameter spheres fit on the bottom?.
10 x 10
____100_______ containers
b.
How many rows are possible?
________20_____ rows
c.
Total # of containers:
___2000___ 1L containers
Summarizing:
Surface Area:
Cube: ___600 cm2__
Sphere: _483.6 cm2_
Containers per Shipping Unit:
Cube: 3600 containers_
Sphere: _2000 cont._
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4.
Which shape is more efficient; the cube or the sphere?
This is a toss up. A cube takes 24% more material to make but is
shipped for nearly half the cost.
5.
Are there other factors that need to be considered? Explain.
Which container is the most economical to manufacture and which
product fits most efficiently on a store shelf.
6.
Assume that the cubic shaped containers are shipped in cases; 24 to a
case. The cases are then arranged on a pallet that is 120cm by 100cm by
120 cm high. Only consider cases that are either 6 by 4 or the 8 by 3.
Design a stacking arrangement that will allow for the most cases to be
shipped per pallet.
a.
Make a sketch showing how the cases are arranged on the bottom row of
the pallet.
The 6 x 4 case has dimensions 60 x 40 cm
120
b.
40
40
60
40
100
40
60cm
60cm
Find the following:
cases per layer: _5_layers per pallet: _12
c.
Compare your results with others in class.
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# of cases per Pallet: _60_
Global Bottled Water Market
Teacher Background Information: Data for this
unit can be viewed at:
www.bottledwater.org/public/statistics_main.htm
Goals: To use statistics, linear algebra and
regression models to consider the use of bottled
water.
Objectives: Students will…
 Consider bottled water and its impact on the
environment.
 Analyze global water markets using pie charts
Procedure:
 Show the Water-Disaster video.
 Lead a discussion with the students about
bottled water, if they drink it and why.
 Explain to students that they are going to work
with some numbers that really show the
impact of bottled water consumption in the
world.
 Hand out the student sheet.
Content Area:
Statistics, Linear Algebra,
Functions, Regression
Models
Prerequisites: Linear
Algebra, Equations of a
Line
Standards met:
NM-Num.9-12.1a
NM-Num.9-12.2a
NM-Num.9-12.3a,b
NM-Alg.9-12.1b,c,e,f
NM-Alg.9-12.2a,b,c,e
NM-Alg.9-12.3a,b.c
NM-Alg.9-12.4
NM-Data.9-12.1a,b,c,d,e
NM-Data.9-12.2a,b,c,e
NM-Prob.Pk-12.1,2,3,4
NM-Prob.Comm.Pk-12.1,2,3,4
NM-Prob.Conn.Pk-12.1,2,3
NM-Prob.Rep.Pk-12.1,3
Time required:
Flexible: 30 minutes to 3
days.
-:
©2010 Beyond Benign – All Rights Reserved.
The Global Bottled Water Market
Analyze Data Using Pie Charts
Name: ________________________ Hour:_____
In this problem you will compare and contrast the consumption of bottled
water by creating two pie charts from the data set below;
-
one for bottled water consumption in 2002
-
and the second for bottled water consumption in 2007.
Begin by;
a.
sorting the data by continent
b. calculate the percent of total
c.
calculate the size of the pie slice d. make and label a pie chart for
each year.
CAGR = Compound Annual Growth Rate
Marketing Corporation
©2010 Beyond Benign – All Rights Reserved.
Source: Beverage
Round all data to the nearest tenth of a trillion gallons. Also note that only
the top 10 countries of the 220 countries are represented in this survey.
1.
North America
2002
# of gallons
(millions)
2. South America
Country
2002
of gallons
(millions)
Brasil
2.5
3.6
Sub total
2.5
3.6
% of Total
2.5÷ 25.5
= 9.8%
Country
Slice Size
degrees)
3.
2007
# of gallons
(millions)
(in
2007
# of gallons
(millions)
.098 x 360°
= 35°
Europe
Country
#
4. Asia
2002
# of gallons
2007
# of gallons
Sub total
% of Total
Slice Size
(in degrees)
©2010 Beyond Benign – All Rights Reserved.
Country
2002
# of gallons
2007
# of gallons
Create your pie charts on the circles below. Use a protractor to approximate
each slice. ‘Fudging’ is a little OK. Be sure to give each graph a title and
label each sector.
Questions:
1.
Which continent experienced the greatest increase in the
gallons of water consumed?
number of
2.
Which continent experienced the greatest increase in their share of
the pie from 2002 to 2007?
3.
Give at least two reasons that you feel are leading to the
consumption of bottled water.
©2010 Beyond Benign – All Rights Reserved.
increased
Calculating the percent increase from 2002 to 2007 can help us make
predictions about consumption in 2012. Fill in the table below.
percent increase =
Continental
Totals

North America
U.S.
Mexico
(2007 - 2002)
x 100
2002
2002
2007
Increase
%
increase
2007
Multiplier
2012 Total
(Projected)
% of Total
9.7
14.7
5.0
5 ÷ 9.7
14.7
1.515
22.3
22.3 ÷ _____
= 51.5%
South America
Brazil
Europe
Italy, Germany,
France, Spain
Asia
China, Thailand,
Indonesia
4.
Which continent experienced the greatest percent increase in
the number of gallons of water consumed from 2002 to 2007?
5.
Which continent experienced the greatest increase in the number of
gallons of water consumed from 2007 to 2012?
6.
Do you think that Asia’s bottled water consumption will exceed the
U.S. consumption of bottled water by the year 2017? Explain.
©2010 Beyond Benign – All Rights Reserved.
= _________
The Global Bottled Water Market
Analyze Data Using Pie Charts
Teacher Answer Key
Name: _______________________________
Hour: _____
In this problem you will compare and contrast the consumption of bottled
water by creating two pie charts from the data set below;
-
one for bottled water consumption in 2002
-
and the second for bottled water consumption in 2007.
Begin by;
a.
sorting the data by continent
b. calculate the percent of total
c.
calculate the size of the pie slice d. make and label a pie chart for
each year.
CAGR = Compound Annual Growth Rate
Marketing Corporation
©2010 Beyond Benign – All Rights Reserved.
Source: Beverage
Round all data to the nearest tenth of a trillion gallons. Also note that only
the top 10 countries of the 220 countries are represented in this survey.
1.
North America
2. South America
Country
2002
# of gallons
(Trillions)
2007
# of gallons
(Trillions)
Country
2002
of gallons
(Trillions)
U.S.
5.8
8.8
Brazil
2.5
3.6
Mexico
3.9
5.9
Sub total
9.7
14.7
2.5
3.6
% of Total
38.0%
40.2%
2.5÷ 25.5
= 9.8%
9.9%
137˚
144˚
.098 x 360°
= 35°
36˚
Slice Size
degrees)
3.
(in
Europe
#
2007
# of gallons
(Trillions)
4. Asia
Country
2002
# of gallons
2007
# of gallons
Country
2002
# of gallons
2007
# of gallons
Italy
2.6
3.1
China
2.1
4.8
Germany
2.3
2.7
Indonesia
1.6
2.4
France
2.2
2.3
Thailand
1.3
1.5
Spain
1.2
1.3
Sub total
8.3
9.4
5.0
8.7
% of Total
32.5%
25.8%
19.6%
23.8%
117˚
93˚
71˚
86˚
Slice Size
degrees)
(in
©2010 Beyond Benign – All Rights Reserved.
Create your pie charts on the circles below. Use a protractor to approximate
each slice. ‘Fudging’ a little is OK. Be sure to give each graph a title and
label each sector.
Bottled Water Consumption by
Continent
South
America
9.8%
2002*
2007*
North America
38%
North America
40.2%
South
America
9.9%
Asia 19.6%
Europe 25.8%
Asia 23.8%
Europe 32.5%
Questions:
1.
Which continent experienced the greatest increase in the number of
gallons of water consumed?
N.A. increased 5 Trillion
S.A. 1.1 Trillion
2.
Asia 3.7 Trillion
Europe 1.1 Trillion
Which continent experienced the greatest increase in their share of
the pie from 2002 to 2007?
Europe: The greatest percent (of total) increase: Europe 6.7%,
Asia4.2%, N.A. 2.2%, S.A. 0.1%
©2010 Beyond Benign – All Rights Reserved.
3.
Give at least two reasons that you feel are leading to the increased
consumption of bottled water.
Contaminated water supplies
Global population increase
Calculating the percent increase from 2002 to 2007 can help us make
predictions about consumption in 2012. Fill in the table below.
percent increase =
Continental
Totals
(2007 - 2002)
x 100
2002
2002
trillion
gallons
2007
trillion
gallons
Increase
%
increase
2007
trillion
gallons
Multiplier
2012 Total
(Projected)
trillion gal.
% of Total
North America
U.S.
Mexico
9.7
14.7
5.0
5 ÷ 9.7
14.7
1.515
22.3
22.3 ÷ 53.3
South America
Brazil
-
2.5
3.6
1.1
1.1 ÷
2.5= 44%
3.6
1.44
5.2
5.2 ÷ 53.3 =
9.8%
Europe
Italy, Germany,
France, Spain
8.3
9.4
1.1
1.1 ÷ 8.3
= 13.3%
9.4
1.133
10.7
10.7 ÷ 53.3 =
20.1%
Asia
China, Thailand,
Indonesia
5
8.7
3.7
3.7 ÷ 5 =
74%
8.7
1.74
15.1
15.1 ÷ 53.3 =
28.3%

= 51.5%
= 41.8%
Total 53.3
4.
Which continent experienced the greatest percent increase in
the number of gallons of water consumed from 2002 to 2007?
Asia with a 74% increase
5.
Which continent experienced the greatest increase in the number of
gallons of water consumed from 2007 to 2012?
North America’s total increased by 7.6 trillion gallons
©2010 Beyond Benign – All Rights Reserved.
6.
Do you think that Asia’s bottled water consumption will exceed the
U.S. consumption of bottled water by the year 2017? Explain. (Hint you
could project amounts by assuming the same % increase as is evidenced in
the data you already have.)
NA
22.3 x 1.515
Asia
15.1 x 1.74
= 33.78
= 26.274
No Asia’s total has yet to exceed NA’s. NA’s projects to consume 22.78
trillion, Asia 26.274 trillion.
©2010 Beyond Benign – All Rights Reserved.
The Global Bottled Water Market
A Statistical Analysis of Data
Name: ____________________________ Hour:_____
The consumption of bottled water has been increasing across the globe. The
increase in bottled water production also leads to the increase in empty
plastic water bottle waste. These plastic bottles are sometimes recycled but
more often end up in landfills or as litter.
In this problem you will compare and contrast per capita bottled water
consumption data for the top twenty countries in the years 2002 and 2007.
Using a graphing calculator;
1.
Find the mean and median for each data set.
2002:
mean: _________
median: _________
2007:
mean: _________
median: _________
2.
Find the standard deviation for both sets.
2002:
____________
2007: _____________
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3.
Make a box and whisker plot for 2002 and 2007. Clearly mark the low,
Q1,median, Q3, and the high on each.
2002:
_________________________________________________
2007:
_________________________________________________
4.
Make a frequency table for both data sets.
Range: Gallons/capita
Frequency: 2002
12 to 17
17 to 22
22 to 27
27 to 32
32 to 37
37 to 42
42 to 47
47 to 52
52 to 57
57 to 62
62 to 67
Above 67
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Frequency: 2007
5.
Use the information from the frequency table above to make a
histogram for each data set. Label each axis. Draw a vertical line on each
graph to show the location of the mean.
2002
2007
6. Is either set of data skewed left or right?
7. Mark off two standard deviations to the right of the mean. What do
you call data points that are more than two standard deviations from the
mean?
8.
Are there any of these data points in either set?
9.
Which country’s per capita consumption is represented by this data
point? Are you surprised by this? Explain.
10.
Canada is missing from the top 20 list. Does this surprise you?
Explain.
©2010 Beyond Benign – All Rights Reserved.
The Global Bottled Water Market
A Statistical Analysis of Data
Teacher Answer Key
Name: ____________________________
Hour:_____
The consumption of bottled water has been increasing across the globe. The
increase in bottled water production also leads to the increase in empty
plastic water bottle waste. These plastic bottles are sometimes recycled but
more often end up in landfills or as litter.
In this problem you will compare and contrast per capita bottled water
consumption data for the top twenty countries in the years 2002 and 2007.
Using a graphing calculator;
1.
Find the mean, median, and mode for each data set.
2002:
mean: ____25.02_____
median: ____22.6_______
2007:
mean: ____32.4______
median: __28.4_________
2.
Find the standard deviation for both sets.
©2010 Beyond Benign – All Rights Reserved.
2002:
3.
_ 8.43____
2007: _____12.18________
Make a box and whisker plot for 2002 and 2007. Clearly mark the low,
Q1,median, Q3, and the high on each.
2002:
0
12.4 20 22
31.2
44.2
70
2007:
0
4.
22.4 24.2
28.4
35
70
Make a frequency table for both data sets.
Range:
Gallons/capita
Frequency: 2002
Frequency: 2007
12 to 17
3
0
17 to 22
7
0
22 to 27
3
9
27 to 32
2
5
32 to 37
2
2
37 to 42
2
1
42 to 47
1
0
47 to 52
0
0
52 to 57
0
2
57 to 62
0
0
62 to 67
0
0
©2010 Beyond Benign – All Rights Reserved.
Above 67
0
1
5.
Use the information from the frequency table above to make a
histogram for each data set. Label each axis. Draw a vertical line on each
graph to show the location of the mean.
2002
12-17
17-22 22-27
27- 32 32-37 37-42
42-47
47-52 52-57
Mean 25.02 + 2 (8.43) =41.88
16.86
2007
Mean 32.4 + 2(12.18) = 56.76
24.36
6. Is either set of data skewed left or right?
Both sets of data are skewed to the right. The data set for 2007 is more
skewed right than data for 2002.
7. Mark off two standard deviations to the right of the mean. What do you
call data points that are more than two standard deviations from the mean?
These data points are called outliers
©2010 Beyond Benign – All Rights Reserved.
8.
Are there any of these data points in either set?
Yes. Italy in the 2002 data. The UAE in 2007
9. Which country’s per capita consumption is represented by this data
point? Are you surprised by this? Explain.
10. Canada is missing from the top 20 list. Does this surprise you?
Explain.
©2010 Beyond Benign – All Rights Reserved.