The Water Bottle Unit Is Divided Into 3 Sections

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.

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.

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 non-sparkling 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) = ______also find N(13) = ______

5.What does N(13) represent?

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.

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.

Domestic Sparkling Bottled Water: S(x) = ______

Pearson Correlation Coefficient: r = ______

Imported Bottled Water: I(x) = ______

Pearson Correlation Coefficient: r = ______

11. Find: S(9) = ______I(9) = ______

12.What do the values S(9) and I(9) represent?

13.Which prediction is more reliable? Why?

The U.S. Bottled Water Market

Trends and Trend Lines

Name: ______Hour:_____

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

b.2008 = year 12 of the study. Evaluate your equation from question #5.

Your equation: y = _____ (12) + _____y = ______

c. LinReg equation: y = ______(12) + ______y = ______

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.Is one estimate more reliable than the other? Which one do you think is the most reliable? Explain.

The U.S. Bottled Water Market

A Graphical Analysis–Teacher Answer Key

Name: ______Hour:______

2000 2001 2002 2003 2004 2005 2006 2007 200

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 non-sparkling 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 MillionGallons also find N(13) = 11,234 Million Gallons

5.What does N(13) represent? N(13) represents the projected numberof gallons of bottled water consumed in the U.S

6. On the same graph make a connected line graph of the sales volume data for:

a.) Domestic,

b.) Sparkling and

c.) Imports

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?

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: r = 0.966

Imported Bottled Water: I(x) = 7.68x + 137.3

Pearson Correlation Coefficient: r = 0.5683

11. Find: 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.

The U.S. Bottled Water Market

Trends and Trend Lines –

Teacher Answer Key

Name: ______Hour:_____

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.

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

1.59 and 1.75 about a 10% difference.

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 35 Answers vary

b.2008 = year 12 of the study. Evaluate your equation from question #5.

Your equation: y = 1.75 (12) + 11y = 32

Answers will vary.

c. LinReg equation: y = 1.59 x (12) + 11.06y = 30.14

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 = 32c = 30.14

Compare: a and b

Compare: a and c

Compare: b and c

b.Is one estimate more reliable than the other? Which one do you think is the most reliable? Explain.

Answers vary.

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:

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 E-factor = Mass of packaging / Mass of consumable product.

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.)One each of the different half-liter bottles b.) Scale c.) 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 Second: full with caps/tops on.

Calculate and record the information below

Brand / Bottle width / 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.

( ______+ ______) ÷ 2 = ______grams/0.5L bottle

4.Calculate the average weight of the two heaviest bottles.

( ______+ ______) ÷ 2 = ______grams/0.5L bottle

5.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

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)

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

The Packaging E-Ratio

A Study of 0.5-Liter Plastic Water Bottles-

Teacher 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.)One each of the different half-liter bottles b.) Scale c.) 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 Second: full with caps/tops on.

Calculate and record the information below –

answers will vary depending on the brand of water used.

Brand / 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%

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____ + __30___ ) ÷ 2 = _29.25__ grams/0.5L bottle

4.Calculate the average weight of the two heaviest bottles.

( __15.7___ + __16__ ) ÷ 2 = __15.85_ grams/0.5L bottle

5.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

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 x # of g /0.5L bottle

= __37,672,000,000___ x ___29.25__

= _1,102,094,360,000___ grams = __1,102,094,360___ kg

= __1,102,000__ metric tons = ______1,215,000____ U.S. tons

c. 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 # of g /0.5L bottle

= __37,672,000,000_____ x __15.85______

= _59,710,120,000____ grams = _59,710,120____ kg

= ___597,101.2___ metric tons = ___658,200___ U.S. tons

d. 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)

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

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 = ______

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.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

b.How many rows are possible?______rows

c.Total # of containers:______1L containers

2.Spheres:

a.How many 12.4 cm diameter spheres fit on the bottom?.

______containers

b.How many rows are possible?______rows

c.Total # of containers:______1L containers

3.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.

b. Find the following:

cases per layer: ___layers per pallet: ____# of cases per Pallet: _____

c.Compare your results with others in class.

How shape influences packaging an Efficient Packaging Study

Teacher Answer Key

Name: ______Hour:______

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.