Municipal Waste Generation – Part I
Teacher Background Information:
Use the pdf document for Municipal Waste Generation found on the following
website. http://www.epa.gov/epawaste/nonhaz/municipal/pubs/msw07rpt.pdf
Content Area:
http://www.factmonster.com/us/census/national-1790Reading line graphs
2000.html
Goals: To… assess or review the students’ ability to read
line graphs and calculate the percent of change in data.
Objectives: Students will . . .
Read and interpret graphs and tables
Determine percent of increase/decrease
Procedure: (for the teacher)
Ask students if they can estimate how many things
they have thrown in the trash can so far today.
Explain that it is a significant amount and that
everyone on the planet is doing the same thing.
Explain that you are going to explore a little deeper
about the concept of waste using math data and
concepts.
Hand out the student sheet.
Review and answer questions.
Give students time to complete the worksheet.
Show students the PPT presentation – you may want to
and make it into a competition.
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Calculating percent
of change
Standards met:
NM-NUM.9-12.3
NM-ALG.9-12.4
NM-COMM.PK-12.1
Time required:
20-30 minutes
Materials: (per
student)
MSW Generation
Rates graph
handout
U.S. populations
table handout
Calculator
needed:
make teams
Municipal Waste Generation Part I:
Student Worksheet
Name: ____________________________________Class period: ________
Use the figure 1 graph and the US population chart to answer the following.
1. Calculate the percent of increase/decrease for each 5-year period (6-year
period from 2000 – 2006) for both graphs. (show your calculations)
MSW Total
Per Capita
1960 – 1965:
_______
________
1965 – 1970:
__________
1970 – 1975:
_________
_________
1975 – 1980:
_________
_________
1980 – 1985:
_________
_________
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__________
MSW Total
Per Capita
1985 – 1990:
________
_________
1990 – 1995:
_________
_________
1995 – 2000:
_________
_________
2000 – 2006:
_________
_________
2. Give an explanation for why the rates of change for Total MSW are not
the same as the rates of change for Per Capita Waste from 1960 – 2006.
3. State whether the following statement is “true” or “false” and explain:
“If the per capita generation of waste decreases, then the total MSW
generation will decrease also.”
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4. Which graph (“Total MSW generation” or “Per Capita generation”)
gives more cause for concern and why?
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Municipal Waste Generation: Student
Data –
Figure 1
Name:____________________________________ Class period:_________
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Municipal Waste Generation: Student
Data – US Population Chart
Name:_________________________________ Class period:_______
National Censuses, 1790–20001
Resident
Year population
Land area, Pop. per
2
sq mi
sq mi
1790
3,929,214
864,746
4.5
1800
5,308,483
864,746
6.1
1810
7,239,881
1,681,828
4.3
1820
9,638,453
1,749,462
5.5
1830 12,866,020
1,749,462
7.4
1840 17,069,453
1,749,462
9.8
1850 23,191,876
2,940,042
7.9
1860 31,443,321
2,969,640
10.6
1870 39,818,449
2,969,640
13.4
1880 50,155,783
2,969,640
16.9
1890 62,947,714
2,969,640
21.2
1900 75,994,575
2,969,834
25.6
1910 91,972,266
2,969,565
31.0
1920 105,710,620 2,969,451
35.6
1930 122,775,046 2,977,128
41.2
1940 131,669,275 2,977,128
44.2
1950 150,697,361 2,974,726
50.7
1960 179,323,175 3,540,911
50.6
1970 203,302,031 3,540,023
57.4
1980 226,545,805 3,539,289
64.0
1990 248,709,873 3,536,278
70.3
2000 281,421,906 3,537,441
79.6
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Municipal Waste Generation Part I:
Student Worksheet – Teacher
Answer Key
Use the figure 1 graph and the US population chart to answer the following.
1. Calculate the percent of increase/decrease for each 5-year period (6-year
period from 2000 – 2006) for both graphs. (show your calculations)
MSW Total
Per Capita
1960 – 1965:
18.7 %
10.6 %
(88.1 + 121.1)/2 = 104.6
(2.68 + 3.25)/2 = 2.965
(104.6 – 88.1)/88.1 = .187
(2.965 – 2.68)/2.68 = .106
1965 – 1970:
15.8 %
(88.1 + 121.1)/2 = 104.6
(2.68 + 3.25)/2 = 2.965
(121.1 - 104.6)/104.6 = .158
(3.25 - 2.965)/2.965 = .096
1970 – 1975:
12.6 %
(121.1 + 151.6)/2 = 136.35
(3.66 + 3.25)/2 = 3.455
(136.5 – 121.1)/121.1 = .126
(3.455 – 3.25)/3.25 = .063
1975 – 1980:
11.2 %
(121.1 + 151.6)/2 = 136.35
(3.66 + 3.25)/2 = 3.455
(151.6 – 136.5)/136.5 = .112
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9.6%
6.3%
10.6 %
(3.66 – 3.455)/3.455 = .106
MSW Total
Per Capita
1980 – 1985:
(151.6 + 205.2)/2 = 178.4
– 151.6)/151.6 = .177
17.7 %
5.9 %
(4.5 + 3.66)/2 = 4.08(178.4
4.08 – 3.66)/3.66 = .059
1985 – 1990:
15.0 %
(151.6 + 205.2)/2 = 178.4
(4.5 + 3.66)/2 = 4.08
(205.2 - 178.4)/178.4 = .150
(4.5 - 4.08)/4.08 = .103
1990 – 1995:
4.4 %
(214.3 – 205.2)/205.2 = .044
(4.46 – 4.50)/4.50 = -0.009
1995 – 2000:
11.2 %
(238.3 – 214.3)/214.3 = .112
(4.64 – 4.46)/4.46 = 0.040
2000 – 2006:
5.5 %
(251.3 – 238.3)/238.3 = .055
(4.60 – 4.64)/4.64 = -0.009
10.3 %
-0.9 %
_4.0 %
-0.9 %
2. Give an explanation for why these rates of change (percents) for each
period are not the same for the two graphs.
While the per capita generation of waste levels, the total amount of waste
increased because the population continues to increase.
3. State whether the following statement is “true” or “false,” and explain:
“If the per capita generation of waste decreases, then the total MSW
generation will decrease also.”
False. As seen, the per capita generation decreased but the total MSW did
not. This is because the per capita generation is affected by the changes in
population.
4. Which graph (“Total MSW generation” or “Per Capita generation”) gives
more cause for concern and why?
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Total MSW: It’s the amount of waste that causes the immediate concern. It
is a good thing that the per capita generation is decreasing – it just isn’t
enough to cause the total waste to decrease.
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Municipal Waste Generation – Part II
Teacher Background Information:
Use the PDF document for Municipal Waste Generation found on the
following website.
http://www.epa.gov/epawaste/nonhaz/municipal/pubs/msw07-rpt.pdf
Goals: To assess or review students’ ability to
interpret pie charts, and successfully perform
operations with percents and fractions.
Objectives: Students will . . .
Read and interpret graphs
Determine the fraction of the total for various
parts of a pie graph
Use percentages to determine the amount
associated with each part of a pie graph
Solve problems using fractions
Procedure: (for the teacher)
If you have not already done the first waste
lesson you may want to start this lesson with
the warm-up and culminating activity from
the last lesson.
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Content Area:
Reading pie charts
Renaming percents as
fractions
Operations with
percents
Standards met:
NM-NUM.9-12.3
NM-PROB.REP.PK-12.1
Time required: 20 –
30 minutes
Materials: (per
student)
Figure 5 Total MSW
Generation pie chart
handout
Calculator
:
Municipal Waste Generation – Part
II: Student Worksheet
Name:_____________________ Class period:_________
Use the pie chart to answer the following questions. (show all calculations)
1. What is the approximate number of tons for each category of material in
this graph? (First write the fraction of the total waste generated for each
category)
Paper:
Glass:
Metals:
Plastics:
Rubber/leather & textiles:
Wood:
Yard trimmings:
Food scraps:
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2. Identify up to three combinations of categories:
a) one-tenth of the total waste?
b) one-fifth of the total waste?
c) one-fourth of the total waste?
d) nine-twentieths of the total waste?
e) one-half of the total waste?
3. If all of the percentages in the graph are added together, what is the
total that you would expect to have? Is this true for the graph in this
problem? If not, explain a possible reason?
©2010 Beyond Benign – All Rights Reserved.
Municipal Waste Generation – Part
II: Student Worksheet – Teacher
Key
Name:_____________________ Class period:_________
Use the figure 5 pie chart to answer the following questions. (show all
calculations)
1. What is the approximate number of tons for each category of material in
this graph? (First write the fraction of the total waste generated for each
category)
Paper:
327/1000 x 254,000,000
tons
83,058,000
Glass:
53/1000 x 254,000,000
tons
13,462,000
Metals:
82/1000 x 254,000,000
tons
20,280,000
Plastics:
121/1000 x 254,000,000
tons
30,734,000
Rubber/leather & textiles:
76/1000 x 254,000,000
tons
Wood:
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19,304,000
56/1000 x 254,000,000
tons
14,224,000
Yard trimmings:
128/1000 x 254,000,000
tons
32,512,000
Food scraps:
125/1000 x 254,000,000
tons
31,750,000
2. Identify up to three combinations of categories (showing all of your
calculations) that account for approximately . . .
(the top three combinations are shown below)
a) one-tenth of the total waste?
(Accept combinations from 9% - 11%)
Rubber, Leather, and Textiles (RLT) & Other
(7.6% + 3.2%)
10.8%
Wood & Glass
(5.6% + 5.3%)
10.9%
b) one-fifth of the total waste?
(Accept combinations from 19% - 21%)
Food & RLT
(12.5% + 7.6%)
20.1%
Plastics & Metals
(12.1% + 8.2%)
20.3%
Plastics & RLT
19.7%
(12.1% + 7.6%)
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c) one-fourth of the total waste?
(Accept combinations from 24% - 26%)
Yard Trimmings & Plastics
(12.8% + 12.1%)
24.9%
Yard Trimmings & Food
(12.8% + 12.5%)
25.3%
Food & Plastics
(12.5% + 12.1%)
24.6%
d) nine-twentieths of the total waste?
(Accept combinations from 44% - 46%)
Paper & Plastics
(32.7% + 12.1%)
44.8%
Paper & Food
(32.7% + 12.5%)
45.2%
Paper & Yard Trimmings
(32.7% + 12.8%)
45.5%
e) one-half of the total waste?
(Accept combinations from 49% - 51%)
Paper & Plastic & Glass
12.1% + 5.3%)
50.1%
(32.7% +
Paper & Food
12.5% + 5.3%)
50.4%
(32.7% +
Paper & Yard Trimmings
12.8% + 5.3%)
50.5%
(32.7% +
3. If all of the percentages in the graph are added together, what is the
total that you would expect to have? Is this true for the graph in this
problem? If not, explain a possible reason?
The total percentage should be 100%. Yes, the total for this graph is 100%
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Municipal Waste Generation:
Student Data – Figure 5
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Municipal Waste Generation – Part
III
Teacher Background Information:
Use the PDF document for Municipal Waste Generation found on the
following website.
http://www.epa.gov/epawaste/nonhaz/municipal/pubs/msw07-rpt.pdf
Goals: To…..
Assess or review students’ understanding of how
regression analysis can be used to represent data in a
way that predictions can be made concerning that data.
Objectives: Students will . . .
Fit a curve to given data
Use function notation to identify a function
Use interpolation and extrapolation to estimate
data that is not provided in the data set
Use the correlation coefficient (r) to comment on
the goodness of fit of their function (extension)
Procedure: (for the teacher)
All procedures are reflected in the student
handout
Content Area:
Reading bar graphs
Function notation
Curve fitting (calculator
active)
Interpolation &
Extrapolation
Goodness of fit using the
correlation coefficient
(extension)
Prerequisites:
Using graphic display
calculator/computer to
conduct regression
analysis
Standards met:
NM-ALG.9-12.2
NM-ALG.9-12.3
NM-PROB.COMM.PK-12.1
Time required: 20-30
minutes
Materials: (per student)
Number of landfills in the
United States bar graph
handout
Graphic Display
Calculator:
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Municipal Waste Generation – Part
III: Student Worksheet
Name:___________________________________ Class period:_________
Use the Landfills bar graph and your available technology (calculator or
computer) to:
1. Determine the function (equation) that best models the data in the
graph. Write this equation using the function notation L(x), where x is the
year and L(x) is the number of landfills.
2. Use your function to estimate L(2003) and L(2004).
3. Use your function to estimate L(2020). Comment on the reasonableness
of your answer.
(extension): Comment on how well your function fits the data (including
your “r value” in your comment.)?
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Municipal Waste Generation: Student
Worksheet – Landfills bar graph
Name: _____________________________
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Class period:_________
Student Worksheet:
STAT CALC menu on TI-83 calculator
4.
LinReg
Fits a linear model to data
(Xlistname, Ylistname, freqlist, regequ)
LinReg
5.
QuadReg
Fits a quadratic model to data
(Xlistname, Ylistname, freqlist, regequ)
QuadReg
6.
CubicReg
Fits a cubic model to data
(Xlistname, Ylistname, freqlist, regequ)
CubicReg
7.
QuartReg
Fits a quartic model to data
(Xlistname, Ylistname, freqlist, regequ)
QuartReg
9.
LnReg
Fits a logarithmic model to data
(Xlistname, Ylistname, freqlist, regequ)
LnReg
10. ExpReg
Fits an exponential model to data
(Xlistname, Ylistname, freqlist, regequ)
ExpReg
A.
PwrReg
Fits a power model to data
(Xlistname, Ylistname, freqlist, regequ)
PwrReg
B.
logistic
Fits a logistical model to data
(Xlistname, Ylistname, freqlist, regequ)
Logistic
C.
SinReg
SinReg
Fits a sinusoidal model to data
(iterations, Xlistname, Ylistname, period, regequ)
When using the TI-83 calculator to find an equation that will model data using
one of the regression models above, you should set the “DiagnosticOn” by
pressing 2nd catalog and select “diagnosticon”, then press enter. This will
display the diagnostics r and r2 with the results when you execute a regression
model.
©2010 Beyond Benign – All Rights Reserved.
The Correlation (r) measures the strength and direction of the linear
association between two quantitative variables x and y. The calculator linearly
transforms the data to allow us to use r with non-linear data.
The Coefficient of determination (r2) is the proportion of the total variability
that is explained by the least squares regression of y on x. (0 ≤ r2 ≤ 1) The
value r2 tells us what percent of the total variation of the y-values about their
mean can be explained by the terms of the model (x-values). (1 - r2) is the
percentage of variation that is unexplained by the model.
The closer is to one, the better the fit of the model to the data. In the r2
scale, a correlation of ±.7 is about halfway between 0 and 1. (In other words,
when r = ±.7, r2 = ±.5)
©2010 Beyond Benign – All Rights Reserved.
Municipal Waste Generation – Part
III: Student Worksheet – Teacher
Key
Use the Landfills bar graph and your available technology (calculator or
computer) to:
1. Determine the function (equation) that best models the data in the
graph. Write this equation using the function notation L(x), where x is the
year and L(x) is the number of landfills.
Using the quadratic regression function on the TI-83 calculator, the
equation:
L(x) = 28.52855x2 – 114284.09x + 114455841.7 models the data with a
correlation coefficient (r) of .99674.
Using the exponential regression function: L(x) = (8.69117 x 1085)(.90930x)
models the data with a correlation coefficient of .96183.
2. Use your function to estimate L(2003) and L(2004).
Quadratic model: L(2003) ≈ 1630
L(2004) ≈ 1659
Exponential model: L(2003) ≈ 1701
L(2004) ≈ 1547
3. Use your function to estimate L(2020). Comment on the reasonableness
of your answer.
Quadratic model: L(2020) ≈ 9896
Not very reasonable, or desirable.
Exponential model: L(2020) ≈ 338
landfills will be gone some day.
Reasonable. It is our hope that all
(extension): Comment on how well your function fits the data (including
your “r value” in your comment.)? The quadratic model fits the data very
well, with a correlation coefficient (r-value) of ≈.99674, but it would have
the number of landfills increase in the years to come. This is not reasonable
or desirable. The exponential model fits the data pretty well, with a
correlation coefficient of ≈.96183. The closer the r-value is to 1 or -1, the
better the fit of the model to the data.
©2010 Beyond Benign – All Rights Reserved.
Municipal Waste Generation – Part IV
Teacher Background Information:
Use the pdf document for Municipal Waste Generation found on the following
website.
http://www.epa.gov/epawaste/nonhaz/municipal/pubs/msw07-rpt.pdf
Goals: To…..
Assess or review students’ understanding of reading
and interpreting tables and graphs, constructing
specialty graphs, and the use of percentages in such
areas.
Objectives: Students will . . .
Read and interpret graphs and tables
Calculate the percentage of the whole for
various parts
Construct graphs (pie, and stacked bar)
Procedure: (for the teacher)
All procedures are reflected in the student
handout
Content Area:
Reading tables
Renaming fractions as
percents
Creating pie charts and
stacked bar graphs
Prerequisites:
Knowledge of
constructing pie charts
and “stacked” bar
graphs
Standards met:
NM-NUM.9-12.3
NM-MEA.9-12.1
NM-DATA.9-12.3
NM-PROB.REP.PK-12.1
Time required:
30 – 45 minutes
Materials: (per
student)
Table 3 Generation
Materials recovery
Composting,
Combustion with
energy recovery
Discards of MSW
handout
Graph paper and circle
graph paper
Rulers and protractors:
©2010 Beyond Benign – All Rights Reserved.
Municipal Waste Generation – Part
IV: Student Worksheet
Name:___________________________________ Class period:_________
1. Use the generation materials recovery table to determine the
“percentage of the total generation” for the following categories for 1960
and 2006: (show all calculations)
Recovery for recycling:
Recovery for composting:
Total materials recovery:
Combustion with energy recovery:
Discards to landfill/other disposal:
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2. Construct pie charts (graphs) 1960 and 2006 using the percentage of the
total generation from problem #1. Show your calculations, on a separate
sheet of paper, for determining the angle measures needed to construct
each graph. Remember titles and labels.
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3.
Construct a stacked bar graph. Your graph will show the amount of
waste recovery (in millions of tons) from the different activities, for the
years 1960 and 2006, “stacked” to form one bar for each year. Your
categories should include: recycling, composting, combustion, and
landfill/other. Remember titles and labels for your graph.
4. Identify and describe any trends that you see in the stacked bar graph.
©2010 Beyond Benign – All Rights Reserved.
STAT CALC menu on TI-83 calculator
4.
LinReg
Fits a linear model to data
(Xlistname, Ylistname, freqlist, regequ)
LinReg
5.
QuadReg
Fits a quadratic model to data
(Xlistname, Ylistname, freqlist, regequ)
QuadReg
6.
CubicReg
Fits a cubic model to data
(Xlistname, Ylistname, freqlist, regequ)
CubicReg
7.
QuartReg
Fits a quartic model to data
(Xlistname, Ylistname, freqlist, regequ)
QuartReg
9.
LnReg
Fits a logarithmic model to data
(Xlistname, Ylistname, freqlist, regequ)
LnReg
10. ExpReg
Fits an exponential model to data
(Xlistname, Ylistname, freqlist, regequ)
ExpReg
A.
PwrReg
Fits a power model to data
(Xlistname, Ylistname, freqlist, regequ)
PwrReg
B.
Logistic
Fits a logistical model to data
(Xlistname, Ylistname, freqlist, regequ)
Logistic
C.
SinReg
Fits a sinusoidal model to data
(iterations, Xlistname, Ylistname, period, regequ)
SinReg
When using the TI-83 calculator to find an equation that will model data
using one of the regression models above, you should set the “DiagnosticOn”
by pressing 2nd catalog and select “diagnosticon”, then press enter. This will
display the diagnostics r and r2 with the results when you execute a
regression model.
©2010 Beyond Benign – All Rights Reserved.
The Correlation (r) measures the strength and direction of the linear
association between two quantitative variables x and y. The calculator
linearly transforms the data to allow us to use r with non-linear data.
The Coefficient of determination (r2) is the proportion of the total variability
that is explained by the least squares regression of y on x. (0 ≤ r2 ≤ 1)
The value r2 tells us what percent of the total variation of the y-values about
their mean can be explained by the terms of the model (x-values). (1 - r2)
is the percentage of variation that is unexplained by the model.
©2010 Beyond Benign – All Rights Reserved.
Municipal Waste Generation – Part
IV: Student Worksheet – Teacher
Key
Name: ______________________________
Class period: _________
1. Use the materials generation recovery table to determine the
“percentage of the total generation” for the following categories for 1960
and 2006: (show all calculations)
Recovery for recycling:
1960
6.36%
2006
24.27%
Recovery for composting:
1960
2006
0.0%
8.28%
Combustion with energy recovery:
1960
0.0%
2006
12.50%
Discards to landfill/other disposal:
1960
93.64%
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2006
54.99%
2. Construct pie charts (graphs) 1960 and 2006 using the percentage of the
total generation from problem #1. Show your calculations, on a separate
sheet of paper, for determining the angle measures needed to construct
each graph. Remember titles and labels. (The graph should include the
following categories: Recycling, Composting, Combustion, & Landfill/other.)
1960
Recycling:
360 x .0636 = 23°
Composting:
360 x 0 = 0°
Combustion:
360 x 0 = 0°
Landfill/Other:
360 x .9364 = 337°
2006
Recycling:
360 x .2427 = 87°
Composting:
360 x .0828 = 30°
Combustion:
360 x .125 = 45°
Landfill/Other: 360 x .5499 = 198°
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3. Construct a stacked bar graph. Your graph will show the amount of waste
recovery (in millions of tons) from the different activities, for the years 1960
and 2006, “stacked” to form one bar for each year. Your categories should
include: recycling, composting, combustion, and landfill/other. Remember
titles and labels for your graph.
4. Identify and describe any trends that you see in the stacked bar graph.
Recycling & Composting (total materials recovery) has increased the most,
but has begun slowing its growth to about .6% per year.
Combustion with energy recovery peaked in 1990 and has since declined at
a small, but increasing, rate.
Discards to landfill/other decreased dramatically at first, but now seem to
have leveled off at about 55% of the total waste generated.
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Municipal Waste Generation: Student
Worksheet - Generation materials
recovery
Name:____________________________________ Class period:_________
©2010 Beyond Benign – All Rights Reserved.
