Municipal Waste Generation – Part I



Municipal Waste Generation – Part I

Teacher Background Information:

Use the pdf document for Municipal Waste Generation found on the following website.



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 make teams and make it into a competition.

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: _________ _________

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.”

4. Which graph (“Total MSW generation” or “Per Capita generation”) gives more cause for concern and why?

Municipal Waste Generation: Student Data –

Figure 1

Name:____________________________________ Class period:_________

[pic]

[pic]

Municipal Waste Generation: Student Data – US Population Chart

Name:_________________________________ Class period:_______

National Censuses, 1790–20001

|Year |Resident |Land area, |Pop. per |

| |population2 |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 |

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 % 9.6%

(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 % 6.3%

(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 % 10.6 %

(121.1 + 151.6)/2 = 136.35 (3.66 + 3.25)/2 = 3.455

(151.6 – 136.5)/136.5 = .112 (3.66 – 3.455)/3.455 = .106

MSW Total Per Capita

1980 – 1985: 17.7 % 5.9 % (151.6 + 205.2)/2 = 178.4 (4.5 + 3.66)/2 = 4.08(178.4 – 151.6)/151.6 = .177 4.08 – 3.66)/3.66 = .059

1985 – 1990: 15.0 % 10.3 %

(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 % -0.9 %

(214.3 – 205.2)/205.2 = .044 (4.46 – 4.50)/4.50 = -0.009

1995 – 2000: 11.2 % _4.0 %

(238.3 – 214.3)/214.3 = .112 (4.64 – 4.46)/4.46 = 0.040

2000 – 2006: 5.5 % -0.9 %

(251.3 – 238.3)/238.3 = .055 (4.60 – 4.64)/4.64 = -0.009

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?

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.

Municipal Waste Generation – Part II

Teacher Background Information:

Use the PDF document for Municipal Waste Generation found on the following website.



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.

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:

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?

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 83,058,000 tons

Glass:

53/1000 x 254,000,000 13,462,000 tons

Metals:

82/1000 x 254,000,000 20,280,000 tons

Plastics:

121/1000 x 254,000,000 30,734,000 tons

Rubber/leather & textiles:

76/1000 x 254,000,000 19,304,000 tons

Wood:

56/1000 x 254,000,000 14,224,000 tons

Yard trimmings:

128/1000 x 254,000,000 32,512,000 tons

Food scraps:

125/1000 x 254,000,000 31,750,000 tons

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 10.8% (7.6% + 3.2%)

Wood & Glass 10.9% (5.6% + 5.3%)

b) one-fifth of the total waste?

(Accept combinations from 19% - 21%)

Food & RLT 20.1% (12.5% + 7.6%)

Plastics & Metals 20.3% (12.1% + 8.2%)

Plastics & RLT 19.7%

(12.1% + 7.6%)

c) one-fourth of the total waste?

(Accept combinations from 24% - 26%)

Yard Trimmings & Plastics 24.9% (12.8% + 12.1%)

Yard Trimmings & Food 25.3% (12.8% + 12.5%)

Food & Plastics 24.6% (12.5% + 12.1%)

d) nine-twentieths of the total waste?

(Accept combinations from 44% - 46%)

Paper & Plastics 44.8% (32.7% + 12.1%)

Paper & Food 45.2% (32.7% + 12.5%)

Paper & Yard Trimmings 45.5% (32.7% + 12.8%)

e) one-half of the total waste?

(Accept combinations from 49% - 51%)

Paper & Plastic & Glass 50.1% (32.7% + 12.1% + 5.3%)

Paper & Food 50.4% (32.7% + 12.5% + 5.3%)

Paper & Yard Trimmings 50.5% (32.7% + 12.8% + 5.3%)

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%

Municipal Waste Generation: Student Data – Figure 5

Municipal Waste Generation – Part III

Teacher Background Information:

Use the PDF document for Municipal Waste Generation found on the following website.



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

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.)?

Municipal Waste Generation: Student Worksheet – Landfills bar graph

Name: _____________________________ Class period:_________

[pic]

Student Worksheet:

STAT CALC menu on TI-83 calculator

4. LinReg Fits a linear model to data LinReg (Xlistname, Ylistname, freqlist, regequ)

5. QuadReg Fits a quadratic model to data QuadReg (Xlistname, Ylistname, freqlist, regequ)

6. CubicReg Fits a cubic model to data CubicReg (Xlistname, Ylistname, freqlist, regequ)

7. QuartReg Fits a quartic model to data QuartReg (Xlistname, Ylistname, freqlist, regequ)

9. LnReg Fits a logarithmic model to data LnReg (Xlistname, Ylistname, freqlist, regequ)

10. ExpReg Fits an exponential model to data ExpReg (Xlistname, Ylistname, freqlist, regequ)

A. PwrReg Fits a power model to data PwrReg (Xlistname, Ylistname, freqlist, regequ)

B. logistic Fits a logistical model to data Logistic (Xlistname, Ylistname, freqlist, regequ)

C. SinReg Fits a sinusoidal model to data SinReg

(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.

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)

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 Reasonable. It is our hope that all landfills will be gone some day.

(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.

Municipal Waste Generation – Part IV

Teacher Background Information:

Use the pdf document for Municipal Waste Generation found on the following website.



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

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:

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.

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.

STAT CALC menu on TI-83 calculator

4. LinReg Fits a linear model to data LinReg (Xlistname, Ylistname, freqlist, regequ)

5. QuadReg Fits a quadratic model to data QuadReg (Xlistname, Ylistname, freqlist, regequ)

6. CubicReg Fits a cubic model to data CubicReg (Xlistname, Ylistname, freqlist, regequ)

7. QuartReg Fits a quartic model to data QuartReg (Xlistname, Ylistname, freqlist, regequ)

9. LnReg Fits a logarithmic model to data LnReg (Xlistname, Ylistname, freqlist, regequ)

10. ExpReg Fits an exponential model to data ExpReg (Xlistname, Ylistname, freqlist, regequ)

A. PwrReg Fits a power model to data PwrReg (Xlistname, Ylistname, freqlist, regequ)

B. Logistic Fits a logistical model to data Logistic (Xlistname, Ylistname, freqlist, regequ)

C. SinReg Fits a sinusoidal model to data SinReg (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.

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.

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 2006

[pic] [pic]

6.36% 24.27%

Recovery for composting:

1960 2006

[pic] [pic]

0.0% 8.28%

Combustion with energy recovery:

1960 2006

[pic] [pic]

0.0% 12.50%

Discards to landfill/other disposal:

1960 2006

[pic] [pic]

93.64% 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°

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.

Municipal Waste Generation: Student Worksheet - Generation materials recovery

Name:____________________________________ Class period:_________

[pic]

-----------------------

Content Area:

Reading line graphs

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:

Content Area:

Reading pie charts

[pic]%&'FGHQq›œÛÜ " Ž ? › û ü |

M

òîãØÍëá։ÉáÍ}ØÍ}qÍ–Ã}hQhî-jhZ?ª5?CJ OJQJRenaming 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

:

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-M.PK-12.1

Time required: 20-30 minutes

Materials: (per student)

Number of landfills in the United States bar graph handout

Graphic Display Calculator:

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:

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download