# 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 TotalPer Capita

1960 – 1965:______

1965 – 1970:______

1970 – 1975:______

1975 – 1980:______

1980 – 1985:______

MSW TotalPer 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.”

- 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:______

**Municipal Waste Generation: Student Data – US Population Chart**

Name:______Class period:______

**National Censuses, 1790–20001**

population2 / Land area,

sq mi / Pop. per

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 TotalPer 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 TotalPer 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 254,000,00083,058,000 tons

Glass:

53/1000 x 254,000,00013,462,000 tons

Metals:

82/1000 x 254,000,00020,280,000 tons

Plastics:

121/1000 x 254,000,00030,734,000 tons

Rubber/leather & textiles:

76/1000 x 254,000,00019,304,000 tons

Wood:

56/1000 x 254,000,00014,224,000 tons

Yard trimmings:

128/1000 x 254,000,00032,512,000 tons

Food scraps:

125/1000 x 254,000,00031,750,000 tons

- 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) & Other10.8% (7.6% + 3.2%)

Wood & Glass10.9% (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 & Metals20.3%(12.1% + 8.2%)

Plastics & RLT19.7%

(12.1% + 7.6%)

c)one-fourth of the total waste?

(Accept combinations from 24% - 26%)

Yard Trimmings & Plastics24.9%(12.8% + 12.1%)

Yard Trimmings & Food25.3%(12.8% + 12.5%)

Food & Plastics24.6%(12.5% + 12.1%)

d)nine-twentieths of the total waste?

(Accept combinations from 44% - 46%)

Paper & Plastics44.8%(32.7% + 12.1%)

Paper & Food45.2%(32.7% + 12.5%)

Paper & Yard Trimmings45.5%(32.7% + 12.8%)

e)one-half of the total waste?

(Accept combinations from 49% - 51%)

Paper & Plastic & Glass50.1%(32.7% + 12.1% + 5.3%)

Paper & Food50.4%(32.7% + 12.5% + 5.3%)

Paper & Yard Trimmings50.5%(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:______

**Student Worksheet: **

**STAT CALC menu on TI-83 calculator**

4.LinRegFits a linear model to dataLinReg (Xlistname, Ylistname, freqlist, regequ)

5.QuadRegFits a quadratic model to dataQuadReg (Xlistname, Ylistname, freqlist, regequ)

6.CubicRegFits a cubic model to dataCubicReg (Xlistname, Ylistname, freqlist, regequ)

7.QuartRegFits a quartic model to dataQuartReg (Xlistname, Ylistname, freqlist, regequ)

9.LnRegFits a logarithmic model to dataLnReg (Xlistname, Ylistname, freqlist, regequ)

10.ExpRegFits an exponential model to dataExpReg (Xlistname, Ylistname, freqlist, regequ)

A.PwrRegFits a power model to dataPwrReg (Xlistname, Ylistname, freqlist, regequ)

B.logisticFits a logistical model to dataLogistic (Xlistname, Ylistname, freqlist, regequ)

C.SinRegFits a sinusoidal model to dataSinReg

(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) ≈ 1630L(2004) ≈ 1659

Exponential model: L(2003) ≈ 1701L(2004) ≈ 1547

3. Use your function to estimate L(2020). Comment on the reasonableness of your answer.

Quadratic model: L(2020) ≈ 9896Not very reasonable, or desirable.

Exponential model: L(2020) ≈ 338Reasonable. 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.LinRegFits a linear model to dataLinReg (Xlistname, Ylistname, freqlist, regequ)

5.QuadRegFits a quadratic model to dataQuadReg (Xlistname, Ylistname, freqlist, regequ)

6.CubicRegFits a cubic model to dataCubicReg (Xlistname, Ylistname, freqlist, regequ)

7.QuartRegFits a quartic model to dataQuartReg (Xlistname, Ylistname, freqlist, regequ)

9.LnRegFits a logarithmic model to dataLnReg (Xlistname, Ylistname, freqlist, regequ)

10.ExpRegFits an exponential model to dataExpReg (Xlistname, Ylistname, freqlist, regequ)

A.PwrRegFits a power model to dataPwrReg (Xlistname, Ylistname, freqlist, regequ)

B.LogisticFits a logistical model to dataLogistic (Xlistname, Ylistname, freqlist, regequ)

C.SinRegFits a sinusoidal model to dataSinReg (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

6.36% 24.27%

Recovery for composting:

1960 2006

0.0% 8.28%

Combustion with energy recovery:

1960 2006

0.0% 12.50%

Discards to landfill/other disposal:

1960 2006

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:______

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