1. Students will be able to systematically collect, organize, and describe data through construction and interpretation of graphs.
2. Students will be able to make inferences, formulate convincing arguments and evaluate those arguments based on data analysis.
3. Students will gain an appreciation for statistical methods as a powerful tool in decision-making.
(These objectives coincide with National Council of Teachers of Mathematics Standard #10: statistics for grades 5-8.)
In the mathematics portion of the "You Make It Happen" module students study how energy use varies over time. Monthly utility bills covering a one year period provide data for student analysis. Students construct and interpret graphs of monthly energy usage. They then practice making inferences and developing convincing arguments based on their data as to the causes of monthly fluctuations in energy use.
For activities 2 and 4, you will need multiple copies of utility bills spanning a one year period. To make this unit most realistic for students, it would be best if each student could bring a copy of their family's monthly utility bill for the past year. These utility bills will then serve as the data base for several activities. Approximately one week before beginning the energy unit, send a letter home with students asking for monthly utility figures (See sample letter in Appendix B). Have sample utility bills available for students who are unable to bring their own bills. While a 12-month sample is provided in Appendix B, it would be best to secure bills from your own local utility, as the format differs with each company. You may be able to get sample bills covering a one year period from your local utility. Ask for bills representing a variety of situations. For example, from a grain farmer, a large family, an apartment, a large home and a small home. This will provide students with a variety of data from which they may make inferences about energy consumption patterns.
Throughout this module, students should be given the opportunity to work in small groups. It is suggested that the group size be kept at two students and that all students make their own graphs, rather than making graphs as a group. This will help to ensure maximum involvement by all students.
Each of the five questions posed below could be used as an authentic assessment measure following completion of the 4 activities.
1. A new family has moved into your school district. Explain in writing what they need to know to understand their utility bill. (Purpose: to evaluate student's ability to interpret a utility bill)
2. The following graph is an example of annual energy usage in the form of natural gas. What conclusions can you make from this data? (Purpose: to evaluate the student's ability to make inferences and interpret graphs.)
3. The graph below shows the annual electrical energy use of a sample household. What conclusions can you make from this data about the household's electricity use behaviors? Be as specific as possible in trying to explain the monthly fluctuations in electricity.
4. Create a January through December graph/record of energy use based on the scenario presented below.....extra fun: circle any energy terms you find in the paragraph (Purpose: to evaluate the student's ability to use written material to develop graphs)
The D.C. Watts are a family of four currently living in our community. Their home has electric heat and air conditioning. They had a shocking experience in July when their grandparents, Mr. and Mrs. A.C. Lumens, came to spend the entire month with them. Fortunately, they brought their own mobile home in which to stay. Unfortunately, they plugged their mobile home into the Watt's power supply. The D.C. Watts were powerless in their efforts to get them to shorten their stay. Although it was an enlightening experience, the family needed to re-charge so they surged ahead on a three week vacation that included stops at the Hoover Dam, the oil fields of Texas, the turbine valleys in California and other illuminating places. After completing this circuit, they returned home. The remainder of the year was normal in regard to temperature and precipitation. However, the month of January generated the coldest temperatures on record.
Teacher Notes
Objective:
List at least five different types of information which are contained on a local utility bill.
Materials:
local utility bills (one copy per student group)
It would be best if each group is given a different bill. You may secure copies of local utility bills from your local utility, or may wish to use some of the
bills which students have brought in from their homes.
Suggested Teaching Strategies:
Give each group of students a copy of a local utility bill (one month only)
along with the student worksheet entitled "Bill Me". Directions are provided on the student worksheet. You may wish to save on paper copies by presenting
students with an overhead of the problem (Let's Investigate) and the Summing Up questions.
After students have been allowed some time to work on the Let's Investigate, get student groups to share their ideas. Generate a class list of the information provided on a utility bill. Remind students to make additions to their own lists as each group shares their ideas.
Discuss student answers to the "Summing Up" questions. Be sure to ask students to give reasons for their answers. Students should have had a great deal of difficulty coming up with good guesses to these questions. They simply do not have enough data to answer the questions. The point of asking these questions at this stage is to allow students to come to the realization that they can not make very good inferences based on this limited amount of data. One month's energy consumption does not allow students to see a pattern.
Student Page
A utility bill contains a lot more information than how much money you owe for your energy consumption. By closely examining a typical month's bill, you can see the types of information which the bill gives you about energy use patterns.
Let's Investigate:
Exam your copy of a utility bill. As a group, make a list of the types of information the bill provides. List even the most obvious things.
Following the class discussion, make additions to your group's list to reflect the ideas that were added from your teacher and other members of your class.
Summing Up:
Based on the data contained on your sample utility bill, answer the following questions:
1. Do you think the owner has gas or electric heat? How can you tell?
2. Do you think the owner has a gas or electric water heater? How can you tell?
3. How many people do you think live in this home? Why?
4. Do you think this home has air conditioning? How can you tell?
Teacher Notes
Objective:
Graph energy consumption based on data contained in monthly energy bills and formulate inferences about the target home.
Materials:
12-month supply of utility bills (One per student group)
You will need one set of bills per student group. Each set of bills should be
from the same household. Use the bills which students have brought from their homes. Make certain that you have extra sets available in case some students are not able to bring their bills from home.
Suggested Teaching Strategies:
Break students into think pairs. Give each pair of students a one-year
collection of utility bills along with the student page for this activity. Directions are provided on the student worksheet. You may wish to save paper by presenting the problem (Let's Investigate) and the Summing Up questions on the
overhead.
Please refrain from telling students which data should be graphed and which types of graphs would be most appropriate for this data. One of the major benefits of this investigation is that students are able to discuss the pros and cons of different types of graphs. Not all groups will make the same types of graphs. This will make for interesting discussion following completion of the "Summing Up" questions.
After the graphs have been completed, analyze and discuss the range (highs and lows) and the mean or average values. It is likely that some groups will have prepared bar graphs and others line graphs. Some groups may have decided to prepare pie graphs. Have groups display their graphs and discuss their reasons for choosing a particular type of graph. Perhaps a consensus can be reached about which graph most clearly illustrates the trends in energy consumption.
What conclusions can the students make from the data? Students were asked to answer the same set of questions posed earlier. This time, students should immediately realize that with more data, they are able to make more logical inferences. Students are also asked to notice when water consumption is highest and what might be the cause of the increased water usage? In most homes, water usage goes up during summer months due to increased use of water for watering lawns, washing cars, and other outdoor activities.
At the conclusion of this discussion, be sure to ask students why it was easier to devise answers to these questions with this additional data than it was with only one month's bill.
Sample Answers to Summing Up:
1. Student answers will vary, but will likely list bar and line graphs as the easiest way to illustrate the patterns on energy use.
2. If the sample bills have significantly higher gas consumption during winter months, it is likely that the home is heated with gas.
3. It will be more difficult for students to make a logical inference for this question since hot water is used with some regularity throughout the year. The important thing is to check student answers for logical reasoning.
4. This is a difficult question to answer, even with a year's worth of data. Students should realize that to answer this question, they might need to compare the bill to other homes and to also know the size of the home.
5. If the electricity usage goes up significantly during summer months, it is likely that the home has air conditioning.
6. If water consumption is highest during summer months, it might be a function of increased water usage for outdoor purposes such as watering the lawn and washing cars.
Student Page
Utility bills are not standardized across the United States or even throughout Iowa. Some bills may not even include the same information. The electricity is measured in units called kilowatt-hours (the number of kilowatts in one hour). The utility company then charges a fee for each kilowatt-hour consumed. The fee can vary from place to place and from month to month.
Natural gas measurement may be expressed in therms representing 100 cubic feet or as mcf representing 1000 cubic feet. The utility company charges a fee for each therm or mcf consumed. Check your bill carefully to see which units are used.
Materials:
graph paper
ruler
utility bills
calculator
markers or colored pencils
Let's Investigate:
Your group has been given monthly utility bills covering one year for a local family. Your job is to come up with graphing techniques that will clearly
represent the monthly changes in kilowatt-hours of electricity consumed. At this point we will tell you that the homeowners consist of a family who live in a house in a typical residential area. You will be surprised to learn that the
collection of numbers on their utility bills can tell you a great deal about the family to whom this bill belongs. Use the data from your bills to prepare the graph. Prepare a second graph illustrating the monthly use of natural
gas.
Summing Up:
1. Which type of graph (pie, pictograph, bar, line) do you think best represents the data? Explain your answer.
2. Do you think the owner has gas or electric heat? Why?
3. Do you think the owner has a gas or electric water heater? Why?
4. How many people do you think live in this home? Explain your reasoning.
5. Do you think this home has air conditioning? Explain your reasoning.
6. Notice when water consumption is highest. What might be the cause of the increased water usage?
Teacher Notes
Objectives:
Prepare and interpret scattergrams.
Materials:
Student copies of utility bills(one-year supply) Use the same sets of bills students worked with in Activity 2.
Suggested Teaching Strategies:
This activity has no accompanying student page, as the procedure is best explained by the teacher. You may wish to begin with some of the discussion questions suggested below.
Do you think there is a relationship between energy consumption and number of people in a given household? Ask students to hypothesize as to whether the amount of energy consumed in a home is related to the number of individuals living in the household. How might these two factors be related? After students have made their predictions and stated their reasons for the suspected relationship, ask students how they might go about discovering if their prediction is correct. Hopefully students will suggest that they look at the amount of energy used by different families.
Explain how a scattergram (scatterplot) is set up and for what purposes it is typically used. Ask students to set up a scattergram relating amount of energy consumed and number of individuals living in a household. Set up a method of sharing the data that was collected from students' homes. Let students determine which numbers should be plotted. For example, they may want to sum all monthly consumption and graph the total yearly energy consumption. If they choose to ` graph consumption during one month only, they must all choose the same month. It is best that students discover these potential problems on their own, rather than having the teacher simply tell them what to plot.
Display the plots in a prominent area. Challenge students to look for patterns and to attempt to explain the reasons for the patterns. When income is not controlled, a clear pattern may or may not emerge. If no pattern emerges, students should be asked to explain the lack of a pattern.
Teacher Notes
Objective:
Explain patterns of energy consumption in various homes given monthly utility bills.
Materials:
monthly utility bills (1-year supply per student)
Suggested Teaching Strategies:
It is best to have each student work with the utility bills they have brought from their home. If this is not possible, give students an "extra set" of data. Try to secure utility bill data from some of the other teachers or
administrators in your school. Student interest will remain higher if they know the person whose bills they are analyzing.
Break students into think pairs, such that each group has at least one person with a complete set of utility bill records. Give students copies of the students worksheet entitled "Energy Highs and Lows".
Students should be able to come up with some logical explanations for differences in electrical and gas energy consumption. Sharing data on the number of individuals living in their home, size of house or apartment, when it was built, types of appliances they have, and other personal use habits provides useful information for comparison. It would be preferable to have each student graph their own data, assuming enough students brought their data to class.
Sample Answers to Summing Up:
Student answers to the "Summing Up" questions will vary depending on their energy usage and on with whom they compare their graphs. Look for logic in
student answers. It is likely that students will mention seasonal temperature differences as the major cause of the differences between high and low use of both gas and electricity.
Extensions/Assessment:
Challenge students to make inferences about the fluctuations in the energy use plots shown below.
In Household A, there is a marked increase in electricity use during the summer months. This is likely due to increased use of the air conditioning. Students should also be able to conclude that Household A has gas or fuel oil heat. This conclusion is based on the fact that the energy consumption does not increase during the cold Iowa winter months. If the heat was electrical, this would not be the case.
For Household B students should notice the large increase in energy consumption during the month of October and November on Graph B. This is a plot of energy consumption on a grain farm. During the fall months, much electricity is used in the grain dryer during harvest time. This accounts for the large increase in electricity during these months.
Challenge students to devise their own fictitious plots of energy consumption and to have other students make inferences about the causes if the energy consumption fluctuations in the plots. Encourage students to make a decision about the type of heating and cooling, the number of individuals in the household and their ages prior to preparing their graphs.
Student Page
Now that you have become skilled at graphing data, it is time to try your hand at interpreting patterns in those graphs. Everyone's home energy use follows patterns. These patterns may be related to the weather, to the personal habits of those living in the home, or to a host of other factors. In this activity you will be looking for patterns in your family's energy use. You will then compare your family's energy use patterns to those of one of your classmates.
Materials:
graph paper
monthly utility bills from your home
Let's Investigate:
Prepare a graph of the monthly electrical use for your set of home utility bills. Prepare a second graph of your home's natural gas consumption.
Compare your graphs to those made by another student. Notice the overall pattern of highs and lows for your graphs and your classmate's graphs. Talk with your classmate about his/her home. Ask questions about the number of persons living in the home, the size of the home, when it was built, and the types of appliances they have. By comparing this information to your home, point out at least three similarities between the patterns on your graphs and those of your classmate. Come up with some reasons that would explain these patterns.
Describe at least three things that are different between your graphs and those of your classmate. What reasons can you think of to explain these differences?
Summing Up:
1. Locate the highest and the lowest months of electricity consumption. State at least three factors that you believe could have caused the energy consumption between these two months to differ so much. Please be specific.
2. During which month was gas consumption the highest and when was it the lowest? State at least three factors that could have caused the gas consumption between these two months to differ so much. Again be specific.
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