MODULE TITLE - Steelton-Highspire High School



Compact Fluorescent Lights: A Bright Idea

Overview

I. Learning situation/issues

A. Grade level

B. Mathematical topics

Relevant PSSA standards

D. Curriculum connection

E. Steelton-Highspire curriculum connections

F. Career considerations

II. Underlying context

A. Initial setting

B. Detailed context

C. Context Q&A

III. Lesson ideas

A. Open-ended project

B. Free-response items

C. Variety items

IV. Particular Materials

A. Mathematics tasks

B. Mathematics handouts

C. Technology guides

D. Visual components

E. Web “in-sites”

F. Materials and equipment needed

V. About this module

A. Motivation

B. History of use

C. Credits/disclaimer

Module Components

Overview

The CFL module is the prototype module for the GE Math Excellence: Math in a “New Technology” Context project. The module contains a collection of items that can be used with middle-school students to reinforce whole number operations, to connect rational number operations to whole number operations, to compare numbers, to apply geometric formulas, and to express patterns involving number calculations as a precursor to algebraic symbolism. For an explanation of how and why CFLs became the topic of this module, please see the section on the motivation for this module.

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Learning situation/issues

This section provides the basic background for this module and its use in middle school mathematics settings. For additional particular insights about how this module has been used in various settings, please see the history of use section.

Grade level

The primary intended audience for this module is Grade 6 students of various abilities. The items are particularly focused on having students use number operations and then reflect on how different operations relate to each other. This reflective work develops a sound understanding of operations and an abstraction of operations as the basis for algebraic topics. As with many curriculum materials, this module may be used in its entirety or in part with many different learners.

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Mathematical topics

This module addresses several topics of middle school mathematics. It is particularly related to number and algebra with some attention to geometry and data analysis. The topics are described in the following sections in terms of Pennsylvania Mathematics Standards and Curriculum Connections for at least one school district.

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Relevant Pennsylvania Mathematics Standards

|Standard Number |Standard |Related Items in Module |

|2.8. |Algebra and Functions | |

|2.8.8.C. |Create and interpret expressions, equations or inequalities |CFL Module: |

| |that model problem situations. |Variety Items |

|2.1 |Number, Number Systems and Number Relationships | |

|2.1.8.B. |Simplify numerical expressions involving exponents, scientific | Students have several |

| |notation and using order of operations. |opportunities to work with |

| | |expressions of the forms ___. |

|2.2.8 |Computation and Estimation | |

|2.2.8.A. |Complete calculations by applying the order of operations. |CFL Module: |

| | |Evaluate Problems with formulas |

| | |(light emission, Kelvin |

| | |Temperature, etc.) |

|2.2.8.E. |Determine the appropriateness of overestimating or |CFL Module: |

| |underestimating in computation. |School Lighting Project, and |

| | |Classroom Lighting Project |

|2.4 |Mathematical Reasoning and Connections | |

|2.4.8.B. |Combine numeric relationships to arrive at a conclusion. |CFL Module: |

| | |Addressed throughout the entire |

| | |module. |

|2.5 |Mathematical Problem Solving and Communication |CFL Module: |

| | |School Lighting Project, and |

| | |Classroom Lighting Project |

|2.5.8.B. |Verify and interpret results using precise mathematical |CFL Module: |

| |language, notation and representations, including numerical |Interpretation of Graphs of |

| |tables and equations, simple algebraic equations and formulas, |Various Aspects of CFLs (bulb |

| |charts, graphs, and diagram. |diameter, Arc Length vs. Lumens, |

| | |Arc Length vs. Voltage, light |

| | |emission intensities, |

|2.5.8.C. |Justify strategies and defend approaches used and conclusions |CFL Module: |

| |reached. |School Lighting Project, and |

| | |Classroom Lighting Project |

|2.5.8.D. |Determine pertinent information in problem situations and |CFL Module: |

| |whether any further information is needed for solution. |School Lighting Project, and |

| | |Classroom Lighting Project |

|2.6.8 |Statistics and Data Analysis | |

|2.6.8.C. |Fit a line to the scatter plot of two quantities and describe |CFL Module: |

| |any correlation of the variables. |Free-Response Scatter Plot |

| | |Problems. |

|2.6.8.F. |Use scientific and graphing calculators and computer |CFL Module: |

| |spreadsheets to organize and analyze data. |Organize, plot and analyze various|

| | |sets of data relevant to real-life|

| | |problems relevant to CFLs and |

| | |their usage. |

|2.9.5 |Geometry | |

| | | |

| | |CFL Module: |

| | |School Lighting Project, & |

| | |Classroom Lighting Project (areas |

| | |of rooms) |

| | |Comparison Problems of Varying CFL|

| | |bulb (surface area) |

| | | |

|2.11.8 |Concepts of Calculus | |

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Curriculum connections

This module particularly fits with the study of real numbers and serves as a bridge to algebra. It might also be used in Algebra courses in a review of real numbers and operations, extending to other topics such as dimensional analysis.

Number and operation

Many of the items in this module require students to operate on whole numbers or rational numbers. Some of the items (e.g., F1, V1, V2)[1] provide opportunities for students to think about number operations beyond the actual computations.

Algebra, pattern and function

There are several opportunities (e.g., F2) for students to generalize operations on numbers and to write expressions with informal or formal variables, such as 7 times price plus 150 or 7p+150, respectively.

Measurement

Students will have several opportunities (e.g., V5) in using dimensional analysis as they think through what they are multiplying or dividing and how the units of measure appear in the calculations and the answers.

Geometry

Students will have some opportunities to use geometric principles of area (e.g., V1) and surface area (e.g., V3). Geometry is not central to this module.

Data analysis

The projects offer students venues in which to design and implement data collection schemes. Throughout all items, students use data of several kinds. Some data are information on pages (e.g., F2) or information the students gather (e.g., P3). The information may involve measure they recognize (e.g., diameter of a circle in F3) or measures that are not familiar (e.g., energy in F2).

Steelton-Highspire curriculum match

There are particularly fruitful uses of the materials in this module in the Steelton-Highspire curriculum. The district uses the following textbooks:

• Grade 6 Altieri, M. B., Bezuk, N., Cole, P. B., Ferguson, B. W., Harrell, C. P., & Lubcker, D. H. (2002). Mathematics. New York: McGraw Hill.

• Pre-Algebra Davison, D. M., Landau, M. S., McCracken, L., & Thompson, L. (2001). Pre-Algebra. Needham, MS: Prentice Hall.

• Algebra Bellman, A., Bragg, S. C., Chapin, S. H., Gardella, T. J., Hall, B. C., Handlin, W. G., & Manfre, E. (2001). Algebra. Needham, MS: Prentice Hall.

• Geometry Bass, L. E., Charles, R. I., Johnson, A., & Kennedy, D. (2004). Geometry. Needham, MS: Prentice Hall.

The specific connections for these grades and textbooks include the following:

| | | |Module Connections |

| |Chapter |Clusters (Grade 6 Mathematics) |P=Open-ended Project Items |

| | |or |F=Free Response Items |

| | |Section numbers |V=Variety Items |

| |1 |Add and Subtract Decimals (Clusters A & B) |P2 – Room Lighting Project |

|Mathematics | | |P3 – Home Lighting Project |

| | | |F4 – Comparison Chart |

| | | |V6 – Register Tape Questions |

| |2 |Multiply and Divide Decimals (Cluster A) |F2 – CFL Conversion Questions (part |

| | | |a, b, c) |

| | | |F3 – Circular CLF’s |

| | | |F4 – Comparison Chart |

| | | |V6 – Register Tape Questions |

| |3 |Data Statistics and Graphs (Clusters A&B) |F2 – CFL Conversion Questions (part |

| | | |d) |

| | | |V6 – Register Tape Questions |

| |7 |Measurement (Clusters A&B) |P1 – School Lighting Project |

| | | |P2 – Room Lighting Project |

| | | |P3 – Home Lighting Project |

| |8 |Algebra: Functions and Equations (Clusters A&B) |F3 – Circular CLF’s |

| | | |F4 – Comparison Chart |

| | | |V4 – The Lifetime of a CFL |

| | | |V5 – Conversions to Find Cost |

| | | |V6 – Register Tape Questions |

| |9 |Integers and Rational Numbers (Cluster B) |V1 – Comparing Bulb Life |

| | | |V2 – Savings |

| | | |V4 – The Lifetime of a CFL |

| | | |V6 – Register Tape Questions |

| |11 |Perimeter, Area, and Volume (Clusters A&B) |P1 – School Lighting Project |

| | | |F3 – Circular CLF’s |

| | | |V3 – CFL Surface Area |

|Pre-Algebra |1 |Algebraic Expressions and Integers (1, 2, 3, 7, 8, & |F4 – Comparison Chart |

| | |9) |V1 – Comparing Bulb Life |

| | | |V2 – Savings |

| | | |V4 – The Lifetime of a CFL |

| | | |V5 – Conversions to Find Cost |

| | | |V6 – Register Tape Questions |

| |2 |Solving One-Step Equations and Inequalities (1-10) |V6 – Register Tape Questions |

| |3 |Decimals and Equations (4, 5, 6, & 8) |F2 – CFL Conversion Questions (parts|

| | | |a, b, c) |

| | | |F4 – Comparison Chart |

| | | |V6 – Register Tape Questions |

| |7 |Solving Equations and Inequalities (1, 2, 3, 4, 5, 6, |F1 – CFL Replacement Question |

| | |& 7) |F2 – CFL Conversion Questions (parts|

| | | |a, b, c) |

| | | |F3 – Circular CLF’s |

| | | |F4 – Comparison Chart |

| | | |V5 – Conversions to Find Cost |

| | | |V6 – Register Tape Questions |

| |8 |Linear Functions and Graphing (1, 2, 3, 4, 7, & 8) |F2 – CFL Conversion Questions (part |

| | | |d) |

| |9 |Area and Volume (1, 2, 3, 5, 6, 7, 8, 9) |P1 – School Lighting Project |

| | | |F3 – Circular CLF’s |

| |12 |Data Analysis and Probability (3) |F2 – CFL Conversion Questions (part |

| | | |d) |

| | | |F4 – Comparison Chart |

| |13 |Nonlinear Functions and Polynomials (1, 2, & 8) | |

|Algebra |1 |Tools of algebra (1, 3, 4, 5, 6, 9) |F1 – CFL Replacement Question |

| | | |F3 – Circular CLF’s |

| | | |F4 – Comparison Chart |

| | | |V4 – The Lifetime of a CFL |

| | | |V5 – Conversions to Find Cost |

| | | |V6 – Register Tape Questions |

| |2 |Functions and Their Graphs (2) |F2 – CFL Conversion Questions (part |

| | | |d) |

|Geometry |1 |Tools of Geometry (1 & 7) | |

| |2 |Reasoning and Proof (4) |F4 – Comparison Chart |

| | | |V3 – CFL Surface Area |

| | | |V4 – The Lifetime of a CFL |

| |7 |Area (1, 4, 5, & 7) |P1 – School Lighting Project |

| |10 |Surface Area and Volume (3, 4, 5, 6, 7, & 8) |P1 – School Lighting Project |

| | | |P2 – Room Lighting Project |

| | | |P3 – Home Lighting Project |

| | | |F3 – Circular CLF’s |

| | | |V3 – CFL Surface Area |

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Career considerations

There are number of mathematical applications in this module. Facility in determining how to minimize cost or to weigh one product against another is useful in a variety of business and industry settings. Comparisons of surface areas are useful in a range of jobs from painting to engineering.

The science behind CFLs includes a blend of heat, light and energy.

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Underlying context

Initial setting

Think about a light bulb. What image comes to mind? Does it look like the photo to the right? People have used incandescent light bulbs like this one to light their homes, schools, and other buildings. Recently, compact fluorescent lights (CFLs) became available. CFL manufacturers and others who are familiar with this new technology claim that replacing incandescent bulbs with CFLs gives better lighting and saves money in the long run. Mathematics helps us to understand and to support or refute this claim.[2]

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Detailed context

The brief introduction above likely is enough for students to know as they begin working on the tasks in this module. Addition information about the CFL context may be useful. Among the topics addressed here are energy use, shape of CFLs.

Energy use and CFLs. The major technology advantage of CFL is the reduced amount of energy consumed to get the same amount of the light (illumination) brightness (in the unit of Lumens). The electric energy is first emitted from the two electrodes at the end of the tube in the form of flow of electrons. Then the energy is transferred into ultraviolet light (invisible to human eye) when the electrons bombard the mercury atoms inside the CFL tubes. Finally the energy is conveyed in the form of illuminating light when the pre-deposited phosphors (on the inner surface of the CFL tube) give off light under the exposure of the ultraviolet light. All these processes are very efficient and the undesired heat generation and energy loss is much less compared with incandescent light.

Shape of CFL. Depending on the specific design priorities among energy efficiency, size, visual appeal, and brightness requirement, the CFLs are designed either with extended tubular shape, U shape or twisted shape. CFLs with extended tubular shape will yield more lumens and are brighter. For extended tube shape, it could be either U-shape, extended tubular or circular shape. All of them have extended total tube length. However, an extended tubular CFL generally has larger tube diameter thus generally better efficiency. People may also choose twisted shape for its visual appearance and it is generally even more compact than the other shape with the same brightness. However, the twisted shape generally suffers diffuse problem and may only good for close lighting.

Advantages and disadvantages. There are several advantages of CFLs over incandescent bulbs, yet CFLs are not a perfect solution to the lighting problem.

|Advantages |Disadvantages |

|The biggest benefit of CFL is the |Older CFLs need extended warm-up time (1 to 2 minutes) to reach the optimal working |

|efficient energy transfer (from |condition and the designed brightness. |

|electricity to light) and energy |Some CFL may produce annoying audible buzz. |

|saving feature. |The working temperature of CFL is rather limited (about 50F to 120F). |

|CFLs last 8 to 10 times longer than |CFLs have shorter lifetimes when they are switched on and off very often. |

|the incandescent light bulb. |CFLs cannot be used on dimmer switches. |

|A CFL generally can be made to |Incandescent bulbs project light farther and therefore may be better for some uses, |

|produce any color of light needed. |such as high-hanging fixtures. |

| |CFL bulbs have to be properly disposed due to the toxic mercury vapor used in the tube.|

A helpful source for students to quickly find the meaning of terms is the glossary of lighting terminology available at .

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Context Q&A

There are two things that make the CFL context of this module both intriguing and challenging to use in the classroom. Cost of the materials and production change and other details about this new technology continue to evolve and emerge. To reflect the changes in the context, this module will continue to evolve and this Context Q&A section will be the place to gather more information about the context as the module is used in mathematics teaching and learning.

Q1: Why do incandescent light bulbs lose so much energy?

There are two major reasons for energy loss in the incandescent light bulb: (1) heat conduction to the wire and the environment; and (2) the undesired irradiation in the spectrum range outside the visible regime.

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Lesson ideas

There are three types of lesson ideas. Open-ended projects are major activities that engage students in answering non-trivial questions about the real-world contexts. These activities could be treated as projects that take several days or class meetings. Free-response items are individual problems or sets of problems. They require students to make decisions, calculate values, and do other things to construct their own answers. For all or at least most of these open-ended items, there are specific suggestions about how the items may play out in the classroom. Variety items are stand-alone problems that could be used in many different ways, including review and practice. These items may be used to revisit previously learned materials while students are working either on a project or on several open-ended items related to CFLs. The variety items also may be incorporated as applications of mathematics into lessons in a standard mathematics curriculum and used separately from the projects and free-response items. However, some of the variety items may provide insights into things to consider in the projects or free-response answers.

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Open-ended projects

P1. School Lighting Project

Lighting is important in a school. Your school likely pays a large amount of money for electricity to light the hallways, classrooms, and other spaces in your school. In addition to these monthly electric bills, your school also paid to purchase the light fixtures and to replace light bulbs in those fixtures. A current claim is the a relatively new type of light bulb may help your school – as well as other schools, offices, and homes – to save money on lighting costs over time.

This new type of light bulb is a compact fluorescent light bulb, or CFL for short. Should your school save money if it replaces its incandescent light bulbs with CFLs? Explain your recommendation. Write a report to your principal that informs the school about what to do and why the plan makes sense. Be sure to explain in detail how your plan will help the school save money over the next several years.

Answer: It is very clear that the details of students’ projects will vary from one school to another. It is also clear that the answers may vary from student to student. The expected conclusion in all typical cases (e.g., not a case where the particular school building is about to be closed, making the replacement task a waste of time and resources) is that changing to CFLs will lead to savings eventually but not immediately. Minimally, the students’ explanations should include sources of fixed costs (e.g., cost of purchasing the new CFLs, installation costs) and sources of savings (e.g., decreased electricity consumption). Students will need data about the current light use in their school. Graphs and charts may be used effectively to convey the comparisons. Geometry may come into play if students need to decide where to locate fixtures or to determine the area lit by a particular light source.

Enactment:

• Take time to develop the context and to motivate the project. Perhaps the principal or central office person could visit the class in person or via video to set-up the school’s need and to provide students with a sense of the real dollar values attached to the cost of lightening the school.

• It is tempting to give students answers to all of their questions. It often would be more beneficial to student to encourage them to seek the information rather than to receive it. There are several potential resources (web sites, books, etc.). If students have difficulty locating information, it may help to share the Web “in-sites” with them.

• It is tempting to present the students with a data set rather than having students collect the data. However, this move defeats the spirit of the intended lesson. In collecting the data students negotiate several measurement issues (e.g., how to measure parts of the CFLs). They also have to make decisions that involve various areas of mathematics (e.g., rounding, sampling). However, it may be reasonable to have information for the students about who to ask about the school and to have these people ready to respond. For example, the custodian may tell them how frequently light bulbs are changed and an office staff person may know the school’s cost of purchasing replacement bulbs.

• Students may need to develop some clever ways around particular data collection problems. Here are some issues that might arise and ideas about how to address the issues:

o Students likely will ask, How many incandescent light bulbs are in the school? If it is not possible to count all of the lights in the school, students can be asked about the number of light bulbs in some small part of the school (e.g., the auditorium). It is important that chosen space (auditorium) has a large number of bulbs. Note that a CFL does not provide exactly the same area of light as an incandescent bulb. Also, CFLs can be purchased for use in standard (incandescent) light fixtures; CFLs that do not fit standard fixtures also exist. Students may need to consider the relative prices of these different kinds of CFLs.

o Students likely can see the light fixtures but they may not be able to see the number of incandescent bulbs in each fixture. If they can see the number of bulbs, they likely cannot see the size of the bulb (e.g., 60 watt versus 100 watt). This may be a good time to consult with the building staff responsible for the lighting. They may be able to tell students, for example, what size bulbs are used where.

• If students have difficultly getting started, it might help to ask them what factors they think they need to include. If students continue to struggle, or as a way of helping students to think about how these factors relate to their project, it might be useful to ask questions about the existing and proposed lighting. Some questions that students may need to answer in their work on this activity are:

o How many incandescent bulbs are in the school?

o How much light do the incandescent bulbs provide?

o How many CFLs would be needed to provide this amount of light?

o What amount of power do the existing bulbs use?

o Will this be enough power for the replacement CFLs?

o What will be the initial cost of installing the CFLs?

o Will any new light fixtures be needed?

o How much energy will the new bulbs save in a month? in two months? In three months? In n months?

o And then there is the ultimate question: is it a good idea for the school to switch to CFLs?

• Students may have to deal with the fact that they cannot merely replace one incandescent bulb with one CFL. So, they will have to determine how they will deal with the temptation to claim one CFL is the equivalent to so many incandescent bulbs. As a result, students see that they cannot simply divide the number of incandescent bulbs by some number to get the number of CFLs needed – after all, some of the bulbs may be lone bulbs in small rooms while other bulbs may be in large collections (such as several dozen bulbs in the auditorium).]

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P2. Room Lighting Project

A smaller version of the School Lighting Project is to have students determine whether and how to change the lighting in their classroom, the library, or some other specific room or portion of the school.

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P3. Home Lighting Project

A variation on the School or Room Lighting Projects would have students determine whether and how to change the lighting in their homes. This option adds the obvious opportunity for parental involvement.

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Free-response items

F1. CFL Replacement Questions

CFLs fit in 29 of the 35 old light fixtures in a house in central Iowa.[3] Is it correct to say CFLs fit in more than half of the fixtures? Explain your answer in at least two mathematically different ways. Tell how the answers are mathematically different.

Answer:

Way (: [pic] So, the CFLs fit in more than one-half of the fixtures.

Way (: [pic]

Way (: [pic] So, the CFLs fit in more than half of the fixtures.

Way (: [pic] The CFLs fit in more than half of the fixtures.

Explanation of differences and similarities: Ways ( and ( use fractions to make the comparison. Way ( compares the fraction of fixtures to one-half using percents; 50% represents one-half. Way ( compares the fraction of fixtures to one-half expressed as an equivalent fraction with an even denominator. Ways ( and ( use whole number relationships to make the comparisons. Way ( compares the number of fixtures the CFLs fit to half of the fixtures available. Way ( compares the number of fixtures fit to the number not fit with the understanding that the number fit and the number not fit would be equal if exactly CFLs fit exactly half of the fixtures.

Enactment: Students should discuss which ways are easier than other ways for the given problem and for related problems. In the given problem, for example, comparing 29/35 (Way () to 1/2 is easy when 29/35 is written as an equivalent fraction with an even denominator, 58/70. 58/70 would also be a useful form of 29/35 if students had to compare 29/35 to a number of tenths since 10 divides 70 but 10 does not divide 35. For example, given 58/70, it is easy to see that 29/35 is greater than 4/10=28/70 with 58>28. However, 29/35 is already in a handy form if the comparison is to some number of fifths. For example, is 29/35 less than 2/5 can be done by quickly expressing 2/5 as 14/35 and seeing 29 is not less than 14. This discussion may be a useful reminder to students about how and why common denominators are used to compare two fractions.

F2. CFL Conversion Questions

One type of CFL is a spiral tube with a base that screws into a typical light fixture, much like an incandescent bulb. CFLs of this type come in different sizes, as shown in the photo to the right. On each of these packages (or in on-line catalogs), there is a variety of information printed on each size. Here is a sample of that information for the smallest CFL shown in the photo:

Uses less energy

Utiliza menos energia

7w 25w

375. ( 160

Lumens Lumens

a. The “7w”, or 7 watts, on the left side is a measure of the size of the CFL. The “25w” in the column on the right indicates that this CFL corresponds to a 25-watt incandescent bulb, a common size for a small incandescent bulb. Other common sizes for incandescent bulbs are 75 watts and 100 watts. What size CFL (in watts) would you expect to correspond to a 75-watt incandescent bulb? What size CFL would you expect to correspond to a 100-watt incandescent bulb?

Answer:

Way (: 21-watt and 28-watt CFLs correspond to 75-watt and 100-watt incandescent bulbs, respectively. The mathematical reasoning for this answer may be 75 watts would be 3 times 25 watts for the incandescent bulbs and so for the CFLs one would expect 3 times 7 or 21 watts. Similarly, 100=4x25 implies 4x7=28.

Way (: [pic] and rewriting fractions with common denominators suggest a 75-watt incandescent bulb matches a 7x3=21-watt CFL. Similarly, [pic] suggests a 7x4=28-watt CFL matches a 100-watt incandescent bulb.

Enactment: Students at this grade level likely can apply multiplicative thinking or constant ratio as suggested in the sample answer. Students learn in the later parts of this item that this mathematical reasoning may not quite match the real-world context. Have students present these different methods and compare them, noting that factor-product relationship between 25 and 75=25x3 or between 25 and 100=25x4 makes it easy to arrive at 21=7x3 and 28=7x4. If students do not suggest one of the methods, it may be useful to introduce that method after students attempt the next part.

b. Another common type of incandescent bulb is a 60-watt incandescent bulb. What number of watts would be appropriate for the corresponding CFL?

Answer:

Way (: 60÷25=2.4 and 2.4 x7=16.8. A 16.8-watt CFL would correspond to the 60-watt incandescent bulb.

Way (: [pic], 60x7÷25=16.8. A 16.8-watt CFL matches the 60-watt incandescent bulb.

Enactment: Students should see that this question is answered in a way that is nearly identical to the questions in part a. Both questions ask for a prediction. The fact that 60 is not a multiple of 25 makes part b more difficult than part a.

c. According to information on the package, a 19-watt CFL corresponds to a 75-watt incandescent bulb and a 23-watt CFL corresponds to a 100-watt incandescent bulb.

i. Compare this information with your results in part a.

Answer:

The package information gives watt values that are less than the values I calculated for the incandescent bulbs.

Enactment: Ensure students know their mathematical thinking in part a could be absolutely perfect and the lack of a match to this answer in part ei has to do with the real-world issues yet to be considered.

I student know two point – not one point – completely defines a line, now may be a good time to have them think about why only the one data point, (7,25), was not enough information to get an answer that would match reality. A more general point is that having information about only one thing (i.e., one package) simply is not always enough information on which to base a general conclusion about all such things.

ii. Assume the package information is correct. What would you expect to see on a package as the CFL wattage that corresponds to a 60-watt incandescent bulb?

Answer:

Way (: For the incandescent bulbs, 60 watts is greater than 25 watts and less than 75 watts, but closer to 75 watts than to 25 watts. So, the CFL should be more than 7 watts and less than 19 watts, and probably closer to 19 watts.

Way (: [pic]. The CFL should be labeled as 19x60÷75=15.2 watts.

Way (: [pic]. The CFL would be marked 23x60÷100=13.8 watts.

Way (: Using [pic] and [pic], the value for the CFL could be something like 13.8 or 15.2 watts.

Way (: [pic] The value of the ratio seems to decrease as the number of watts becomes larger. For the 60-watt incandescent bulb, the value seems to be between 0.25 and 0.28 but closer to 0.25. Suppose the value is 0.26. The CFL would be labeled 0.26x60 or 15.6 watts. However the number of watts in all other cases is a whole number. So, the CFL may be labeled 16 watts.

Enactment: Students may be flustered when they come up with clearly conflicting answers when using what they should know are mathematically correct calculations. This item leads students to the data analysis technique in part d, thought it may be possible for students to stop with part e. In preparation for future work, have students present their answers in the order of greater precision. The order of precision from least to most for the given methods is Way (, Way ( or Way (, Way (, then Way (. In Way (, there is the essence of simultaneously considering all data points, as students would learn to do in part d. Be sure students justify Ways ( and ( as mathematically correct despite the fact both of the obviously unequal numerical answers could not be correct in the context. Creating the scatter plot in the next item may help students understand why these conflicting answers happen.

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d. Another way to figure out what number of watts for a CFL would match the 60-watt incandescent bulb involves using a graph. The following data came from CFL packages like those in the photograph.

|CFL watts |Incandescent watts |Lumens |

|7 |25 |375 |

|19 |75 |1200 |

|23 |100 |1600 |

It is possible to use the information to study the relationship between the watts of CFLs and the watts of incandescent bulbs.

i. Enter the CFL watt values as L1, the incandescent watt values as L2, and the lumen values as L3.

Answer:

The values should appear in the lists as indicated.

[pic]

Enactment: For instructions on how to enter data and plot points, see Plotting Data Points and Fitting Curves. Students may need substantial guidance in this calculator work. They will have opportunities to practice these calculator skills.

ii. Plot the CFL watts on the horizontal axis and the incandescent bulb watts on the vertical axis. Be sure to determine a good window to use before creating the graph.

Answer:

The CFL watt values range from 7 to 23. One good window would have x-values from 0 to 25 in increments of 1. The incandescent bulb watt values range from 25 to 100. One reasonable window would have y-values from 0 to 120 in increments of 10.

[pic][pic]

Enactment: One nice aspect of using a the value from 0 to 120 in steps of 10 is that 60 will appear exactly as a y-value when the cursor moves around the window. This happens because the number 60 is in the sequence {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120}. Notice that 60 would also appear for a window with y-values from 0 to 120 in steps of 20, as 60 appears in the sequence {0. 20. 40. 60. 80. 100. 120}. However, 60 does not show up as a y-value if the window runs from 0 to 120 in steps of 25; 60 does not appear in the sequence {0, 25, 50, 75, 100}. While discussing students’ strategies for this problem set, it would be reasonable to have students talk about how they can predict if 60 would show up as an exact value in the window.

[pic]

iii. Fit a linear function to the data. Record an equation to represent the graph.

Answer:

The graph of the fitted function appears below, with the expression in x for y at the top of the screen.

[pic]

iv. What is the slope of the line? What is the intercept of the line? What do these values mean in terms of the CFLs?

The slope is approximately 1.7 and the intercept is approximately 10. This slope implies that an incandescent light uses 1.7 watts for every 1 watt used by the CFL. The intercept indicates that a 10-watt incandescent light uses the energy of a 0-watt CFL. This does not seem to make sense in reality.

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A second way to use information in the chart and now in your calculator is to find a mathematical way to associate watts and lumens. This would involve the relationship between the energy needed by the light and the amount of light the bulb produces.

iv. Create the scatter plot and fit a line to the data for CFL watts (in L1) and lumens (in L3).

Answer:

The scatter plot and its window information appear first, followed by the fitted line’s equation as Y2 and its graph.

[pic][pic]

[pic][pic]

v. Use the scatter plot and graph to determine how many watts correspond to 870 lumens.

Answer:

Moving the tracer until 870 (or a value close to 870) appears as the value for y. The number of watts is approximately 13.8, or close to 14 watts.

[pic]

Enactment: Students may notice by now that the watts are given in integer values. So, rounding the result of the calculator work makes sense in the situation.

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F3. Circular CFLs

CFLs come in different shapes. One type of CFL has a circular tube. The greatest distance across the entire CFL is 8 inches. The greatest distance across the inside of the CFL is [pic] inches. Estimate the surface area of the CFL.

[pic]

Answer:

The CFL does not have a shape that matches the usual formulas for surface area. The rounded nature of the CFL makes it impossible to calculate the surface area as a sum of the area of flat surfaces. So, to estimate the surface area, a reasonable method is to use a more common figure as a model of the CFL.

One way to think about the CFL in a simpler form is to image that the CFL is ‘flat’ on top and on the bottom and has vertical sides. The visual image is that of a three-dimensional “disk”, as shown here:

[pic]

The surface area of this model would be the sum of areas of the top, the bottom, the inside, and the outside. These areas can be calculated as follows:

Top: area of a large circle – area of a smaller circle

= [pic]= [pic]

Bottom: same as top

Inside vertical part: height x circumference of smaller circle

= [pic]=[pic]

Outside vertical part: height x circumference of larger circle

= [pic]=[pic]

Sum: 92.6+92.6+78.4+106≈370

An estimate of the surface area is 370 square inches.

Enactment: Students may have other strategies for computing the surface area. Many valid methods are possible. If students have difficulty getting started, it may be useful to have them think first of what two-dimensional object reminds them of the CFL. Circle would be an expected response. They may then see the region of the top of the figure as the area between two concentric circles. This task may be used either for students to apply their understanding of the areas of familiar shapes or to introduce the need for surface area. Years later in their mathematics experience, students could return to this task and compute the volume and surface area of this figure (a torus) using calculus techniques.

F4. Comparison Chart Completion

The following chart appears on a web site.[4] All of the numbers in the chart are related to other numbers in the chart. Explain how the person who made this chart could have computed each of the following numbers.

[pic]

a. $40.60

Answer:

($5.91 x 4.5 years) + $14.00 = $40.60

Enactment: Students should be able to discuss the importance of including the initial cost of the lamp in their calculation. Note: Because the Ti-73 and any other graphing calculator will perform order of operations on expressions presented, this may be a place to pursue the topic of order of operations.

b. $103.55

Answer:

($21.90 x 4.5 years) + (10 lamps x $0.50) = $103.55

Enactment: Students may encounter difficulties in the reasoning necessary for this calculation due to the difference between the lamp lives of the CFL and incandescent lights.

c. $62.95

Answer:

$103.55 - $40.60 = $62.95

d. 10

Answer:

A 100-Watt bulb lasts for only 167 days. The 27-watt CFL lasts 1642.5 days. So, it takes 1642.5÷167 or approximately 10 days.

Enactment: The value obtained through this calculation is actually 9.8. This could lead to a valuable discussion on the issues involved with rounding.

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Variety items

These items are short-answer tasks that may be used alone or in combination. For each item, the student should be encouraged to articulate the answer in the CFL context, and not to settle for a numerical or other mathematical result devoid of the context. In some cases, this means the students may have to interpret an answer (e.g., round to the nearest unit) to give the mathematical result meaning in the context.

V1. Comparing Bulb Life

A CFL lasts an average of 10,000 hour. A typical incandescent bulb lasts 750 hours. How many incandescent bulbs would you need to last as long as one CFL?[5]

Answer:

10000÷750=13.33…. You should expect to use 14, or at least 13, incandescent bulbs to last as long as one CFL.

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V2. Savings

Replacing a 100-watt incandescent bulb with a 32-watt CFL can save at least $30 in energy costs over the life of the bulb. [6] If a business in town replaces 17 100-watt incandescent bulbs with 32-watt CFLs, what would be the savings over the life of these bulbs?

Answer:

To estimate the savings, multiply the $30 savings for each replacement by the number of replacements, 17. [pic] The savings would be at least $510. It is mathematically important to say the savings are at least $510 because the savings on each replacement should be at least $30. However, in terms of the context, the duration of some bulbs may be more or less than that of other bulbs. The prediction may not be accurate enough to guarantee “less than” is appropriate.

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V3. CFL Surface Areas

For any one CFL, the total surface area of the tube(s) determines how much light the CFL produces. Some CFLs have 2, 4 or 6 tubes. Some CFLs have circular or spiral shape tubes.[7] Should a CFL with 4 tubes produce twice as much light as a CFL with 2 tubes? Explain.

Answer:

At first glance it seems the 4-tube CFL should produce twice as much light at the 2-tube CFL because the surface area of twice as many tubes would be twice the surface area of the 2 tubes. However, the CFL with four tubes may or may not produce twice as much light as a CFL with two tubes. If we know all of the tubes are congruent and have the same electrical power, the CFL with four tubes should produce twice as much light as the CFL with two tubes. However, if the tubes are not of the same size with the same power, one CFL with four tubes may not produce as much light as a bulb with two tubes.

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V4. Lifetime of CFLs

A tube in a CFL lasts approximately 10000 hours.[8] If a CFL is installed in your classroom today, should you expect the CFL to last until the end of the school year?

Answer path:

Students likely will use specific numbers in their responses. The answer here is given as a generic formula although students likely will use particular numbers. Estimate the number of hours, h1, of light per school day (number of school days is sd) and the number of hours, h2, of light per non-school day (number of which is nd). Estimate how many of each type of day exists between now and the end of the school year. Calculate the total amount of light time needed using h1*sd+h2*nd.

Enactment: The expectation is for students to answer this question with particular numbers based on whatever day the task is given to them. It would be natural to ask them how the calculations they do would change if they were asked the question one month later or one month earlier. Thinking about how they would change the numbers but still do the same operations leads them to algebraic thinking about variables. In this particular problem, the total amount of light time needed would be calculated as h1*sd+h2*nd. Students who are new to thinking about generalized arithmetic might only be able to express this as number of hours on a school day times number of school days plus number of hours on a non-school day times number of non-school days. As students begin to use variables, subscripts may be a problem; writing the expression as hsd*sd+hnd*nd might be more accessible to them.

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V5. Conversions to Find Costs

The following figure is part of a chart that appears in a web page.[9] [pic]

Determine how they calculated $21.90 for the Annual Energy Cost of a 100-Watt Incandescent bulb. Assume six hours per day and electric rate of 10 cents per 1-kilowatt hour.

Answer: [pic] is how they seemingly calculated $21.90.

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V6. Register Tape Questions

The following portion of a register tape[10] shows the prices of several types of CFLs. Use this information to answer the following questions:

LOWE'S

STATE COLLEGE, PA

(814)237-2100

-SALE-SALES #; S0273SM1 77947 09-17-04 TE#; 1840 PENN STATE UNIVERSITY

76223 100W 4-pk. 1.92

76510 60W 4-pk. 0.78

51430 60W 0.49

51800 100W 0.59

156922 13W MINI CFL 3-pk. 11.98

67196 13W MINI CFL 4.98

44258 23W MINI TWIST CFL 6.97

VISA XXXXXXXXXXXX1234 064231 AMOUNT: 27.71

0273 TERMINAL; 07 09/17/04 12:27:34

[pic]

THANK YOU PENN STATE UNIVERSITY FOR SHOPPING LOWE'S

RECEIPT REQUIRED FOR CASH REFUND. CHECK PURCHASE REFUNDS REQUIRE 15 DAY WAIT PERIOD FOR CASH BACK. STORE MGR: RAY FORZIAT

WE HAVE THE LOWEST PRICES, GUARANTEED! IF YOU FIND A LOWER PRICE, WE WILL BEAT IT BY 10%. SEE STORE FOR DETAILS

a. The 13-watt mini-twist CFL comes in a package of three bulbs. What is the customer paying for each 13-watt bulb, excluding sales tax?

Answer:

11.98÷3 yields approximately $3.99 per 13-watt bulb.

b. What would it cost to buy three 23-watt CFLs with 6% sales tax?

Answer:

3x6.97=20.91, 1.06x20.91≈22.1646. OR 1.06x6.97x3≈22.1646. It would cost approximately $22.16.

c. What would the cost of one 60-watt bulb be if you purchased them in a package of 4?

Answer:

0.78÷4 = 0.195. One of these bulbs would be $0.20.

Enactment: Students should discuss the issue of rounding. This discussion may be useful to address the rounding capabilities of the TI-73 or any other graphing calculator.

d. The custodian will be replacing each light fixture in your classroom with one 13W Mini CFL. This means that one CFL bulb will replace each light fixture in your room. Estimate the total of this replacement. Then calculate the actual cost. How did your estimate compare to the actual cost? Show your work and explain your reasoning.

Answer:

Estimate will vary depending on the number of light fixtures in the classroom. A reasonable student response would be rounding $4.98 to $5.00 and multiplying by the number of light fixtures. Actual cost for a given classroom will be $4.98 multiplied by the number of light fixtures. In their comparison of estimate and actual, students should realize that the estimate value will be slightly more than the actual cost.

Enactment: Students should discuss the reasonableness of their estimation of $5.00 for the cost of one 13W Mini CFL. Students should discuss the relationship between the estimated and actual costs.

e. The register tape here was from a purchase made through Penn State. No sales tax was included. What would be the sales tax on this purchase if the sales tax rate is 6%?

Answer:

$27.71 x 6% = $1.66 and $27.71 + $1.66 = $29.37

f. At the bottom of the register tape receipt, Lowe’s guarantees the lowest prices. If these prices are not the lowest, Lowe’s will beat any other stores prices by 10%.If a customer found all of the bulbs at a lower price at another store, how much money would Lowe’s need to give back to the customer?

Answer:

$27.71 x 10% = $2.77

Enactment: There is a nice chance here to do a bit of rounding. The calculation of 10% of $27.71 is easy. So, attention could be given to how we ‘round’ $2.771 to $2.77 to get the amount of the tax.

g. You have $30 to purchase bulbs. Create a shopping list of the bulbs you would buy to get as close to $30 without overspending. (Note: There will be no sales tax added t o this purchase.)

Answer:

There are multiple solutions to this problem. Following are four possible solutions:

Way (:

|Number |Description |Unit Price |Total |

|2 |13W Mini CFL 3-pk. |$11.98 |$23.96 |

|1 |13W Mini CFL |$4.98 |$4.98 |

|2 |60W |$0.49 |$0.98 |

| | | |$29.92 |

Way(:

|Number |Description |Unit Price |Total |

|6 |13W Mini CFL |$4.98 |$29.88 |

| | | |$29.88 |

Way (:

|Number |Description |Unit Price |Total |

|4 |23W Mini Twist CFL |$6.97 |$27,88 |

|4 |60W |$0.49 |$1.96 |

| | | |$29.84 |

Way (:

|Number |Description |Unit Price |Total |

|2 |100W 4-pk. |$1.92 |$3.84 |

|1 |60W 4-pk. |$0.78 |$0.78 |

|1 |60W |$0.49 |$0.49 |

|1 |100W |$0.59 |$0.59 |

|1 |13W Mini CFL 3-pk. |$11.98 |$11.98 |

|1 |13W Mini CFL |$4.98 |$4.98 |

|1 |23W Mini Twist CFL |$6.97 |$6.97 |

| | | |$29.63 |

Enactment: Students strategies may use different combinations of addition and multiplication. For example, Way ( is a multiplicative approach while Way ( is an additive approach. It would be important to draw students’ attention to these differences. Most students might use an additive approach, given that one “adds up” the prices to find the “total” amount. This is a time when multiplicative thinking could be encouraged!

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Particular materials

Mathematics Tasks

Free-Response Items

F1. CFL Replacement Questions

CFLs fit in 29 of the 35 old light fixtures in a house in central Iowa.[11] Is it correct to say CFLs fit in more than half of the fixtures? Explain your answer in at least two mathematically different ways. Tell how the answers are mathematically different.

F2. CFL Conversion Questions

One type of CFL is a spiral tube with a base that screws into a typical light fixture, much like an incandescent bulb. CFLs of this type come in different sizes, as shown in the photo to the right. On each of these packages (or in on-line catalogs), there is a variety of information printed on each size. Here is a sample of that information for the smallest CFL shown in the photo:

Uses less energy

Utiliza menos energia

7w 25w

376. ( 160

Lumens Lumens

a. The “7w”, or 7 watts, on the left side is a measure of the size of the CFL. The “25w” in the column on the right indicates that this CFL corresponds to a 25-watt incandescent bulb, a common size for a small incandescent bulb. Other common sizes for incandescent bulbs are 75 watts and 100 watts. What size CFL (in watts) would you expect to correspond to a 75-watt incandescent bulb? What size CFL would you expect to correspond to a 100-watt incandescent bulb?

b. Another common type of incandescent bulb is a 60-watt incandescent bulb. What number of watts would be appropriate for the corresponding CFL?

c. According to information on the package, a 19-watt CFL corresponds to a 75-watt incandescent bulb and a 23-watt CFL corresponds to a 100-watt incandescent bulb.

i. Compare this information with your results in part a.

ii. Assume the package information is correct. What would you expect to see on a package as the CFL wattage that corresponds to a 60-watt incandescent bulb?

d. Another way to figure out what number of watts for a CFL would match the 60-watt incandescent bulb involves using a graph. The following data came from CFL packages like those in the photograph.

|CFL watts |Incandescent watts |Lumens |

|7 |25 |375 |

|19 |75 |1200 |

|23 |100 |1600 |

It is possible to use the information to study the relationship between the watts of CFLs and the watts of incandescent bulbs.

i. Enter the CFL watt values as L1, the incandescent watt values as L2, and the lumen values as L3.

ii. Plot the CFL watts on the horizontal axis and the incandescent bulb watts on the vertical axis. Be sure to determine a good window to use before creating the graph.

iii. Fit a linear function to the data. Record an equation to represent the graph.

iv. What is the slope of the line? What is the intercept of the line? What do these values mean in terms of the CFLs?

A second way to use information in the chart and now in your calculator is to find a mathematical way to associate watts and lumens. This would involve the relationship between the energy needed by the light and the amount of light the bulb produces.

• Create the scatter plot and fit a line to the data for CFL watts (in L1) and lumens (in L3).

* Use the scatter plot and graph to determine how many watts correspond to 870 lumens.

F3. Circular CFLs

CFLs come in different shapes. One type of CFL has a circular tube. The greatest distance across the entire CFL is 8 inches. The greatest distance across the inside of the CFL is [pic] inches. Estimate the surface area of the CFL.

Variety items

V1. Comparing Bulb Life

A CFL lasts an average of 10,000 hour. A typical incandescent bulb lasts 750 hours. How many incandescent bulbs would you need to last as long as one CFL?

V2. Savings

Replacing a 100-watt incandescent bulb with a 32-watt CFL can save at least $30 in energy costs over the life of the bulb. [12] If a business in town replaces 17 100-watt incandescent bulbs with 32-watt CFLs, what would be the savings over the life of these bulbs?

V3. CFL Surface Areas

For any one CFL, the total surface area of the tube(s) determines how much light the CFL produces. Some CFLs have 2, 4 or 6 tubes. Some CFLs have circular or spiral shape tubes.[13] Should a CFL with 4 tubes produce twice as much light as a CFL with 2 tubes? Explain.

V4. Lifetime of CFLs

A tube in a CFL lasts approximately 10000 hours.[14] If a CFL is installed in your classroom today, should you expect the CFL to last until the end of the school year?

V5. Conversions to Find Costs

The following figure is part of a chart that appears in a web page.[15] [pic]

Determine how they calculated $21.90 for the Annual Energy Cost of a 100-Watt Incandescent bulb. Assume six hours per day and electric rate of 10 cents per 1-kilowatt hour.

V6. Register Tape Questions

The following portion of a register tape[16] shows the prices of several types of CFLs. Use this information to answer the following questions:

[pic]

a. The 13-watt mini-twist CFL comes in a package of three bulbs. What is the customer paying for each 13-watt bulb, excluding sales tax?

b. What would it cost to buy three 23-watt CFLs with 6% sales tax?

c. What would the cost of one 60-watt bulb be if you purchased them in a package of 4?

d. The custodian will be replacing each light fixture in your classroom with one 13W Mini CFL. This means that one CFL bulb will replace each light fixture in your room. Estimate the total of this replacement. Then calculate the actual cost. How did your estimate compare to the actual cost? Show your work and explain your reasoning.

e. The register tape here was from a purchase made through Penn State. No sales tax was included. What would be the sales tax on this purchase if the sales tax rate is 6%?

f. At the bottom of the register tape receipt, Lowe’s guarantees the lowest prices. If these prices are not the lowest, Lowe’s will beat any other stores prices by 10%.If a customer found all of the bulbs at a lower price at another store, how much money would Lowe’s need to give back to the customer?

g. You have $30 to purchase bulbs. Create a shopping list of the bulbs you would buy to get as close to $30 without overspending. (Note: There will be no sales tax added t o this purchase.)

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Mathematics handouts

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Technology guides

Quick Tricks

Plotting Data Points and Fitting Curves

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Visual components

Picture of incandescent light bulb

[pic]

Picture of CFL

[pic]

Register tape with prices of various CFLs:

[pic]

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Web “in-sites”

CFL introductory video. To initiate discussion of CFLs, one might use the GE Lighting video available at . The video has an animated speaker (a male scientist?) and it lasts less than two minutes. At the end of this video, students may gather information about different types of CFLs. This information would be very useful to students in designing their plan about what kind of lighting changes should be made in various locations and for various purposes throughout their school or home (as in the major project). [Caution: As long as the site is open in the browser window, it continues to make a sound (similar to sandpaper rubbing against wood) every few seconds. If leaving the site open makes sense, it may be good to turn the volume down or off, particularly if students are seated close to the machine or speakers.]

What is light? Students may raise this question as they think about CFLs and compare them to other lighting materials. A very short but accessible description of what is light (first sentence and first long paragraph) appears at [17]:

Introduction to Lighting

Simply put, light is a form of traveling energy.

Light from the sun brings energy to the earth… energy that can be absorbed by plants for photosynthesis, by the oceans to evaporate water and cause rain, by photocells and solar panels to create electricity, and so on.

When light enters the human eye and falls on the retina, it sets off photochemical and neurological processes that result in seeing. Radio waves, television transmissions, microwaves, ultra violet light, X-rays are all forms of electromagnetic waves just like light, but with a different wavelength. The human eye cannot perceive these wavelengths, but instruments can pick them up.

Thomas Edison invented the first practical electric lamp in 1879. He also invented the phonograph, moving pictures, the mimeograph machine, carbon microphones and so on. Edison’s original lamp used a carbon filament in a vacuum. Today we use tungsten wire in a bulb filled with argon gas.

Edison’s original lamp converted less than 1% of the electricity into light. Today’s household bulbs convert 6% to 7% into light, the rest being wasted as heat. Compact fluorescent lamps today can be 50 times more efficient than Edison’s original lamp and will last for years.

The background on Edison and the details about the amount of electricity converted to light may provide additional motivation for why CFLs are an appealing alternative to incandescent bulbs.

Science connection via on-line quiz. Classroom mathematics conversation around CFLs may connect nicely with science conversations about heat, light, energy, and environment. A particularly nice way to connect this module to science topics is through the “Fun Lighting Quiz” offered by Energy Star[18]. The quiz is on line at . For example, question number 4 () opens the door to a nice opportunity to challenge a basic mal-conception of heating/cooling.

[pic]

[pic]

Question 5 of the 10-question quiz provides nice motivation to understand why CFLs matter as well as to help students negotiate heat and light as different forms of energy.

[pic]

[pic]

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Materials and equipment needed

Students would need the following materials and equipment to work on the items in this module:

|Item |Materials and equipment |

|All |Paper and pencil for notes and calculations; Calculators for computations |

|??? |Graphing calculator with ability to plot data points (Plot Data Points Lab Guide) |

| |IS THIS TYPE OF CHART USEFUL? |

In addition, it would be helpful for students to have access to actual CFLs for curiosity, for motivation, or to better understand the context for some items (e.g., F3, V3). Minimally, pictures of the objects would be useful – See Normal Light Bulb Photo.

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About this module

Motivation

CFLs came to mind as the topic of this first module because CFLs seem to have many advantages (e.g., less power use for same amount of light), but they cost MUCH more than traditional light bulbs. People resist change in almost everything, and higher costs will keep many consumers away from buying something new. Consumers definitely have “sticker shock” when they see the price of a CFL compared to the price of a traditional light bulb. The price of CFLs is decreasing, but it is likely CFLs will always cost more than normal light bulbs.

There also is an interesting engineering twist to the CFL story. Engineers needed to do some new, challenging design work to get the electronics of the CFL into each light bulb. For example, standard fluorescent lights (like those in many schools and offices) have a special power unit in the light fixture for the light bulb. Recent advances in technology and manufacturing lead to bulbs that warm up quickly and can be used in the light fixtures made for incandescent bulbs. Lastly, most of us tend to be users of technology – even things as common as electric lighting – with no insight into how these things actually work. This module helps people not only to make wise decisions about using CFLs but also to know a bit more about light, lighting, and technology we take for granted.

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History of use

The anticipated first classroom trials of this module will be in the Steelton-Highspire middle-grades mathematics classrooms in 2004-2005.

Teachers in the Bellefonte School District will review the module in Fall 2004.

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Credits/disclaimer

This module was developed under the GE Math Excellence: Math in a “New Technology” Context project, funded by the GE Foundation. The idea for a module on CFLs came from Liz Kisenwhether. Jianwu Ding lent technology context details about CFLs. The mathematical problems for students were generated by Rose May Zbiek. Shari Heller and Rose Zbiek developed the curriculum connections.

Add GE disclaimer to all modules.

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[1] To translate these codes to item in this module, please see Lesson Ideas.

[2] Refuting or supporting this claim is the essence of Projects 1, 2 and 3.

[3] (p. 2)

[4] , p. 1

[5] (p. 2)

[6] (p. 1)

[7] , p. 1

[8] , pp. 1-2

[9] , p. 1

[10] Register tape is based on actual purchase from Lowes’, September 2004.

[11] (p. 2)

[12] , p. 1

[13] , p. 1

[14] No permission yet to use the following clip from the web site – it is here temporarily only to give us an idea of what the site holds. In web version, excerpts from sites may be replace by a link to the site that then appears as a pos-up box.

[15] ENERGY STAR® is a collaboration between the U.S. Department of Energy, the U.S. Environmental Protection Agency, and participating companies with the goal to prevent pollution by giving consumers energy-efficient product choices without sacrificing on quality. The ENERGY STAR® label makes it easy to identify products that will save money and help protect the environment. The Energy Star Partner of the Year Award announced February 5, 2004 went to GE.

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