• 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 that model problem situations.

    CFL Module:

    Variety Items

    2.1

    Number, Number Systems and Number Relationships

     

    2.1.8.B.

    Simplify numerical expressions involving exponents, scientific notation and using order of operations.

     Students have several 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 underestimating in computation.

    CFL Module:

    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 language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs, and diagram.

    CFL Module:

    Interpretation of Graphs of Various Aspects of CFLs (bulb diameter, Arc Length vs. Lumens, Arc Length vs. Voltage, light emission intensities,

     

    2.5.8.C.

    Justify strategies and defend approaches used and conclusions reached.

    CFL Module:

    School Lighting Project, and Classroom Lighting Project

    2.5.8.D.

    Determine pertinent information in problem situations and whether any further information is needed for solution.

    CFL Module:

    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 any correlation of the variables.

    CFL Module:

    Free-Response Scatter Plot Problems.

    2.6.8.F.

    Use scientific and graphing calculators and computer spreadsheets to organize and analyze data.

    CFL Module:

    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:

     

     

    Chapter

     

    Clusters (Grade 6 Mathematics)

    or

    Section numbers

    Module Connections

    P=Open-ended Project Items

    F=Free Response Items

    V=Variety Items

     

    Mathematics

    1

     

    Add and Subtract Decimals (Clusters A & B)

    P2 – Room Lighting Project

    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, & 9)

    F4 – Comparison Chart
    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, & 7)

    F1 – CFL Replacement Question
    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.



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