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Sales Projections Templates

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					                                   Math-Related Credit Crosswalk
                                                 for
                                  Career Technical Education Classes
                                         in Macomb County

                                         Program Information
                                 District:   Van Dyke
                         Program Name: Finance
                      CIP Code Number:       52.0800
                         Career Pathway: Accounting
                        Instructor Name:     Heath
                                    Date: December 15, 2008
Strand              STANDARDS                                               CTE APPLICATION and PRACTICE
L1
                      REASONING ABOUT NUMBERS, SYSTEMS AND QUANTITATIVE LITERACY

L1.1                                             Number Systems and Number Sense

L1.1.2              Explain why the multiplicative inverse of a     Example=Budget
                    number has the same sign as the number,
                    while the additive inverse has the opposite     Revenues – Expenses = 0
                    sign.
L1.1.3              Explain how the properties of associativity,    Grouping of numbers on Financial Statements
                    commutativity, and distributivity, as well as   Ratios (e.g.) % of sales
                    identity and inverse elements, are used in      Taxes - Distributivity
                    arithmetic and algebraic calculations.
L1.1.4              Describe the reasons for the different          Sales Projections
                    effects of multiplication by, or
                    exponentiation of, a positive number by a
                    number less than 0, a number between 0
                    and 1, and a number greater than 1.
L1.2                                               Representations and Relationships

L1.2.1              Use mathematical symbols (e.g., interval        Ratio analysis
                    notation, set notation, summation notation)
                    to represent quantitative relationships and
                    situations.
L1.2.4              Organize and summarize a data set in a          Income Statements
                    table, plot, chart, or spreadsheet; find        Balance Sheets
                    patterns in a display of data; understand       Ratio Analysis
                    and critique data displays in the media.        Pie Charts - % of Sales
L1.3                                            Counting and Probabilistic Reasoning
L1.3.2              Define and interpret commonly used              “What are the chances”
                    expressions of probability (e.g., chances of    Supply and demand
                    an event, likelihood, odds).

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L1.3.3              Recognize and explain common probability        Stock market trends/projections
                    misconceptions such as “hot streaks” and        Profitability trends
                    “being due.”                                    Luck vs. Work
                                                       Multiply and Divide Fractions

N.MR.06.01          Understand division of fractions as the         Explain that dividing by 3 is the same as multiplying
                    inverse of multiplication.                      by 1/3.
N.MR.06.03          Solve for the unknown.                          Accounting Equation

                                  Solve Decimal, Percentage and Rational Number Problems

N.MR.06.13          Solve contextual problems involving             Payroll Taxes
                    percentages such as sales taxes and tips.
N.FL.06.15          Solve applied problems that use the four        Continually
                    operations with appropriate decimal
                    numbers.
                          Understand Rational Numbers and Their Location on the Number Line

N.ME.06.17          Locate negative rational numbers (including     The concept of net loss.
                    integers) on the number line. Know that
                    numbers and their negatives add to 0 and
                    are on opposite sides and at equal distance
                    from 0 on a number line.
N.ME.06.18          Understand that rational numbers are            Ratios. Scaling up or down fractions.
                    quotients of integers (non zero
                    denominators).
N.ME.06.19          Understand that 0 is an integer that is         Break-even. Revenues and expenses are equal.
                    neither negative nor positive.

                                                      Understand Derived Quantities

N.MR.07.02          Solve problems involving derived quantities     Rates of changes. Simple v. Compound Interest
                    such as density, velocity and weighted
                    averages.
                       Understand and Solve Problems Involving Rates, Ratios, and Proportions

N.FL.07.03          Calculate rates of change including speed.      Horizontal Analysis. Ex. % of increase in sales from
                                                                    one year to the next.

N.MR.07.04          Convert ratio quantities between different      Currency exchange in a global economy.
                    systems of units, such as feet per second to
                    miles per hour.
N.FL.07.05          Solve proportion problems using such            Payroll Taxes that are proportional (or at least within
                    methods as unit rate, scaling, finding          a range) Ex. State Income and FICA.
                    equivalent fractions, and solving the
                    proportion equation a/b = c/d; know how to      Unit Cost Analysis – As revenues increase, variable
                    see patterns about proportional situations in   costs can be projected to increase proportionally.
                    tables.
                                                     Compute with Rational Numbers

N.FL.07.07          Solve problems involving operations with        Continually
                    integers.
N.FL.07.08          Add, subtract, multiply and divide positive     Continually
                    and negative rational numbers fluently.
N.FL.07.09          Estimate results of computations with           Continually
                    rational numbers.

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                                                                   Solve Problems

N.MR.08.08          Solve problems involving percent increases         Calculating increased payroll taxes resulting from
                    and decreases.                                     pay increases.
N.FL.08.09          Solve problems involving compounded                Compound Interest
                    interest or multiple discounts.
N.FL.08.11          Solve problems involving ratio units, such         Sales and/or costs per unit.
                    as miles per hour, dollars per pound or
                    persons per square mile.
L2                  STANDARDS                                                CTE APPLICATION and PRACTICE

                                        CALCULATION, ALGORITHMS, AND ESTIMATION

L2.1                                       Calculation Using Real and Complex Numbers

L2.1.1              Explain the meaning and uses of weighted           CPI, GDP
                    averages (e.g., GNP, consumer price index,
                    grade point average).
L2.1.6              Recognize when exact answers aren’t                Budgets, projected financial statements
                    always possible or practical. Use
                    appropriate algorithms to approximate
                    solutions to equations (e.g., to approximate
                    square roots).
L2.2                                                      Sequences and Iteration

L2.2.1              Find the nth term in arithmetic, geometric, or     Simple v. Compound Interest
                    other simple sequences.
L2.2.2              Compute sums of finite arithmetic and              Simple v. Compound Interest
                    geometric sequences.
L2.2.3              Use iterative processes in such examples           Calculating Compound Interest one period at a time.
                    as computing compound interest or
                    applying approximation procedures.
L3                  STANDARDS                                                CTE APPLICATION and PRACTICE

                                               MEASUREMENT AND PRECISION
L3.1                                       Measurement Units, Calculations, and Scales

L3.1.1              Convert units of measurement within and            Currency exchange in a global economy.
                    between systems; explain how arithmetic
                    operations on measurements affect units,
                    and carry units through calculations
                    correctly.
L3.2                                                         Understanding Error

L3.2.1              Determine what degree of accuracy is               Rounding of financial statements and payroll taxes. A
                    reasonable for measurements in a given             column of rounded numbers will likely not equal the
                    situation; express accuracy through use of         rounded sum of the same numbers.
                    significant digits, error tolerance, or percent
                    of error; describe how errors in
                    measurements are magnified by
                    computation; recognize accumulated error
                    in applied situations.
L3.2.2              Describe and explain round-off error,              Rounding of financial statements and payroll taxes. A
                    rounding, and truncating.                          column of rounded numbers will likely not equal the

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                                                                     rounded sum of the same numbers.

L4.1                                                      Mathematical Reasoning

L4.1.1              Distinguish between inductive and                Basing on results v. Looking at factors to project
                    deductive reasoning, identifying and
                    providing examples of each.
A1                  STANDARDS                                              CTE APPLICATION and PRACTICE

                                        EXPRESSIONS, EQUATIONS, AND INEQUALITIES

A1.1                      Construction, Interpretation, and Manipulation of Expressions (linear,
                          quadratic, polynomial, rational, power, exponential, logarithmic, and
                                                      trigonometric)
A1.1.1              Give a verbal description of an expression       Cost projections, breakeven analysis, sales tax
                    that is presented in symbolic form, write an
                    algebraic expression from a verbal
                    description, and evaluate expressions given
                    values of the variables.
A1.2                    Solutions of Equations and Inequalities (linear, exponential, logarithmic,
                                      quadratic, power, polynomial, and rational)
A1.2.1              Write and solve equations and inequalities       Cost projections, breakeven analysis, sales tax
                    with one or two variables to represent
                    mathematical or applied situations.
A1.2.8              Solve an equation involving several              Compound interest
                    variables (with numerical or letter
                    coefficients) for a designated variable.
                    Justify steps in the solution.
A1.2.9              Know common formulas (e.g., slope,               Compound Interest
                    distance between two points, quadratic           Rate of change (slope)
                    formula, compound interest, distance = rate      Earnings Per Share
                    · time), and apply appropriately in              Return on Equity
                    contextual situations.
A2                  STANDARDS                                               CTE APPLICATION and PRACTICE

                                                                   FUNCTIONS

A2.1                               Definitions, Representations, and Attributes of Functions

A2.1.1              Recognize whether a relationship (given in       Break-even analysis, compound interest
                    contextual, symbolic, tabular, or graphical
                    form) is a function and identify its domain
                    and range.
A2.1.2              Read, interpret, and use function notation       Identifying the domain and range of breakeven
                    and evaluate a function at a value in its        analysis and
                    domain.
A2.1.3              Represent functions in symbols, graphs,          Break-even analysis, compound interest
                    tables, diagrams, or words and translate
                    among representations.
A2.1.7              Identify and interpret the key features of a     Break-even analysis
                    function from its graph or its formula(e),
                    (e.g., slope, intercept(s), asymptote(s),
                    maximum and minimum value(s), symmetry,
                    and average rate of change over an
                    interval).

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A2.5                                            Exponential and Logarithmic Functions

A2.5.1              Write the symbolic form and sketch the            Compound Interest
                    graph of an exponential function given
                    appropriate information (e.g., given an initial
                    value of 4 and a rate of growth of 1.5, write
                                  x
                    f(x) = 4 (1.5) ).
A2.5.2              Interpret the symbolic forms and recognize        Compound interest
                    the graphs of exponential and logarithmic
                                              x
                    functions (e.g., f(x) = 10 , f(x) = log x, f(x)
                        x
                    = e , f(x) = ln x).
A2.5.4              Understand and use the fact that the base         Compound Interest
                    of an exponential function determines
                    whether the function increases or
                    decreases and how base affects the rate of
                    growth or decay.
A2.5.5              Relate exponential and logarithmic                Compound Interest
                    functions to real phenomena, including half-
                    life and doubling time.
A3                  STANDARDS                                               CTE APPLICATION and PRACTICE

                                                       MATHEMATICAL MODELING

A3.1                Models of Real-world Situations Using Families of Functions Example: An
                    initial population of 300 people grows at 2% per year. What will the population be in
                    10 years?

A3.1.1              Identify the family of functions best suited      Compound Interest
                    for modeling a given real-world situation
                    [e.g., quadratic functions for motion of an
                    object under the force of gravity or
                    exponential functions for compound
                    interest. In the example above, recognize
                    that the appropriate general function is
                                           t
                    exponential (P = P0a )].
A3.1.2              Adapt the general symbolic form of a              Compound Interest
                    function to one that fits the specifications of
                    a given situation by using the information to
                    replace arbitrary constants with numbers.
                    In the example above, substitute the given
                    values P0 = 300 and a = 1.02 to obtain P =
                               t
                    300(1.02) .
A3.1.3              Using the adapted general symbolic form,          Compound Interest
                    draw reasonable conclusions about the
                    situation being modeled. In the example
                    above, the exact solution is 365.698, but for
                    this problem, an appropriate approximation
                    is 365.
                                                          Calculate Rates - Algebra

A.PA.06.01          Solve applied problems involving rates,           Compound Interest, depreciation rates, graduated
                    including speed.                                  payroll rates.
                                                    Understand the Coordinate Plane
A.RP.06.02          Plot ordered pairs of integers and use            Breakeven analysis
                    ordered pairs of integers to identify points in
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                    all four quadrants of the coordinate plane.
                      Use Variables, Write Expressions and Equations, and Combine Like Terms

A.FO.06.03          Use letters with units, to represent                Accounting equations, variable costs
                    quantities in a variety of contexts.

A.FO.06.04          Distinguish between an algebraic                    Financial statements, financial ratios, payroll
                    expression and an equation.
A.FO.06.05          Use standard conventions for writing                Compound Interest
                    algebraic expressions.
A.FO.06.06          Represent information given in words using          Accounting equation, calculating owner’s equity
                    algebraic expressions and equations.
A.FO.06.07          Simplify expressions of the first degree by         FICA = Social security + medicare
                    combining like terms and evaluate using
                    specific values.
                             Represent Linear Functions Using Tables, Equations, and Graphs

A.RP.06.08          Understand that relationships between               Sales versus variable expenses. Pie chart of
                    quantities can be suggested by graphs and           disposition of net sales.
                    tables.

A.RP.06.10          Represent simple relationships between              Sales versus variable expenses. Pie chart of
                    quantities using verbal descriptions,               disposition of net sales.
                    formulas or equations, tables and graphs.
                                                                   Solve Equations

A.FO.06.12          Understand that adding or subtracting the           Accounting equation
                    same number to both sides of an equation
                    creates a new equation that has the same
                    solution.
A.FO.06.13          Understand that multiplying or dividing both        Finding errors in trial balances
                    sides of an equation by the same non-zero
                    number creates a new equation that has the
                    same solutions.
                        Understand and Apply Directly Proportional Relationships and Relate to
                                          Linear Relationships - Algebra

A.AP.07.01          Recognize when information given in a               Break-even analysis, variable costs
                    table, graph or formula suggests a directly
                    proportional or linear relationship.
A.RP.07.02          Represent directly proportional and linear          Payroll taxes
                    relationships using verbal descriptions,
                    tables, graphs and formulas and translate
                    among these representations.
A.PA.07.04          For directly proportional or linear situations,     Breakeven analysis, payroll
                    solve applied problems using graphs and
                    equations.
                                            Understand and Represent Linear Functions

A.PA.07.06          Calculate the slope from the graph of a             Compound interest, growth rates
                    linear function as the ratio of “rise/run” for a
                    pair of points on the graph and express the
                    answer as a fraction and a decimal;
                    understand that linear functions have slope
                    that is a constant rate of change.


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                     Understand and Solve Problems about Inversely Proportional Relationships

A.PA.07.09          Recognize inversely proportional                  Supply and demand
                    relationships in contextual situations; know
                    that quantities are inversely proportional if
                    their product is constant.
                               Apply Basic Properties of Real Numbers in Algebraic Contexts

A.PA.07.11          Understand and use basic properties of real       Taxes
                    numbers: additive and multiplicative
                    identities, additive and multiplicative
                    inverses commutativity, associativity, and
                    the distributive property of multiplication
                    over addition.
S1                     STANDARDS                                              CTE APPLICATION and PRACTICE

                                        UNIVARIATE DATA - EXAMINING DISTRIBUTIONS

S1.1                                                Producing and Interpreting Plots

S1.1.1              Construct and interpret dot plots,                Identify appropriate types of charts (e.g. pie charts,
                    histograms, relative frequency histograms,        bar graphs, line graphs) to facilitate analysis of
                    bar graphs, basic control charts, and box         financial results.
                    plots with appropriate labels and scales;
                    determine which kinds of plots are
                    appropriate for different types of data;
                    compare data sets and interpret differences
                    based on graphs and summary statistics.
S2                     STANDARDS                                              CTE APPLICATION and PRACTICE

                                         BIVARIATE DATA - EXAMINING RELATIONSHIPS

S2.1                                                    Scatterplots and Correlation

S2.1.4              Differentiate between correlation and             Understanding whether economic conditions,
                    causation. Know that a strong correlation         industry developments, supplier and customer
                    does not imply a cause-and-effect                 behavior directly impact the bottom line or whether
                    relationship. Recognize the role of lurking       they simply correlate.
                    variables in correlation.
S4                     STANDARDS                                              CTE APPLICATION and PRACTICE

                                 PROBABILITY MODELS AND PROBABILITY CALCULATION

S4.1                                                                Probability

S4.1.2              Define mutually exclusive events,                 The conditional impact of economic conditions,
                    independent events, dependent events,             industry developments, supplier and customer
                    compound events, complementary events,            behavior on the profitability of a business.
                    and conditional probabilities; and use the
                    definitions to compute probabilities.

S4.2                                                 Application and Representation


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S4.2.2              Apply probability concepts to practical        Projections of revenues, expenses and rates of
                    situations, in such settings as finance,       return based upon the conditional impact of
                    health, ecology, or epidemiology, to make      economic conditions, industry developments,
                    informed decisions.                            supplier and customer behavior.
                                                       Represent and Interpret Data

D.RE.07.01          Represent and interpret data using circle      Identify appropriate types of charts (e.g. pie charts,
                    graphs, stem and leaf plots, histograms,       bar graphs, line graphs) to facilitate analysis of
                    and box-and-whisker plots and select           financial results.
                    appropriate representation to address
                    specific questions.
                           Understand Probability Concepts for Simple and Compound Events

D.PR.08.06          Understand the difference between              The conditional impact of economic conditions,
                    independent and dependent events and           industry developments, supplier and customer
                    recognize common misconceptions                behavior on the profitability of a business. Analyzing
                    involving probability.                         whether events are dependent or independent.




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