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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). D:\Docstoc\Working\pdf\f91e4343-98a5-4eba-a352-d14dfd50db62.doc 1 07/27/2011 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. D:\Docstoc\Working\pdf\f91e4343-98a5-4eba-a352-d14dfd50db62.doc 2 07/27/2011 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 D:\Docstoc\Working\pdf\f91e4343-98a5-4eba-a352-d14dfd50db62.doc 3 07/27/2011 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). D:\Docstoc\Working\pdf\f91e4343-98a5-4eba-a352-d14dfd50db62.doc 4 07/27/2011 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 D:\Docstoc\Working\pdf\f91e4343-98a5-4eba-a352-d14dfd50db62.doc 5 07/27/2011 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. D:\Docstoc\Working\pdf\f91e4343-98a5-4eba-a352-d14dfd50db62.doc 6 07/27/2011 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 D:\Docstoc\Working\pdf\f91e4343-98a5-4eba-a352-d14dfd50db62.doc 7 07/27/2011 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. D:\Docstoc\Working\pdf\f91e4343-98a5-4eba-a352-d14dfd50db62.doc 8 07/27/2011

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