Business+Model+Application

[Module materials drafted by Washington Applied Math Council team at summer 2010 conference in Richland, WA, June 21-25] · How can we use mathematics to create models and make decisions about statistical data? · Productivity and production costs? || · Students will be able to graph functions of inequalities to solve problems · Students will understand quadratic and polynomial equations and their graphs || Ability to use a calculator. Understanding of the coordinate plane and graphing. ||
 * **Business Model Applications** ||
 * **Mathematics Frame: Algebra 2** ||
 * **CTE Frame: Applied Math** ||
 * **Time Expectation: 24 learning hours** ||
 * **Desired Results** ||
 * **Understandings** ||
 * Linear equations and inequalities are used to calculate and graph sales quantities and maximizations of sales. Quadratic and cubic equations are used to calculate maximums. Polynomials are used to predict manufacturing costs, total revenue, and profit and loss. ||
 * **Mathematics Essential Questions** ||
 * · How do linear equations and inequalities help business to predict maximum sales?
 * **Mathematics Essential Questions** ||
 * · How do linear equations and inequalities help business to predict maximum sales?
 * **Concepts:** The students will know… ||
 * Students will gain knowledge of mathematical models to predict, determine, and enhance business decisions. Students will gain an understanding of how statistics are used to make business and marketing decisions. ||
 * **Knowledge:** The students will know… ||
 * Students formalize their study of linear equations, quadratics, and polynomials to calculate cost, revenue, profit/loss, and volume. They extend their use of statistics to graph data and analyze its shape to make predictions. Students prepare for the further study of mathematical models as they are used in business operations. ||
 * **Skills:** The students will be able to… ||
 * · Students will be able to work problems with multiple variables
 * **Standards Addressed** ||
 * A1.1.A Select and justify functions and equations to model and solve problems. ||
 * A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. ||
 * A1.1.C Solve problems that can be represented by a system of two linear equations or inequalities. ||
 * A1.1.D Solve problems that can be represented by quadratic functions and equations. ||
 * A1.1.E Solve problems that can be represented by exponential functions and equations. ||
 * A1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. ||
 * A1.2.C Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions. ||
 * A1.2.E Use algebraic properties to factor and combine like terms in polynomials. ||
 * A1.2.F Add, subtract, multiply, and divide polynomials. ||
 * A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. ||
 * A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. ||
 * A1.3.C Evaluate //f//(//x//) at //a// (i.e., //f//(//a//)) and solve for //x// in the equation //f//(//x//) = //b//. ||
 * A1.4.D Write and solve systems of two linear equations and inequalities in two variables. ||
 * A1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations. ||
 * A1.6.B Make valid inferences and draw conclusions based on data. ||
 * A2.1.A Select and justify functions and equations to model and solve problems. ||
 * A2.1.B Solve problems that can be represented by systems of equations and inequalities. ||
 * A2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities. ||
 * A2.2.B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents. ||
 * A2.2.C Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions. ||
 * A2.3.C Solve quadratic equations and inequalities, including equations with complex roots. ||
 * A2.5.D Plot points, sketch, and describe the graphs of cubic polynomial functions of the form //f(x) = ax3 + d// as an example of higher order polynomials and solve related equations. ||
 * A2.7.A Solve systems of three equations with three variables. ||
 * A2.8all All Core Processes Covered ||
 * **Presenting Theme Problem:** ||
 * Use of mathematical models in various business operations. ||
 * **Formative Assessment:** ||
 * There will be on going question and answer sessions, observations, and potential games and competitions. ||
 * **Summative Assessment:** ||
 * End of unit quiz and/or company finance project. Maybe have the students in teams start a business of their choice. Have them stock their business with three different items. They can buy 100 items to start. Assuming each item has a 75% mark-up, determine which three items will be stocked, how many of each item will be purchased and what the profit will be if all 100 iems are sold. Use newspaper articles, web sources, or actual prices from suppliers/stores for iem prices. Have the teams share their findings. (Guest speakers such as buyers, etc.can come and explain how they decide what to buy) ||
 * **Necessary Prior Knowledge and Skills:** ||
 * Basic understanding of equations and manipulation of algebraic equations.
 * **Scope and Sequence of Instructional Activities:** ||
 * Linear equations, inequalities, quadratics, polynomials. ||
 * **Necessary Materials:** ||
 * Copies of student worksheets, access to computers for research and excel ||
 * **Printed Resources:** ||
 * Business materials to create supplemental problems ||
 * **Supplies:** ||
 * Calculators, rulers, graph paper ||
 * **Electronic Resources:** ||
 * None used ||
 * **Other (speakers, field trips, etc.):** ||
 * Small Business Owner. Sales Manager. Operations Manager. ||