Mathematics, Grade 9 - 12, Algebraic Connections, 2010 ALGEBRAModeling 1.) Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) Example: The amount of sales tax on a new car is directly proportional to the purchase price of the car. If the sales tax on a \$20,500 car is \$1,600, what is the purchase price of a new car that has a sales tax of \$3,200?                 Answer: The purchase price of the new car is \$41,000. 2.) Solve application-based problems by developing and solving systems of linear equations and inequalities. (Alabama) 3.) Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) Example: Solve problems involving compound interest, bacterial growth, carbon-14 dating, and depreciation. Graphing 4.) Determine maximum and minimum values of a function using linear programming procedures. (Alabama) Example: Observe the boundaries x ≥ 0, y ≥ 0, 2x - 3y + 15 ≥ 0, and x ≤ 9 to find the maximum and minimum values of f(x,y) = 3x + 5y 5.) Determine approximate rates of change of nonlinear relationships from graphical and numerical data. (Alabama) a. Create graphical representations from tables, equations, or classroom-generated data to model consumer costs and to predict future outcomes. (Alabama) 6.) Use the extreme value of a given quadratic function to solve applied problems. (Alabama) Example: Determine the selling price needed to maximize profit. Finance 7.) Use analytical, numerical, and graphical methods to make financial and economic decisions, including those involving banking and investments, insurance, personal budgets, credit purchases, recreation, and deceptive and fraudulent pricing and advertising. (Alabama) Examples: Determine the best choice of certificates of deposit, savings accounts, checking accounts, or loans. Compare the costs of fixed- or variable-rate mortgage loans. Compare costs associated with various credit cards. Determine the best cellular telephone plan for a budget. a. Create, manually or with technological tools, graphs and tables related to personal finance and economics. (Alabama) Example: Use spreadsheets to create an amortization table for a mortgage loan or a circle graph for a personal budget. GEOMETRYModeling 8.) Determine missing information in an application-based situation using properties of right triangles, including trigonometric ratios and the Pythagorean Theorem. (Alabama) Example: Use a construction or landscape problem to apply trigonometric ratios and the Pythagorean Theorem. Symmetry 9.) Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) Example: Identify the symmetry found in nature, art, or architecture. Measurement 10.) Critique measurements in terms of precision, accuracy, and approximate error. (Alabama) Example: Determine whether one candidate has a significant lead over another candidate when given their current standings in a poll and the margin of error. 11.) Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama) Example: Use a blueprint or scale drawing of a house to determine the amount of carpet to be purchased. STATISTICS AND PROBABILITYGraphing 12.) Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) Examples: Create models of election results as a function of population change, inflation or employment rate as a function of time, cholesterol density as a function of age or weight of a person. a. Predict probabilities given a frequency distribution. (Alabama)