Mathematical Models with Applications

Apply mathematics to problems arising in everyday life, society, and the workplace; October 2015 Update Page 17 §111.C. High School.

Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Create and use representations to organize, record, and communicate mathematical ideas.

Analyze mathematical relationships to connect and communicate mathematical ideas.

Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Use rates and linear functions to solve problems involving personal finance and budgeting, including compensations and deductions.

Solve problems involving personal taxes.

Analyze data to make decisions about banking, including options for online banking, checking accounts, overdraft protection, processing fees, and debit card/ATM fees.

Use formulas to generate tables to display series of payments for loan amortizations resulting from financed purchases.

Analyze personal credit options in retail purchasing and compare relative advantages and disadvantages of each option.

Use technology to create amortization models to investigate home financing and compare buying a home to renting a home.

Use technology to create amortization models to investigate automobile financing and compare buying a vehicle to leasing a vehicle.

Analyze and compare coverage options and rates in insurance.

Investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans.

Analyze types of savings options involving simple and compound interest and compare relative advantages of these options.

Use proportionality and inverse variation to describe physical laws such as Hook's Law, Newton's Second Law of Motion, and Boyle's Law; Page 18 October 2015 Update.

Use exponential models available through technology to model growth and decay in areas, including radioactive decay.

Use quadratic functions to model motion.

Use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture.

Use scale factors with two-dimensional and three-dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields.

Use the Pythagorean Theorem and special right-triangle relationships to calculate distances.

Use trigonometric ratios to calculate distances and angle measures as applied to fields.

Use trigonometric ratios and functions available through technology to model periodic behavior in art and music.

Use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and photography.

Use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music.

Use scale factors with two-dimensional and three-dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields.

Determine the number of ways an event may occur using combinations, permutations, and the Fundamental Counting Principle.

Compare theoretical to empirical probability.

Use experiments to determine the reasonableness of a theoretical model such as binomial or geometric.

Interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, dot plots, stem-and-leaf plots, and box and whisker plots, to draw conclusions from the data and determine the strengths and weaknesses of conclusions.

Analyze numerical data using measures of central tendency (mean, median, and mode) and variability (range, interquartile range or IQR, and standard deviation) in order to make inferences with normal distributions.

Distinguish the purposes and differences among types of research, including surveys, experiments, and observational studies.

Use data from a sample to estimate population mean or population proportion; October 2015 Update Page 19 §111.C. High School.

Analyze marketing claims based on graphs and statistics from electronic and print media and justify the validity of stated or implied conclusions.

Use regression methods available through technology to model linear and exponential functions, interpret correlations, and make predictions.

Formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions.

Communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation.