Math Models with Applications
Fall Semester | ||||
Unit Title | Unit 1: Introduction to Problem-Solving and Mathematical Models | Unit 2: Linear Function Models and Problem-Solving | Unit 3: Problem-Solving with Quadratic and Variation Function Models | Unit 4: Modeling with Exponential Functions |
Time | ~ 3 weeks | ~ 4 weeks | ~ 7 weeks | ~ 3 weeks |
Understandings | Problem-solving strategies can be applied to a wide range of mathematical situations. Problems and their solutions can be represented in multiple ways, strengthening understanding and flexibility. Mathematics is a tool for interpreting and solving problems in real-world settings. Mathematical relationships can be expressed verbally, algebraically, numerically, and graphically. Understanding multiple representations deepens conceptual understanding.
| Slope represents a line’s rate of change, measured as vertical change over horizontal change.
The relationship between two lines can be determined by comparing their slopes and y-intercepts, which allows meaningful comparisons when evaluating multiple options. Financial situations—such as bank accounts, loans, and credit cards—can be analyzed using graphs, tables, and equations. Simple interest is based only on the principal. Compound interest is based on the principal plus accumulated interest. Scatter plots show how one variable may affect another, and the correlation coefficient measures the strength of a linear relationship. | Quadratic functions model nonlinear relationships and can be written in various forms. Their key attributes (such as intercepts and vertex) can be identified both graphically and algebraically, and their solutions correspond to the factors of the function.
Functions serve as models for real-world data, helping determine solutions and make predictions. In context, a reasonable domain includes independent values that make sense in the situation, and a reasonable range includes dependent values that fit the scenario. | Exponential Models can be used to reflect exponential growth or decay in finance situations. Percent increase/decrease can be represented in real-life situations such as indicating sales tax and discounts, respectively.
Exponential models can be used to make critical judgements from a given graph.
Lines of best fit can help determine if data sets represent linear or exponential models. Predictions can be made using regression models.
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TEKS | M.1 A, B, C, D, G M.2 A, B | M.2 A, B, C M.4 B, C M.9 A, F M.10 A, B | M.5 A, C | M.2 A, C M.3 A, D M.5 B M.9 F |
Process Standards | 1 A, B, C, D, E, F, G | |||
Math Models with Applications
Spring Semester | ||||
Unit Title | Unit 5: Problem-Solving with Financial Models | Unit 6: Using Geometric Models to Solve Problems | Unit 7: Problem-Solving with Probability and Statistical Models | Unit 8: Modeling with Trigonometric Functions |
Time | ~ 5 weeks | ~ 4 weeks | ~ 4 weeks | ~ 4 weeks |
Understandings | Interest significantly affects loan repayment, and individuals can (and should) shop for loan options that best support their financial goals.
Financial comparisons—such as buying versus renting or leasing—should be carefully analyzed to determine the most beneficial option. Investment opportunities may include annuities, stocks, bonds, and insurance products, each carrying different levels of risk and return. | Perimeter measures the distance around a polygon, and changes in a figure’s dimensions affect its measurements predictably.
Transformations create relationships between the vertices of a preimage and its image, preserving or altering specific properties depending on the transformation. Measurement of three-dimensional figures extends these ideas to include area, surface area, and volume, connecting geometric structure to quantitative reasoning. | Investment options can be represented in multiple ways and may sometimes mislead the consumer Comparisons should be made when shopping for investment opportunities
Theoretical probability considers the likelihood of an event occurring without an experiment.
Experimental probability considers the likelihood of an event occurring using the results of an experiment.
Data can be skewed to portray a particular outcome. Bias should be considered when making critical judgements for a given situation.
| The Distance Formula determines the length between two points and leads to the Pythagorean Theorem, which can be used to verify whether a triangle is a right triangle. Similar figures contain congruent angles and proportional sides, reinforcing consistent geometric relationships. Trigonometric functions exhibit repeating patterns. The period represents the cycle length of the function. The amplitude represents the height of the function.
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TEKS | M.2 A, B, C M.3 A, B, C, D M.4 A, B, C M.9 E | M.6 A, B M.7 B, C, D | M.4 B M.8 A, B, C M.9 A, B, C, D M.10 A, B | M.6 A, C, D M.7 A, C |
Process Standards | 1 A, B, C, D, E, F, G | |||