M 315C addresses the following portions of SBEC Standards II (Patterns and Algebra), IV (Probability and Statistics), V (Mathematical Processes), and VII (Mathematical Learning and Instruction)

"The beginning teacher of mathematics is able to:

• (2.1s) use inductive reasoning to identify, extend, and create patterns using concrete models, figures, numbers, and algebraic expressions;
• (2.2s) formulate implicit and explicit rules to describe and construct sequences verbally, numerically, graphically, and symbolically;
• (2.3s) illustrate concepts of relations and functions using concrete models, tables, graphs, and symbolic expressions;
• (2.4s) apply relations and functions to represent mathematical and real-world situations; …
• (2.6s) model and solve problems , including proportions problems, using concrete, numeric, tabular, graphic, and algebraic methods; and
• (2.7s) recognize misleading patterns….
• (2.9s) make, test, validate, and use conjectures about patterns and relationships in data presented in tables, sequences, or graphs;
• (2.10s) use linear and nonlinear functions and relations, including polynomial, absolute value, trigonometric, rational, radical, exponential, logarithmic, and piecewise functions, to model problems;
• (2.11s) use a variety of representations and methods (e.g., numerical methods, tables, graphs, algebraic techniques) to solve linear and nonlinear equations, inequalities, and systems;
• (2.12s) use transformations to illustrate properties of functions and relations and to solve problems; …
• (2.14s) relate the concept of limit as a conceptual foundation of calculus to middle school mathematics;
• (2.15s0 relate the rate of change as a conceptual foundation of calculus to middle school mathematics;
• (2.19s0 use methods of recursion and iteration to model and solve problems;
• (2.20s) analyze the properties of sequences and series and use them to solve problems involving finite and infinite processes; …
• (2.23s) analyze attributes of functions … and their graphs;
• (2.24s) describe linear, quadratic, and other polynomial functions, analyze their algebraic and graphical properties, and use these to model and solve problems using a variety of methods, including technology;
• (2.25s) describe exponential, logarithmic, and logistic functions algebraically and graphically, analyze their algebraic and graphical properties, and use theses to model and solve problems using a variety of methods, including technology;
• (2.26s)describe trigonometric and circular functions algebraically and graphically, analyze their algebraic and graphical properties, and use these to model and solve problems using a variety of methods, including technology;
• (2.27s) describe rational, radical, absolute value, and piecewise functions algebraically and graphically, analyze their algebraic and graphical properties, and use these to model and solve problems using a variety of methods, including technology; … (pp. 6 - 9)
• (4.1s) investigate and answer questions by collecting, organizing , and displaying data from real-world situations;
• (4.2s) support arguments, make predictions, and draw conclusions using summary statistics and graphs to analyze and interpret one-variable data; … (p. 13)
• (5.7s) recognize that a mathematical problem can be solved in a variety of ways, evaluate the appropriateness of various strategies, and select an appropriate strategy for a given problem;
• (5.8s) evaluate the reasonableness of a solution to a given problem;
• (5.9s) use physical and numerical models to represent a given problem or mathematical procedure;
• (5.10s) recognize that assumptions are made when solving problems and identify and evaluate those assumptions;
• (5.11s) investigate and explore problems that have multiple solutions;
• (5.12s) apply content knowledge to develop a mathematical model of a real-world situation and analyze and evaluate how well the model represents the situation; …
• (5.13s) develop and use simulations as a tool to model and solve problems; and
• (5.14s) develop and use iteration and recursion to model and solve problems.
• (5.15s) explore problems using verbal, graphical, numerical, physical, and algebraic representations;
• (5.16s) recognize and use multiple representations of a mathematical concept…
• (5.17s) apply mathematical methods to analyze practical situations; and
• (5.18s) use mathematics to model and solve problems in other disciplines, such as art, music, science, social science, and business….
• (5.21s) translate mathematical statements among developmentally appropriate language, standard English, mathematical language, and symbolic mathematics;
• (5.22s) provide students with opportunities to demonstrate their understanding of mathematics in a variety of ways using a variety of tools;
• (5.23s) use visual media such as graphs, tables, diagrams, and animations to communicate mathematical information; (pp. 17 - 20) …
• (7.18s) use mathematics labs, simulations, open-ended investigations, research projects, and other activities when appropriate to guide students' learning;
• (7.19s) apply appropriate technology to promote mathematical learning; …
• (7.23s) teach students how to locate, retrieve, and retain content-related information from a range of … technologies; …(pp. 23- 24)