Algebra I Basic Understandings:

How does this course relate to the Texas Essential Elements for secondary mathematics?

This course gives you experience and background in many of the TEKS for secondary mathematics, including:

(3) Function concepts. Functions represent the systematic dependence of one quantity on another. Students use functions to represent and model problem situations and to analyze and interpret relationships.
(5) Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, numerical, algorithmic, graphical), tools, and technology, including, but not limited to, powerful and accessible hand-held calculators and computers with graphing capabilities and model mathematical situations to solve meaningful problems.
(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling, and justification and proof.

Algebra I Knowledge and Skills: "The student …

(b.1 B) gathers and records data, or uses data sets, to determine functional (systematic) relationships between quantities;
(b.2 D) in solving problems, collects and organizes data, makes and interprets scatterplots, and models, predicts, and makes decisions and critical judgments.
(b.3 B) given situations, looks for patterns and represents generalizations algebraically.
(c.2 A) develops the concept of slope as rate of change and determines slopes from graphs, tables, and algebraic representations;
(c.2 B) interprets the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;
(d.3 C) analyzes data and represents situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

Algebra II Basic Understandings:

(3) Functions, equations, and their relationship. The study of functions, equations, and their relationship is central to all of mathematics. Students perceive functions and equations as means for analyzing and understanding a broad variety of relationships and as a useful tool for expressing generalizations.
(5) Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, numerical, algorithmic, graphical), tools, and technology, including, but not limited, to powerful and accessible hand-held calculators and computers with graphing capabilities and model mathematical situations to solve meaningful problems.
(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling, and justification and proof.

Algebra II Knowledge and Skills:

(b.1 B) in solving problems, collects data and records results, organizes the data, makes scatterplots, fits the curves to the appropriate parent function, interprets the results, and proceeds to model, predict, and make decisions and critical judgments.
(f.1 E) analyzes a situation modeled by an exponential function, formulates an equation or inequality, and solves the problem.

Geometry Basic Understandings:

(5) Tools for geometric thinking. Techniques for working with spatial figures and their properties are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, algebraic, and coordinate), tools, and technology, including, but not limited to, powerful and accessible hand-held calculators and computers with graphing capabilities to solve meaningful problems by representing figures, transforming figures, analyzing relationships, and proving things about them.
(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling, and justification and proof.

Precalculus Knowledge and Skills: The student is expected to:

(3 A)use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;
(3 B) use regression to determine a function to model real-life data;
(3 C) use properties of functions to analyze and solve problems and make predictions
(4 A) represent patterns using arithmetic and geometric sequences and series;
(4 B) use arithmetic, geometric, and other sequences and series to solve real-life problems;
(4 C) describe limits of sequences and apply their properties to investigate convergent and divergent series;

Mathematical Models with Applications Knowledge and Skills: The student is expected to:

(1 A) compare and analyze various methods for solving a real-life problem;
(1 B) use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines; and
(1 C) select a method to solve a problem, defend the method, and justify the reasonableness of the results.
(2 A) interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, and scatterplots to draw conclusions from the data;
(2 D) use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most appropriate model, and use the model to interpret information.
(8 A) use geometric models available through technology to model growth and decay in areas such as population, biology, and ecology;