Algebra 1 Honors

Description

Algebra I is the first mathematics course in high school and the focal point is functions; specifically linear, quadratic, and exponential functions. By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. In Algebra I, students:

• analyze and explain precisely the process of solving an equation

• develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities and make conjectures about the form that a linear equation might take in a solution to a problem

• reason abstractly and quantitatively by choosing and interpreting units in the context of creating equations in two variables to represent relationships between quantities

• master the solution of linear equations and apply related solution techniques and the properties of exponents to the creation and solution of simple exponential equations

• learn the terminology specific to polynomials and understand that polynomials form a system analogous to that of integers. Students learn function notation and develop the concepts of domain and range

• explore many examples of functions, including sequences; they interpret functions represented graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations

• build on their understanding of integer exponents to consider exponential functions with integer domains. They compare and contrast linear and exponential functions, looking for structure in each and distinguishing between additive and multiplicative change

• explore systems of linear and quadratic equations and linear inequalities, and they find and interpret their solutions

• interpret arithmetic sequences as linear functions and geometric sequences as exponential functions focusing in on the explicit forms of sequences written in subscript notation

• analyze the key features of a graph or table of a function

• strengthen their ability to discern structure in polynomial expressions

• create and solve equations involving quadratic and cubic expressions

• reason abstractly and quantitatively in interpreting parts of an expression that represent a quantity in terms of its context

• learn to make sense of problems and persevere in solving them by choosing or producing equivalent forms of an expression

• consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions

• learn through repeated reasoning to anticipate the graph of a quadratic function by interpreting the structure of various forms of quadratic expressions

• identify the real solutions of a quadratic equation as the zeros of a related quadratic function, which may require students to write solutions in simplest radical form

• expand their experience with functions to include more specialized functions—linear, exponential, quadratic, square, and those that are piecewise-defined, including absolute value and step

• select from among these functions to model phenomena using the modeling cycle

• build upon prior experiences with data, and are introduced to working with more formal means of assessing how a model fits data

• display and interpret graphical representations of data, and if appropriate, choose regression techniques when building a model that approximates a linear relationship between quantities

• analyze their knowledge of the context of a situation to justify their choice of a linear model, compute and interpret the correlation coefficient, and distinguish between situations of correlation and causation