**Course: Algebra I**

This course focuses on the mastery of five critical areas: (1) developing understanding and investigating relationships between quantities and reasoning with equations; (2) developing understanding and applying linear and exponential relationships; (3) investigating trends and modeling with descriptive statistics; (4) performing arithmetic operations on polynomial expressions, solving equations, inequalities, and systems of equations; and (5) using properties of rational and irrational numbers to develop an understanding of quadratic functions.

**Unit 1: Representing Functional Relationships**

By the end of the previous course, 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. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. All of this work is grounded on understanding quantities and on relationships between them.

**Unit 2: Linear and Exponential Relationships**

In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They move beyond viewing functions as processes that take inputs and yield outputs and start viewing functions as objects in their own right. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that, depending upon the context, these representations are likely to be approximate and incomplete. Their work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. Students explore systems of equations and inequalities, and they find and interpret their solutions. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.

**Unit 3:**Quadratic Functions and ModelingIn preparation for work with quadratic relationships students explore distinctions between rational and irrational numbers. They consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students learn that when quadratic equations do not have real solutions the number system must be extended so that solutions exist, analogous to the way in which extending the whole numbers to the negative numbers allows

*x*+1 = 0 to have a solution. Formal work with complex numbers comes in Algebra II. Students expand their experience with functions to include more specialized functions—absolute value, step, and those that are piecewise-defined.

Unit 4:

Unit 4:

**Descriptive Statistics**

Students will choose and create an appropriate data representation for a given set of data. They will be able to read and interpret the representations they create as well as others that are given to them. These data representations will include bar graphs, histograms, box-and-whisker plots, stem and leaf plots (including back-to-back stem plots) as well as frequency tables. For categorical data, students will be able to use two-way frequency tables to find joint, marginal and conditional relative frequencies.

Students will calculate and use summary statistics such as mean, median, range, lower and upper quartile, interquartile range and standard deviation to help describe the shape of the data. The processes by which mean and median are calculated have been previously taught. Students have not been introduced to standard deviation, and must understand the process behind the calculation. However, technology should be used to calculate the standard deviation. Students will build on their understanding of these calculations to comment on possible outliers in a data set and to make well-informed decisions about the best summary statistics to represent given data. When data is notably skewed or when meaningful outliers are present, the median and 5-Number Summary should be used to describe the distribution. Alternately, the mean and standard deviation should be used to describe unimodal and symmetric data. Throughout this unit, students should use these summary statistics and/or graphical representations to write critical analyses of a situation within the context of the given data.

**Unit 5:**

**Modeling with Other Functions**

As an extension of their work with various function families, students will begin to investigate the graphs of simple nonlinear functions. Students will explore the graphical representations of other models, to include square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Students will be able to graph these functions by hand in simple cases and by using technology in more complex cases. In all cases, students should identify key features of their graphs. Students should identify parent functions and describe or sketch the effects of simple transformations on those parent functions.