# ALGEBRA 1 RESOURCES

### Module 1: Sequences

In Module 1, students develop an understanding of Arithmetic Sequences and Geometric Sequences by looking at multiple representations (patterns/context, tables, equations, and graphs).

By the end of this module, students should be able to do the following:

• Identify a sequence as being arithmetic (adding), geometric (multiplying), or neither.
• Determine the constant difference (growth) of an arithmetic sequence.
• Determine the common ratio (growth factor) of a geometric sequence.
• Determine the initial value of a sequence (both when n=0 and n=1).
• Write an explicit equation and recursive equation for arithmetic and geometric sequences.
• Solve problems involving arithmetic and geometric sequences.

Module 1 Resources:

### Module 2: Linear and Exponential Functions

In Module 2, students will work with continuous linear and exponential functions in various representations (context, table, equation, graph). They will also compare these functions to arithmetic and geometric sequences to understand the difference between continuous and discrete.

By the end of this module, students should be able to do the following:

• Identify whether a situation/context is continuous or discrete.
• Identify whether a problem (context, table, equation, graph) is linear, exponential, or neither.
• Identify a function’s rate of change and compare it to another function’s rate of change.
• Use the linear Point-Slope Form to graph and solve problems.
• Make tables, write equations, and graph problems of linear functions.
• Make tables, write equations, and graph problems of exponential functions.

Module 2 Resources:

### Module 3: Features of Functions

In Module 3, students identify a function’s key features (continuous, discrete, increasing, decreasing, domain, range, maximum, minimum, intercepts, rate of change, step-functions, function values, and more).

By the end of this module, students should be able to do the following:

• Determine if a function is continuous or discrete.
• Identify intervals where a function is increasing or decreasing from a table or graph.
• Identify the domain and range of a function.
• Locate local maximum values and local minimum values of a function.
• Identify intercepts of a function.
• Determine the rate of change of a function.
• Determine function values, including using function notation.
• Interpret the key features as they relate to a context.
• Write intervals in interval notation and inequality notation.

Module 3 Resources:

### Module 4: Equations and Inequalities

In Module 4, students build on prior knowledge of solving linear equations and inequalities. They work with more complicated equations/inequalities (multi-step) and examine the meaning of the symbols as applied to a context.

By the end of this module, students should be able to do the following:

• Solve multi-step linear equations using equivalent (simplified) equations to isolate the unknown. (i.e. “Keep the equation balanced”).
• Solve multi-step linear inequalities using properties of inequalities.
• Solve literal equations (“formulas” or equations with letter coefficients).
• Write and solve an equation or inequality for a context/application.
• Write solutions to inequalities in both interval notation and set notation.
• Graph solutions to one-variable inequalities on a number line.

Module 4 Resources:

### Module 5: Systems of Equations and Inequalities

In Module 5, students work with systems of equations and systems of inequalities to solve application problems. After developing methods within contexts, students work on problems out of context by using strictly mathematical symbols.

By the end of this module, students should be able to do the following:

• Find the solution to a system using tables, equations, or graphs.
• Describe what the solution to a system of equations or system of inequalities represents in a context.
• Solve a system of equations using the Elimination method (or Linear Combinations).
• Solve a system of equations using the Substitution method.
• Identify the sample space (shaded region) of a system of inequalities by graphing.

Module 5 Resources:

In Module 6, students will work with a new type of function – Quadratic functions. Contextual problems familiarize students with how quadratics grow and how they compare to linear or exponential functions from HS Math 1.

By the end of this module, students should be able to do the following:

• Identify whether a table, equation, or graph is linear, exponential, or quadratic.
• Write an explicit equation for a quadratic relationship.
• Write a recursive equation for a quadratic relationship.
• Evaluate function values for a quadratic function.

Module 6 Resources:

### Module 7: Structure of Expressions

In Module 7, students will continue to work with Quadratic functions. They will explore different ways of writing quadratics (Standard Form, Vertex Form, and Factored Form) as well as identify the features of quadratics illuminated by each form.

By the end of this module, students should be able to do the following:

• Transform (move and change) the graph of the original parabola y=x^2 by shifting left, right, up, down, stretching, or flipping.
• Identify the vertex and the axis-of-symmetry for the graph of a parabola.
• Write the Vertex Form (or Graphing Form) for the graph of a quadratic.
• Quickly make an accurate graph by hand of a quadratic function written in Vertex Form (or Graphing Form).
• Take a quadratic in Standard Form and turn it into Vertex Form (or Graphing Form) by Completing the Square.
• Factor a quadratic function given in Standard Form to create the Factored Form.
• Identify the x-intercept(s), y-intercept, and vertex of a quadratic function.

Module 7 Resources:

### Module 8: More Functions and Features

In Module 8, students will begin working with piecewise functions and absolute value functions. Function features from last year’s High School Math 1 class are revisited while describing these new functions. Students will work with the piecewise functions and absolute value functions within multiple representations (graphs, equations, tables, and context). Module 4 also introduces the idea of inverse and determining if the inverse is a function.

By the end of this module, students should be able to do the following:

• Write a piecewise equation for the graph of a piecewise function.
• Evaluate piecewise functions (both from graphs and equations).
• Identify features of functions including: domain, range, intervals of increasing, intervals of decreasing, rate of change, etc.
• Graph absolute value functions.
• Write the equation for the graph of an absolute value.
• Solve absolute value equations.
• Find the inverse of a function from various representations (tables, equations, graphs, situations).
Identify if the inverse is a function or not.

Module 8 Resources:

### Module 9: Modeling Data

In Module 9, students work with data displayed in various ways – a simple list, histogram, stem-and-leaf, two-way table, scatter plot, and more. Emphasis is placed on interpreting the data display within a context and making informed decisions after analyzing the data.

By the end of this module, students should be able to do the following:

• Describe data set by describing shape, center, and spread.
• Interpret two-way frequency tables.
• Interpret relative frequency tables.
• Estimate the line of best fit and the correlation coefficient.
• Use technology to calculate the line of best fit (linear regression) and the correlation coefficient.

Module 9 Resources: