# 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:

- MVP Algebra 1 Curriculum: MVP Website
- Helpful Videos: Khan Academy – Sequences
- Helpful Explanations: Purple Math – Sequences

### 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:

- MVP Algebra 1 Curriculum: MVP Website
- Helpful Videos: Khan Academy – Linear Functions
- Helpful Videos: Khan Academy – Exponential Functions
- Helpful Explanations: Purple Math – Exponential Functions

### 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:

- MVP Algebra 1 Curriculum: MVP Website
- Helpful Videos: Khan Academy – Functions and Features
- Helpful Practice: Math Bits Notebook – Features of Functions

### 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:

- MVP Algebra 1 Curriculum: MVP Website
- Helpful Videos (REVIEW): Khan Academy – Linear Equations (REVIEW)
- Helpful Videos: Khan Academy – Linear Equations and Inequalities
- Helpful Explanations: Purple Math – Solving Multi Step Linear Equations

### 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:

- MVP Algebra 1 Curriculum: MVP Website
- Helpful videos: Khan Academy – Linear Equations and Graphs
- Helpful videos: Khan Academy – Solving Systems of Equations
- Helpful videos: Khan Academy – Systems of Inequalities
- Helpful explanations: Math Planet – System of Inequalities
- Helpful explanations: Math Planet – Graphing Linear Systems
- Helpful explanations: Math Planet – Substitution Method
- Helpful explanations: Math Planet – Elimination Method (or Linear Combinations)

### Module 6: Quadratic Functions

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:

- MVP Algebra 1 Curriculum: MVP Website
- Helpful videos: Khan Academy – Quadratics
- Helpful explanations: Determine if Table is Linear, Quadratic, or Exponential
- Helpful explanations: Writing Explicit Equation for Quadratic from a Table

### 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:

- MVP Algebra 1 Curriculum: MVP Website
- Helpful videos: Khan Academy – Quadratics
- Helpful explanations: Math Warehouse – Standard and Vertex Form
- Interactive Demo: Manipulating a Quadratic in Vertex Form
- Virtual Algebra Tiles and Manipulative: CPM Technology Tools – Algebra Tiles

### 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:

- MVP Algebra 1 Curriculum: MVP Website
- Helpful videos: Khan Academy – Absolute Value and Piecewise Functions
- Helpful videos: Khan Academy – Intro to Inverse Functions

### 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:

- MVP Algebra 1 Curriculum: MVP Website
- Helpful videos: Khan Academy – Data Distributions
- Helpful videos: Khan Academy – Two-way Tables
- Helpful videos: Khan Academy – Scatterplots (Line of Best Fit)