Welcome to Algebra 1

**Below is a brief synopsis of what will be covered during the 5th Six Weeks. For detailed student expectations see below. **

**Unit 1 – The Study of Functions (17 days)**

This unit bundles student expectations that address the exploration of linear and non-linear data, their representations, and their relationships. Functional relationships are the basis of algebra and will be the focus of Algebra 1 throughout the course. The exploration of functions through data collection and analysis is a foundation for this study, and is introduced at the beginning of Algebra 1.

Prior to this unit, in Grade 8, students were introduced to arithmetic sequences, mathematical relationships, and multiple forms of representations. During this unit, those topics are extended to include the development of the concept of function and an exploration of the representations and characteristics of functions. Graphing calculator technology is incorporated to collect and analyze data throughout the unit. After this unit, linear and quadratic functions will be explored in more depth.

**Unit 2 - Algebraic Expression and Equations (8 days)**

This unit bundles student expectations that focus on simplifying expressions using properties of algebra, solving equations, and representing solution methods. Students extend the methods used to solve equations in middle school to include functional analysis of graphs and tables using technology.

Prior to this unit, in Grades 7 and 8, students solved equations using concrete models and algebraic manipulation. During this unit, students review these methods and also solve equations by analyzing tables and graphs of functions. The properties of algebra are used to simplify algebraic expressions. Students explain and differentiate between expressions and equations. After this unit, students will apply multiple methods for solving equations and inequalities.Students will also apply properties of algebra to simplify and perform operations with polynomials. These skills are necessary not only in Algebra 1, but in subsequent courses in mathematics.

Rose Math Champions Class Blog*(Ask teacher for class code)*

**Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to:**

A.1A Describe independent and dependent quantities in functional relationships.

A.1B Gather and record data and use data sets to determine functional relationships between quantities.

A.1D Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal

descriptions, and equations.

A.1E Interpret and make decisions, predictions, and critical judgments from functional relationships.

**Foundations for functions. The student uses the properties and attributes of functions. The student is expected to:**

A.2B Identify mathematical domains and ranges and determine reasonable domain and range values for given

situations, both continuous and discrete.

A.2D Collect and organize data, make and interpret scatterplots and model, predict, and make decisions and

critical judgments in problem situations.

**Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to:**

A.3A Use symbols to represent unknowns and variables.

A.3B Look for patterns and represent generalizations algebraically.

**Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems in problem situations. The student is expected to:**

A.4A Find specific function values as necessary in problem situations.

A.4B Use the commutative, associative, and distributive properties to simplify algebraic expressions.

A.4C Connect equation notation with function notation, such as *y *= *x *+ 1 and *f(x) *= *x *+ 1.

**Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:**

A.7A Analyze situations involving linear functions and formulate linear equations to solve problems. * *

A.7B Investigate methods for solving linear equations and inequalities using concrete models, graphs, and the

properties of equality, select a method, and solve the equations.

A.7C Interpret and determine the reasonableness of solutions to linear equations .

A.11B Analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or

algebraic methods.

A.11C Analyze data and represent situations involving exponential growth and decay using concrete models,

tables, graphs, or algebraic methods.

Animations - Multiple Representations

Glencoe Animations - Is this a Function?

Glencoe Animations - Graphing Linear Equations

Glencoe Interactive Lab - Graphing Relations and Functions

Glencoe Animations - Families of Linear Equations

Glencoe Animations - Families of Quadratic Equations

Glencoe Personal Tutor - Representing Relations

Glencoe Personal Tutor - Representing Functions

Glencoe Personal Tutor - Linear Functions

Glencoe Personal Tutor - Two Step Equations

Cosmeo Personal Tutor - Domain and Range

Personal Tutor: Solving Multi-Step Equations

Personal Tutor: Solving Equations with Variable on Each Side

Personal Tutor: Solving for a Specific Variable

BrainPop: Two-Step Equations

PH Personal Tutor: Writing and Solving Two-Step Equations

PH Personal Tutor: Consecutive Integer Problems

PH Personal Tutor: Solving Equations with Variable on Each Side

PHSchools Personal Tutor: Consecutive Numbers

Animations: Solving Inequalities

Interactive Lab: Solving Inequalities

PHSchools Personal Tutor: Graphing Inequalities

PHSchools Personal Tutor: Writing Inequalities from a Graph

BrainPop: Solving Inequalities

Glencoe Personal Tutor: Solving Inequalities by Addition and Subtraction

Glencoe Personal Tutor: Solving Inequalities by Multiplication and Division

Glencoe Personal Tutor: Solving Multi-Step Inequalities

Animation: Adding and Subtracting Polynomials

BrainPop: Polynomials

Glencoe Personal Tutor: Adding and Subtracting Polynomials

PHSchool Personal Tutor: __Finding the GCF of a Polynomial__

PHSchool Personal Tutor: __Using the GCF of a Polynomial__

PHSchool Personal Tutor: __Factoring the Differences of Squares__

PHSchool Personal Tutor: Factoring Trinomials when b is positive

PHSchool Personal Tutor: Factoring Trinomials when b is negative

PHSchool Personal Tutor: Factoring Trinomials when c is negative

PHSchool Personal Tutor: Factoring Trinomials when leading coefficient is not equal to 1 (c is positive)

PHSchool Personal Tutor: Factoring Trinomials when leading coefficient is not equal to 1 (c is negative)

PHSchool Personal Tutor: Factoring Trinomials with Grouping

PHSchool Personal Tutor: Factoring Trinomials in Real World Situations (volume)

PHSchool Personal Tutor: Solving Quadratic Equations by Graphing

PHSchool Personal Tutor: Graphing Quadratic Equations (using a table)

PHSchool Personal Tutor: Using the Quadratic Formula

Glencoe Personal Tutor: Solving Quadratic Equations

Glencoe Personal Tutor: Graphing Quadratic Equations