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Linear Equations and Inequalities

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LINR Module 1 - Linear Relationships

Module 1 develops a conceptual understanding of linear situations, graphs, tables, and equations.  In this module, students will calculate slope, write linear equations, and graph linear equations in the form: y = mx + b both in context and abstract representations.

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Lesson 1: Linear Patterns in Multiple Representations

Lesson 2: Graphs and Equations of Linear Situations

Lesson 3: Graphs in Slope-Intercept Form

Lesson 4: Writing Equations of Lines

LINR Module 2 - Solving Equations and Inequalities

Module 2 develops the understanding of solutions to linear equations and inequalities, including literal and absolute values. In this module, students will solve systems of equations and inequalities. They will be comfortable with both the symbolic and graphic solutions and able to translate between them. Several lessons have links to Desmos. If an activity, you can sign in as a guest.

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Lesson 1: Solving Equations including Absolute Value

Lesson 2: Solving Equations and Inequalities (Including Absolute Value)

Lesson 3: Linear Inequalities in Two Variables

LINR Module 3: Solving Systems

Module 3 develops the understanding of systems of equations and inequalities. Lesson 3 includes the development of absolute value functions as well as the system including an absolute value function and a linear function. Lesson 4 makes connections of systems to polygons in a plane as the region bound by the lines that include their side

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Lesson 1: Analyzing, Writing, and Solving Linear Systems

Lesson 2: Writing, Solving, Interpreting Linear Systems of Inequalities

Lesson 3: Understanding and Using Absolute Value

Lesson 4: Solving Linear Systems with Geometric Applications


Rational Numbers and Equations

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RATL Module 1 : Fractions and Percents

In this module, students will review addition and subtraction of fractions both symbolically and with graphs/tables. They also compute percentages, products, and quotients of fractions symbolically and with graphs/tables.

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Lesson 1: Operations on Fractions

Lesson 2: Using Percentages

Lesson 3: Multiplicative Thinking

Lesson 4: Proportional Reasoning

RATL Module 2 : Rational Expressions and Equations

In this module students make the connection between calculations on fractions and simplifying rational expressions. They use the arithmetic model as a means of simplifying, as well as adding, subtracting, multiplying and dividing rational expressions. In lesson 4, they solve rational equations as well as solve rate problems. There are several lessons where linked to LearnZillion.

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Lesson 1: Introduction to Rational Expressions

Lesson 2: Adding and Subtracting Rational Expressions

Lesson 3: Multiplying and Dividing Rational Numbers

Lesson 4: Solving Rational Equations and Writing Rational Equations from Context

RATL Module 3: Solve Rational Inequalities and Graph Rational Functions

In this module, students evaluate rational expressions and solve rational inequalities. They graph rational functions, by first finding asymptotes and the zeros of the function.

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Lesson 1: Evaluating Rational Expressions

Lesson 2: Solving Rational Inequalities

Lesson 3: Zeros and Asymptotes of Rational Functions

LLesson 4: Graphing Rational Functions


Polynomials & Quadratic Equations & Functions

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POLQ Module 1: Combining Polynomials

The module begins with multiplying and dividing polynomials. While multiplying, the distributive property patterns are recognized. These recognized patterns are then used in factoring.

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Lesson 1: Multiplication of Polynomials

Lesson 2: Division of Polynomials

Lesson 3: Factoring Polynomials

Lesson 4: Summative Polynomial Performance Task

POLQ Module 2: Factoring and Solving Quadratics

Special factoring patterns are noted in the beginning of the module, especially the trinomial square. The second lesson introduces completing the square as a means of finding solutions to an equation. This leads to the development of the Quadratic Formula as a means of finding solutions to any quadratic equation.

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Lesson 1: Special Factoring Patterns

Lesson 2: Completing the Square to Solve Quadratic Equations

Lesson 3: Solving Radical Equations

Lesson 4: Deriving the Quadratic Formula

POLQ Module 3: Analysis of Polynomials

In this module, graphic representation of polynomial equations are analyzed and features are noted. Roots of the polynomial are found in a number of methods as well as finding multiplicity and end behavior. In the last lesson connections to other graphs and applications are made.

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Lesson 1: Introduction to Graphing Polynomials

Lesson 2: Roots of Polynomials and Polynomial Theorems

Lesson 3: Polynomials Features: Multiplicity, Degree, End Behavior

Lesson 4: Applications of Polynomials



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GEOM Module 1: 2D & 3D Figures

In this module, area and perimeter formulas are developed. Once the formulas are established and connections made, they are applied. In the last two lessons volume and surface area formulas are developed and used.

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Lesson 1: Developing Formulas for Area of Multiple Shapes

Lesson 2: Extending and Applying Area and Perimeter

Lesson 3: Developing Formulas for Volume of multiple shapes

Lesson 4: Application of Area vs. Volume

GEOM Module 2: Triangles

The module begins with classification of triangles with respect to angle measure and or side lengths. A discussion of special right triangles is used to develop the trigonometric ratios. By examining these ratios connections among sine, cosine and tangent are made. Problems are then solved by using the trigonometric ratios. The module ends with developing and applying the properties and characteristics of triangles.

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Lesson 1: Classifying Triangles

Lesson 2: Introduction to Trigonometry

Lesson 3: Extending Trigonometry

Lesson 4: Properties and Characteristics of Triangles

GEOM Module 3: Similarity & Congruence

The transformations of a rigid shape are used to discussion congruence. This leads into methods of proving congruence, especially in triangles. Congruence of triangles is used to find congruence in quadrilaterals. Later in the module, dilations are used to introduce similarity. The module ends with similarity proofs and applications.

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Lesson 1: Discovering Congruence

Lesson 2: Applying Congruence

Lesson 3: Developing Similarity

Lesson 4: Applying Similarity


Functions and Their Graphs

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FNGR Module 1: Exponential Functions

The attributes of exponential functions are examined in this module. Students find that in contrast, exponential functions grow multiplicatively whereas linear functions grow additively. The growth patterns in exponential functions are identified and connections made. These connect the graph to the equation, including transformations of the parent function.

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Lesson 1: Identifying Exponential Functions

Lesson 2: Identifying Exponential Growth and Decay

Lesson 3: Transformations of Parent Functions, focus on Exponential

Lesson 4: Transformations, Vertical and Horizontal, of Parent functions

FNGR Module 2: Functional Relationships

The module begins with a distinction of what is and what is not a function. The emphasis in this module is on quadratic functions. Connections are made between the equation and the graph. This includes transformations, i.e., identifying horizontal and vertical shifts. In the third lesson, students build functions from other functions.

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Lesson 1: Identify Functional Relationships

Lesson 2: Identify Horizontal and Vertical Shifts of Quadratics

Lesson 3: Build Functions

Lesson 4: Recognize Algebraic Representation of Quadratics and Transformations

Lesson 5 : Inverse Functions



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EXPS Module 1 : Exponents and Roots

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Lesson 1 : Integer Exponents

Lesson 2 : Rules of Exponents

Lesson 3 : Scientific Notation