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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
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)
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
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
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
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
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
Geometry
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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
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
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
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 4: Recognize Algebraic Representation of Quadratics and Transformations
Exponents
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