The Pythagorean Theorem

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This seminar will teach you about the Pythagorean Theorem. It will also teach you how to use the converse of the theorem and how to identify Pythagorean triples. You will have to apply the techniques you have learned to simplify radicals, and you will learn how to apply exponential properties. You will be shown visual demonstrations of the Pythagorean Theorem and be asked to connect them to the algebraic models of the Theorem.StandardsCC.2.3.8.A.3.Understand and apply the Pythagorean Theorem to solve problems.

Material Type: Lesson Plan

Authors: Bonnie Waltz, Deanna Mayers, Tracy Rains

Simplifying Square Roots

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In this seminar you will learn how to simplify square roots whose radicands contain factors that are perfect squares. You will learn how to perform these operations on both integers and variables. You will be able to do this by learning how to identify factors that are perfect squares. These will be necessary skills as you continue to perform operations that contain radical expressions. StandardsCC.2.2.8.B.1Apply concepts of radicals and integer exponents to generate equivalent expressions.

Material Type: Lesson Plan

Authors: Bonnie Waltz, Deanna Mayers, Tracy Rains

Operations With Radical Expressions

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This seminar will teach you how to perform the four basic mathematical operations on expressions containing radicals. It will also show you how to rationalize the denominator of a fraction that contains radicals. You will apply your knowledge of factorization and perfect squares of both integers and variables in order to simplify the radicals. You will extend your knowledge of simplifying expressions to include those that contain radicals. You will rationalize denominators in order to place expressions in simplest radical form.StandardsCC.2.2.8.B.1Apply concepts of radicals and integer exponents to generate equivalent expressions.

Material Type: Lesson Plan

Authors: Bonnie Waltz, Deanna Mayers, Tracy Rains

Solving Systems of Equations Using Elimination

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This seminar will explore how to solve systems of equations using elimination. You will discover the most efficient methods of preparing a system to be solved using elimination and how to identify the best variable to eliminate.StandardsCC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

Material Type: Lesson Plan

Authors: Bonnie Waltz, Deanna Mayers, Tracy Rains

Substitution

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This seminar will explore how to solve a system of linear equations using substitution. It will also describe what it means for a system of equations to have no solution or infinitely many solutions. Applications of systems of equations will also be explored.StandardsCC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

Material Type: Lesson Plan

Authors: Bonnie Waltz, Deanna Mayers, Tracy Rains

Graphing Systems of Linear Equations

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This seminar will allow you to solve a system of linear equations by graphing. It will help you to understand what it means when the lines in a system of equations are parallel, and also what it means for the graphs to be the same line. You will learn how to visually identify information about the system of equations simply by examining the graphs of the lines that make up the system.StandardsCC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

Material Type: Lesson Plan

Authors: Bonnie Waltz, Deanna Mayers, Tracy Rains

Problem Based Module: GMOs and Farming

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In this project, you will explore a real-world problem, and then work through a series of steps to analyze that problem, research ways the problem could be solved, then propose a possible solution to that problem. Often, there are no specific right or wrong solutions, but sometimes one particular solution may be better than others. The key is making sure you fully understand the problem, have researched some possible solutions, and have proposed the solution that you can support with information / evidence.Begin by reading the problem statement in Step 1. Take the time to review all the information provided in the statement, including exploring the websites, videos and / or articles that are linked. Then work on steps 2 through 8 to complete this problem-based learning experience.

Material Type: Lesson Plan

Author: Tracy Rains

Graphing Linear Equations

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In this seminar, you will learn how to graph linear equations that have been written in any form. You will learn the characteristics of intercepts, and also of horizontal and vertical lines. You will discover the various types of information that can be discovered by looking at the graph of a linear equation.StandardsCC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically

Material Type: Lesson Plan

Author: Tracy Rains

Number Properties

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In this seminar you will look at the commutative, associative, and distributive properties to better understand how they are used in mathematics. You may see some similarities among these properties, but you will find large differences as well. These differences are important to recognize when completing problems, or else you will find yourself getting wrong answers. You will also explore identity and inverses, which are used so often in math (often without your even knowing it!). A majority of the time will be spent on the distributive property as it tends to be the property used most moving forward in math. Understanding these basic number properties is important in working with numbers and equations later in the course.StandardsCC.2.2.HS.D.2Write expressions in equivalent forms to solve problems.

Material Type: Lesson Plan

Author: Tracy Rains

Order of Operations

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In this seminar you will review the order of operations to ensure that you understand the importance of the order in which to complete addition, subtraction, multiplication, and division, as well as handling exponents and grouping symbols. You will apply techniques you have learned about each of these operations. You will then use the techniques learned in this seminar to verify solutions to various other types of problems and use these ideas in nearly all mathematical problems and formulas moving forward. When using order of operations, you will identify which operation must be completed first, which second, and so on, depending on the problem given. You will also see how not using the Order of Operations can severely change an answer.StandardsCC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.

Material Type: Lesson Plan

Author: Tracy Rains

Variables, Expressions, & Combining Like Terms

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In this seminar, you will learn about variables and how they are used in mathematical expressions. You will also learn what it means to be a like term and how to combine like terms. You will pull variables, expressions, and like terms together so that you can apply them moving forward.StandardsCC.2.2.HS.D.1Interpret the structure of expressions to represent a quantity in terms of its context.CC.2.2.HS.D.2Write expressions in equivalent forms to solve problems.

Material Type: Lesson Plan

Author: Tracy Rains

Problem Based Module: The Evolving World of Retail

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Material Type: Lesson Plan

Author: Tracy Rains

Absolute Value

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In this seminar you will learn about the absolute value of numbers. You will learn how taking the absolute value affects both positive and negative numbers. You will use the techniques learned in this seminar to verify solutions to various other types of problems involving absolute value as you move forward. When looking at absolute value, you will identify how it can change a solution and the compare the difference that it makes in equations when there are multiple negative signs.StandardsCC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problemsLearning TargetI can find the absolute value of a given number or numbers.Habits of MindPersistingCritical Thinking SkillAnalyze/evaluateAcademic/Concept VocabularyAbsolute valueNegativeNumber linePositive

Material Type: Lesson Plan

Author: Tracy Rains

Rational & Irrational Number

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In this seminar you will explore different types of numbers in math. You will learn to classify numbers into the categories of natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. You will see how some numbers can be classified in a few of these categories. Some important things to consider will be whether or not a decimal number terminates or repeats.StandardsCC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problems.

Material Type: Lesson Plan

Author: Tracy Rains

Square Roots

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In this seminar you will explore square roots and see how they are used throughout mathematics. You will see how “squaring” a number and “taking the square root” relate to each other. Also presented will be how to estimate square roots when given a number. You will have plenty of opportunity to try practice problems, review, and even create a short presentation. You will apply techniques you have learned involving estimating. You will use the techniques learned in this seminar to solve problems involving square roots moving forward and ultimately be able to verify solutions. When working with square roots, you will identify the patterns in perfect square numbers, as well as in techniques such as squaring and cubing numbers. By the end, you should have a better understanding of what a square root is and how to handle expressions that involve square roots.StandardsCC.2.1.HS.F.1Apply and extend the properties of exponents to solve problems with rational exponents.CC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite in equivalent forms.

Material Type: Lesson Plan

Author: Tracy Rains

Problem Based Module: Automobile Travel

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Material Type: Lesson Plan

Author: Tracy Rains

Multi-Step Equations

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In this seminar you will learn how to complete multiple step equations. You will apply techniques you have learned about inverse operations to solve for a missing variable. You will use the techniques learned in this seminar to verify solutions to various other types of problems as you move forward. When solving multiple step equations, you will identify which operation to address first, which second, and so on, until you have the variable all alone and a solution for it. The best part? You can always substitute your answer into the original problem to make sure your answer is correct.StandardsCC.2.2.HS.D.8Apply inverse operations to solve equations or formulas for a given variable.

Material Type: Lesson Plan

Author: Tracy Rains

One Step Equations

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In this seminar you will learn how to solve single step equations. You will apply techniques you have learned regarding addition, subtraction, multiplication and division. You will use the techniques learned in this seminar to verify solutions to various other types of problems as you move forward and solve for missing variables. When solving single step equations, you will use inverse operations to find missing variables and then use substitution to check each problem to verify that your answer is correct.StandardsCC.2.2.HS.D.8Apply inverse operations to solve equations or formulas for a given variable.

Material Type: Lesson Plan

Author: Tracy Rains

Variables on Both Sides of an Equation

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In this seminar you will learn how to solve problems where variables are on each side of the equation. You will apply techniques you have learned to this point involving inverse operations. You will use the techniques learned in this seminar to verify solutions to various other types of problems as you move forward, primarily when solving for any unknown variable. When solving equations with a variable on each side, you will first want to isolate the variable to one side and then use inverse operations to solve for it. StandardsCC.2.2.HS.D.8Apply inverse operations to solve equations or formulas for a given variable.

Material Type: Lesson Plan

Author: Tracy Rains