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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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

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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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.This project focuses on the following:Habits of Mind: Thinking about thinking (metacognition)Critical Thinking Skills: Analyze/evaluate

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

Problem Based Module: How Much to Tip?

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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

Adding & Subtracting Polynomials

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It is important to understand polynomials and to be able to classify them based on the number of terms, as well as recognize the coefficients, and degrees. You must also understand how to perform mathematical operations on them. This seminar will focus on combining polynomials using addition and subtraction. It will be important to understand the rules to make sure you are combining only like terms. You will apply techniques you have learned involving exponents and general addition and subtraction rules. You will use the techniques learned in this seminar to verify solutions to various other types of polynomial problems as you move forward. When adding and subtracting polynomials, you will first identify the like terms to combine polynomials to their simplest form.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomials.

Material Type: Lesson Plan

Author: Tracy Rains

Classifying Polynomials

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Mathematics involves many different types of numbers. It is important that you can classify and name numbers and expressions. In this seminar you will go beyond the basics and learn about various types of expressions called polynomials. You will explore terminology affiliated with polynomials and classify them based on their degree.  You will also use past knowledge on how to simplify and combine like terms. You will use the techniques learned in this seminar to then perform operations on various types of polynomials such as adding, subtracting, and multiplying moving forward.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomials.CC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite in equivalent forms.  

Material Type: Lesson Plan

Author: Tracy Rains

Multiplying Polynomials

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In the world of mathematics you can always count on encountering problems involving multiplication. With polynomials, things are no different. It is imperative to look at various types of multiplication problems since there are many different polynomials such as: monomials, binomials, trinomials, and more. This seminar covers the various forms of multiplication with these different types of polynomials.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomials.

Material Type: Lesson Plan

Author: Tracy Rains

Problem Based Module: Start Saving for Retirement Now?

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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

Factoring Monomials

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In this seminar you will learn how to factor monomials using prime factorization. You will apply prior knowledge about factoring integers. You will use the techniques learned in this seminar to factor polynomials with multiple terms as you move forward. When factoring monomials using this method, you will identify what product of prime numbers and variables will create the expression. This seminar will also begin finding the greatest common factor among multiple monomials, which is a skill that will be used moving forward on polynomials with multiple terms.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomialsCC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite in equivalent forms.

Material Type: Lesson Plan

Author: Tracy Rains

Factoring Polynomials: Common Factor

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In this seminar you will learn how to factor polynomials by looking for a common factor. You will apply the concepts of factoring integers, as well as factoring monomials and looking for the greatest common factor among terms. The techniques learned in this seminar will allow you to factor polynomials with multiple terms, and find solutions using factoring.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomialsCC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite in equivalent forms

Material Type: Lesson Plan

Author: Tracy Rains

Factoring Quadratics

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In this seminar you will learn how to factor quadratic equations. You will apply the concepts of factoring integers, factoring monomials, and looking for the greatest common factor among terms. The techniques learned in this seminar will allow you to use factoring to find solutions to quadratics and help with graphing.StandardsCC.2.2.HS.D.3Extend the knowledge of arithmetic operations and apply to polynomialsCC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite in equivalent forms.CC.2.2.HS.C.5Construct and compare linear, quadratic, and exponential models to solve problems

Material Type: Lesson Plan

Author: Tracy Rains

Problem Based Module: Conventional vs. Green Construction

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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

Dividing Polynomials

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In this seminar you will further your work with polynomials, by learning how to divide them.  You will identify which strategy is best for each type of polynomial and you will be able to identify the number of real solutions each polynomial will have. You will also be able to use this process in real world situations.StandardsCCSI: HS: Algebra: HSA-SSE.A. Interpret the structure of expressions.CCSI: HS: Algebra: HSA-SSE.B. Write expressions in equivalent forms to solve problems. 

Material Type: Lesson Plan

Author: Tracy Rains

Rational Equations and Functions

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In this seminar you will learn how to identify, simplify and solve rational equations and functions.  You will understand how to use rational equations to solve real-world problems.StandardsCCSI: HS: Algebra: HSA-SSE.A. Interpret the structure of expressions.CCSI: HS: Algebra: HSA-SSE.B. Write expressions in equivalent forms to solve problems.

Material Type: Lesson Plan

Author: Tracy Rains