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

Rational Equations with Polynomials

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In this seminar you will learn continue your study of rational equations.  These equations will contain polynomials and be a little more difficult than the previous seminar.  You will also further your understanding of how rational equations are used 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

Problem Based Module: Baby Booming the Economy

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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

Multiplying and Dividing Rational Expressions

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In this seminar you will learn what rational expressions are and how to work with them.  You will also be able to recognize real-world situations that involve rational expressions and how to apply the use of rational expressions to a variety of day-to-day situations.  You will come to understand strategies for taking complex situations and simplifying them in order to find solutions for them.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

Adding and Subtracting Rational Expressions

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In this seminar you will continue your learning of rational expressions adding and subtracting them as stand alone problems, as well as in real-world situations  You will continue to use strategies for simplifying complex situations into more solvable 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

Simplifying Radical Expressions

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In this seminar you will learn what radical expressions are and how to simplify them.  You will also be able to recognize real-world situations that involve radical expressions and how to apply the use of radical expressions to a variety of day-to-day situations you may face as you get older.  You will come to understand strategies for taking complex situations and making them more simple in order to find solutions for them.StandardsCCSI: HS: Algebra: HSA-SSE.B. Write expressions in equivalent forms to solve problems.CCSI:  HS: Algebra: HSA-APR.D. Rewrite rational expressions

Material Type: Lesson Plan

Author: Tracy Rains

Problem Based Module: Weather Worries? Are natural disasters on the rise?

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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

Percents

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In this lesson you will learn how to convert between decimal, percent and fraction; calculate percent of change; and apply percents to real-world situations.  You will be able to discuss the importance of writing numbers in different formats; how to determine a percent increase or decrease; and how percents are an integral part of daily living.StandardsCC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problems.MP.1. Make sense of problems and persevere in solving them.MP.4. Model with mathematics.MP.5. Use appropriate tools strategically.

Material Type: Lesson Plan

Author: Tracy Rains

Ratio and Proportion

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In this seminar you will have a better understanding of how to identify and write ratios and proportions,understand their relationship to each other, and use them in real-world contexts.StandardsMathematical PracticeCC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problems.MP.1. Make sense of problems and persevere in solving them.MP.4. Model with mathematics.MP.5. Use appropriate tools strategically.

Material Type: Lesson Plan

Author: Tracy Rains

Variation

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In this seminar you will learn about variation.  There are two types - direct and inverse- and you will be able to identify and calculate each type.  You will also learn how to solve real-world problems involving each type of variation, to better understand the importance of variation.StandardsCC.2.2.HS.D.8Apply inverse operations to solve equations or formulas for a given variable.CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities.MP.1. Make sense of problems and persevere in solving them.MP.2. Reason abstractly and quantitatively.MP.3. Construct viable arguments and critique the reasoning of others.MP.4. Model with mathematics.MP.5. Use appropriate tools strategically.MP.6. Attend to precision.MP.7. Look for and make use of structure.MP.8. Look for and express regularity in repeated reasoning.

Material Type: Lesson Plan

Author: Tracy Rains

Problem Based Module: Inventory Investments- How much inventory is enough?

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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