OER Commons - Keywords: Factoring
https://www.oercommons.org
daily12000-01-01T12:00+00:00Lesson 13: Completing the Square
https://www.oercommons.org/courses/lesson-13-completing-the-square
This lesson introduces completing the square as a means of expanding the set of quadratic equations that may be solved beyond the extraction of roots and factoring. Simpler cases are first presented and then towards the end of the lesson a procedure for completing the square of ax^2 + bx + c = 0 is given.MathematicsComputing and InformationEducation2014-11-02T13:20:21.248039Course Related MaterialsLesson 35: Polynomial Functions
https://www.oercommons.org/courses/lesson-35-polynomial-functions
Beginning with the definition of a polynomial, polynomial multiplication and degree of polynomial products are introduced. Special products and factoring cubics are presented before modeling with polynomials is discussed.MathematicsComputing and InformationEducation2014-11-02T13:20:19.551258Course Related MaterialsLesson Plan: Rational Expressions
https://www.oercommons.org/courses/lesson-plan-rational-expressions
With our initial teaching plan, the findings showed that even though students were successful at the beginning problems in the homework, they were intimidated by the "difficult look" of the later homework problems and simply did not attempt them. This was evident in the analysis of the homework where the amount of incomplete problems drastically increased at a certain problem when the difficulty level was higher. In the revised lesson, more difficult examples were used, and it was stressed that the steps remain the same even though it looked much harder than previous examples. Several days later when the students had to use the lesson to solve equations involving rational expressions their confidence level was greater and the majority of students got the correct answers.Mathematics2014-11-02T13:20:17.680122Course Related MaterialsLesson 37: Operations on Algebraic Fractions
https://www.oercommons.org/courses/lesson-37-operations-on-algebraic-fractions
The four arithmetic operations on fractions are given here, but in each case examples of using the operation on ordinary fractions is first reviewed, helping to ground the new material in the understanding of the familiar older content. Finding the least common denominator and rewriting the new equivalent fraction is also presented. The lesson concludes with a motion application problem.MathematicsComputing and InformationEducation2014-11-02T13:20:16.535458Course Related MaterialsLesson 41: Conic Sections: Ellipses
https://www.oercommons.org/courses/lesson-41-conic-sections-ellipses
Beginning with a general introduction to conics and how they are formed, circles are first presented and then ellipses are motivated by looking at the general equation of a circle centered at the origin. After central ellipses, translated ellipses are discussed, followed by a procedure for writing the equation of the ellipse in standard form. The lesson concludes with a procedure for finding the equation of an ellipse given its vertices.MathematicsEducation2014-11-02T13:20:16.103242Course Related MaterialsLesson 42: Conic Sections: Hyperbolas
https://www.oercommons.org/courses/lesson-42-conic-sections-hyperbolas
This lesson begins with centralized hyperbolas and then moves into translated hyperbolas. A review of conic sections is presented before exercises in determining the type of conic section from its equation are given.MathematicsComputing and InformationEducation2014-11-02T13:20:11.812603Course Related MaterialsAlcohol in Your Body (Rational functions)
https://www.oercommons.org/courses/alcohol-in-your-body-rational-functions
The functions that model the process of the elimination of alcohol from the body serve as an introduction to a study of rational functions at an intermediate algebra level. The lesson focuses on graphs of the functions with an emphasis on interpretation of the horizontal and vertical asymptotes in the context of elimination of alcohol from the body. Other mathematics involved is algebraic manipulation of the rational functions, solution of equations with rational expressions, realistic domain of a function, inverse functions, and equilibrium state of a dynamic process.MathematicsComputing and InformationEducation2014-11-02T13:20:08.638031Course Related MaterialsIntroduction to Functions - Basics and Applications
https://www.oercommons.org/courses/introduction-to-functions-basics-and-applications
The purpose of this activity is to reinforce the concept of function and the use of functional notation rather than to teach the concepts. This lab looks at input/output pictures to emphasize that a function has only one output for every input even through the output need not be unique. Using functional notation, students determine both range and domain values from a graph and then do the same for a variety of given functional equations. The real world applications include a piecewise function (cell phone costs) and require the student to find a variety of values as well as determining realistic domains.MathematicsSocial SciencesEducation2014-11-02T13:20:08.490519Course Related MaterialsLesson 38: More Operations on Fractions
https://www.oercommons.org/courses/lesson-38-more-operations-on-fractions
The lesson begins with a definition of a "complex" fraction and then presents a procedure for simplifying them (multiplying the numerator and the denominator by the lcd of all fractions contained in the complex fraction). Exercises with negative exponents are covered before applications are presented. The lesson concludes with division of polynomials.MathematicsComputing and InformationEducation2014-11-02T13:20:08.144611Course Related MaterialsLesson 39: Equations with Algebraic Fractions
https://www.oercommons.org/courses/lesson-39-equations-with-algebraic-fractions
The lesson begins with using the lcd to clear the fractions in the equation, and then a review of proportions follows to motivate the "shortcut" of cross multiplication for equations containing only a fraction on each side of the equation. The possible existence of extraneous solutions and solving the equations graphically is discussed before application problems are presented. The lesson concludes with exercises in manipulating formulas.MathematicsComputing and InformationEducation2014-11-02T13:20:05.945922Course Related MaterialsQuadratic Equations: From Factored to Standard Form
https://www.oercommons.org/courses/quadratic-equations-from-factored-to-standard-form
This activity leads students to understand the utility in the factored form of a quadratic equation. Students then express quadratic equations in standard form in the corresponding factored form. The activity is concluded with four critical-thinking questions. website: http://www.mathedpage.org/ copyright information: http://www.mathedpage.org/rights.htmlMathematicsEducation2014-11-02T13:20:05.404638Course Related MaterialsA Study of Malaria and Sickle Cell Anemia
https://www.oercommons.org/courses/a-study-of-malaria-and-sickle-cell-anemia
This investigation of the genetics of the Sickle Cell trait via a mathematical model uses probability and teaches properties of quadratic functions and the concept of optimization of a function. The properties of quadratic functions brought out by this investigation are -the relationship between the zeros of the function and its factors, -the relationship between the zeros and the location of its vertex, -the symmetry of its graph, and the location of its extreme point, -factors of quadratics of the form ax^2 + bxMathematicsLife ScienceEducation2014-11-02T13:20:04.899868Course Related MaterialsLesson 11: Intercepts, Solutions, and Factors
https://www.oercommons.org/courses/lesson-11-intercepts-solutions-and-factors
The lesson begins with a situation where the height of a pop fly in baseball is modeled using a quadratic equation. This motivates an inquiry into finding a method for obtaining solutions beyond the a(x-p)^2 = q case, to the general quadratic ax^2 + bx + c = o. Using factoring and the zero product principle is then presented as a method for solving quadratic equations. Area application problems are covered and at the end of the lesson a method for finding a quadratic equation when given the solutions is presented.MathematicsEducation2014-11-02T13:20:04.207313Course Related MaterialsLesson 36: Algebraic Fractions
https://www.oercommons.org/courses/lesson-36-algebraic-fractions
The lesson begins with the definition of an algebraic fraction and then a quick review of the fundamental principle of fractions. Exercises in reducing fractions follow before a brief procedure for reducing algebraic fractions is provided. Opposites of binomials are reviewed before rational functions are defined and a motion application problem is discussed.MathematicsComputing and InformationEducation2014-11-02T13:20:03.413178Course Related Materials