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| Credit- Not degree applicable | | Effective Quarter: Fall 2020 | I. Catalog Information
| MATH 212 | College Math Preparation Level 2: Beginning Algebra | 5 Unit(s) |
| | Formerly: Requisites: Advisory: EWRT 211 and READ 211, or ESL 272 and 273. Hours: Lec Hrs: 60.00
Out of Class Hrs: 120.00
Total Student Learning Hrs: 180.00 Description: Application of linear functions, quadratic functions and linear systems to problems. Emphasis on the development of models of real-world applications and interpretation of their characteristics. |
| Student Learning Outcome Statements (SLO)
| | | • Student Learning Outcome: Evaluate real-world situations and distinguish between and apply linear and quadratic function models appropriately. |
| | | • Student Learning Outcome: Analyze, interpret, and communicate results of linear and quadratic models in a logical manner from four points of view - visual, formula, numerical, and written. |
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II. Course Objectives | A. | Develop, throughout the course as applicable, systematic problem-solving methods |
| B. | Explore the function concept algebraically, numerically, verbally and graphically |
| C. | Explore the graphical and numerical characteristics of linear relationships and describe their meaning in the context of a problem |
| D. | Develop linear function models to solve problems |
| E. | Use systems of two linear equations to solve real-world problems |
| F. | Explore the graphical and numerical characteristics of quadratic relationships and describe their meaning in the context of a problem |
| G. | Develop quadratic function models to solve problems |
| H. | Use inequalities to solve real world problems |
| I. | Explore arithmetic sequences and series |
| J. | Investigate, throughout the course as applicable, how mathematics has developed as a human activity around the world |
III. Essential Student Materials IV. Essential College Facilities V. Expanded Description: Content and Form | A. | Develop, throughout the course as applicable, systematic problem-solving methods |
| 1. | Devise a strategy or plan |
| 2. | Organize information, including identification and definition of known and unknown quantities |
| 3. | Translate verbal expressions into mathematical format |
| 4. | Apply mathematical tools to formulate a solution |
| 5. | Clearly communicate the solution |
| B. | Explore the function concept algebraically, numerically, verbally and graphically |
| 1. | Identify relations which are and are not functions |
| 2. | Identify the domain and range of a function |
| a. | to express a function relationship using f(x) notation |
| b. | to evaluate function values using f(x) notation |
| c. | to identify points on a two-dimensional graph |
| C. | Explore the graphical and numerical characteristics of linear relationships and describe their meaning in the context of a problem |
| 1. | Graph linear relationships |
| a. | by plotting ordered pairs from tables |
| b. | by using the slope and a point |
| c. | by using properties of parallel lines |
| 2. | Identify the main characteristics of linear functions including: |
| 1. | its definition as the change in the dependent variable to the change in the independent variable |
| 2. | its meaning as a constant rate of change |
| 3. | its use in determining whether a linear function is increasing or decreasing |
| 4. | the slopes of vertical and horizontal lines |
| 5. | its use in determining parallel lines |
| 1. | as a point at which the graph crosses an axis |
| 2. | as the corresponding value of one variable when the other is zero |
| D. | Develop linear function models to solve problems |
| 1. | Develop the equation of a linear function |
| a. | numerically from tables of values |
| b. | graphically by determining the slope and vertical intercept from a graph |
| c. | algebraically by determining the slope and vertical intercept from two points |
| d. | algebraically from a parallel line and a point |
| e. | verbally from a description |
| 2. | Determine an appropriate domain to fit the constraints of a problem |
| 3. | Determine the corresponding values of the range |
| 4. | Determine a line by choosing two points and deriving the equation |
| 5. | Use a linear model to obtain values |
| a. | of the dependent variable by substitution |
| b. | of the independent variable by solving a linear equation |
| 6. | Interpret the results of a linear model in the context of the problem |
| c. | values of the independent and dependent variables |
| E. | Use systems of two linear equations to solve real-world problems |
| 1. | Identify the solution of a system of linear equations in two variables |
| a. | graphically as the intersection of two lines |
| b. | numerically as those values, if any, which satisfy both equations |
| 2. | Solve a system of linear equations in two variables |
| 2. | by elimination/addition |
| 3. | Develop system models to solve problems |
| a. | identify a situation as a system of linear equations in two variables |
| b. | develop the equations of a linear system which models the given situation |
| d. | interpret the results in the context of the problem |
| F. | Explore the graphical and numerical characteristics of quadratic relationships and describe their meaning in the context of a problem |
| 1. | Distinguish between linear and quadratic functions |
| 2. | Graph quadratic relationships |
| a. | recognize that the graph of a quadratic function has a parabolic shape |
| b. | graph by plotting ordered pairs from tables (optional) |
| c. | graph by using the vertex and the intercepts or other symmetric points |
| 3. | Identify the main characteristics of quadratic functions |
| a. | the vertex as the maximum or minimum point on the graph of the function |
| b. | the intercept(s), if they exist |
| d. | whether the graph opens up or down |
| G. | Develop quadratic function models to solve problems |
| 1. | Factor quadratic expressions in one variable |
| b. | trinomial expressions with leading coefficient 1 |
| c. | trinomial expressions with leading coefficient other than 1 |
| d. | differences of perfect squares |
| 2. | Determine the algebraic formula for a quadratic function |
| a. | as a product of binomial expressions |
| b. | as a perfect square of a binomial |
| c. | converting from graphing/vertex form to standard function form |
| 3. | Find the vertex of a quadratic function algebraically |
| 4. | Find the zeros, if they exist, of a quadratic function |
| a. | graphically as horizontal intercepts |
| 2. | by using the quadratic formula |
| 3. | by extracting roots (optional) |
| 4. | by completing the square (optional) |
| 5. | Use quadratic models to solve problems |
| a. | obtain values and solutions |
| 1. | of the dependent variable by substitution |
| 2. | of the independent variable by solving a quadratic equation |
| b. | find maximum or minimum values of a quadratic function |
| 6. | Interpret the results of a quadratic model in the context of a problem |
| b. | maximum or minimum values |
| H. | Use inequalities to solve real world problems |
| 1. | Identify the main characteristics of linear inequalities in one variable |
| a. | utilize inequality notation |
| b. | find solutions to linear inequalities using the properties of addition and multiplication |
| c. | identify solutions of linear inequalities graphically on a number line |
| d. | use inequality and interval notation to express solutions algebraically |
| 2. | Identify the main characteristics of linear inequalities in two variables |
| a. | verify a solution to a linear inequality in two variables |
| b. | graph the solution set of a linear inequality in two variables |
| c. | graph the solution set of a system of linear inequalities in two variables |
| 3. | Solve real world problems involving inequalities |
| I. | Explore arithmetic sequences and series |
| 1. | Investigate sequences as discrete function models |
| 2. | Explore the numerical and algebraic characteristics of arithmetic sequences |
| b. | recognize the connections to linear functions |
| c. | determine the formula for the general term |
| 3. | Define arithmetic series and determine the sum of the first n terms |
| J. | Investigate, throughout the course as applicable, how mathematics has developed as a human activity around the world
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| 1. | Investigate the use and development of algebraic concepts throughout history. Some possibilities are: |
| a. | explore the development and use of irrational numbers by various cultures such as those of Arabia, Babylonia, China, Greece and Europe |
| b. | explore the development and use of imaginary and complex numbers |
| c. | investigate the development of algebra, especially as it relates to linear and quadratic equations and functions, in ancient times |
| 2. | Explore algebraic applications that are of historical and/or contemporary interest. Some possibilities are: |
| a. | investigate the uses of linear and quadratic functions and inequalities in various disciplines such as the sciences and business |
| b. | investigate the uses of linear and quadratic functions and inequalities that may occur in everyday life, e.g. cost, revenue and profit functions, quadratic position functions and trajectories. |
VI. Assignments | A. | Reading of text explanations and examples |
| B. | Written assignments which may include |
| 2. | Problems requiring written explanations of key concepts, analysis of problem solving strategies and use of mathematical vocabulary |
| 3. | Projects such as labs or "big problems" that require research or data collection |
| C. | Class participation which may include |
| 1. | Collaborative activities |
VII. Methods of Instruction | | Lecture and visual aids
Discussion and problem solving performed in class
Quiz and examination review performed in class
Collaborative learning and small group exercises
Computer lab assignments |
VIII. Methods of Evaluating Objectives | A. | Periodic quizzes and/or problem assignments from the text which will be evaluated for accuracy and completion in order to assess student’s comprehension of material covered in lecture and to provide feedback to students on their progress. Questions may also require the student to
communicate ideas and conclusions in short essay format.
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| B. | Examinations will be composed of both computational and concept-based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format. |
| C. | Projects/activities, group or individual, that include written descriptions of methods and results, and justification of conclusions. Projects/activities may be based upon real, simulated, or collected data, or other methods. They will be assessed on proper use of methods and accuracy of results. |
| D. | Portfolios evaluated by a rubric created by the instructor |
| E. | Problem-solving journals assessed on completeness and accuracy of notation |
| F. | Two hour comprehensive final examination composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format. |
IX. Texts and Supporting References | A. | Examples of Primary Texts and References |
| 1. | Intermediate Algebra 7th Ed.; Blitzer, Prentice Hall 2017 |
| 2. | Intermediate Algebra, 2nd edition, Mark Clark and Cynthia Anfinson, Cengage 2017 |
| 3. | Beginning Algebra Student Workbook, Bambhania, 2017 (OER) |
| 4. | Lehmann, Jay. "Elementary and Intermediate Algebra, Functions and Authentic Applications" 2nd Ed. Pearson Education Inc. 2014. |
| B. | Examples of Supporting Texts and References |
| 1. | Mathematics Multicultural Bibliography available on the De Anza College Mathematics Resources website. |
| 2. | Gerdes, Paulus, "Geometry from Africa, Mathematical and Educational Explorations." MAA 1999 |
| 3. | Gerdes, Paulus, "Women, Art and Geometry in Southern Africa." 1998, Africa World Press. |
| 4. | Gillings, Richard J., "Mathematics in the Time of the Pharaohs." 1982, Dover Publications. |
| 5. | Joseph, George Gheverghese, "The Crest of the Peacock: Non-European Roots of Mathematics." 2010, Princeton University Press. |
| 6. | Lumpkin, Beatrice, "Algebra Activities from Many Cultures." 1997, Walch Education. |
| 7. | McLeish, John, "Number, the History of Numbers and How They Shape Our Lives." 1991, Fawcett Columbine. |
| 8. | Moses, Robert P and Cobb Jr., Charles E.; "Radical Equations, Math Literacy and Civil Rights." 2001, Beacon Press. |
| 9. | Nahin, Paul, "An Imaginary Tale, The Story of Sqrt(-1)." 1998, Princeton University Press. |
| 10. | Secada, Walter G. ed., "Changing Faces of Mathematics, Perspectives on Multiculturalism and Gender Equity;" 2000, NCTM. |
| 11. | Voolich, Erica Dakin, "A Peek into Math of the Past, Mathematical and Historical Investigations for Middle School and Pre-Algebra Students." 2001, Dale Seymour Publications. |
| 12. | Zaslavsky, Claudia, "The Multicultural Math Classroom." 1996, Heinemann Publishers. |
| 13. | ALEKS Assesment & Learning System. Aleks Corporation, 2013. |
| 14. | Crump, Thomas, "The Anthropology of Numbers." 1990, Cambridge University Press. |
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