MATH 0000G - B-STEM Intermediate Algebra
http://catalog.sierracollege.edu/course-outlines/math-0000g/
Catalog Description Course Student Learning Outcomes CSLO #1: Simplify expressions and solve equations of the following types: linear, quadratic (including some with complex solutions), rational, radical, absolute value, exponential, and logarithmic. CSLO #2: Interpret and construct graphs of linear, quadratic, rational, exponential, and logarithmic functions and their inverse functions. CSLO #3: Translate, model, and solve applied problems using linear, quadratic, rational, radical, exponential, and logarithmic functions, systems of equations. CSLO #4: Critically solve problems in a variety of contexts using the tools of mathematics, including technology. CSLO #5: Construct clear, complete and accurate solutions to mathematical problems and logically communicate solutions in a variety of ways including written, graphically and verbally. CSLO #6: Identify individual attitudes towards mathematics and demonstrate specific learning strategies, study techniques, and a fluency in mathematical communication. Effective Term Fall 2024 Course Type Credit - Degree-applicable Contact Hours 90 Outside of Class Hours 180 Total Student Learning Hours 270 Course Objectives 1. Solve equations including linear, quadratic, polynomial, rational and absolute value, exponential, logarithmic, or radical, and their associated applied problems. 2. Solve inequalities including linear, quadratic, polynomial, rational and absolute value. 3. Analyze and determine the domain for polynomial, radical, rational, logarithmic and exponential functions. 4. Graph linear, absolute value, quadratic, radical, exponential, logarithmic and piecewise functions. 5. Write equations from graphs of linear and quadratic functions. 6. Utilize function notation, perform operations on functions, determine if a function is invertible, and find the inverse of functions both graphically and in function notation. 7. Use graphic, numeric and analytic methods to solve linear and quadratic equations and inequalities, applying technology when appropriate. 8. Simplify and perform operations on complex numbers and solve equations with non-real solutions. 9. Simplify and perform operations on algebraic expressions including polynomials, rational expressions, complex fractions, radicals, rational and integral exponents, and logarithms. 10. Solve linear and nonlinear systems of equations and inequalities with two variables and applied problems associated with such systems, including finding feasible regions. 11. Solve linear systems of equations with three variables and applied problems associated with such systems. 12. Graph and write equations of the elementary conic sections: parabola and circle. 13. Demonstrate fluency with mathematical vocabulary, terminology, and notation through written and oral presentation. 14. Implement student-specific learning strategies and study techniques. General Education Information Approved College Associate Degree GE Applicability AA/AS - Comm & Analyt Thinking AA/AS - Mathematical Skills CSU GE Applicability (Recommended-requires CSU approval) Cal-GETC Applicability (Recommended - Requires External Approval) IGETC Applicability (Recommended-requires CSU/UC approval) Articulation Information Not Transferable Methods of Evaluation Classroom Discussions Example: The following is an example of a classroom discussion that would lead into a group project started in class and finished for homework. The final product would be a group report turned in at the completion of the project. Student performance would be evaluated based on the detail provided about the students' specific project, each student's contribution to the group and the correctness of the solutions given. As a class, the instructor will facilitate a discussion about catapults and trajectories. Through the discussion the instructor will talk about the different ways to write an equation of a parabola. The class will then break up into small groups with the goal of finding an equation to model the trajectory of a catapult (catapult will be provided by the instructor). The groups will discuss and come up with a strategy for collecting data and then head outside to shoot the catapult and find data. Ultimately, each group will be asked to test the accuracy of their equations by determining where in the trajectory to place a basket or trash can so that a bouncy ball will land directly in the basket or trash can. The class will hold a competition at the end of the activity. Each group will be given the following assignment: a. Determine the information you would need to collect to model the trajectory of your catapult. Write out a plan for your group to find this information. b. Head outside to shoot your catapult and collect data. c. Using the data you collected, find a quadratic equation that models the trajectory of your catapult. Define your variables (x and y) and state the domain and range of the model. d. Measure the height of the given objects (basket and/or trash cans) and then determine where to place the objects so that the bouncy ball will fall into them when launched. Include all calculations. e. Test your predictions! Objective Examinations Example: The following is an example of a problem from an exam which would entail problem solving, written explanations and objective solutions. Student performance would be evaluated based on the correctness of the solutions and on the depth of understanding displayed in written explanations to the questions asked in the problem. Using the data from the last several years of the ever increasing cost of a 30 second Super Bowl Ad: a. Identify the independent and dependent variables. b. Graph the data on a Cartesian coordinate system and label your axes and intercept(s). Write a sentence or two to describe the trend and the intercept(s) in context of the data given. c. Draw a line of best fit through the points. d. Determine the slope of the line through the years 2012 and 2017. Describe the slope in context. e. Use the equation you found to predict the cost of a 30 second ad in 2025. f. Do you think the trend will continue? At the same rate? Explain your reasoning. Problem Solving Examinations Example: The following is an example of a problem from an exam which would entail problem solving, written explanations and objective solutions. Student performance would be evaluated based on the correctness of the solutions and on the depth of understanding displayed in written explanations to the questions asked in the problem. Using the data from the last several years of the ever increasing cost of a 30 second Super Bowl Ad: a. Identify the independent and dependent variables. b. Graph the data on a Cartesian coordinate system and label your axes and intercept(s). Write a sentence or two to describe the trend and the intercept(s) in context of the data given. c. Draw a line of best fit through the points. d. Determine the slope of the line through the years 2012 and 2017. Describe the slope in context. e. Use the equation you found to predict the cost of a 30 second ad in 2025. f. Do you think the trend will continue? At the same rate? Explain your reasoning. Projects Example: The following is an example of a classroom discussion that would lead into a group project started in class and finished for homework. The final product would be a group report turned in at the completion of the project. Student performance would be evaluated based on the detail provided about the students' specific project, each student's contribution to the group and the correctness of the solutions given. As a class, the instructor will facilitate a discussion about catapults and trajectories. Through the discussion the instructor will talk about the different ways to write an equation of a parabola. The class will then break up into small groups with the goal of finding an equation to model the trajectory of a catapult (catapult will be provided by the instructor). The groups will discuss and come up with a strategy for collecting data and then head outside to shoot the catapult and find data. Ultimately, each group will be asked to test the accuracy of their equations by determining where in the trajectory to place a basket or trash can so that a bouncy ball will land directly in the basket or trash can. The class will hold a competition at the end of the activity. Each group will be given the following assignment: a. Determine the information you would need to collect to model the trajectory of your catapult. Write out a plan for your group to find this information. b. Head outside to shoot your catapult and collect data. c. Using the data you collected, find a quadratic equation that models the trajectory of your catapult. Define your variables (x and y) and state the domain and range of the model. d. Measure the height of the given objects (basket and/or trash cans) and then determine where to place the objects so that the bouncy ball will fall into them when launched. Include all calculations. e. Test your predictions! Repeatable No Methods of Instruction Lecture/Discussion Distance Learning Lecture: Using an interactive lecture format, the instructor will develop the concept of a function, function notation and domain and range. Instructor will begin with definitions and examples, then students will work in groups to evaluate sets of data, graphs and equations to determine if they represent functions and state the domain and range of each given example. The instructor will write the same sets of data, graphs and equations on whiteboards around the classroom and call on groups to share and write their solutions on the whiteboards. (Objectives 6 & 13) Collaborative Learning: Using an in-class small group collaborative learning activity, students will discuss the strategies for factoring different types of polynomial expressions and create a flow chart to help them determine the best approach. Given a list of polynomials, they will use their flow chart to determine the complete factorization. The instructor will circulate and ask clarifying questions as the students complete this task. (Objectives 9 & 13) Distance Learning A cumulative project is given to the students at the end of the unit on quadratic functions. Students are presented with a digital image of the Golden Gate Bridge. Using the measurements given they must create a mathematical model of the suspension bridge. Using this model are asked to determine where 100 foot high cameras should be placed on the cables to monitor traffic. Students will work on this problem independently and then share their solutions with small groups through the Discussion Boards. After a period of time to clean up any errors that were found during their small group discussion on the Discussion Board, students will make final individual submissions for the project to the teacher through the gradebook. (Objectives 1, 5 & 13) Typical Out of Class Assignments Reading Assignments 1. Find and read an article utilizing measurements in scientific or engineering notation. State the numbers used in the article in both the given scientific/engineering form and in the equivalent standard decimal format. Describe why the authors chose to describe the numbers in this format rather than in standard decimal notation. 2. Read an article describing the growth and/or decline of different social media platforms such as MySpace, Facebook, Instagram, Snapchat and Twitter. Research historical records of user data per month and make independent tables for each company, clearly labeling your independent and dependent variables. Using a graphing calculator, Excel or Desmos (a free app that is a powerful graphing calculator) create a graph of each company’s growth curve. Explain the type of growth experienced by each company, the factors that led to this growth and any conditions that did or will hinder future growth. Model the data with a function that best fits the type of growth (linear, exponential or piecewise function) and make predictions with your model. Writing, Problem Solving or Performance 1. Solve applied mathematical problems that use exponential models. Example: Assume that on the day you were born, your uncle put $8,000 into an account that grew at a rate of 3.7% annual interest compounded continuously. How much money would you have in the account on your 21st birthday? 2. Solve an applied mathematics problem using a system of equations. Example: A wine company needs to blend a California wine with a 5% alcohol content and a French wine with a 9% alcohol content to obtain 200 gallons of wine with 6.5% alcohol content. How many gallons of each kind of wine must be used? Other (Term projects, research papers, portfolios, etc.) Required Materials Intermediate Algebra for College Students Author: Blitzer Publisher: Pearson Publication Date: 2017 Text Edition: 7th Classic Textbook?: No OER Link: OER: Intermediate Algebra Author: Marecek Publisher: OpenSTAX Publication Date: 2017 Text Edition: 1st Classic Textbook?: No OER Link: OER: Other materials and-or supplies required of students that contribute to the cost of the course.
