## MATH 0000E - Practical Mathematics

http://catalog.sierracollege.edu/course-outlines/math-0000e/

Catalog Description Course Student Learning Outcomes CSLO #1: Apply the concept of numeracy in multiple contexts. (Numeracy) CSLO #2: Recognize proportional relationships and use proportional reasoning to solve problems. (Proportional Reasoning) CSLO #3: Use algebra to recognize and write relationships involving variables; interpret those relationships and solve problems. (Algebraic Reasoning) CSLO #4: Analyze and interpret data critically in multiple formats including graphs, tables, equations, formulas and be able to communicate reasoning verbally and in writing. (Data Analysis) CSLO #5: Critically solve contextual problems by making generalizations based on observations and repeated reasoning. (Critical Thinking) CSLO #6: Identify individual mindsets towards mathematics and apply student specific learning strategies, study techniques, and procedural fluency in mathematics. (Math Confidence) CSLO #7: Work effectively as a team member and work collaboratively within small groups. (Team Building) Effective Term Fall 2024 Course Type Credit - Degree-applicable Contact Hours 108 Outside of Class Hours 216 Total Student Learning Hours 324 Course Objectives Numeracy 1. Execute basic order of operations and demonstrate the effects of common operations with signed numbers, fractions and decimals in both words and symbols. 2. Apply estimation techniques using technology in a manner mathematically appropriate for the context of the situation. 3. Demonstrate the ability to measure and perform dimensional analysis with variety of units of measure such as length, area, volume and weight. 4. Demonstrate competency in the use of magnitude in the context of place values, fractions and numbers written in scientific, engineering and pre-fix notation. 5. Read, interpret, analyze and make decisions based upon data collection and computer processed results given including from line graphs, quadratic graphs, exponential graphs, logarithmic graphs, scatter plots, charts, and tables. Proportional Reasoning 6. Recognize and compare proportional relationships presented in different ways. 7. Apply quantitative reasoning to solve applied problems with proportional relationships. Algebraic Reasoning 8. Understand the use of variables to represent quantities or attributes in a variety of forms such as equations, formulas, tables and graphs. 9. Describe the effects of changes in variable values on algebraic and basic trigonometric relationships. 10. Construct and solve equations and inequalities representing relationships involving one or more unknown quantities for applied problems. Trigonometric Reasoning 11. Apply the Pythagorean Theorem in a variety of contexts to solve applied problems. 12. Estimate and measure angles and solve practical problems involving missing angle measurements. 13. Construct and solve basic right triangle trigonometric equations representing relationships that arise in a variety of applied settings. Data Analysis 14. Translate data using technology from a variety of sources including from linear graphs, quadratic graphs, exponential graphs, logarithmic graphs, scatter plots, charts, and tables into mathematical representations. 15. Convert mathematical representations including linear, quadratic, exponential and logarithmic equations into visual, graphical interpretations. 16. Describe the behavior of common types of functions (including linear, polynomial, exponential and logarithmic) using words, algebraic symbols, graphs and tables generated manually and with technology. 17. Use appropriate terms and units to describe a rate of change for a variety of applied settings. 18. Identify the appropriate mathematical models for a given set of data and consider alternative models. 19. Demonstrate an understanding of the error involved when using mathematical models to estimate real world scenarios. Critical Thinking 20. Use online and print resources to construct mathematical models, apply estimation techniques, analyze data and appraise validity of claims. 21. Operate appropriate mathematical tools such as calculators, computer algebra systems (CAS), electronic graphing and modeling tools, and measuring tools to solve applied problems. 22. Demonstrate critical thinking by analyzing ideas, patterns and principles. 23. Demonstrate flexibility with mathematics through various contexts, modes of technology and presentations of information. Math Confidence 24. Demonstrate fluency with mathematical vocabulary, terminology, and notation through written and oral presentation. 25. Implement student-specific learning strategies and study techniques. 26. Develop the ability to work effectively as a member of a team. 27. Develop a growth mindset towards mathematics that enables the student to continue to persevere through problem solving. 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 the different ways to measure the height of very tall objects such as buildings or trees. If not brought up during the discussion, the instructor will introduce tools (including applications for cell phones) and mathematical formulas from trigonometry that can be used to determine heights and angles. The class will then take a field trip outside the classroom to find heights of specific objects around campus. The initial object measured will be demonstrated by the instructor and done together as a class. Then small groups will split off to find other objects around campus and determine the measurements necessary to find the height of the specified objects. The groups will use this data collection to complete an in class worksheet. At the end of class, each small group will be given the following assignment: a. Find five objects off campus and determine the heights of these objects, pick objects that would otherwise be difficult to measure them with standard measuring tools (i.e. do not use the bookshelf in your room). b. List all five objects, along with the subsequent measurements you found necessary to determine the height of the object. c. Show all equations and calculations used. d. Write a conclusion paragraph about this project. Include your contribution to the group data collection, how accurate your measurements were and discuss any difficulties your group encountered. 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 given the specific data set and on the depth of understanding displayed in written explanations to the question asked in the problem. Given the data set of Instagram users after 2010 (when Instagram was initially launched): 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 intercept(s) in context of the data given. c. Determine which type of algebraic equation would best fit your data. Then find the appropriate equation. d. Use the equation you found to predict the number of Instagram users in 5 years, in 10 years and in 100 years. e. Does your algebraic model have restrictions in this context? Why or why not? 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 given the specific data set and on the depth of understanding displayed in written explanations to the question asked in the problem. Given the data set of Instagram users after 2010 (when Instagram was initially launched): 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 intercept(s) in context of the data given. c. Determine which type of algebraic equation would best fit your data. Then find the appropriate equation. d. Use the equation you found to predict the number of Instagram users in 5 years, in 10 years and in 100 years. e. Does your algebraic model have restrictions in this context? Why or why not? 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 the different ways to measure the height of very tall objects such as buildings or trees. If not brought up during the discussion, the instructor will introduce tools (including applications for cell phones) and mathematical formulas from trigonometry that can be used to determine heights and angles. The class will then take a field trip outside the classroom to find heights of specific objects around campus. The initial object measured will be demonstrated by the instructor and done together as a class. Then small groups will split off to find other objects around campus and determine the measurements necessary to find the height of the specified objects. The groups will use this data collection to complete an in class worksheet. At the end of class, each small group will be given the following assignment: a. Find five objects off campus and determine the heights of these objects, pick objects that would otherwise be difficult to measure them with standard measuring tools (i.e. do not use the bookshelf in your room). b. List all five objects, along with the subsequent measurements you found necessary to determine the height of the object. c. Show all equations and calculations used. d. Write a conclusion paragraph about this project. Include your contribution to the group data collection, how accurate your measurements were and discuss any difficulties your group encountered. Repeatable No Methods of Instruction Lecture/Discussion Distance Learning Lecture: Interactive lecture format will be used to perform data analysis, graph real world information and model the behavior with an algebraic equation. Data will be projected to the class and graphed through a Computer Algebra System (CAS) such as Excel or Desmos. The class will discuss the trends in the data and which type of algebraic curve would best describe the data. Through lecture, discussion and demonstration the class guided by the instructor will develop the appropriate algebraic modeling equation. (Objectives 14 & 18) Small group collaborative learning activity: In small groups, students will be asked to design and build a seal-able container that will hold 3 ounces of popcorn. Each group will be given a piece of poster board, scissors, tape and a scale. There will be a large bag of popcorn at the front of the room, but there is no measurement given on the bag. The instructor will move around the room observing and guiding groups as needed. At the end of the activity, each group will get to test their container by pouring exactly 3 ounces of popcorn into the container to determine how close they met the criteria. As the groups are testing their containers, the instructor will facilitate a class discussion about the pros and cons of each design and the process of designing the containers. (Objectives 2 & 21) Distance Learning Interactive lecture format will be used to present data analysis, graph real world information and model the behavior with an algebraic equation. Data will be presented to the class and graphed through a Computer Algebra System (CAS) such as Excel or Desmos. a discussion board will host a discuss about the trends in the data and which type of algebraic curve would best describe the data. (Objectives 14 & 18) Small virtual group collaborative learning activity: In small virtual groups, students will be given an activity to create a demonstrations for the class, guided by the instructor, that will develop the appropriate algebraic modeling equation given a data set. The instructor will moderate and guide groups as needed. At the end of the activity, each group will post their demonstration, the instructor will facilitate a discussion board about the pros and cons of each demonstration and the process of analyzing a data set. (Objectives 2 & 21) 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 of different social media such as Facebook, Instagram, 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 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. Writing, Problem Solving or Performance 1. Using a thermometer and a cup of boiling water, take the temperature of the water every 4 minutes for at least an hour. Record the data, graph the relationship between time elapsed and temperature of the water, determine what is a model of best fit (linear, power, exponential or logarithmic), include a justification for your choice. Using either Desmos or Excel, graph the data and find the equation of best fit to use to answer: How long will it take for a cup of boiling hot coffee take to reach 140 degrees (considered an ideal temperature for drinking coffee)? How long will it take for a cup of boiling water to reach the room temperature? 2. Determine the number of grains of rice in a 20lb bag. First, make a guess as to how many grains you would estimate in the 20lb bag, then discuss in your group different strategies and methods for solving this problem. Summarize the steps your group members will take to find the number of grains of rice in a 20lb bag. Using the tools provided (scales, cups, rice samples, plates, etc.) and proportions to solve this problem. Other (Term projects, research papers, portfolios, etc.) Material Cost Project: Determine the cost to manufacture a product of your choice. The materials you use and the type of manufacturing is your choice. You may construct/build, weld, sew, design, etc. -Write a paragraph explaining your project, design, the tools needed and how you would manufacture this product. -Create a blueprint of your project complete with measurements of each piece. -On the blueprint, state each measurement in both US customary units and metric units. -On the blueprint, state your measurements in both fractional and decimal equivalents. (Note: Your design must include at least 5 fractional measurement, you may not use only whole numbers) -On a separate sheet of paper, determine exact amount of material needed to manufacture your product. Include all areas and volumes necessary to complete your design. -Using technological resources, determine the cost to manufacture your product based on the amount of material needed. Answer the following questions: -- Can you purchase the exact amount of material needed? If not, what is the waste? -- Would it be cheaper to produce more products? -- What issues did you run into? How did you resolve these issues? Required Materials Math Lit: A Pathway to College Mathematics Author: Almy and Foes Publisher: Pearson Publication Date: 2017 Text Edition: 2nd Classic Textbook?: No OER Link: OER: Math E: Practical Math Volumes 1 and 2 (course Pack) Author: Doug Gardner Publisher: XanEdu Publication Date: 2018 Text Edition: 3rd Classic Textbook?: No OER Link: OER: Other materials and-or supplies required of students that contribute to the cost of the course.