Sep 09, 2024
2023-2024 College Catalog and Student Handbook
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# MATH 0075 - Foundations of Mathematical Reasoning

3 Credit(s)
Foundations of Mathematical Reasoning is a quantitative literacy course designed to provide students with the skills and conceptual understanding to succeed in a college-level statistics course.  Foundations of Mathematical Reasoning is organized around big mathematical and statistical ideas.  The course will help students develop conceptual understanding and acquire multiple strategies for solving problems.  The course will prepare students for success in future courses and will help them develop skills for the workplace and as productive citizens.   UG
3 Lecture Hour(s);
Required Concurrent Course(s): MATH 0030

College Wide Outcomes
 College-Wide Learning Outcome Assessments - - How it is met & When it is met Communication – Written Communication – Speech Intercultural Knowledge and Competence Critical Thinking Information Literacy Quantitative Literacy

Student Learning Outcomes for Course
 Outcomes Assessments – How it is met & When it is met 1. Represent large numbers in various ways. Scale measurements. Convert between units of measure. Practice Assignments – Week 1 Test 1 – Week 4 Final Exam – Week 16 2. Use data to estimate doubling time. Compare and contrast growth via doubling times. Convert between scientific notation and standard notation. Recognize when it is appropriate to express a ratio as a percentage. Calculate and estimate ratios of large numbers. Preview Assignments – Week 1 Practice Assignments – Week 1 Test 1 – Week 4 Final Exam – Week 16 3. Evaluate reasonableness of statements in the media. Rewrite statements to improve clarity. Estimate and calculate percentages. Determine when an estimate or an exact calculation is appropriate. Preview Assignments – Weeks 1 and 2 Practice Assignments – Week 2 Test 1 – Week 4 Final Exam – Week 16 4. Write a calculation in different ways. Apply mathematical properties and operations in using spreadsheet technology. Calculate absolute and relative change from a line graph. Interpret information from pie charts. Preview Assignments – Weeks 2 and 3 Practice Assignments – Weeks 2 and 3 Test 1 – Week 4 Final Exam – Week 16 5. Compare mean and median from the shape of a distribution. Preview Assignment – Week 3 Practice Assignment – Week 3 Test 1 – Week 4 Final Exam – Week 16 6. Apply skills and concepts to consumer credit. Use spreadsheets to compute credit card interest. Perform and rewrite multi-step calculations using information from a real-world source. Preview Assignments – Weeks 3 and 4 Practice Assignments – Weeks 3 and 4 Test 1 – Week 4 Final Exam – Week 16 7. Express and interpret ratios in non-standard and standard forms. Make quantitative comparisons between data. Create graphs that show absolute change calculated from a rate. Compute absolute changes. Create graphs that show relative changes in a rate. Compute relative changes. Preview Assignments – Weeks 4 and 5 Practice Assignments – Week 5 Test 2 – Week 8 Final Exam – Week 16 8. Calculate percentages and convert from a decimal representation to a percent. Correctly identify the quantities involved in a general verbal statement about percentages. Extract relevant information from a two- way table. Select the appropriate values to compute probabilities. Calculate and interpret probabilities of errors. Preview Assignments – Weeks 5 and 6 Practice Assignments – Weeks 5 and 6 Test 2 – Week 8 Final Exam – Week 16 9. Calculate a unit rate. Compare and contrast populations using their population densities. Calculate population densities. Calculate population density proportions from density ratios. Solve a proportion by first finding a unit rate and then multiplying appropriately. Calculate a unit rate. Explain the difference between a relative change and an absolute change. Preview Assignments – Weeks 6 and 7 Practice Assignments – Weeks 6 and 7 Test 2 – Week 8 Final Exam – Week 16 10. Solve complex problems requiring multiple pieces of information and steps. Use formulas from geometry and perform calculations that involve rates and measures to support financial decisions. Evaluate an expression. Preview Assignments – Weeks 7 and 8 Practice Assignments – Weeks 7 and 8 Test 2 – Week 8 Final Exam – Week 16 11. Use units to determine which conversion factors are needed for dimensional analysis. Use a conversion factor to convert a rate. Write a rate as a fraction. Use a unit factor to convert a rate. Preview Assignments – Weeks 8 and 9 Practice Assignments – Week 9 Test 3 – Week 12 Final Exam – Week 16 12. Evaluate an expression involving a square root. Identify a sequence of calculations defined by an equation. Evaluate a rational expression. Establish a strategy to explore the pattern of changes in one variable while holding other variables fixed. Preview Assignments – Weeks 9 and 10 Practice Assignments – Week 10 Test 3 – Week 12 Final Exam – Week 16 13. Explicitly write out the order of operations to evaluate a given formula. Solve for a variable in an equation. Determine the effect of a variable on the size of an expression based on its location. Preview Assignments – Weeks 10 and 11 Practice Assignments – Week 11 Test 3 – Week 12 Final Exam – Week 16 14. Set up and solve a proportion based on a contextual situation. Solve a proportion using algebraic methods. Solve equations that require simplification before solving. Solve for a variable in terms of other variables. Solve quadratic equations. Set up a proportion based on a contextual situation. Preview Assignments – Weeks 12 and 13 Practice Assignments – Week 13 Final Exam – Week 16 15. Calculate slope in direct variation situations. Express slope with appropriate units. Interpret slope in a problem situation. Compare slopes in a problem situation. Calculate slope from two data points in a linear relationship. Determine the y-intercept and equation of a linear relationship. Calculate the y- intercept of any linear relationship given two points. Write an equation that represents a linear relationship given two data points. Use the linear equation to make predictions. Preview Assignments – Weeks 13 and 14 Practice Assignments – Week 14 Final Exam – Week 16 16. Express linear relationships in multiple forms. Identify appropriate use of each form of linear relationships. Compare two relationships. Translate between representations of a line. Make decisions based on different forms of linear equations. Identify approximately linear data. Write a linear equation to model approximately linear data. Preview Assignments – Weeks 14 and 15 Practice Assignments – Week 15 Final Exam – Week 16 17. Write and interpret an expression that models a percentage increase or decrease. Preview Assignments – Week 15 Practice Assignments – Week 15 Final Exam – Week 16

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