# MATH-131: Mathematics for the Modern World

School
Science, Technology, Engineering & Math
Course Subject
Mathematics
Course Number
131
Course Title
Mathematics for the Modern World
Credit Hours
4.00
Instructor Contact Hours Per Semester
62.00 (for 15-week classes)
Student Contact Hours Per Semester
62.00 (for 15-week classes)
A-E
Pre-requisites
(MATH-080 OR MATH-081 OR MATH-089 OR MATH-0894 OR MATH-103 with a C grade or better, MATH-100 or MATH-101 with a B- grade or better, a satisfactory score on the Math placement test, OR eligible to take gateway MATH courses at HFC) AND Eligible to take ENG courses at HFC
Catalog Course Description

For students pursuing a liberal arts curriculum or a program without a specified mathematics requirement. Topics include linear and exponential growth; statistics; personal finance; and geometry, including scale and symmetry. Emphasizes techniques of problem-solving and application of modern mathematics to understanding quantitative information in the everyday world.

### Goals, Topics, and Objectives

Goal Statement
1. To generate an appreciation of the quantitative tools that help to present and explain issues arising in the media and students' daily lives.
2. To heighten communication skills, both written and oral, of mathematical ideas so that students can express quantitative evidence in support of an argument or purpose of a work.
3. To increase the ability to explain information presented in mathematical forms such as equations, graphs, diagrams, tables, and paragraphs and to convert relevant information between the forms.
4. To strengthen the ability to make judgments and draw appropriate conclusions based on the quantitative analysis of data, while recognizing the limits of this analysis.
5. To enhance mathematical competence in performing appropriate calculations and communicating results in the specific areas of modeling, personal finance, basic statistics, and geometry.
Core Course Topics
1. Linear and Exponential Change
1. Recognize linear functions.
2. Find the slope of a linear function or model.
3. Interpret the slope of a linear function or model.
4. Find an exponential formula modeling data or a percentage-growth situation.
5. Solve problems involving exponential functions, such as growth, decay, doubling time, and half-life.
6. Describe how exponential and logarithmic functions are related.
7. Solve problems involving logarithms, such as sound volume and earthquake magnitude.
2. Personal Finance
1. Calculate simple and compound interest.
2. Solve problems about Annual Percentage Rate and Annual Percentage Yield.
3. Use formulas and amortization tables to solve problems about loans.
4. Use tables and formulas to solve problems about savings and annuities.
5. Calculate the interest paid on a credit card transaction.
7. Solve problems about income taxes.
3. Basic Statistics
1. Calculate mean, median, and mode, and choose the most representative number from among these.
2. Classify a data value as an outlier.
3. Calculate a five-number summary and use it to construct a box plot.
4. Calculate the standard deviation for a data set.
5. Interpret the standard deviation for a data set.
6. Construct a histogram.
7. Determine whether data are distributed normally.
8. Apply properties of the normal distribution, including calculating z-scores.
9. Calculate percentiles.
10. Interpret percentiles.
11. Apply the terms "margin of error," "confidence interval," and "confidence level."
12. Apply the terms “population”, “sample”, “control group”, and “experimental group”.
13. Describe the steps in a statistical study.
14. Identify common sampling methods and describe why statisticians strive for representative samples.
15. Identify whether a study is observational or experimental.
16. Apply guidelines for evaluating a statistical study including: getting a big picture, reviewing sources, looking for bias, considering confounding variables, and checking for fairness of questions and result presentation.
17. Read data from frequency charts.
18. Read data from graphics with multiple data sets such as double bar charts, multiple line graphs and stack plots.
19. Provide a plausible reason the author of a graphic chose the particular graphic and scale.
20. Calculate the sample size necessary for a particular confidence level.
21. Determine whether results are statistically significant.
22. Describe correlation and distinguish it from causation.
4. Geometry
1. Calculate perimeters and areas of plane figures.
2. Solve problems involving the Pythagorean Theorem.
3. Calculate surface areas and volumes of three-dimensional figures.
4. Recognize rotational symmetry and reflectional symmetry.
5. Apply properties of rotational symmetry and reflectional symmetry.
5. Mathematics and Music

Additional Topics in Geometry: Teachers should choose one of the three sets of objectives (5, 6, or 7) for their class to master or allow students to choose one of the sets of objectives in which to demonstrate mastery.

1. Describe the relation between pitch and frequency.
2. Explain that an octave corresponds to a doubling of frequency.
3. Calculate the frequency of a note on a twelve-note scale given the frequency of a lower frequency note.
6. Fractals

Additional Topics in Geometry: Teachers should choose one of the three sets of objectives (5, 6, or 7) for their class to master or allow students to choose one of the sets of objectives in which to demonstrate mastery.

1. Determine whether an object in the real world can be modeled with a fractal.
2. Find the fractal dimension given a ruler reduction factor and element increase factor.
3. Draw the first three iterations of an approximation of a self-similar fractal given an algorithm.
7. Proportion and the Golden Ratio

Additional Topics in Geometry: Teachers should choose one of the three sets of objectives (5, 6, or 7) for their class to master or allow students to choose one of the sets of objectives in which to demonstrate mastery.

1. Solve proportions involving the Golden Ratio.
2. List occurrences of the Golden Ratio in human history and nature
3. Find terms in the Fibonacci Sequence.
4. Describe the relationship between the Fibonacci Sequence and the Golden Ratio.

### Assessment and Requirements

• All students will be required to complete a comprehensive final examination that assesses the learning of all course objectives. This exam must be weighted in a manner so that this exam score is worth a minimum of fifteen percent (15%) of the final course grade.
• Additional assessment of student achievement may include assignments, quizzes, and exams.
• Application problems must not only be included on chapter exams but also on the final exam.
General Course Requirements and Recommendations
• A scientific calculator is required of each student.
• Application problems must be covered in all mathematics courses. Every section of any course outline that includes application problems must be covered.

### Outcomes

General Education Categories
• Mathematics
Institutional Outcomes
• Quantitative Literacy
MTA Categories
• Category 3: Mathematics (Quantitative Literacy Track)
Satisfies Wellness Requirement
No

### Credit for Prior College-Level Learning

Options for Credit for Prior College-Level Learning
Other Exam
Other Exam Details

50, CLEP College Mathematics exam, taken at any certified Testing Center, such as HFC’s Workforce & Professional Development’s Testing Center (313) 317-6600.

Other Details

A student may receive credit for Math-131 by earning a minimum score of 50 on the CLEP College Mathematics exam.

### Approval Dates

Effective Term
Winter 2022
ILT Approval Date
08/30/2021
AALC Approval Date
09/15/2021
Curriculum Committee Approval Date
10/04/2021