Course Descriptions & Syllabi

Course Descriptions & Syllabi

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Note: some or all of the courses in the subjects marked as "Transfer" can be used towards a transfer degree: Associate of Science and Arts or Associate of Engineering Science at DACC. Transferability for specific institutions and majors varies. Consult a counselor for this information.

Areas of Study | | MATH107 syllabus




COURSE NUMBER: MATH107
COURSE TITLE:Applied Mathematical Concepts
DIVISION:Sciences
IAI CODE(S):
SEMESTER CREDIT HOURS:5
CONTACT HOURS:75
STUDENT ENGAGEMENT HOURS:225
DELIVERY MODE:Online, In-Person, Hybrid

COURSE DESCRIPTION:
This course is intended for students who are pursuing applied science degrees (not requiring college algebra). The emphasis is on applications and problem solving. The following topics are introduced through solving practical problems which involve the modeling of natural phenomena. Topics of study include numerical analysis, variation, modeling with functions and equations, operations with polynomials, greatest common factor, introduction to functions, graphical analysis, and models of growth, linear equations and inequalities, and polynomials as related to applied sciences such as nursing, criminal justice, accounting, commercial floriculture, floral design, landscape design/construction, management, and marketing.

PREREQUISITES:
Place into MATH107 with approved and documented math placement test scores or by completing DEVM099 or DEVM100 with an ‘S’.

NOTES: This course involves group-work. Students must have access to the internet, word processing, Microsoft Excel, and printing capabilities. A TI-83/83+ or TI-84/84+ graphing calculator is required for all sections. After successful completion of this course, students will be able to take MATH115 Survey of Statistics or MATH108 Intermediate Algebra.


STUDENT LEARNING OUTCOMES:
Upon completion of this course, students will be able to:
  • Identify and interpret and evaluate solutions using graphs, charts, and tables, and report these solutions in the appropriate form (decimal, percent, fractional) and with appropriate unit labelling.
  • Use technology such as Excel, graphing calculators, and online platforms to complete data calculations, representations, and problem solving.
  • Explain the meaning of mathematical concepts using appropriate terminology and symbols
  • Apply Polya's problem solving and mathematical reasoning skills to solve practical real-life problems.
  • Apply the correct type of relationship (linear, quadratic, exponential growth/decay) in a described real-life application, to produce and analyze a solution.
  • Perform units of measure calculations and/or conversions using scales, graphs, and dimensional analysis.
  • Calculate a percentages, measures of average, area, volume, relative difference, and relative error.
  • Correctly label answers for area, volume, percentages, and relative difference/error
  • Apply the Pythagorean Theorem by calculating distances, reading contour maps, and calculating grade.
  • Apply computational procedures to practical problem solving, including explanation of specific operations.

TOPICAL OUTLINE:
  • Functions (1 contact hour)
    • Distinguish between inputs (independent variables) and outputs (dependent variables)
    • Use function notation when writing and solving functions
  • Life Skills (3 contact hours)
    • Identify and interpret elements of bank statements
    • List and describe important skills for college students to have
    • List and apply strategies for preparing for and taking math tests
    • Discuss the impact of a single question on an exam grade or a single exam on a semester average
    • Assess major life decisions that involve answering "Which is Better?" Justify an answer to this question using verbal reasoning and/or numerical computations
  • Graphing (12 contact hours)
    • Create & Interpret pie charts using Excel and by hand
    • Create & Interpret bar graphs using Excel and by hand
    • Plot points on a number line
    • Interpret and use rates of change
    • Use a rectangular coordinate system
    • Display data using graphs and use graphs to report data relationships and solutions
    • Define slope as a constant rate of change
    • Define the y intercept of a line
    • Interpret the meaning of slope and y intercept in an applied problem
    • Create a story based on the graph of a line
    • Compare and contrast solution identification using tables, graphs, and equations
    • Create equations of lines by recognizing slope and y intercept
    • Create a linear equation that models data from a description, table, or graph.
    • State the connection between zeros of a function and x intercepts of the function’s graph
    • Graph lines from a given equation
    • Find the line of best fit for data using spreadsheets and/or calculators
  • Geometry (3 contact hours)
    • Calculate the perimeter of rectangles and triangles
    • Correctly identify and apply the use of units for area and volume
    • State the Pythagorean Theorem and report the criteria for applying its use
    • Apply the Pythagorean Theorem to produce solutions
    • Develop the distance formula and apply it to find the distance between two points
  • Arithmetic (4.5 contact hours)
    • Successfully complete addition & subtraction problems with positive and negative numbers
    • Compute sums using Excel
    • Interpret multiplication as repeated addition
    • Correctly apply multiplication and division skills
    • Interpret exponents as repeated multiplication
    • Demonstrate correct use of exponents in calculations
    • State and correctly apply the order of operations
    • Compute Percentages
    • Apply inequality symbols to demonstrate comparative sizes in quantities
  • Unit Conversion (4 contact hours)
    • Convert units by multiplying and dividing
    • Convert units using dimensional analysis
    • Convert units involving rates
    • Find conversion factors for square and cubic units
  • Reasoning (1 contact hour)
    • Recognize patterns and use them to make predictions
    • Approximate square roots
  • Expressions (2 contact hours)
    • Write and interpret expressions
    • Identify when it’s appropriate to add quantities
    • Combine expressions using addition, subtraction, and multiplication
    • Evaluate expressions using provided values for variables
  • Problem Solving (4 contact hours)
    • State and describe the four steps in Polya’s problem-solving procedure
    • Solve problems using a diagram
    • Solve problems using trial-and-error
    • Solve problems requiring using numerical calculations
    • Construct and use equations to solve applied problems
    • Produce a table and/or graph to illustrate a problem
  • Variation (4 contact hours)
    • Identify quantities that vary directly
    • Identify quantities that are related by inverse variation
    • Write and use variation equations
    • Write and use inver variation equations
    • Solve problems involving direct and inverse variation
  • Quadratic Equations and Expressions (5 contact hours)
    • State the qualities that identify a graph as parabollic
    • Identify a graph that is parabolic
    • Identify solutions to problems using the graph of a quadratic equation
    • Identify quadratic functions and quadratic equations
    • Apply the quadratic formula to solve a quadratic equation
    • Produce the vertex of a parabola from a graph or equation
    • Use quadratic functions to illustrate and study physical phenomena
    • Describe what factoring is and explain why it’s useful in algebra
    • Use techniques to factor expressions
  • Growth and Decay (5.5 contact hours)
    • Distinguish between linear and exponential growth
    • Identify simple interest and know that it is an example of linear growth
    • Identify complex interest and know that it is an example of exponential growth
    • Distinguish between simple and compound interest
    • Construct expressions to calculate simple interest over time
    • Construct expressions to calculate compound interest over time
    • Identify solutions for exponential growth and decay using graphs
  • Maps and scale (2.5 contact hours)
    • Interpret and apply scale in models and maps
    • Contrast and convert percentages and scales
    • Interpret contour maps and calculate grade
  • Systems of equations (3.5 contact hours)
    • Decide when one option is better by constructing and evaluating tables
    • Decide when one option is better from graphs
    • Decide when one option is better using calculations and inequalities
  • Relative difference and relative error (2 contact hours)
    • Compare difference to relative difference
    • Calculate relative difference
    • Apply and calculate relative error
  • Measures of average, standard deviation, and normal distribution (5 contact hours)
    • Calculate and interpret measures of average
    • Describe the meaning of standard deviation
    • Recognize normal distribution graphs
    • Calculate values related to a mean and standard deviation in the normal distribution
    • Understand and apply the Empirical Rule

TEXTBOOK / SPECIAL MATERIALS:

CHBA: Online program that includes an e-book copy of Pathways to Math Literacy, Sobecki and Mercer,2nd ed

TI-83/83+ or TI-84/84+ calculator

See bookstore website for current book(s) at https://www.dacc.edu/bookstore

EVALUATION:
Tests & Quizzes
General Assessment
Final Exam
60%
20%
20%


Grade Scale:
A- 90-100%
B- 80-89%
C- 70-79%
D- 60-69%
F- 00-59%



BIBLIOGRAPHY:

STUDENT CONDUCT CODE:
Membership in the DACC community brings both rights and responsibility. As a student at DACC, you are expected to exhibit conduct compatible with the educational mission of the College. Academic dishonesty, including but not limited to, cheating and plagiarism, is not tolerated. A DACC student is also required to abide by the acceptable use policies of copyright and peer-to-peer file sharing. It is the student’s responsibility to become familiar with and adhere to the Student Code of Conduct as contained in the DACC Student Handbook. The Student Handbook is available in the Information Office in Vermilion Hall and online at: https://www.dacc.edu/student-handbook

DISABILITY SERVICES:
Any student who feels s/he may need an accommodation based on the impact of a disability should contact the Testing & Academic Services Center at 217-443-8708 (TTY 217-443-8701) or stop by Cannon Hall Room 103. Please speak with your instructor privately to discuss your specific accommodation needs in this course.

REVISION:
Fall 2019

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