MS 090MS O95MS 098
  1. Course Objectives or Learning Outcomes
    1. Program student learning outcomes
      Students will be able to:
      • define mathematical concepts, calculate quantities, estimate solutions, solve problems, represent and interpret mathematical information graphically, and communicate mathematical thoughts and ideas.
    2. Course student learning outcomes
      Students will be able to:
      1. add and subtract whole numbers
      2. multiply and divide whole numbers
      3. find factors and calculate multiples
      4. perform operations with fractions
      5. perform operations with decimals
      6. calculate ratios, proportions, and percentages
      7. measurement, geometry, statistics and the usage of formulas
      8. solve basic algebraic expressions
    3. Specific student learning outcomes
      Students will be able to:
      1. add and subtract whole numbers
        1. add and subtract whole numbers
        2. determine decimal place values
        3. round, estimate, and put whole numbers into order
        4. borrow and carry
        5. list and describe the properties of addition
        6. solve applications involving addition and subtraction
      2. multiply and divide whole numbers
        1. list and describe the properties of multiplication
        2. multiply and divide by numbers with more than one digit
        3. demonstrate usage of the long division algorithm
        4. solve applications involving multiplication and division
      3. find factors and calculate multiples
        1. distinguish between prime and composite numbers
        2. write composite numbers as products of prime numbers
        3. find the Greatest Common Factor
        4. find the Least Common Multiple
      4. perform operations with fractions
        1. identify and distinguish proper & improper fractions, and mixed numbers
        2. convert improper fractions to mixed numbers and vice-versa
        3. determine whether fraction are equivalent simplify fractions
        4. multiply and divide fractions
        5. multiply fractions and mixed numbers
        6. simplify and dividing fractions
        7. add and subtraction fractions
        8. find the Least Common Denominator
        9. add and subtract fractions with different denominators
        10. add and subtract mixed numbers
        11. solve applications involving fractions
      5. perform operations with decimals
        1. add and subtract of decimals
        2. determine place value in decimal fractions
        3. round decimals
        4. convert decimals to fractions
        5. multiply and divide decimals
        6. multiply and divide decimals by whole numbers
        7. multiply and divide decimals by powers of 10
        8. perform operations using scientific notation
      6. calculate ratios, proportions, and percentages
        1. define the terms used with ratios and proportions
        2. solve ratio and proportion problems
        3. define the meaning of percent
        4. changing percent to fractions and decimals and back
        5. identify rate, base, and amount
        6. solve applications and word problems with ratios, proportions, and percent
      7. measurement, geometry, statistics and the usage of formulas
        1. define the English system of measurement
        2. define the metric system of measurement
        3. describe the units of these systems
        4. describe the correlation of weight, volume, and length
        5. identify and distinguish lines, angles, and simple geometric figures
        6. describe the parts of a graph including the quadrants, axes, and ordered pairs
        7. recognize graphs of geometric figures
        8. find perimeter and circumference
        9. find area and volume from formulas
        10. Calculate square roots and the Pythagorean Theorem
        11. define and calculate basic terms of statistics
        12. determine mean, mode, range, and median
      8. solve basic algebraic expressions
        1. distinguish real numbers and subsets
        2. calculate using positive and negative values and the rules of operation
        3. solve problems using the steps for solving equations
        4. evaluate algebraic expressions
        5. converti statements to equations
        6. solve basic equations with positive and negative values
  2. Course content
    1. Addition and Subtraction of Whole Numbers
      1. Addition and Subtraction
      2. Decimal Place Value System
      3. Rounding, Estimation, and Order
      4. Borrowing and Carrying
      5. Properties of Addition
      6. Applications Involving Addition and Subtraction
    2. Multiplication and Division of Whole Numbers
      1. Properties of Multiplication
      2. Multiplication and Division by Numbers with more than one digit
      3. Long Division Algorithm
      4. Applications involving multiplication and division
    3. Factors and Multiples
      1. Prime and Composite Numbers
      2. Composite Numbers as Products of Prime Numbers
      3. Finding the Greatest Common Factor
      4. Finding the Least Common Multiple
    4. Fractions
      1. Introduction to Fractions
      2. Proper & Improper Fractions, and Mixed Numbers
      3. Converting Improper Fractions and Mixed Numbers
      4. Equivalent Fractions and Simplifying Fractions
      5. Multiplication and Division of Fractions
      6. Multiplying Fractions and Mixed Numbers
      7. Simplifying and Dividing Fractions
      8. Addition and Subtraction of Fractions
      9. Finding the Least Common Denominator
      10. Adding and Subtracting Fractions with Different Denominators
      11. Addition and Subtraction of Mixed Numbers
      12. Applications Involving Fractions
    5. Decimals
      1. Addition and Subtraction of Decimals
      2. Place Value in Decimal Fractions
      3. Rounding Decimals
      4. Converting Decimals to Fractions
      5. Multiplication and Division of Decimals
      6. Multiplication and Division of Decimals By Whole Numbers
      7. Decimals By Powers of 10
      8. Decimals with Scientific Notation
    6. Ratios, Proportions, and Percents
      1. Language of Ratios and Proportions
      2. Ratio and Proportion Problems
      3. Meaning of Percent
      4. Changing Percent to Fractions and Decimals
      5. Identifying Rate, Base, and Amount
      6. Solving Applications and Word Problems with Ratios, Proportions, and Percent
    7. Measurement, Geometry, Statistics and the usage of formulas
      1. The English System of Measurement
      2. The Metric System of Measurement
      3. Units of these Systems
      4. Correlation of Weight, Volume, and Length
      5. Lines, Angles, and Simple Geometric Figures
      6. Basics of Graphing, Quadrants, and Ordered Pairs
      7. Graphs of Geometric Figures
      8. Finding Perimeter and Circumference
      9. Finding Area and Volume
      10. Square Roots and the Pythagorean Theorem
      11. Basic Terms of Statistics
      12. Determining Mean, Mode, Range, and Median
    8. Introduction to Algebra
      1. Real Numbers and Subsets
      2. Positive and Negative Values and Rules of Operation
      3. Steps for Solving Equations
      4. Evaluating Algebraic Expressions
      5. Converting Statements to Equations
      6. Solving Basic Equations with Positive and Negative Values
  1. General Objectives: Students will acquire the basic mathematical tools that will enable them to develop long-range intellectual abilities including:
    1. engaging in substantial mathematical problem solving
    2. learning mathematics through modeling real-world situations
    3. expanding their mathematical reasoning skills
    4. developing the view that mathematics is a growing discipline, interrelated with human culture, and understand its connections to other disciplines
    5. acquiring the ability to read, write, listen to, and speak mathematics
    6. using appropriate technology to enhance their mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of their results
    7. developing mathematical power by engaging in rich experiences that encourage independent, nontrivial exploration in mathematics, develop and reinforce tenacity and confidence in their abilities to use mathematics, and inspire them to pursue the study of mathematics and related disciplines as related to their personal life-time goals.
  2. Specific Objectives: The student will demonstrate understanding of the following topics at least 70% of the time:
    1. Working With Whole Numbers
      1. Place Value
      2. Addition/Subtraction
      3. Multiplication/Division
      4. Exponents
      5. Rounding and Estimation
      6. Factors/Prime Factorization
      7. Least Common Multiple/Greatest Common Factor
      8. Order of Arithmetic Operations
      9. Formulas and Applications
    2. Working With Integers
      1. Order Relations Between Integers
      2. Absolute Value
      3. Addition/Subtraction
      4. Multiplication/Division
      5. Order of Arithmetic Operations
      6. Applications
    3. Working With Fractions
      1. Proper/Improper Fractions, Mixed Numbers
      2. Equivalence
      3. Order Relations Between Fractions
      4. Addition/Subtraction
      5. Multiplication/Division
      6. Exponents
      7. Complex Fractions
      8. Order of Arithmetic Operations
      9. Applications
      4. Working With Decimals and Real Numbers
      1. Place Value
      2. Order Relations Between Decimals
      3. Rounding and Estimation
      4. Addition/Subtraction
      5. Multiplication/Division
      6. Conversions Between Fractions and Decimals
      7. Real Numbers and the Real Number Line
      8. Inequalities of One Variable
      9. Applications and Formulas
    4. Working With Variable Expressions
      1. Simplifying Expressions Using the Properties of Addition and Multiplication
      2. Applying the Distributive Property
      3. General Variable Expressions
      4. Using Formulas
        1. for Perimeter and Area of Geometric Figures
        2. for Volume and surface Area of Solids
      5. Translating Verbal Expressions into Variable Expressions
      6. Applications
    5. Working With Equations and Inequalities
      1. Solutions of an Equation
        1. of the form x + a = b
        2. of the form ax = b
        3. of the form ax + b = c
        4. of the form ax + b = cx + d
        5. equations containing parentheses
      2. Translations of Sentences into Equations and Solving
      3. Applications
        1. Basic Percent Equations
        2. Percent Increase and Percent Decrease
        3. Geometry: Lines, Angles, and Triangles
        4. Mixture, Investment,and Motion Problems
      4. Inequalities
        1. Addition and Multiplication Properties
        2. General Inequalities
        3. Applications
  1. General Objectives:Students will acquire the basic mathematical tools that will enable them to develop long-range intellectual abilities including:
    1. Engaging in substantial mathematical problem solving.
    2. Learning mathematics through modeling real-world situation.
    3. Expanding their mathematical reasoning skills.
    4. Developing the view that mathematics is a growing discipline, interrelated with human culture, and understand its connections to other disciplines.
    5. Acquiring the ability to read, write, listen to, and speak mathematics
    6. Using appropriate technology to enhance their mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of their results
    7. Developing mathematical expertise by engaging in experiences that encourage independent, nontrivial exploration in mathematics, develop and reinforce confidence in their abilities use mathematics, and inspire them to pursue the study of mathematics and related disciplines as related to their personal life-time goals.
  2. Specific Objectives: Students will demonstrate acquisition of basic mathematical tools listed in the Course Content category below. The students will demonstrate by successful (70% accuracy or better) performance in:
    1. Classroom discussion and practice of the mathematical tools
    2. Homework used to reinforce classroom discussion
    3. Projects (including computerized projects) used to expand on and synthesize the tools discussed
    4. Multiple test or quizzes (as a minimum, one per chapter) covering the course content
    5. Mid-Term and Final that will be a comprehensive assessments of students’ understanding of the course content.
  3. Course Content:
    1. Graphs and Linear Equations
      1. Rectangular coordinate system
      2. Solutions of Linear Equations in two variables<
      3. Graph equations of the following forms:
        1. y = mx + b
        2. Ax + B = C
      4. The slope of a straight line
      5. Graph a line using the slope and y-intercept
      6. Find the equation of line given:
        1. a point and a slope
        2. two points
      7. Solve a system of linear equations by:
        1. graphing
        2. substitution method
        3. addition method
      8. Apply the above concepts with real problems
    2. Polynomials
      1. Operation with Polynomials:
        1. Addition
        2. Subtraction
        3. Multiplication, concentrating on methods for
          1. monomials
          2. binomials
        4. Division, concentrating on methods for
          1. monomials
          2. long division of polynomials
      2. Working with Exponents
        1. Negative and zero exponents
        2. Positive exponents
        3. Scientific notation
      3. Applications of polynomials
    3. Factoring Polynomials
      1. Finding the greatest common factor of two or more monomials
      2. Factoring a monomial from a polynomials
      3. Factoring a trinomial of the forms
        1. Perfect squares
        2. Difference of squares
        3. Multi-step factoring completely
      4. Solving equations by factoring
      5. Application using factoring
    4. Algebraic Fractions
      1. Simplifying fractions
      2. Multiplication of fractions
      3. Division of fractions
      4. Addition/Subtraction using the Least Common Multiple
      5. Solving equations (and applications) containing fractions
        1. Variation problems
        2. Literal equations
        3. Unit rates and proportions
        4. Similar triangles
        5. Work problems
        6. Uniform motion problems
    5. Radical Expressions
      1. Operations on radical expressions
        1. Addition/subtraction of radical expressions
        2. Multiplication/division of radical expressions
      2. Equations with radical expressions<
      3. Solving right triangles
    6. Quadratic Equations
      1. Solving quadratic equations by the following methods:
        1. Factoring
        2. Taking square roots
        3. Completing the square
        4. Quadratic formula
      2. Graphing quadratic equations in two variables

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