Integrated Arithmetic and Algebra

Topical Outline with Specific Course Objectives

  1. Focus on Math Study Skills
    1. Develop awareness of preferred learning styles and learn to make adaptations for other instructional styles.
    2. Develop mathematical study skills that can be utilized in college-level math courses.
    3. Utilize support systems (faculty office hours, labs, SI, advising, etc.) to maximize learning opportunities.
    4. Utilize critical thinking skills to solve problems and determine reasonableness of solutions.
  2. Arithmetic
    1. Classify sets of numbers
    2. Identify and apply the properties of real numbers
    3. Write the prime factorization of a number
    4. Perform operations with integers (with applications)
    5. Perform operations with fractions (with applications)
    6. Perform operations with decimals (with applications)
    7. Perform operations on whole number (with applications, including area and perimeter)
    8. Convert among percents, fractions, and decimals
    9. Identify place value and round decimals
    10. Identify place value and round whole numbers
    11. Simplify fractions
    12. Perform order of operations including absolute values
    13. Evaluate exponents with whole numbers
    14. Evaluate exponents with integers
    15. Compare magnitude of real numbers
    16. Convert between scientific notation and standard notation
  3. Expressions and Equations
    1. Solve percent equations with applications
    2. Evaluate absolute value expressions
    3. Solve application problems involving geometry (circumference of circle, perimeter of           polygons, area of triangles, parallelograms, circles)
    4. Solve formulas with given values
    5. Set up and solve ratios and proportions with simple algebraic expressions
    6. Covert units of measurements with same measurement system
    7. Define variables and write an expression to represent a quantity in a problem
    8. Evaluate algebraic expressions
    9. Simplify algebraic expressions involving one variable
    10. Solve linear equations involving the addition and multiplication property of equalities
    11. Solve multi-step problems involving fractions and percentages (include situations such as simple interest, tax, markups/markdowns, gratuities and commissions, fees, percent increase and decrease, percent error, expressing rent as a percentage of take home pay)
    12. Recognize proportional relationships and solve problems involving rates and ratios
    13. Apply the order of operations to evaluate algebraic expressions, including those with parentheses and exponents
    14. Solve application problems involving geometry (Pythagorean Theorem)
    15. Solve application problems involving geometry (perimeter and area with algebraic expressions)
    16. Convert units of measurements across measurement systems
    17. Solve literal equations for a given variable with applications (geometry, motion [d=rt], simple interest [i=prt]
    18. Solve linear equations in one variable using manipulations guided by the rules of arithmetic and the properties of equality
    19. Simplify an expression with integer exponents
    20. Simplify radical expressions – square roots only
  4. Graphing Linear Equations and Inequalities
    1. Graph an inequality on a number line
    2. Identify the slope of a line (from slope formula, graph, and equation)
    3. Solve linear inequalities in one variable and graph the solution set on a number line
    4. Graph linear equations using table of values, intercepts, slope intercept form
    5. Identify the intercepts of a linear equation
  5. Polynomials and Rational Expressions
    1. Add, subtract, multiply, and divide polynomials. Division by monomials only
    2. Add, subtract, and multiply square roots of monomials
    3. Factor polynomial expressions (GCF, grouping, trinomials, difference of squares)
    4. Solve quadratic equations in one variable by factoring
    5. Rationalize the denominator (monomials only)
    6. Simplify, multiply, and divide rational expressions
    7. Add and subtract rational expressions with monomial denominators

Department Policies

  • Comprehensive common final
  • Four function basic calculator allowed
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