Developmental Math Modules
Math 095: Modules 1 – 5
Math 098: Modules 11 – 15
Math 096: Modules 6 – 10
Math 099: Modules 16 - 20
(Corresponding course outcomes in parentheses)
0. Student Attributes for College Readiness
1. Whole Numbers (Math 095)
 Describe numbers using standard notation, place values, word names, and
expanded form (#1, 4)
 Add and subtract whole numbers(#2)
 Multiply and divide whole numbers(#2)
 Compare, round, and estimate whole numbers (#3)
 Convert exponential notation to standard notation (#5)
 Apply the Order of Operations Agreement to simplify whole number expressions
(#6)
 Interpret data representations such as charts and graphs (#7, 12)
 Translate and solve whole number application problems that involve one or
more operations (#12)
2. Fractions (Math 095)
 Identify and convert types of fractions (#2)
 Determine whether a whole number is prime, composite, or neither (#9)
 List factors and provide prime factorization of whole numbers (#2, 9)
 Recognize and generate equivalent fractions through simplifying and Least
Common Multiple (#2)
 Classify order relations of two or more fractions using inequality operations (#4)
 Multiply and divide fractions (#2)
 Add and subtract fractions (#2)
 Apply the Order of Operations Agreement to simplify expressions with fractions
(#6)
 Translate and solve fraction application problems that involve one or more
operations (#12)
3. Decimals (Math 095)
 Read, write and compare decimals (#1, 4)
 Use place value understanding to round decimals to a specific place value (#3)
 Add and subtract decimals (#2)
 Multiply and divide decimals (#2)
 Convert between decimals and fractions (#13)
 Translate and solve decimal application problems that involve one or more
operations (#12)
 Apply the Order of Operations Agreement to simplify expressions with decimals
(#6)
4. Ratios, Proportions, Percents I (Math 095)
 Write and interpret ratios, rates and unit rates (#10)
 Solve basic proportion problems (#11)
 Convert the percent of a quantity as a rate per 100 (#13)
 Convert between percents, decimals and fractions (#13)
 Interpret data representations such as circle graphs, bar graphs, histograms, and
line graphs (#7)
 Use measure of central tendency (mean, median, mode) and spread (range) of a
given set of numbers including whole numbers, fractions, decimals and percents
to summarize data (This objective may also be presented in modules #1, 2, 3)
(#8)
5. Rational Numbers (Math 095)
 Read, write and compare rational numbers (#1)
 Add and subtract rational numbers (#2)
 Multiply and divide rational numbers (#2)
 Translate and solve rational number application problems that involve one or
more operations (#12)
 Apply the Order of Operations Agreement to simplify expressions with rational
numbers (#6)
6. Linear Equations and Inequalities I (Math 096)
 Use Order of Operations Agreement to evaluate algebraic expressions and
formulae at specific rational values (#1, 2)
 Use appropriate properties to simplify an algebraic expression (#2)
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Use properties of equality to solve linear equations through a series of
equivalent equations (#3)
Extract and apply information given by data representations or graphically (#9)
Translate application problems into algebraic equations to solve (#4)
Solve first degree inequalities in one variable (#10)
7. Proportions and Percents II (Math 096)
 Write and interpret ratios (#3)
 Use the proportion method to solve for an unknown quantity (#3, 6)
 Translate and solve proportion application problems (#4, 5)
 Solve percent problems finding the base, amount or percent given two of the
other parts using the basic percent equation and the proportion method (#5, 6,
#2 – 098)
 Translate and solve percent application problems including problems with
percent increase and decrease (#4, 5)
8. Basic Geometry I – (Math 096)
 Identify and compare types of angles and their relationships (#8)
 Identify and compare types of triangles (#8)
 Apply the applicability of proportions in problem-solving situations of similar
triangles (#6)
 Use the Pythagorean Theorem when appropriate to compute unknown distances
(#8)
 Distinguish between an exact answer and an approximate answer when solving
problems involving Pythagorean Theorem (#3)
 Translate and solve application problems involving Pythagorean Theorem (#4, 8)
9. Basic Geometry II – (Math 096)
 Identify the base and the height of various geometric shapes (#8)
 Identify and compare the components of a circle (#8)
 Calculate the perimeter/circumference of various geometric figures including
circles, triangles and quadrilaterals (#8)
 Calculate the area of various 2-D figures, including circles, triangles and
quadrilaterals (#8)
 Calculate the volume of various 3-D figures, including spheres, right rectangular
prisms, right circular cylinders, right pyramids and right cones (#8)
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Translate and solve application problems involving perimeter, area and volume
of various geometric figures (#4, 8)
10. Measurement/Conversions – (Math 096)
 Use ratio reasoning (solving proportions or dimensional analysis) to convert
measurement units (#7)
 Convert between units of time (#7)
 Convert between Celsius and Fahrenheit temperatures (#3, 4)
 Convert between U.S. System units of length, mass and capacity (#7)
 Convert between metric units of length, mass and capacity (#7)
 Conversions between U.S. System and metric units of length, mass and capacity
(#7)
 Translate and solve application problems involving conversion of units of length,
mass and capacity (#4, 7)
11. Linear Equations II – (Math 098)
 Solve applications using first-degree linear equations (#1)
 Solve literal equations (formula) for a particular variable (#1)
 Translate percentage problems into linear equations when an unknown base
must be combined with percent change (#2)
 Solve direct and inverse variation problems, including applications (#13)
12. Graphing Linear Equations – (Math 098)
 Define and label the relevant features of the rectangular coordinate system,
including intercepts (#14)
 Create an appropriate linear graph for a given set of data (#1, 16)
 Determine slope and grade both from geometric representations and from given
points (#16)
 Identify the characteristics of the slope-intercept form of linear equations and
apply to problem-solving (#17)
 Graph linear equations by table, intercepts, and slope-intercept (#1, 15, 17)
 Identify and apply the relationships between parallel and perpendicular lines
(#16)
13. Polynomials – (Math 098)
 Recognize the difference between factors and terms (#3, 5)
 Evaluate and simplify polynomial expressions (#3)
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Apply polynomial expressions to geometric representations (#3)
Define and apply properties of integer exponents of real numbers, including
scientific notation (#4)
Add and subtract polynomials of varying degree of single variable and several
variables then simplify result (#5)
Multiply and divide polynomials of varying degree of single variable and several
variables then simplify result if applicable (#5)
14. Factoring – (Math 098)
 Factor completely integers, monomials and polynomials using greatest common
factor (#3, 6)
 Identify prime expressions (#6)
 Utilize applicable techniques to factor binomial expressions (including difference
of squares, sum and difference of cubes) , trinomial expressions and 4-term
polynomial expressions (#6)
 Solve quadratic equations by factoring, including finding x-intercepts (#1, 7)
 Translate application problems into quadratic equations and solve (#8)
15. Rational Expressions and Equations – (Math 098)
 Determine values for which rational expressions are undefined (#9)
 Simplify rational expressions, including complex rational expressions (#10)
 Multiply and divide rational expressions (#11)
 Determine the Least Common Denominator of a set of rational expressions (#11)
 Add and subtract rational expressions (#11)
 Solve rational equations with polynomial denominators (#12)
 Translate application problems to rational equations, including work problems
and proportions and solve (#13)
16. Functions (including exponential and logarithmic) – (Math 099)
 Recognize whether a relationship given in various forms is a function (#1)
 Determine the domain and range of a function (#1)
 Understand and interpret function notation (#1)
 Evaluate functions to generate a graph (#1)
 Construct new functions using addition, subtraction, and composition (#12)
 Translate application problems to function notation equations and solve (#1)
 Graph and solve exponential functions (#13)
 Solve application problems involving exponential functions (#13)
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Find the inverse of a function (#11)
Define and identify one-to-one functions algebraically and graphically (#11)
Convert exponential expressions to logarithmic form and convert logarithms to
exponential form (#14)
Calculate the value of logarithms and natural logarithms
Convert logarithms of products, quotients and powers to the sum, difference or
product of logarithms, and conversely (#14)
Graph and solve logarithmic equations (#15)
17. Systems of Equations – (Math 099)
 Solve 2x2 systems of linear equations graphically (#2)
 Solve 2x2 systems of linear equations by substitution (#2)
 Solve 2x2 systems of linear equations by elimination (#2)
 Solve 3x3 systems of linear equations (#2)
 Translate application problems to 2x2 or 3x3 systems of equations and solve (#2)
18. Compound Inequalities – (Math 099)
 Identify the union and intersection of two or more data sets (#3)
 Solve linear inequalities in one variable, including those involving “and” and “or”,
state answers using interval notation (#3)
 Solve linear inequalities in two variable graphically (#3)
 Solve absolute value equations (#4)
 Solve absolute value inequalities (#4)
 Translate application problems to linear inequalities in one variable and solve
(#3)
19. Radical Expressions and Equations – (Math 099)
 Convert radical expressions to expressions with rational exponents (#5)
 Simplify rational exponent expressions (#5)
 Multiply and divide rational exponent expressions (#5)
 Simplify radical expressions, rationalizing denominator if necessary (#5)
 Add and subtract radical expressions (#5)
 Multiply and divide radical expressions (#5)
 Solve equations in one variable containing one or two radicals (#6)
 Add and subtract complex numbers (#7)
 Multiply and divide complex numbers (#7)
20. Quadratic Equations – (Math 099)
 Solve quadratic equations by square root property (#8)
 Solve quadratic equations by completing the square (#8)
 Solve quadratic equations by quadratic formula (#8)
 Determine the number of solutions to a quadratic equation by calculating the
discriminant (#8)
 Solve application problems using quadratic equations (#9)
 Solve quadratic equations graphically by completing the square (#10)
 Solve quadratic equations graphically by calculating the vertex (#10)