MAT 027 - Mastery of Math III
Course Department: Mathematics
Last Date of Approval: Summer 2018
3 Credits
Total Lecture Hours: 45
Total Lab Hours: 0
Total Clinical Hours: 0
Total Work-Based Experience Hours: 0
Course Description:
The first unit of this course includes the study of basic operations on integers, the properties of arithmetic, slope of a line, and simple word problems. The second unit includes the study of exponents; simplifying and solving algebraic expressions and equations; calculating perimeter, area, and volume of geometric figures; and graphing linear equations. The third unit includes the study of exponents, scientific notation, triangles, and their angles, and solving and graphing linear equations, inequalities, and systems. This course will also help students gain mathematical literacy which will be of vital significance when making important life decisions. In addition, this course will help with any career that involves mathematics, decision making, or problem solving. This course does not meet graduation requirements for certificate, diploma, general studies, or associate degree programs.
Prerequisites: ALEKS score from 10 to 14, or C grade in MAT 026 - Mastery of Math II , or B grade in MAT 023 - Mastery of Math I
Mode(s) of Instruction: traditional/face-to-face, virtual, and/or online
Credit for Prior Learning: There are no Credit for Prior Learning opportunities for this course.
Course Fees: ebook/Access Code: $120.00
Common Course Assessment(s): Students take a final exam within the ALEKS software for each module over the topics assigned to that module. Students are required to pass the final with 75% or higher to move on to the next module.
Student Learning Outcomes and Objectives:
Module 3:
Outcome 1: Calculate accurately (add, subtract, multiply, and divide) with real numbers.
Task 1: Add and subtract integers and signed fractions.
Task 2: Multiply and divide integers and signed fractions.
Task 3: Evaluate expressions using the order of operations.
Task 4: Solve problems using ratios and percentages.
Task 5: Estimate a sum, difference, product, or quotient.
Outcome 2: Solve linear equations using properties of real numbers.
Task 1: Combine like terms to simplify expressions.
Task 2: Use the additive property to solve equations.
Task 3: Use the multiplicative property to solve equations.
Task 4: Use the distributive property to solve equations.
Task 5: Add fractions with variables and common denominators.
Outcome 3: Use the Cartesian coordinate system to identify points and slopes.
Task 1: Read a point in the coordinate plane.
Task 2: Create an x-y table for a linear equations.
Task 3: Find the slope of a line given the graph.
Module 4:
Outcome 1: Calculate the perimeter, area, and volume of polygons/polyhedrons.
Task 1: Calculate the perimeter and area of polygons.
Task 2: Calculate the length of a side of a polygon from the perimeter or area.
Task 3: Calculate the surface area and volume of rectangular prisms and cubes.
Task 4: Identify properties of geometric figures.
Outcome 2: Apply properties of real numbers and exponents to solve linear equations and inequalities.
Task 1: Find percentages and use them to solve problems.
Task 2: Use similar triangle and proportions to solve problems.
Task 3: Simplify expressions containing exponents.
Task 4: Solve linear inequalities.
Task 5: Solve linear equations.
Task 6: Translate real-world situations into mathematical expressions and equations.
Outcome 3: Construct graphs of linear equations and inequalities.
Task 1: Determine the equation of a line using the slope and y-intercept.
Task 2: Graph linear equations.
Task 3: Find intercepts.
Task 4: Graph linear inequalities on a number line.
Module 5:
Outcome 1: Solve problems involving geometric area and angles.
Task 1: Calculate area of inscribed figures.
Task 2: Identify acute, obtuse, and right angles.
Task 3: Obtain an angle measure for a triangle with an extended side.
Task 4: Identify parallel and perpendicular lines.
Outcome 2: Solve linear equations and inequalities in one variable and solve formulas for a specified variable.
Task 1: Solve a linear equation.
Task 2: Solve a linear inequality.
Task 3: Graph inequalities (including compound inequalities) on the real number line.
Task 4: Solve an absolute value equation.
Task 5: Solve a formula for a specified variable, in terms of the other variable(s).
Outcome 3: Solve and graph systems of linear equations and inequalities in two variables.
Task 1: Obtain the slope and intercept(s) of a line, given its equation in one or two variables.
Task 2: Obtain the equation of a line in two variables, given a slope and a point, or given two points.
Task 3: Graph a linear equation in one/two variables on the xy plane.
Task 4: Graph linear inequalities in one/two variables on the xy-plane.
Task 5: Identify parallel and perpendicular lines and utilize characteristics of parallel/perpendicular lines to find slope.
Task 6: Classify and solve systems of linear equations algebraically and/or graphically.
Task 7: Solve a system of linear inequalities graphically.
Outcome 4: Express decimal values in scientific notation and exponential form using both positive and negative exponents.
Task 1: Use the product rule of exponents (i.e. adding exponents for expressions with the same base).
Task 2: Use the quotient rule of exponents (i.e. subtracting exponents for expressions with the same base).
Task 3: Use the power rule (aka “power to a power” rule) of exponents.
Task 4: Use the “power of a product or quotient” rule.
Task 5: Use a combination of two or more rules of exponents.
Task 6: Employ scientific notation with positive and negative exponents through proper use of power, product and quotient rules of exponents.
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