Developmental Mathematics Redesign Effective January, 2012
Included in this document: • Overview of the redesign plan.............................................................2 • Crosswalk from MTH to MTE courses..................................................4 • Flow of MTE courses...........................................................................6 • Final exam policies, grading scales, and grade reporting.........................7 • Placement testing policies....................................................................9 • Financial aid.......................................................................................9 • Course content summaries................................................................10
Overview of the Redesign Plan The Mathematics Department will be offering the newly developed one-credit MTE courses beginning January, 2012. Each course is a prerequisite to the next. The new courses are as follows: BSK 1 Whole Numbers MTE 1 Operations with Positive Fractions MTE 2 Operations with Positive Decimals and Percents MTE 3 Algebra Basics MTE 4 First Degree Equations and Inequalities in One Variable MTE 5 Linear Equations, Inequalities and Systems of Linear Equations in Two Variables MTE 6 Exponents, Factoring, and Polynomial Equations MTE 7 Rational Expressions and Equations MTE 8 Rational Exponents and Radicals MTE 9 Functions, Quadratic Equations and Parabolas A student may not register for more than one BSK or MTE course in the same four-week session. The only exception would be for students specifically registered for a computer only class. MTE courses will be offered in four-week sessions as follows: Number of Days per Week
Length of Class
1
5 hours
2
2 hours 5 minutes
3 4 (2nd 8 weeks)
1 hour 15 minutes 55 minutes
Breaks
Number of Sessions
Number of Weeks
Final Exam Day
3
3
Day 3
7
3.5
Day 7
11 15
3.67 3.75
Day 11 Day 15
Three 10 minute breaks One 10 minute break None None
The final exam must be administered on the specified day without exception. The different modes of instruction include: • Lecture only • Lecture & Computer • Computer only • Distance learning (very limited for Spring 2012)
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Definitions of Class Structure Beginning Spring Semester 2012 BSK1/MTE 1 – MTE 9 Classes, Sections 01 – 19: Lecture Only Lecture only classes will meet solely in lecture classrooms, with no computer lab. Students may register for and complete only one BSK/ MTE lecture only class in a four-week session. Students must take their final exam on the one scheduled test date for their class section. BSK1/MTE 1 – MTE 9 Classes, Sections 20 – 39: Lecture & Computer Lecture & Computer classes will meet in a combination of lecture classrooms and computer labs. Students may register for and complete only one BSK/MTE lecture & computer class in a four-week session. Students must take their final exam on the one scheduled test date for their class section. BSK1/MTE 1 – MTE 9 Classes Designated as Distance Learning (DL) BSK 1/MTE 1 – MTE 9 sections designated as “distance learning” (DL) will follow different time constraints. Details will be provided by the instructor in the syllabus and in course orientation materials for that section. BSK1/MTE 1 – MTE 9 Classes, Sections 40 – 99: Computer Only Computer only classes will meet solely in computer labs. Instructors of computer only sections will announce to their students the option of registering for, paying for, and completing more than one BSK/MTE class within the four-week session.
Placement for Students Who Have Taken the Compass Placement Test within the Last Two Years, but Have Not Enrolled in a MTH Class
If you score this COMPASS placement level
You may register for this MTE course
1
BSK 1
2
MTE 3
3
MTE 3
3 with a score of 45-47*
MTE 7
*A student placing in Level 3 with a score of 45-47 may be eligible to register for MTE 7. The student should see an advisor. Students placing above level 3 may register for the appropriate college credit level course.
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MTH to MTE Conversions for Spring Semester 2012 for Students Currently (or Previously) Enrolled in MTH Classes
NON-PRISMM CLASSES If you have completed this MTH course with an S
You may enroll in this MTE course
You may enroll in this college level course
MTE 3
MTH 50 MTH 103 MTH 120 MTH 121
MTH 03
MTE 7
MTH 115 MTH 126 MTH 146 MTH 150 MTH 151 MTH 152 MTH 170
MTH 04
N/A
MTH 163 MTH 166
N/A
MTH 115 MTH 150 MTH 151 MTH 152 MTH 163 MTH 166 MTH 170
MTH 02
MTH 05
If you receive an R or U in this MTH course
You must enroll in this MTE course
MTH 02
BSK 1
MTH 03
MTE 3
MTH 04
MTE 7
MTH 05
Must take the new Placement Test to determine the appropriate MTE course in which to enroll
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PRISMM CLASSES If you have successfully completed this module
You may enroll in this MTE course
Module 1
MTE 1 (followed by MTE 3; MTE 2 will not be required)
Module 2
MTE 3
Module 3
MTE 3
Module 4
MTE 3
You may enroll in this college level course
MTE 5
MTH 50 MTH 103 MTH 120 MTH 121 MTH 126
Module 6
MTE 6
MTH 146 MTH 150 MTH 151 MTH 152
Module 7
MTE 6
Module 8
MTE 7
Module 9
MTE 8
Module 10
MTE 9
Module 11
MTE 9
Module 12
N/A
Module 5
MTH 115 MTH 116 MTH 170
MTH 163 MTH 166
Provided the modules have been taken in sequence, a student that unsuccessfully completes a module (<75%) will follow the guidelines for the highest module completed successfully. If the modules were not completed in sequence, the student must follow the guidelines for the highest module completed successfully in sequence. These students may opt to take the new Placement/Diagnostic Test, but must follow the outcome of the test results, regardless of the chart guidelines. Once students begin in the MTE courses, they will follow the chart to flow within MTE courses and outward to credit courses as it appears on the following page.
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Final Exam Policies and Grading Final Exam Who creates the final exam? Common final exams have already been created for each course and will be delivered to the instructor before the test day of each four-week session. Who should take the final exam? All students are required to take the final exam for each BSK and MTE course—there are no exemptions. When should the final exam be administered? The final exam will be administered on the specified day of each section of the four-week session without exception. Each four-week session will have one final exam test date which will occur on the last class meeting for that section. The instructor will provide details of the testing policy on the syllabus and at the first class meeting. For sections using MyMathLab, will there be prerequisites similar to those in PRISMM for a student to move through the homework/quizzes/checkups in MyMathLab? If an instructor imposes prerequisites in MyMathLab similar to PRISMM (i.e. a student must score at least____ on homework 1 to move to homework 2, or score at least_____ on checkup 1 to move, etc.), there can be no prerequisites imposed in order for the student to take the final exam on the specified day, regardless of whether the student has met the requirements in the syllabus. A student cannot be blocked from taking the final exam on the specified day–ready or not. What happens if a student misses the final exam? If a student misses the final exam, a grade of U must be assigned to that student, and grades must be submitted on time. If the student is able to make-up the final exam before the first day of the next four week session, a Change of Grade form may be completed. It will be the instructor’s responsibility to inform the subsequent instructor that the student has fulfilled the prerequisite course, since there will not be enough time for the changed grade to be reflected in PeopleSoft. Are students allowed to retake the final exam? There are no retakes of the final exam. What is the calculator policy for the new classes and the final exam? Students will not be allowed to use calculators for BSK 1 or MTE 1 – MTE 3. Students may use a scientific calculator (with graphing calculators optional) for MTE 4 – MTE 6. Graphing calculators are required for MTE 7 – MTE 9. In what format(s) are the exams? There will be both computer and pencil-and-paper versions of the final exams. Most questions are open-ended questions. If you are teaching a computer-aided or self-paced section that does not happen to meet in a lab on test day, you will give a paper-and-pencil version of the test. How will the final exams be graded? Exams will be hand-graded by the instructor. The student will receive for each problem: full credit half credit no credit
for no mistakes for one minor mistake for major or multiple mistakes
Who retains the completed final exams? Final exams will be submitted to a designated faculty member for review.
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Grading When will grades be awarded? Grades will be awarded at the end of every four week session without exception. Grades must be submitted within 24 hours of completion of the final exam. What grades will be awarded to students in the BSK and MTE courses? Only grades of S or U will be assigned. R is no longer used under any circumstances. What is the weight of the final exam? The final exam must count 75% of the final course grade. What makes up the remaining 25% of the final grade? The remaining 25% of the course grade is determined as the individual instructor deems appropriate. The instructor may use homework, quizzes, or some other academic work. Can attendance be included as part of the final course grade? Each instructor will now be responsible for his/her own attendance certifications. Instructors will be prompted to submit these certifications at the proper point during every four-week session. However, attendance may not be used in determining the final course grade. Is there a minimum score on the final exam? Students must demonstrate mastery by scoring at least 75% on the final exam. This minimum score has been set by the VCCS. How will the final course grade be calculated? The final course grade will be assigned as follows: The student will receive a grade of: S
if the overall average (including the final exam) is at least 75% AND the final exam score is at least 75%
if the overall average (including the final exam) is below 75% or U if the student scores below 75% on the final exam (regardless of the overall average) or if the student misses the final exam When should grades be reported to PeopleSoftâ&#x201E;˘? Grades should be submitted within 24 hours of the completion of the final exam without exception. All grades must be turned in on time in order for appropriate reports to be run before the next four-week session. An instructor may not wait on individual students to make-up the final exam. Each student will be assigned a gradeâ&#x20AC;&#x201D;S or U. I grades will not be assigned. What happens if a student is unsuccessful and must repeat the course? A student may re-register for the same course if unsuccessful on the first attempt. If the student is unsuccessful on the second attempt, the third attempt must be approved by the Dean. If the student is unsuccessful on the third attempt, the student may no longer take that specific course at the College. What happens if a student has registered for all classes at the beginning of the semester and fails a course during any given four-week session? A student must add/drop the classes in the subsequent four-week sessions to re-enroll in the failed course and add/drop to adjust the remaining courses. For example, a student has registered for MTE 1 , MTE 2 , MTE 3 , and MTE 4 at the beginning of the semester to be taken in the first, second, third, and fourth four week sessions respectively. The student passes MTE 1 the first four weeks and proceeds to MTE 2 the second four weeks. The student fails MTE 2. The student must drop MTE 4, move MTE 3 to the fourth four-week session, and re-enroll in MTE 2 for the third four-week session. If there is a section of the repeated course offered in the same mode and during the same time slot for that next four-week session, and a seat is available, the student may enroll. If there is no section of the course to be 8
repeated available the next four-week session, a student has the option of dropping into a lab setting to complete the repeated course and then rotate into a section in the future, or a student can register for the necessary course in either a different time slot or in a different mode (i.e. lecture instead of computer aided). If a student fails a course, will he/she be allowed to pick up at the point at which he/she left off when the course is repeated? As with any other math course, a student who fails a BSK or MTE class must repeat the course in its entirety. The only exception will be for computer only sections. The instructor will provide details in the syllabus and at the first class meeting. Will the attendance certification still be in effect for each four-week session? Attendance certifications will still be required twice during each four-week session. Admissions and Records will prompt instructors for these certifications as they do for semester classes. Each instructor is responsible for the certifications for all students on the roster. Students will be submitted for unofficial withdrawal if they have missed 160 minutes (20% of 800 minutes) of instruction without contacting the instructor and submitting academic work. The following table translates these minutes into class meetings and summarizes them for each of the class meeting scenarios. According to Admissions and Records, a student will be administratively withdrawn if: Number of Days per Week
Number of Class Sessions
Length of Class
Number of Missed Minutes
1 2 3 4 (2nd 8 weeks)
3 7 11 15
5 hours 2 hours and 5 minutes 1 hour and 15 minutes 55 minutes
160 160 160 15
Number of Missed Classes without Contact or Academic Work 1 class meeting 2 class meetings 2 1/2 class meetings 3 class meetings
Placement Testing Policies The current guidelines will apply for the new placement test until the new placement instrument is online for both Math and English: â&#x20AC;˘ A student must wait four months before retaking the test (within a one year period). â&#x20AC;˘ Placement test scores will remain valid for two years. â&#x20AC;˘ A student may retake the new placement test after the two year validity has passed.
Financial Aid Students on financial aid will need to register for all credits at the beginning of the semester. If a student fails a course, the student must add/drop courses to maintain the same total number of credits, or their financial aid may be affected. The following is the handout which was given to Campus Implementation Leads directly from the VCCS.
Financial Aid Implications of Developmental Education Reform Below is a summary of the most pertinent financial aid issues relative to developmental education redesign. Enrollment Status: Enrollment status changes appear to be the most problematic issues resulting from redesign of developmental education. Colleges in the VCCS lock enrollment as of term census date for purposes of calculating the Federal Pell Grant. This practice is in compliance with federal regulations. To be consistent, enrollment status for other aid types is generally determined at the same time. Class additions and partial enrollment withdrawals after census locking are not considered and do not affect aid eligibility. As a result, it is extremely important that students are enrolled in all coursework (developmental or otherwise) as of census date for the term. Substitutions after census are permissible but must be even swaps. On the other hand, if a student is dropped from or drops a course or module (i.e., never attended) which alters the enrollment status, aid eligibility must be reviewed to exclude the course(s) or module(s) never attended. Aid must often be reduced and some aid types removed if status is now too low for that aid type. If the student were to add a course or module after census that resulted in an increased course load, the additional course or module could not be covered. Careful enrollment planning and registration of all anticipated courses by the term census date will be necessary to ensure that all courses and modules can be covered and no aid must be returned.
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Satisfactory Academic Progress (SAP): The changes being considered for developmental education will have a minimal effect on measuring satisfactory academic progress. Colleges will continue to evaluate progress at the end of each semester. As has always been the case, incomplete or unsatisfactory modules will count against students in this evaluation but will not be known until the end of the semester when the SAP process is run. On a more positive note, if the modules consist of only one credit after the redesign, the negative effect on SAP evaluation could be reduced. Instead of a three-credit failure, the student might have a one-credit failure and a two-credit success. Repeated Coursework: Federal regulations relative to repeated coursework have just changed and are effective July 1, 2011. In summary, a student can continue to take a course and receive aid for it until the course is passed. A student may repeat a passed course one time as long as it is for the purpose of meeting an academic standard. All attempts are included in satisfactory academic progress measures. Return to Title IV (R2T4): With the recent changes in R2T4 regulations that become effective July 1, 2011, modular work or compressed courses will be treated differently and will almost certainly result in increased R2T4s for term-based programs. In short, simply completing a single module or compressed course no longer precludes the need for R2T4 as it has in the past. The student must complete all of the days in the payment period or period of enrollment that he/she was scheduled to complete. The student must attend through the 60% point of the scheduled period of enrollment.
J. Sargeant Reynolds Community College Course Content Summary Course Prefix and Number: BSK 1
Credits: 1
Course Title: Whole Numbers
Course Description (as it should appear in the catalog) Covers whole number principles and computations. Develops the mathematical mastery necessary for MTE 1. Credits not applicable toward graduation. Lecture 4 hours per week for Âź semester. General Course Purpose This course is designed to provide understanding and practice in whole numbers and operations on whole numbers. Course Objectives (Each item should complete the following sentence.) Upon completing the course, the student will be able to: a. Identify place value of whole numbers. b. Add whole numbers without aid of a calculator. c. Subtract whole numbers without aid of a calculator. d. Multiply whole numbers without aid of a calculator. e. Divide whole numbers, giving answers in terms of quotient and remainder, without aid of a calculator. f. Use order of operations to simplify numeric expression. g. Determine appropriate whole number operation, given a sample situation. h. Round numbers to the indicated precision. i. Find the average of a list of numbers. j. Find the perimeter and area of a rectangle. Major Topics to be Included a. Place value b. Addition c. Subtraction d. Multiplication e. Division f. Estimation g. Order of operations h. Applications â&#x20AC;&#x201C; area, perimeter, average Effective Date of Course Content Summary: January 2, 2012 10
Course Prefix and Number: MTE 1
Credits: 1
Course Title: Operations with Positive Fractions
Course Description (Each item should complete the following sentence.) Includes operations and problem solving with proper fractions, improper fractions, and mixed numbers without the use of a calculator. Emphasizes applications and includes U.S. customary units of measure. Credit is not applicable toward graduation. Prerequisite: Placement recommendation or BSK1. Lecture 4 hours per week for Âź semester. General Course Purpose This course is designed to provide understanding and practice in fractions and operations on fractions. Course Objectives Upon completing the course, the student will be able to: a. Express parts of a whole using fraction notation. b. Convert between improper fractions and mixed numbers. c. Express repeated factors using exponents. d. Find the prime factorization of a given number. e. Write fractions in simplest form. f. Compare two quantities in the form of a ration or rate in simplest form. g. Find the least common multiple (LCM) of two or more whole numbers. h. Find the least common denominator (LCD) of two or more fractions. i. Determine the relationship (<, >, =) between two fractions with unlike denominators. j. Add and subtract fractions and mixed numbers with like denominators. k. Add and subtract fractions and mixed numbers with unlike denominators. l. Multiply fractions and mixed numbers. m. Divide fractions and mixed numbers. n. Simplify expressions involving fractions using order of operations. o. Solve applications using U.S. customary units of measurement. Major Topics to be Included a. Writing, simplifying, and comparing fractions b. Performing operations with fractions c. Solving applications using U.S. customary units of measurement Effective Date of Course Content Summary: January 2, 2012
Course Prefix and Number: MTE 2
Credits: 1
Course Title: Operations with Positive Decimals and Percents
Course Description (as it should appear in the catalog) Includes operations and problem solving with positive decimals and percents. Emphasizes applications and includes U.S. customary and metric units of measure. Credits not applicable toward graduation. Prerequisite: placement recommendation or MTE 1. Lecture 4 hours per week for Âź semester. General Course Purpose This course is designed to provide understanding and practice in decimals and operations on decimals, to provide understanding and practice using percents and units of measurement. Course Objectives (Each item should complete the following sentence.) Upon completing the course, the student will be able to: 1. Convert decimals between standard notation and word notation. 2. Identify place values in decimals. 3. Add and subtract decimals. 4. Multiply decimals. 5. Divide decimals.
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6. Simplify expressions using order of operations. 7. Round decimals to a specific place value. 8. Estimate sums, differences, products, and quotients with decimals. 9. Write parts of a whole using percent notation. 10. Convert among fractions, decimals and percents. 11. Order a list of fractions and decimals from smallest to largest. 12. Calculate all values in the basic percent problem. 13. Calculate percent increase and percent decrease. 14. Calculate sales tax and commission. 15. Calculate simple interest. 16. Read and interpret information from a pie graph. 17. Calculate the percentage denoted by a pie graph. 18. Read and interpret information from a bar graph. 19. Read and interpret information from a line graph. 20. Convert within the U.S. system. 21. Convert within the metric system. 22. Convert between U.S. and metric units using conversion tables. 23. Convert units of time. 24. Convert between Fahrenheit and Celsius temperatures. 25. Solve application problems using U.S. and metric units of measurement. Major Topics to be Included 1. The meaning of decimal numbers 2. Operations with decimals 3. Estimating decimals 4. Relationship among fractions, decimals, and percents 5. Basic percent problems 6. Basic graphs 7. Units of measurement Effective Date of Course Content Summary: January 2, 2012
Course Prefix and Number: MTE 3
Credits: 1
Course Title: Algebra Basics
Course Description (as it should appear in the catalog) Includes basic operations with algebraic expressions and solving simple algebraic equations using signed numbers with emphasis on applications. Credits not applicable toward graduation. Prerequisite: Placement recommendation or MTE 2. Lecture 4 hours per week for Âź semester. General Course Purpose This course is designed to introduce the student to integers, variables, algebraic expressions, equations and their applications. Course Objectives (Each item should complete the following sentence.) Upon completing the course, the student will be able to: a. Determine the absolute value of a number. b. Express repeated factors using exponents. c. Evaluate powers of numbers. d. Add, subtract, multiply, and divide signed numbers. e. Use the proper order of operations to simplify expression containing multiple operations on signed numbers, including powers and square roots. f. Convert between integer powers of 10 and equivalent decimal numbers. g. Convert numbers between scientific notation and standard notation. h. Identify the properties of real numbers (Commutative, Associative, Distributive, Identity, and Inverse Properties).
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i. Simplify an algebraic expression by combining like terms. j. Simplify algebraic expressions using the order of operations. k. Evaluate a formula or algebraic expression for given values of the variables. l. Solve one-step equations using rational numbers. m. Solve one-step equations using percents. n. Solve problems using proportions. o. Solve application problems including finding perimeter, area, and volume. Major Topics to be Included a. Absolute value b. Square root introduction c. Signed numbers d. Scientific notation e. Algebraic expressions f. Linear equation solutions g. Proportion problems h. Perimeter, area, and volume Effective Date of Course Content Summary: January 2, 2012
Course Prefix and Number: MTE 4
Credits: 1
Course Title: First Degree Equations and Inequalities in One Variable
Course Description (as it should appear in the catalog) Includes solving first degree equations and inequalities containing one variable, and using them to solve application problems. Emphasizes applications and problem solving. Credits not applicable toward graduation. Prerequisite: Placement recommendation or MTE 3. Lecture 4 hours per week for Âź semester. General Course Purpose This course is designed to give the student understanding and practice in solving first degree equations and inequalities (with emphasis on the steps involved) and their applications. Course Objectives (Each item should complete the following sentence.) Upon completing the course, the student will be able to: a. Solve first degree equations in one variable using the Addition or Multiplication properties of Equality. b. Solve first degree equations in one variable using the Addition and Multiplication properties of Equality. c. Solve first degree equations in one variable that contain parentheses. d. Solve first degree equations in one variable with the variable on both sides of the equal sign. e. Solve first degree equations in one variable and identify the solution to an equation as finite, the empty set, or all real numbers. f. Solve a formula or equation for one of its variables using the Addition and/or Multiplication Property of Equality. g. Solve first degree absolute value equations containing a single absolute value. h. Solve first degree inequalities in one variable stating the solution using inequality notation and interval notation. i. Solve first degree inequalities in one variable and graph the solution on a real number line. j. Solve an application using a single first degree equation or inequality. Major Topics to be Included a. First degree equations in one variable b. Formulas c. First degree absolute value equations d. First degree inequalities e. Applications of first degree equations and inequalities Effective Date of Course Content Summary: January 2, 2012 13
Course Prefix and Number: MTE 5 Credits: 1
Course Title: Linear Equations, Inequalities and Systems of Linear Equations in Two Variables
Course Description (as it should appear in the catalog) Includes finding the equation of a line, graphing linear equations and inequalities in two variables and solving systems of two linear equations. Emphasizes writing and graphing equations using the slope of the line and points on the line, and applications. Credits not applicable toward graduation. Prerequisite: Placement recommendation or MTE 4. Lecture 4 hours per week for Âź semester. General Course Purpose This course is designed to give the student understanding and practice in finding equations of lines, graphing lines and inequalities, and solving systems of equations. Course Objectives (Each item should complete the following sentence.) Upon completing the course, the student will be able to: a. Determine the coordinates of a point plotted on the coordinate plane. b. Determine whether an ordered pair is a solution to an equation in two variables. c. Graph a linear equation by finding and plotting ordered pair solutions. d. Identify the x- and y-intercepts of a graph. e. Graph a linear equation by plotting intercepts. f. Graph an equation given in slope-intercept form. g. Graph a horizontal or vertical line given its equation. h. Find the slope of a line given two points on the line. i. Find the slope of a line given its equation or graph. j. Find the slope of horizontal and vertical lines. k. Write an equation of a line in slope-intercept form given the slope and the y-intercept. l. Use point-slope form to write an equation of a line in slope intercept form given the slope and a point on the line or given two points on the line. m. Write the equation of a horizontal or vertical line. n. Find the equation of a line parallel or perpendicular to a given line, through a given point. o. Determine if an ordered pair is a solution of a system of equations in two variables. p. Solve systems of linear equations by graphing. q. Solve by elimination using substitution or addition. r. Identify a system of linear equations as consistent and independent, consistent and dependent, or inconsistent. s. Evaluate y = f(x) for specific values of x. t. Given the graph of y = f(x), evaluate f(x) for specific values of x. u. Given the graph of y = f(x), find x for specific values of f(x). v. Solve application problems that require linear equations, inequalities and systems of linear equations in two variables. Major Topics to be Included a. Rectangular coordinate system b. Graphs of linear equations and inequalities c. Slope d. Equations of lines e. Systems of linear equations f. Function notation g. Applications of linear equations, inequalities and systems of equations Effective Date of Course Content Summary: January 2, 2012
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Course Prefix and Number: MTE 6
Credits: 1
Course Title: Exponents, Factoring and Polynomial Equations
Course Description (as it should appear in the catalog) Includes techniques of factoring polynomials and using these techniques to solve polynomial equations. Emphasizes applications using polynomial equations solved by factoring. Credits not applicable toward graduation. Prerequisite: Placement recommendation or MTE 5. Lecture 4 hours per week for ¼ semester. General Course Purpose This course is designed to give the student understanding and practice in evaluating, combining, and factoring polynomials. Course Objectives (Each item should complete the following sentence.) Upon completing the course, the student will be able to: a. Evaluate the product or quotient of two exponential expressions. b. Evaluate the power of a power of an exponential expression. c. Evaluate exponential expressions that contain negative exponents. d. Evaluate exponential expressions that contain combinations of products, quotients, power of a power, and negative exponents. e. Multiply and divide numbers in scientific notation. f. Identify an expression as a monomial, binomial, trinomial, or polynomial. g. Add, subtract, multiply, and divide monomials using the rules of exponents. h. Add, subtract, and multiply binomials, trinomials, and combinations of binomials and trinomials. i. Find the greatest common factor from a list of terms and from a polynomial. j. Factor a polynomial by grouping. k. Factor trinomials of the form x2 + bx + c. l. Factor trinomials of the form ax2 + bx + c, a≠1. m. Factor a difference of squares. n. Factor a sum or difference of two cubes. o. Solve polynomial equations using factoring techniques. p. Solve application problems involving polynomial equations and factoring. Major Topics to be Included a. Exponents b. Operations on polynomials c. Factoring of polynomials d. Polynomial equations e. Polynomial applications Effective Date of Course Content Summary: January 2, 2012
Course Prefix and Number: MTE 7
Credits: 1
Course Title: Rational Expressions and Equations
Course Description (as it should appear in the catalog) Includes simplifying rational algebraic expressions, solving rational algebraic equations and solving applications that use rational algebraic equations. Credits not applicable toward graduation. Prerequisite: Placement recommendation or MTE 6. Lecture 4 hours per week for ¼ semester. General Course Purpose This course is designed to give the student understanding and practice in simplifying and combining rational expressions, solving rational equations, and using rational equations in applications. Course Objectives (Each item should complete the following sentence.) Upon completing the course, the student will be able to: a. Identify the real values of the variable for which a rational algebraic expression having a linear or quadratic denominator is undefined. b. Express a rational algebraic expression having negative exponents as an equivalent expression without negative exponents. c. Simplify a rational algebraic expression. 15
d. Evaluate a rational algebraic expression given specific integral values for each variable. e. Perform addition and subtraction of rational algebraic expressions having like denominators. f. Find the Least Common Denominator (LCD) of two or more rational algebraic expressions. g. Perform addition and subtraction of rational algebraic expressions with unlike denominators. h. Multiply rational algebraic expressions and express the product in simplest terms. i. Use factorization to divide rational algebraic expressions and express the quotient in simplest terms. j. Simplify complex fractions. k. Divide a polynomial by a monomial. l. Perform polynomial long division having binomial divisors of the form ax + b. m. Solve rational algebraic equations. n. Write a rational equation to match the information given in an application problem. o. Solve an application problem using rational equations. Major Topics to be Included a. Rational algebraic expressions b. Combination of rational algebraic expressions c. Rational algebraic equations d. Applications of rational algebraic equations Effective Date of Course Content Summary: January 2, 2012
Course Prefix and Number: MTE 8
Credits: 1
Course Title: Rational Exponents and Radicals
Course Description (as it should appear in the catalog) Includes simplifying radical expressions, using rational exponents, solving radical equations and solving applications using radical equations. Credits not applicable toward graduation. Prerequisite: Placement recommendation or MTE 7. Lecture 4 hours per week for ¼ semester. General Course Purpose This course is designed to give the student understanding and practice in evaluating radical expressions, combining radical expressions, and solving radical equations. Course Objectives (Each item should complete the following sentence.) Upon completing the course, the student will be able to: a. Convert between radical and rational exponent form. b. Calculate (estimate) square and nth roots using a calculator. c. Simplify using the properties of rational exponents. d. Simplify square and nth roots of variable expressions e. Simplify radicals by using the multiplication and/or division property of radicals. f. Define like radicals. g. Combine and simplify like radicals. h. Multiply and simplify radicals. i. Simplify radicals by rationalizing a denominator with one or two terms. j. Solve radical equations. k. Define i=√-1. l. Define imaginary numbers (e.g. √-25). m. Solve problems involving right triangles and/or the Pythagorean Theorem. n. Solve problems involving the distance formula. Major Topics to be Included a. Radical and rational exponent forms b. Estimation and simplification of radical expressions c. Operations on radical expressions d. Rationalization of denominators e. Radical equations f. Imaginary numbers g. Applications using radicals, including triangles and distance Effective Date of Course Content Summary: January 2, 2012
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Course Prefix and Number: MTE 9
Credits: 1
Course Title: Functions, Quadratic Equations, and Parabolas
Course Description (as it should appear in the catalog) Includes an introduction to functions in ordered pair, graph, and equation form. Also introduces quadratic functions, their properties and their graphs. Credits not applicable toward graduation. Prerequisite: Placement recommendation or MTE 8. Lecture 4 hours per week for ¼ semester. General Course Purpose This course is designed to introduce the student to functions and quadratics and to give them tools for understanding their properties. Course Objectives (Each item should complete the following sentence.) Upon completing the course, the student will be able to: a. Determine if a list of ordered pairs, graph, or equation is a function. b. Determine the domain and range of a function given as a list of ordered pairs. c. Determine the domain and range of a function given as a graph or an equation. d. Evaluate y = f(x) for constant values of x and for specific monomials and binomials. e. Find the roots of quadratic equations of the form ax2 + c = 0. f. Find the roots of quadratic equations of the form ax2 + bx + c = 0 when the discriminant is a positive perfect square, positive but not perfect square, zero, or negative. g. Describe the roots of a quadratic based upon the discriminant in all cases. h. Write a quadratic function in vertex from y = a(x–h)2 + k by completing the square for quadratics. . i. Find the vertex of a quadratic equation y = ax2 + bx + c using the formula method –b , f –b 2a 2a j. Determine whether the parabola opens upward or downward. k. Plot the vertex of the parabola. l. Determine the axis of symmetry for the parabola. m. Plot the x- and y- intercepts of the parabola and complete the graph with additional points as needed. n. Solve problems involving area optimization. o. Solve problems involving revenue optimization. p. Solve problems involving the motion of falling objects.
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Major Topics to be Included a. Functions b. Domain and Range c. Roots of Quadratics d. Features of Parabolas e. Vertex Form of Quadratics f. Applications from Geometry, Economics, Applied Physics and Other Disciplines Effective Date of Course Content Summary: January 2, 2012
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