Technical Math 1A

Course Outcome Summary

Course Information

Description
Topics include: solving linear , quadratic, and rational equations; graphing; formula
rearrangement; solving systems of equations; percent; proportions; and operations on
polynomials. Emphasis will be on the application of skills to technical problems. Successful
completion of College Technical Mathematics 1A and College Technical Mathematics 1B is the
equivalent of College Technical Mathematics 1.CrLf

Types of Instruction

Exit Learning Outcomes

External Standards
AMERICAN MATHEMATICAL ASSOCIATION OF TWO YEAR COLLEGES STANDARDS
STANDARDS FOR CONTENT

Standard C-2: Symbolism and Algebra CrLfStudents will translate problem situations into their
symbolic representations and use those representations to solve problems. CrLf
Standard C-1: Number Sense CrLfStudents will perform arithmetic operations, as well as reason
and draw conclusions from numerical information. CrLf
Standard C-4: Function CrLfStudents will demonstrate understanding of the concept of function
by several means (verbally, numerically, graphically, and symbolically) and incorporate it as a
central theme into their use of mathematics. CrLf
Standard C-3: Geometry CrLfStudents will develop a spatial and measurement sense. CrLf
STANDARDS FOR INTELLECTUAL DEVELOPMENT
Standard I-1: Problem Solving Students will engage in substantial mathematical problem solving.
Standard I-2: Modeling Students will learn mathematics through modeling real-world situations.
Standard I-3: Reasoning CrLfStudents will expand their mathematical reasoning skills as they
develop convincing mathematical arguments. CrLf
Standard I-4: Connecting With Other Disciplines CrLfStudents will develop the view that
mathematics is a growing discipline, interrelated with human culture, and understand its
connections to other disciplines. CrLf
Standard I-5: Communicating CrLfStudents will acquire the ability to read, write, listen to, and
speak mathematics. CrLf
Standard I-6: Using Technology CrLfStudents will use appropriate technology to enhance their
mathematical thinking and understanding and to solve mathematical problems and judge the
reasonableness of their results. CrLf
Standard I-7: Developing Mathematical Power CrLfStudents will engage 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. CrLf

Competencies

A. Perform basic operations with real numbers
You will demonstrate your competence:
A.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
A.1. perform the arithmetic operations in proper sequence
A.2. simplify expressions using the laws of exponents
A.3. evaluate numeric expressions containing exponents
A.4. convert numbers between decimal notation and scientific and/or engineering
notation
A.5. perform arithmetic operations with numbers in scientific notation
A.6. calculate powers and roots with numbers in scientific notation
A.7. apply skill to technical problems
A.8. utilize appropriate technology
A.9. apply the process for solving technical problems according to the problem-solving
criteria (i.e. show work in a clear and logical manner, verify the solution, solution is
within stated range and reflects appropriate accuracy or precision, solution is labeled
with appropriate units)

B. Solve linear equations
You will demonstrate your competence:
B.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
B.1. solve linear equations in one variable
B.2. rearrange a formula to solve for an indicated first-degree variable
B.3. represent unknown (s) with a variable and translate English phrases into
equations
B.4. substitute given number for variables into formula or equation
B.5. apply skill to technical problems
B.6. utilize appropriate technology
B.7. apply the process for solving technical problems according to the problem-solving
criteria (i.e. show work in a clear and logical manner, you verify the solution, solution is
within stated range and reflects appropriate accuracy or precision, solution is labeled
with appropriate units)

C. Solve problems using percent and proportion
You will demonstrate your competence:
C.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
C.1. perform conversions among fractions, decimals, and percent
C.2. write an equation representing the problem
C.3. solve the equation
C.4. apply skill to technical problems
C.5. utilize appropriate technology
C.6. apply the process for solving technical problems according to the problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the solution,
solution is within stated range and reflects appropriate accuracy or precision, solution
is labeled with appropriate units)

D. Solve variation problems
You will demonstrate your competence:
D.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
D.1. identify the type of variation
D.2. write the variation equation
D.3. solve direct variation problems
D.4. solve inverse variation problems
D.5. solve joint and combined variation problems
D.6. apply skill to technical problems
D.7. utilize appropriate technology
D.8. apply the process for solving technical problems according to the problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the solution,
solution is within stated range and reflects appropriate accuracy or precision, solution
is labeled with appropriate units)

E. Perform operations polynomials
You will demonstrate your competence:
E.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
E.1. add, subtract, multiply, and divide polynomials
E.2. utilize appropriate technology
E.3. apply the process for solving technical problems according to the problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the solution,
solution is within stated range and reflects appropriate accuracy or precision, solution
is labeled with appropriate units)

F. Factor algebraic expressions
You will demonstrate your competence:
F.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
F.1. factor using the greatest common factor
F.2. factor binominals and trinominals
F.3. apply skill to technical problems
F.4. utilize appropriate technology
F.5. apply the process for solving technical problems according to the problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the solution,
solution is within stated range and reflects appropriate accuracy or precision, solution
is labeled with appropriate units)

G. Solve quadratic equations over the set of real numbers
You will demonstrate your competence:
G.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
G.1. identify coefficients of a quadratic equation in standard form
G.2. select appropriate method for solving second degree equations
G.3. generate the equation which satisfies the conditions of the problem
G.4. solve second degree equation using the selected method
G.5. select relevant solution(s)
G.6. apply skill to technical problems
G.7. utilize appropriate technology
G.8. apply the process for solving technical problems according to the problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the
solution, solution is within stated range and reflects appropriate accuracy or precision,
solution is labeled with appropriate units)

H. Perform operations with rational expressions
You will demonstrate your competence:
H.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
H.1. add, subtract, multiply, and divide rational expressions
H.2. apply skill to an applied technical problem
H.3. simplify complex fractions
H.4. utilize appropriate technology
H.5. apply the process for solving technical problems according to the problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the solution,
solution is within stated range and reflects appropriate accuracy or precision, solution
is labeled with appropriate units)

I. Solve rational equations
You will demonstrate your competence:
I.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
I.1. apply multiplication property to clear all denominators
I.2. solve equations
I.3. identify extraneous solutions
I.4. apply skill to technical problems
I.5. utilize appropriate technology
I.6. apply the process for solving technical problems according to the problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the solution,
solution is within stated range and reflects appropriate accuracy or precision, solution
is labeled with appropriate units)

J. Graph algebraic functions
You will demonstrate your competence:
J.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
J.1. determine ordered pairs from a given graph
J.2. you differentiate a function from a relation
J.3. you utilize function notation
J.4. identify range and domain of a given function
J.5. graph linear and quadratic functions on the Cartesian plane
J.6. apply skill to technical problems
J.7. utilize appropriate technology
J.8. apply the process for solving technical problems according to the problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the solution,
solution is within stated range and reflects appropriate accuracy or precision, solution
is labeled with appropriate units)

K. Relate the equation of a line to its graph
You will demonstrate your competence:
K.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
K.1. calculate the distance between two points
K.2. calculate the slope of a line given two points on the line
K.3. determine the slope of a line parallel to a given line
K.4. determine the slope of a line perpendicular to a given line
K.5. write the equation of a line using the slope-intercept form, the point-slope form, or
the two-point form
K.6. apply skill to technical problems
K.7. utilize appropriate technology
K.8. apply the process for solving technical problems according to the problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the solution,
solution is within stated range and reflects appropriate accuracy or precision, solution
is labeled with appropriate units)

L. Solve systems of equations
You will demonstrate your competence:
L.1. in an oral, written, or graphic product
Criteria: Performance will be satisfactory when you:
L.1. solve systems of two and three equations or formulas
L.2. check all solutions in the system
L.3. apply skill to technical problems
L.4. utilize appropriate technology
L.5. apply the process for solving technical problems according to the problem-solving
criteria (i.e. you show work in a clear and logical manner, you verify the solution,
solution is within stated range and reflects appropriate accuracy or precision, solution
is labeled with appropriate units)