(a) General requirements. This course is recommended
for students in Grades 11 and 12. Recommended prerequisites: Algebra
I and Geometry. This course satisfies a high school mathematics graduation
requirement. Students shall be awarded one credit for successful completion
of this course.
(b) Introduction.
(1) Career and technical education instruction provides
content aligned with challenging academic standards and relevant technical
knowledge and skills for students to further their education and succeed
in current or emerging professions.
(2) The process standards describe ways in which students
are expected to engage in the content. The placement of the process
standards at the beginning of the knowledge and skills listed for
each grade and course is intentional. The process standards weave
the other knowledge and skills together so that students may be successful
problem solvers and use mathematics efficiently and effectively in
daily life. The process standards are integrated at every grade level
and course. When possible, students will apply mathematics to problems
arising in everyday life, society, and the workplace. Students will
use a problemsolving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying
the solution, and evaluating the problemsolving process and the reasonableness
of the solution. Students will select appropriate tools such as real
objects, manipulatives, paper and pencil, and technology and techniques
such as mental math, estimation, and number sense to solve problems.
Students will effectively communicate mathematical ideas, reasoning,
and their implications using multiple representations such as symbols,
diagrams, graphs, and language. Students will use mathematical relationships
to generate solutions and make connections and predictions. Students
will analyze mathematical relationships to connect and communicate
mathematical ideas. Students will display, explain, or justify mathematical
ideas and arguments using precise mathematical language in written
or oral communication.
(3) Career development is a lifelong pursuit of answers
to the questions: Who am I? Why am I here? What am I meant to do with
my life? It is vital that students have a clear sense of direction
for their career choice. Career planning is a critical step and is
essential to success.
(4) Applied Mathematics for Technical Professionals
uses problemsolving situations, handson activities, and technology
to extend mathematical thinking and engage student reasoning. Situations
relating to technical applications provide students opportunities
to make connections with mathematics and the workplace. In addition,
students will learn the skills necessary to communicate using mathematics.
Handson activities will allow students to model, explore, and develop
abstract concepts applicable to technical careers. (Essential to this
course is the partnership between mathematics and technical teachers.)
(5) Students are encouraged to participate in extended
learning experiences such as career and technical student organizations
and other leadership or extracurricular organizations.
(6) Statements that contain the word "including" reference
content that must be mastered, while those containing the phrase "such
as" are intended as possible illustrative examples.
(c) Knowledge and skills.
(1) The student uses mathematical processes to acquire
and demonstrate mathematical understanding. The student is expected
to:
(A) apply mathematics to problems arising in everyday
life, society, and the workplace;
(B) use a problemsolving model that incorporates
analyzing given information, formulating a plan or strategy, determining
a solution, justifying the solution, and evaluating the problemsolving
process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives,
paper and pencil, and technology as appropriate, and techniques, including
mental math, estimation, and number sense as appropriate, to solve
problems;
(D) communicate mathematical ideas, reasoning, and
their implications using multiple representations, including symbols,
diagrams, graphs, and language as appropriate;
(E) create and use representations to organize, record,
and communicate mathematical ideas;
(F) analyze mathematical relationships to connect
and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas
and arguments using precise mathematical language in written or oral
communication.
(2) The student uses mathematical concepts of algebra
to explain linear and nonlinear applications in business and industry
situations. The student is expected to:
(A) calculate rise and run such as the rise and run
of stair stringers or roof pitch;
(B) distinguish the purpose and difference of a linear
and nonlinear increase and decrease of a variable with time such
as cost or profit;
(C) write systems of equations and inequalities from
reallife situations that compare "best deal opportunities" with
profit and expenses in businesses;
(D) use linear programing to maximize or minimize linear
objective function in reallife situations and determine the reasonableness
of solutions;
(E) express numbers as powers of 10 in business and
industry settings;
(F) determine the powers and roots of numbers;
(G) apply compound interest formulas related to operating
a business; and
(H) use exponential decay models to determine the depreciation
on equipment used in business and industry and explain the meaning
of models.
(3) The student applies geometric concepts to realworld
problems in technical situations. The student is expected to:
(A) identify various geometric figures in order to
identify what formulas are needed to solve situational problems;
(B) compute measurements such as area, surface area,
volume, perimeter, and circumference in order to prepare engineering
drawings for projects;
(C) use trigonometric functions such as sine, cosine,
tangent, cotangent, cosecant, and secant to calculate angles and length
of sides;
(D) apply Heron's formula for finding areas of triangles
when the height is not known;
(E) determine how changing dimensions will affect the
perimeter, area, surface area, or volume in a project;
(F) determine how angles will affect structural strength
and stability;
(G) apply right triangle relationships using the Pythagorean
Theorem, special right triangles, and trigonometry for roof construction,
building the frame of a car, or calculating machined parts;
(H) determine the materials needed for a job or project
by finding missing parts of a circle;
(I) draw orthographic and isometric views and use them
to produce engineering drawings;
(J) use crosssections, including conic sections, of
threedimensional figures to relate to plane figures in specific detail
on an engineered drawing; and
(K) explain and use auxiliary views, revolutions,
intersections, and engineered drawings.
(4) The student applies measurement to all aspects
of business and industry occupations. The student is expected to:
(A) use dimensional analysis to select an appropriate
tool to make measurements;
(B) apply accurate readings of both U.S. customary
and metric measuring devices to a problem situation;
(C) square, measure, and cut materials to specified
dimensions;
(D) draw segments to scale using an accurate scale
and measure segments that are drawn to scales;
(E) convert temperature values between Celsius and
Fahrenheit in situations involving thermodynamics; and
(F) determine length, distance, area, surface area,
volume, and weight with appropriate unit labels.
(5) The student uses mathematical processes with graphical
and numerical techniques to study patterns and analyze data related
to finance. The student is expected to:
(A) use rates and linear functions to solve problems
involving finance and budgeting, including compensations and deductions;
(B) solve problems related to local, state, and federal
taxes;
(C) analyze data to make decisions about banking and
finance;
(D) use mathematical processes with algebraic formulas,
numerical techniques, and graphs to solve problems related to job
cost analysis;
(E) identify what parameters to change such as cost
of materials, cost of labor, and work time required to improve the
overall cost of a project; and
(F) identify the most reasonable mathematical solution
using estimation.
(6) The student applies mathematical processes to design
a study and use graphical, numerical, and analytical techniques to
communicate the results. The student is expected to:
(A) interpret and present situations in terms of given
graphs and that fit graphics;
(B) apply Ohm's Law and Kirchhoff's laws to troubleshoot
electrical circuits;
(C) collect and organize data; make and interpret
scatterplots; and model, predict, and make decisions and critical
judgments; and
(D) prepare technical reports and presentations with
visual media or models, including tables, graphs, and verbal descriptions.
(7) The student applies mathematical principles of
manufacturing processes. The student is expected to:
(A) identify the line types used on engineering drawings;
(B) identify selected symbols commonly used on engineering
drawings;
(C) identify the components of engineering drawings;
(D) read, interpret, and create engineering drawings;
and
(E) use proper nomenclature when identifying engineering
or manufacturing processes.
