(a) General requirements. This course is recommended
for students in Grades 11 and 12. Prerequisite: Algebra II. 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 Science, Technology, Engineering, and Mathematics
(STEM) Career Cluster focuses on planning, managing, and providing
scientific research and professional and technical services, including
laboratory and testing services, and research and development services.
(3) Engineering Mathematics is a course where students
solve and model design problems. Students will use a variety of mathematical
methods and models to represent and analyze problems that represent
a range of real-world engineering applications such as robotics, data
acquisition, spatial applications, electrical measurement, manufacturing
processes, materials engineering, mechanical drives, pneumatics, process
control systems, quality control, and computer programming.
(4) The mathematical 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 problem-solving model that incorporates analyzing
given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving 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.
(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 demonstrates professional standards/employability
skills as required by business and industry. The student is expected
to:
(A) demonstrate knowledge of how to dress appropriately,
speak politely, and conduct oneself in a manner appropriate for the
profession;
(B) show the ability to cooperate, contribute, and
collaborate as a member of a group in an effort to achieve a positive
collective outcome;
(C) present written and oral communication in a clear,
concise, and effective manner;
(D) demonstrate time-management skills in prioritizing
tasks, following schedules, and performing goal-relevant activities
in a way that produces efficient results; and
(E) demonstrate punctuality, dependability, reliability,
and responsibility in performing assigned tasks as directed.
(2) 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 problem-solving model that incorporates analyzing
given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving 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;
(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.
(3) The student uses mathematically based hydraulics
concepts to measure and find pump output, understand pressure versus
cylinder force, and understand flow rate verses cylinder speed. The
student is expected to:
(A) explain how flow rate can be measured in gallons
per minute and liters per minute;
(B) calculate and record data using actual flow rates
from a flow meter chart;
(C) calculate, measure, and illustrate the force output
and speed of an extending and retracting cylinder; and
(D) determine and depict the stroke time of a cylinder
in gallons per minute.
(4) The student uses mathematical concepts of structure
design to define and describe statics, acquire data, apply concepts
of moments and bending stress, and apply concepts of truss design
and analysis. The student is expected to:
(A) calculate a resultant force;
(B) apply the concept of equilibrium to force calculations;
(C) calculate a force using a free-body diagram;
(D) develop an application of strain gauges that determines
mathematically and experimentally the force on a structural element;
(E) calculate the magnitude of force applied to a rotational
system;
(F) apply the moment equilibrium equation to force
calculations;
(G) calculate, measure, and illustrate a bending moment
on a beam;
(H) determine and depict the bending stress in a beam;
(I) calculate forces in truss using a six-step problem-solving
method;
(J) apply modulus of elasticity to the deflection of
beams;
(K) calculate a beam deflection for a given load;
(L) determine and depict the critical load for buckling
using Euler's formula; and
(M) design and apply factors of safety to column and
beam design.
(5) The student understands the role of trigonometry
in spatial applications. The student is expected to:
(A) apply trigonometric ratios, including sine, cosine,
and tangent, to spatial problems; and
(B) determine the distance and height of remote objects
using trigonometry.
(6) The student understands the concepts of design
processes with multi-view computer-aided drafting and design drawings
for facilities layouts, precision part design, process design, injection
mold design, and computer-aided manufacturing, as applied to processes
using 3D printing, laser cutting, and computer numerical control.
The student is expected to:
(A) determine a dimension of an object given a scaled
drawing having no dimensions;
(B) compare and contrast the function of production
time and production rate;
(C) calculate and apply the proper cycle time and analyze
machines required to meet a specified production rate;
(D) demonstrate the calculation and application of
output shaft speed and torque in a gear train;
(E) create a method to determine the direction of a
gear train's output shaft;
(F) design a spur gear train given speed and torque
requirements;
(G) calculate and apply the proper spacing between
the centers of gears in a gear train to a specified tolerance;
(H) apply positional tolerances to assembled parts;
(I) predict the production cost of a product given
process information and a bill of materials;
(J) apply the correct spindle speed for a computer-aided
manufacturing device by calculation;
(K) apply the correct feed rate for a computer-aided
manufacturing device by using calculation;
(L) calculate the pressure drop in an injection mold
system;
(M) design a gate size in an injection mold system
using the gate width and depth formulas;
(N) determine the size of a mold; and
(O) create size runners for a multi-cavity mold.
(7) The student calculates electronic quantities and
uses electrical measuring instruments to experimentally test their
calculations. The student is expected to:
(A) apply common electronic formulas to solve problems;
(B) use engineering notation to properly describe calculated
and measured values;
(C) compare and contrast the mathematical differences
between a direct current and alternating current;
(D) show the effect and give an application of an inductor
in an alternating current circuit;
(E) show the effect and give an application of a capacitor
in an alternating current circuit;
(F) create a resistive capacitive timing circuit in
a time-delay circuit;
(G) calculate the output voltage and current load of
a transformer;
(H) calculate the effective alternating current voltage
root mean square given the peak alternating current voltage and the
peak alternating current voltage given the root mean square value;
and
(I) calculate the cost of operating an electric motor.
(8) The student applies mathematical principles of
pneumatic pressure and flow to explain pressure versus cylinder force,
apply and manipulate pneumatic speed control circuits, and describe
maintenance of pneumatic equipment, centrifugal pump operation and
characteristics, data acquisition systems, pump power, and pump system
design. The student is expected to:
(A) calculate the force output of a cylinder in retraction
and extension;
(B) explain how gage pressure and absolute pressure
are different;
(C) explain the individual gas laws and use the ideal
gas law to solve problems;
(D) convert air volumes at pressures to free air volumes;
(E) compare dew point and relative humidity to explain
their importance;
(F) explain the importance of the two units of pump
flow rate measurement;
(G) convert between mass and volumetric flow rate;
(H) differentiate between unit analysis such as converting
units of pressure between English and SI units and dimensional analysis
such as Force and Pressure;
(I) convert between units of head and pressure;
(J) explain the importance of total dynamic head in
terms of suction and discharge head;
(K) demonstrate the measurement of the total head of
a centrifugal pump;
(L) calculate Reynolds number and determine the type
of fluid flow in a pipe, including laminar flow, transitional flow,
and turbulent flow;
(M) calculate friction head loss in a given pipe length
using head loss tables or charts;
(N) calculate total suction lift, total suction head,
total discharge head, and the total dynamic head of a system for a
given flow rate;
(O) calculate hydraulic power;
(P) calculate centrifugal pump brake horsepower given
pump efficiency and hydraulic power;
(Q) calculate the effect of impeller diameter and speed
on the flow rate of a centrifugal pump and pump head;
(R) predict the effect of impeller diameter on a pump
head capacity curve; and
(S) calculate net positive suction head.
(9) The student applies mathematical principles of
material engineering, including tensile strength analysis, data acquisition
systems, compression testing and analysis, shear and hardness testing
and analysis, and design evaluation. The student is expected to:
(A) calculate stress, strain, and elongation using
the modulus of elasticity for a material or model with a given set
of data;
(B) analyze and explain the importance of sensitivity
in relation to material engineering;
(C) analyze the operation of a data-acquisition application
or program;
(D) mathematically analyze a part for stress and strain
under a compression load;
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