(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;
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