Unit 4: Trigonometry in Spatial Applications In this unit, 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 apply trigonometric ratios, including sine, cosine, and tangent, to spatial problems. (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. Unit 5: Multi-View Computer-Aided Drafting and Design Students will use mathematical relationships to generate solutions and make connections and predictions. In this unit, students will engage in activities such as analyzing mathematical relationships to determine a dimension of an object given a scaled drawing having no dimensions, create a method to determine the direction of a gear train's output shaft, and design a gate size in an injection mold system using the gate width and depth formulas. (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;
the three classes of levers and calculate the coefficient of friction in its proper units of measurement. (C) calculate the magnitude of force applied to a rotational system; (D) calculate the mechanical advantage of first-, second-, and third-class levers; (E) compare the advantages and disadvantages of the three classes of levers for different applications; (F) calculate and analyze the coefficient of friction in its proper of measurement. Unit 10: Mathematical Principles for Mechanical Drives Part II This unit will continue to have students investigate principles for mechanical drives. Culminating activities will have students demonstrate numerous examples of pitch and analyze its proper application, as well as calculate the shaft speed and torque of a belt drive and chain drive system. (10) The student applies mathematical principles for mechanical drives, including levers, linkages, cams, turnbuckles, pulley systems, gear drives, key fasteners, v-belt drives, and chain drives. The student is expected to: (G) analyze and calculate mechanical advantage for simple machines using proper units of measurement; (H) calculate the mechanical advantage of gear drive systems; (I) compare and contrast at least two methods of loading a mechanical drive system; (J) calculate rotary mechanical applied to an application; (K) analyze the mechanical efficiency of a given application; (L) demonstrate various examples of pitch and analyze its proper application; (M) calculate the shaft speed and torque of a belt drive and chain drive system; and (N) calculate sprocket ratio and analyze its importance to various applications.