For Educators: This Guide and the Common Core State Standards

Abstract

The very first Standard for Mathematical Practice asks—requires!—that we educators pay explicit attention to teaching problem-solving: MP1 Make sense of problems and persevere in solving them. And one can argue that several, if not all, of the remaining seven Standards for Mathematical Practice can play prominent roles in supporting this first standard. For example, when solving a problem, students will likely be engaging in the activities of these standards too: MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP7 Look for and make use of structure. These guides on Clever Studying through the MAA AMC align directly with the Standards for Mathematical Practice. And each individual guide directly addresses content standards too! This volume on trigonometry attends to the following standards. (The section numbers refer to the sections of this text in which the standards appear.) 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. (Sections 1 and 14.) 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (Section 1.) 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (Section 1.) F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. (Section 4.) F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. (Sections 2, 3, 4, and 11.) F-TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/ 3, π/ 4 and π/ 6, and use the unit circle to express the values of sines, cosines, and tangents for π - x , π + x , and 2 π - x in terms of their values for x , where x is any real number. (Sections 3 and 7.) F-TF.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. (Sections 3, 5, 6, and 7.) F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.