Rationale
Review/Preview:
This activity is designed to introduce students to the terminology of trigonometry, review the Pythagorean Theorem, and allow them to develop a solid foundation with right triangles, and the corresponding basic trigonometric ratios. The first two Common Core standards (MCC8.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. MCC9‐12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. ) were addressed in this activity. Please note that the students should already have worked with the Pythagorean Theorem before beginning this activity. The purpose of including it was simply to review their knowledge of the theorem. Included in the guided questions is one which specifically addresses the second standard and asks students to make that connection. MCC9‐12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems., the third standard is also used in exploring the basic ratios. It will be better addressed in the next activity. With the exploration of the right triangle and its fixed sides, students are addressing the third mathematical practice listed as well as the second. In solving right triangles using the Pythagorean Theorem, students address the first standard. For both activities, I chose to have the students working on the computer and remaining on this website. The purpose of technology is to enhance learning and make it more efficient. Printing out worksheets seems like a step backwards towards a more primitive form of learning. This is why most of the questions for the students were within the applet webpage. Here, they can focus more of their time contemplating more complex concepts especially through the use of dynamic geometry software. The software saves time by skipping the little time-consuming details and jumps to the broader picture. |
Unit Circle:
As with the previous activity, students are kept on the website working with the dynamic geometry applets. These applets allow the students to make better use of their time exploring the geometry. This activity also fully addresses the final standard especially when it asks students to prove the 45-45-90 triangle using the Pythagorean Theorem. They could then use the theorem to solve for other triangles throughout the unit circle. Again, this activity was not designed to teach the unit circle, so it does not go into much depth. It simply allows students to discover and verify their conjectures about the x and y values corresponding to trigonometric ratios. As for the mathematical practices, this activity addresses all three listed. CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically. CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning. Students are asked to notice patterns in creating the unit circle and the corresponding coordinates. They do have the unit circle applet which gives all the answers, but they must know what angles to search for in order to be successful. Therefore, the applet is a great validation tool. Finally, their proof of the triangle requires that they think with a more abstract mind while using algebra to prove a general idea. |