Contained in my inquiry blog, I am focusing on the law of sine and cosine, including definitions, examples, and proofs of how they are derived. This concept is contained within the high school grade levels. It is not specific due to students flexibility in when a trigonometry course can be taken. The texts I provided below can be used in a plethora of differing ways. However, I would use these texts while introducing the laws of sine and cosine. With that said, explaining how the formula is derived gives students the idea of the connections between differing concepts. In contrast, other texts engage in examples which I would implement after the explanation of the formula and how to decide which information of the triangle goes where. I also think I could use the texts in homework problems, or as a resource for extra help when outside of the classroom. The texts I have provided are a mixture of many different aspects relating to the laws of sine and cosine presented in interesting ways!
PRINT #1
This text is an article that extenuates the law of cosine. However, it exemplifies many aspects, including a definition, proof of how it is derived, and an example. It gives students the opportunity to understand how the law of cosine is derived and not simply being given a formula to plug in numbers. While this article discusses a proof of how the law of cosines is found, the average grade level rating is 9.4. With this, I do agree with the rating given. Ninth grade is typically when students have the opportunity to partake in higher level math courses like trigonometry. Using qualitative aspects, such as knowledge demand, it is assumed that students already have prior knowledge of sine as being equal to opposite over hypotenuse and cosine being equal to adjacent over hypotenuse. It does also assume the student has prior knowledge of the Pythagorean theorem. Therefore, I agree with the 9.4 grade level rating as to infer that a student can prove the law of cosine with the already learned concept of sine, cosine, and Pythagorean theorem which are relatively easier topics in the subject of trigonometry. In terms of qualitative measures of text complexity, the language structure is quite clear and academic. The text/language sticks closely to the law of cosine and does not stray from the topic itself. For example, the article provides the formulas for the law of cosine, a possible proof, and an example to practice. In terms of knowledge demand, like stated prior, it does assume the student has prior knowledge of sine, cosine, and the Pythagorean theorem. However, it also discusses side-side-side (SSS) congruence and the means of solving. The article does state the idea of SSS congruence as "knowing the lengths of all three sides of a triangle" (Law of Cosine). It then walks through solving the triangle in terms of SSS congruence while explaining along the way.
Proof
Trigonometry
Cosine
Congruence
Function
Formula
Equation
The task and reader complexity does not relate to the lives/interests of my students. Students outside of the classroom and in future careers will most likely just know the formula for the law of cosine and be able to solve. The thought of how the formula is derived is not applicable in the given moment. Knowing a proof of the law of cosine is to understand the origin and how it comes to work. The purpose of utilizing the text is to understand the origin and how it is derived from other trigonometric formulas. In math class, students are always taught formulas and how to solve problems respectively. With that, not many classrooms engage in the how a concept came to be known and why it works. Therefore, showing a proof is a good way to open that conversation for students.
PRINT #2
“Proof of the Law of Sines.” Proof of the Law of Sines - Math Open Reference, Math Open Reference, 2011, www.mathopenref.com/lawofsinesproof.html.
PRINT #3
“Law of Sines, Trigonometry of Triangles.” Math Warehouse, www.mathwarehouse.com/trigonometry/law-of-sines/formula-and-practice-problems.php.
MULTIMEDIA #4
mathematicsonline. “Law of Sines and Cosines, Explanation.” YouTube, 26 Apr. 2015, www.youtube.com/watch?v=3jBMymLI8ls&t=4s.
The YouTube video engages in many examples in relation to both sine and cosine. It gives students an opportunity to see how students can engage with the information in the triangles given, to find plug those numbers into the formula in order to find the missing information. The multimedia resource was hard to work with in the StoryToolz resource for calculating grade level. With this being a video, I had to implement the transcript. However, it was calculated as a 5.2 average grade level. I do not agree with this rating. With that said, the knowledge demand is too high to be within a fifth-grade level. Fifth graders are typically not taught sine and cosine until late middle to high school and the video assumes a great deal of conceptual knowledge. For example, the text assumes the student already learned and understands both the sine and cosine formulas in relation to their counterpart over the hypotenuse. Another example is an assumption of students knowing the sum of a triangle, in terms of angle measures, adds up to 180 degrees. Another example is the expectation of knowing inverse sine and inverse cosine prior to conferring with the examples portrayed. The knowledge level is very high for a fifth-grade level and the language structure does not teach the students about the information presented, except give examples to practice.
Triangle
Altitude
Eliminate
Algebra
Hypotenuse
Substitute
Theorem
The task and reader complexity relates highly with the lives of my future students. The text engages with the base knowledge of the laws of sine and cosine. The purpose of the text is to identify parts of a triangle and understand where those parts fit into the equations. With this, students benefit from the practice of the concept. My students might have to use this concept/formulas in their workplace environment. Therefore, with the practice, students are able to perfect their skills and make sure they are ready for the future problems that may arise.
MULTIMEDIA #5
CULTURALLY RELEVANT #6
C, Mrs. “Sine Law Cos Law - Math Parody of Justin Beiber's Baby.” YouTube, 14 Mar. 2011, www.youtube.com/watch?v=o7BkRQw02hQ.
This YouTube video engages in a fun, upbeat music video. With that, the text exemplifies an upbeat explanation and background examples that give students a chance to see how to use the formulas as well. I am unable to retrieve the transcript to implement the text into StoryToolz. However, I would rate the text as having a tenth grade level rating. Tenth grade is when students are able to start partaking in higher level math courses where they learn about the differing aspects of sine and cosine, including the laws of sine and cosine. The knowledge level and language structure both permit this as at a ninth grade comprehension level. The text expects the same prior knowledge of the other texts. However, the language structure does not explain the assumed concepts and does not consist of many vocabulary to work with. With that said, the text expects students to already understand that triangle sum of angle measures adds to 180 degrees. The text also assumes that students understand sine and cosine formulas in relation to opposite or adjacent over the hypotenuse. Finally, students are expected to know inverse sine and inverse cosine. All of which is a lot of information for students to know prior to engaging in the laws. Therefore, with all the prior knowledge, I believe it constitutes as a higher grade level rating.
Triangle
Value
Angle
Dispensed
Crossed Off
Math Law
The task and reader complexity does relate to my students. While the song is overlapping with the ideas of sine and cosine law, there are examples playing in the background. Therefore, students are able to see examples of how to use the formula in terms of triangles being presented in a problem. The task is easily accessible and easy to follow along. The song makes for a very upbeat environment where students can learn a basic understanding of the law of sine and cosine with a background of examples to begin to be engaged with the concept. It is wishful thinking that with the song and background examples, that students would be motivated to learn more about the concept. I think this would be a good text to introduce in the beginning of the lesson as an attention grabber.
CULTURALLY RELEVANT #7
Vilale, Jenina. “The Law of Sines and Cosines Song.” YouTube, 24 Apr. 2018, www.youtube.com/watch?v=FhdOC-ayvOw.
