Micro-Teaching for Nov 30 - the Sine Law

Title: Learning the different cases of the Sine Law
Date: November 30, 2015
Grade Level: Pre-Calculus 11
Prescribed Learning Outcomes: B3. Solve problems, using the cosine law and sine law, including the ambiguous case.
General Purpose: This class will look at how the Sine Law can be used to find the unknown length of the side of a triangle given one angle and the lengths of the other two sides.  We will look at three cases: 1) where there is no solution, 2) where there is one solution, 2) where there are two solutions.
SWBAT: 3.5 Sketch a diagram and solve a problem, using the sine law. 3.6 Describe and explain situations in which a problem may have no solution, one solution or two solutions.
Probing of previous knowledge: We are assuming that in the class previous to the one we are teaching, students learned about the Sine Law and about how to prove it.  They also know basic properties of triangles, like how all the angles add up to 180 degrees.
Objective	Time	Activity	Materials
Introduction/hook	1 minute	Give students a little background information about the use of trigonometry - how it has been used early on as a way of measuring long distances, by calculating angles and smaller distances, and using perspective to approximate the longer distances.
Summary	2  minutes	Review the concept of the Sine Law (presented from a previous class).  Ask the students whether they think they can find an unknown side length of a triangle given the other two lengths and an angle.  Is this always possible?	·
Inquiry project	3x3 = 9 minutes	Illustrate the three different cases for Sine Law (whether one, two or no solutions) by dividing group in three, and having one instructor (Ying Ting, Deeya and Etienne) assigned to each group.  Each instructor will present a different case.  They will give students sets of three sticks, with which they have to make as many different triangles as they can.  Once they have come up with an answer, they have to explain why their solution is correct.  The instructor will help guide the students, writing the problem on the board and explaining why there is indeed only one, two, or no solution. The instructors will spend 3 minutes with each group, and then rotate, for a total of 9 minutes.	Measured sticks with which to make triangles.  Multiple sets for each case.  Three cases.
Handout+ summary	3 minute	Give students the handout on the Sine Law cases.  Go over the handout briefly.  Use it to show students that the three different cases necessarily have one, two or no solutions.  Illustrate this on the board, clearly.  Show the implications of this for when solving the Sine Law.
Summative Evaluation: By having students use the sticks to make up different triangles, students will illustrate their knowledge of the different number of triangles that can be made given certain lengths.