Micro-teaching 2: Lesson Plan for Sine Law

Title: Learning the different cases of the Sine Law
Date: November 30, 2015
Grade Level: Pre-calculus 11
Prescribed Learning outcomes: ·         Be able to understand how to apply Sine Law to solve problems. ·         Introduce oneself of 3 different cases of triangles in applying the Sine Law.
General purpose: The 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 length of the other two sides. We will look at three (3) cases: 1.       Where there is no solution, 2.       Where there is one solution, 3.       Where there are two solutions.
SWBAT 3.5    Sketch a diagram and solve a problem, using the Sine Law. 3.6    Describe and explain situation in which a problem may have no solution, one solution, or two solutions.
Probing of Previous Knowledge ·         The class has already been introduced with the notion of Sine Law (the relationships between the sides and angles) and the proof of Sine Law. ·         The class understands basic properties of triangles and knows how to draw a triangle, such as labelling the angles, sides, and the height, respectively. ·         The class understands the concept of SOH-CAH-TOA; students are expected to know how to calculate the height of a triangle using SOH-CAH-TOA.
Objective	Time	Activity	Materials
Introduction	1 minute	·         Ask students where they see the use of trigonometry in their everyday life. ·         Provide more background info on trigonometry that appeal to them.
Summary	2 minutes	·         Ask students if they can recall what sine law is (just in case not everyone does). ·         Draw a generic, 3-sided triangle. ·         Review the concept of Sine Law. ·         (With a diagram) Ask students if they can find an unknown angle or length of a triangle given the other two lengths and an angle. Is this always possible?	Whiteboard Markers
Inquiry Project	10 minutes The instructor will spend 3 minutes with each group, then rotate for a total of 9-10 minutes.	·         Introduce to class the three (3) different cases of the Sine Law. ·         Divide the class into three groups. Within each group: ·         The instructor presents a different case. ·         The instructor gives each student a set of 3-4 sticks, where students have to make as many different triangles as they can think of. ·         Once students are finished making their answers, they have to explain their answers to the group. ·         The instructor will help to guide the students, writing the problem on the board and explaining why there is indeed only one, two, or no solution.	Measured sticks with which to make triangles. Multiple sets for each of the three cases.
Handout + Summary	3 minutes	·         Provide the class with handout on the three cases of Sine Law. ·         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 whiteboard. ·         Show the implications of this when solving the Sine Law.	Students may need pen and paper for this.
Summary Evaluation: By having the students learn from doing hands-on activities with the sticks (and other visual tools), they can understand better the numbers of triangles that can be made given certain angles and lengths.

2-Sided Puzzle: "Ladies Luncheon"

What is arbitrary and necessary in teaching (math)?

1. What does Hewitt mean by "arbitrary" and "necessary"? How do you decide, for a particular lesson, what is arbitrary and what is necessary?

According to Dave Hewitt, in a learning setting, "arbitrary" means that students are informed of the learning materials through external sources, such as teachers, books, the internet, and many others; "necessary" means that students do not need to be informed of the learning materials through external sources. Often times, they can work through the questions and figure out themselves. As Hewitt writes in his article, what is "arbitrary" is in the "realm of memory", and what is "necessary" is in the "realm of awareness". I have encountered this kind of thinking and reasoning during my short practicum. There were times when students asked why it must be this way and not that, in which I hear my teacher say, "Sometimes, things are just easier this way." I think many of us new and experienced teachers have asked ourselves this kind of question many times during our teaching, and many of these examples have been cleverly brought up by Hewitt.

For my teaching, personally, I would consider math symbols, notations, or any naming conventions as something that is arbitrary. I am unsure of how I can explain why 2 is bigger than 1, for instance. Number symbols (e.g. 1, 2, 3,...) are universal across the world, so explaining that to students would be difficult for me because we have been taught and memorized this way since the beginning.

I would consider proofs, properties and relationships to be necessary because in many of these cases, they can be derived and worked out by students; students within "awareness" that is. For example, understanding why a parabola is shaped a certain way can be understood by graphing and interpreting the formula because parabolic formulas can be revised. Similarly, one can probably also work out why Speed = distance / time, or why chemical formula is written this way because these formulas can be derived and solved from real-life applications, whereas symbols and notations do not.

2. How might this idea influence how you plan for your lessons, and particularly, how you decide "Who does the math" in your math class?

Hewitt's idea of what is arbitrary and what is necessary really blows my mind on thinking to myself and asking "why". There might even be questions that some university professors and teachers cannot answer because they themselves learned concepts arbitrarily. As a teacher, I will try to dig deeper on the materials being taught in class for the curious minds. I might explain, on the side, why we do math a certain way while showing and explaining that there are alternative methods to do math differently, but it would just be harder for some students to grasp (although they are not limited to solving math their own way as long as they derive a right answer in the end). I know that not all students are capable of understanding the "necessary" component to math, but as long as teachers have an answer to "why", they can use simple hints so students can really ponder on it and "think about it".

Exit slip: Reflection on SNAP Math Fair at M.O.A.

Today, our EDCP 342A class had the opportunity as guests to participate the SNAP Math Fair at the Museum of Anthropology. I had a great time meeting talented students from elementary school in Vancouver. What surprised me the most was their ability to reason and think critically on the questions they were presenting. Most of these students were (possibly) in Gr. 6 or maybe even younger, and at that age they could think "beyond the box" with alternate answers and multiple solutions to solve any math problem had even opened my eyes on my own thinking of the questions being presented.

Some of these students were quite eager to present their question. They were able to explain the concepts well that I was able to solve it on my own, and with occasional help from the hints at times. The games were not overly complicated and can be understood easily for their level of learning. As well, I was amazed by how creative and talented these young students were at designing their own math games. Many students had gone out of their way to explore and find common (household) materials and turning them into beautiful and creative art forms!

SNAP Math Fair Response

Ted Lewis, the author of the Math Fair Booklet, poses some very interesting and realistic key points on learning math. Some people fear mathematics because they think that they are incapable of solving problems successfully, so that discourages them to continually pursue math questions. I know a fact that I, for one, feared doing math when I was a younger, especially when I was faced with more abstract math problems. For this reason, problem solving is a great focus to counter the fear of math, especially in Math Fair events because these skill sets can give everyone an opportunity to think and reason beyond the abstract level, into a more concrete and practical area of their lives. Now that the math fair is not been "graded" or awarded, students and visitors will feel less overwhelmed by failures as they are given the chance to perfect their learning continually and gradually.

If I want to incorporate SNAP Math Fair in my practicum high school at Point Grey S.S., I would first start with the younger grades, perhaps the Gr. 8 math classes because students at this age and grade are beginning to step into a more advanced level of math learning, and they are beginning to grasp math even in a more abstract sense. But of course, I should align complexity of math problems that is appropriate for students in Gr. 8 or 9.

The puzzles or brain-teaser math activities such as the ones proposed in the booklet would be a great starting point for those students to work on, and they should be easy enough for students to teach the visitors, such as families and friends, so they can understand the materials as well. I am also a firm believer that math learning should not be dealt alone. Students can think alone first to process the information and try independently, but ultimately, for more difficult questions they are best solved when students work/collaborate with each other. Perhaps, I can mix the Gr. 8s and 9s math together in groups of 3-4 members. For older grades, I can let Gr. 10s and 11s work together on solving the problems and presenting them to others. Finally, the Gr. 12s will have a chance to solve too, maybe with people within their own grade. Students from the mini schools can work independently within themselves too.

Because this school runs on a tight schedule, with each block of class being only 75 minutes long, time can be a constraint that may not work so well in a SNAP math fair (which can run as long as a day!) Because of the time constraint, I may need to simplify problems and puzzles or reduce the numbers of problems given and making them into groups of 3-5 to solve so problems can be solved quicker as students all pour their skills together. Another way to go about doing this is to combine all the students (from all grades) who have a math block at period 1 day 1, for example, together within this 75 min, then divide them based on their grade levels to avoid unfair math competencies. Once that is done, we move on to the next block. For presentations, students can continue to work and perfect their work on a day 1 again so visitors can come and solve themselves with guidance from the students.

November 13: End of Week 2 Reflection

I am writing this blog to describe the summary of my 2-week practicum. Overall, I have to say that I am very thankful of the opportunity to teach at Point Grey secondary school under the guidance of my English and math sponsor teachers and my faculty advisor. The students at PG are always full of energy, either it is the first block of the day, after lunch, or the last block of the day where students are dying to go home, they are always enthusiastic and approachable when it comes to learning.

The second week was a lot busier than the first week because I had to teach multiple of classes. I felt I was more nervous to teach the English classes because I have never taught English in a large setting before. In the past, I had mostly worked with individuals to teach grammar and ESL, so the opportunity to teach a class of roughly 30 students was an eye-opening experience.

I realized that in English, there is really no absolute right and wrong answer - as long as there is evidence to support the argument. This style of teaching is unlike teaching and doing math, where there is always one right answer for every problem, even though there may be more than one way of solving the problem. I understand that while teaching, the questions that I bring to the class should be open questions that give everyone a chance to think and discuss. I also realize that I need to be constantly coming up with real-life questions to stimulate students' thinking process on the spot, and those questions should always tie with the topic of my lesson. In other words, to be able to improvise is important to all teaching professions.

Ultimately, as a teacher, I am here to let students learn, think, and reason. I should be giving students the chance to think for themselves, under the proper guidance and tools. Just as a Bachelor of Education student myself, my faculty advisor, my sponsor teachers, and my Education professors are all here to make me (and the rest of us) a better teacher, for now and the future.

November 9 Reflection

Today, I was supervising and helping English classes in the morning and math classes in the afternoon. From my supervision and assisting the teachers and students, I realize that speaking with a higher volume is very important as a teacher - especially if we are standing in front of 30 something students! We need to make sure that students in the back can hear us clearly so they don't fall behind. Speaking loudly also shows a certain level of assertiveness and confidence in the subject we are teaching.

As well, having a clear instruction for all students is equally important. This ensures that students are all on the same page and clearly know what to do. They would know what is expected of them and what they should accomplish in class.

November 6: End of Week 1 Reflection

In the past couple of days during the week of my practicum, I have been busy preparing lesson plans, meeting the students and teachers, going to various non-math and English classes to learn about different teaching/class management styles.

I have attended a Chemistry 12 class, a Japanese 11 class, and a ELL class. I find that the language-based classes are generally are more interactive and involved than the math and science classes. The math and science classes are more subject-based (subjects and contents are more important), and in language/art classes are more analytical (analysis and thinking are more important).

I have two classes that are repeated for this short practicum, both math and English. I realize that even though they are the same classes, the students' response, thinking and behaviours in that same grade and subject area are all different. In addition, I realize that teachers have slightly different teaching strategies and methods for every class they teach (regardless if they are repeated or not).

For this one week being at a school, I learned about...

• Students are all different at their own levels - their competencies, abilities, personalities, etc.
• Teachers are all different in terms of their teaching and practices.
• The amount of discipline that's needed to control the classrooms are almost consistent from the youngest grade (9) to the oldest grade (12). E.g. some Gr. 9s need more discipline than the Gr. 12s, and some Gr. 12s need more discipline than the Gr. 9s.
• Students at Point Grey are very passionate about what they learn and what their hobbies are. From the clubs that I have attended and observed, students are not only passionate about the big things (e.g. humanitarian clubs) but also about the littlest things that I often don't think about, which amazes me!
• Students do notice me and acknowledge my presence even if they didn't say Hi to me in the classes I observed. (They always come up to me and tell me that I was in his/her's this class and that class, and I didn't even know!)

November 3 Reflection

Today is a very interesting day. My FA, Susan, drop by Point Grey s.s. to resolve some administration situations. I have a new math SA now, which I am very happy about.

I met up with my SA and the two of us talked for awhile about my lesson planning and what content materials her students are learning for each class. I realized that even though she is teaching multiple of the same classes every week, the class atmosphere, environment, structure and the students are very different. For instance, the morning Gr. 11 morning class is very different from her Gr. 11 afternoon class.

Today, I also had the chance to interview the librarians at the school. I never knew they had so much responsibilities to do at the back-end. While I was interviewing them, I never realized how difficult it is to recieve tech support (i.e. fixing computers, software programs, etc.) at this school. They openly admitted to me that tech support is very low, and they needed more staff who can help them resolve any computer/programming issues. The staffs aren't trained on how to resolve tech issues because most of the problems are fixed by and at the central school board. So most of the time when something is down, they have to wait until the school board tech staff fix the issues remotely on their end - so it's really a waiting game.

November 2: First day of short practicum!

Today is my first day of our short practicum at Point Grey Secondary School. I met a few other UBC and SFU teacher candidates who will also be working with sponsor teachers in various subject areas. I am the only math TC at this school.

The morning began with a detailed orientation and breakdown of work procedures in the classrooms. We toured around the school and met different teachers and staff members along the way. Point Grey is a very big school! It is quite old as it was built in the 1920s, but the school has maintained itself very well since then. The staff was very friendly and knows what's going on at school. Our secretary is our go-to person if we ever needed help on admin.

Some other interesting things that I have learned today:

• The school alone has over 60 student clubs! I noticed that there isn't a math club... maybe I can start one!
• I'm really interested in their Comp Sci Club and the Dance Team. I want to check them out! They sound really fun.
• A slight change of plan on who my sponsor teachers are going to be. Hopefully we can resolve this by the end of this week.
• The students in the math and English classes that I have attended are very energetic and friendly. I dropped by a pre-calculus 11 class with fewer than 15 students. It was a quiet class and majority of the class time was devoted to homework time and extra practice. I was able to help out the students whenever I could.
• Students in the AP math class are very ahead and the teaching pace is very fast. Teachers allocated 5-10 min work time before taking up the questions.
• For those who are in enriched or AP classes (especially in Gr.11 or 12), I'm curious as to what they want to pursue in post-grad - maybe I can help them if they want to study math!