342A Gerofsky Lesson Plans I–II–III

Subject: Pre Calculus	Grade: 12	Date: 17 Dec.’17	Duration: 75 to 80 mins
Overview	All the lessons are based from the curriculum text: McGraw-Hill Ryerson Pre-Calculus 12 [pgs. 166 until 324] 15 or 16 pages roughly ought to be covered per day in this unit, for a total of 11 or 10 lessons Every lesson below performs within the new curriculum guidelines, however I.B.-DP content is present within this file
Class Profile	TEO, TBA

Big Idea(s)	Transformations of shapes extend to functions in all of their representations Analyzing the characteristics of functions allows us to solve equations, and model and understand relationships
Curriculum Competencies	Apply flexible strategies to solve problems in both abstract and contextualized situations Model mathematics in contextualized experiences Use mathematical vocabulary and language to contribute to mathematical discussions
Content	Transformations of functions, including (symbols not included) Trigonometric functions and equations with real numbers
Literacy Objectives	I  Investigating Sine & Cosine laws in triangles (with the hour and minute hand on a clock fixed at 3:15) while spinning counterclockwise II  Using the Desmos app, we show how transformations/translations in Trigonometry differ from polynomial functions. III  The final project, where groups investigate Sinusoidal word problems adapting the material taught

Materials and Equipment Needed for this Lesson

Pencil/pen Paper/notebook brought to class Protractor Graphing calculator (will be provided if necessary) Ruler

	Lesson Stages	What the teacher will be doing	What the students will be doing	Time
1	Warm-up	Hook I Let’s hold the time at 3:15, and spin backward (a clock will be provided for every student) Hook II We need to get a more accurate view of why whole number translations are different for polynomials than they are for Trigonometric ones.  Let’s see why Hook III If you were a navigator, and wanted to dock your ship safely, how could you be sure that happens?  We now know amplitudes, phase shifts, and behaviours of sinusoidal functions.	Spinning a non-active clock counterclockwise, discovering obtuse and acute triangles Whole numbers will be converted to radial numbers Use Desmos here Group project (1/2) = class time for research (2/2) = mini presentations	(15 mins) (15 mins) (15 mins)
2	Presentation	I So how does clock spinning relate to angles in a triangle? Remember, we have to connect where the hand counts seconds to the time 3:15 Do we get different triangles every time? And some of the time we don’t even get a triangle at all.  Why is that? II Let’s experiment with what it really means to “move” either the Sine or Cosine curve Left or Right If we take the approach of mapping notation, and compare it to what we did last class with the clocks, then x ~~> (x – π/2) would mean that we’re “moving” every point right by 90o If you brought your spinners today, try it out with the person sitting beside you and get practice converting degrees into radians III (1/2) So to get you started for the project, where can you find some real-world examples (maybe in the subjects of Physics or Music – we could have some students map height on a Ferris wheel.  A musical example would be oscillations in a given pitch) that “look” like a Sine or Cosine curve? Let’s come up with a mind map on the whiteboard here, and I would like you to get into groups of five (we should have around six clusters, presuming an enrollment of 30 students) If we can get everyone doing a separate and unique project, that would be great (2/2) N/A – presentations	If the seconds ticker falls on the 9, it’s merely a straight line	(20 mins) (20 mins) (20 mins)
3	Practice	I Using our protractors and rulers, link up your measurements with the Sine and Cosine laws Can we figure out why for the triangles you made using the clock, both laws work? II I want us to figure out ways/ possibilities for moving Sine and Cosine “around” our graphs here Please get your tablets out, and experiment! (through the Desmos app) What are you finding out when we substitute x ~~> (x – (π / a number)) or x ~~> (x + (π / a number))? Are brackets helpful?  Why or why not? III (1/2) Section devoted researching their particular topic/approach to a sinusoidal problem (2/2) Presentations given by my students		(30 mins) (30 mins) (30 mins)
4	Discussion	I Would anyone like to share their rationale for proving the Sine and Cosine law? What measurements did people from different tables discover their angles were? Was it consistent with what these laws said? II So what did you learn from experimenting with Desmos? That plus (+) and minus (–) some radian number can be tricky, but we just have to be careful, that’s all.  I think we should have a little more practice with it, because when we get to combining everything together, it can get confusing III (1/2) So could everyone get in touch with their group members tonight and inquire about amplitudes, phase shifts, and whether or not you choose to graph using a Sine or Cosine function (2/2) I really enjoyed all of the presentations guys!  What thoughtful ideas on how to connect sinusoidal patterns and behaviours to lifelike situations!		(10 mins) (10 mins) (10 mins)
5	Closure	I Well, we found new ways of demonstrating math connected in clocks, too! II Does everyone feel confident with the material we have just covered today?  Does anyone have a question? (first to five check) III (1/2) N/A – group collaboration (2/2) Can I get everyone to write on a small piece of paper (provided) what they thought of the experiment? Were you surprised at all in anything?		(4 mins) (4 mins) (4 mins)

Reflection:

Having a copy of McGraw-Hill Ryerson Pre-Calculus 12 is helpful, because now I know how to pace all of my lessons. And I believe it was helpful in figuring out what/how a Unit Plan should read, and I definitely will use the holidays for improving my clarity on some lessons

  EDCP 342A Unit planning

EDCP 342A Unit planning: Rationale and overview for planning a 3 to 4 week unit of work in secondary school mathematics

Your name:  Thrasher, Brendan
School, grade & course:  TBA through TEO – 12 – Pre-Calculus 

Topic of unit:  Trigonometry (I.B.-DP component optional)

Preplanning questions:

(1) Why do we teach this unit to secondary school students? Research and talk about the following: Why is this topic included in the curriculum? Why is it important that students learn it? What learning do you hope they will take with them from this? What is intrinsically interesting, useful, beautiful about this topic? (150 words) ------------------------------------------------------------------------------------------------------------ Introducing how to graph the Sine, Cosine, and Tangent functions have always been a core component of Pre-Calculus 12 (or Principles of Math 12 as it formerly was called).  The topic, I would suppose for the first time in their school year, introduces students to “new” shapes – i.e. shapes that are periodic and “wavy”.  This is very important because of applications from physics, music, engineering, etc.  I hope they can learn how to relate the graphs of Sine and Cosine visually with each other (very important!), why the tangent function has asymptotes, what a phase shift/displacement is for one or more of these, and how with a real-life word problem they can combine all the tools taught to solve it.

(2) A mathematics project connected to this unit: Plan and describe a student mathematics project that will form part of this unit. Describe the topic, aims, process and timing, and what the students will be asked to produce, and how you will assess the project. (250 words) ---------------------------------------------------------------------------------------------------------- Even though the question relates to only one particular project (I hope to have mini-projects trough this unit), I will give guidance through an interesting word problem on mapping sinusoidal functions, relating that with tidal wave patterns (high or low) Aims of this project: Have 5 students in a group, and 6 groups (presuming an enrollment of 30) Once they have been taught amplitude, phase shift, and transformations of SOHCAHTOA, they are ready to research a topic and create a (somewhat) realistic graph of a “life-like” problem. Timing:  2 class blocks Class 1/2 (beginning) Say:  “Well now that we’ve learned the behaviour of sinusoidal functions, how can we put this into practice?  Here are some suggested topics on the whiteboard, and I’d like each group to research a different one. Class 2/2 (mini-presentation) Say:  “In your groups, what topic did you research?  Let’s present.

(3) Assessment and evaluation: How will you build a fair and well-rounded assessment and evaluation plan for this unit? Include formative and summative, informal/ observational and more formal assessment modes. (100 words) ---------------------------------------------------------------------------------------------------------- Class 1/2 I would walk around, and observe that each student has a contribution within their group discussion.  More often than not, one or two students will dominate the conversation, while the rest feel “left out” or simply disconnected from the topic. Class 2/2 When students present their topic, I have a rubric that assists me on their level of engagement within the activity Vigilant visual skills (from Opera) certainly help here when I monitor what each student contributes.  I would not expect “perfect” scores in all categories of assessment, but the overall grade/mark would be evident from my judgment.

Elements of your unit plan:

a)  Give a numbered list of the topics of the 10-12 lessons in this unit in the order you would teach them.

Lesson	Topic
1	Review of Right-angled-triangles & SOHCAHTOA
2	Converting degrees into radians and backward
3	Project I:  A spinning COUNTER clock! (how to measure radians)
4	Introduction to Sine & Cosine function graphs
5	Introduction to graphing the Tangent function
6	Project II:  “A tale of two graphs” (phase shift/displacement)
7	Introduction of inverse Sine & Cosine graphs (csc & sec)
8	Cotangent (cot) with rules of asymptotes
9	Word problems involving sinusoidal functions
10	Project III:  Create a sinusoidal function based on everyday situations
(11)	Identities in Trigonometry
(12)	Trigonometric proofs

342A Unit Plan Trigonometry (Pre-Calculus 12) 

Below is a summary of three detailed lessons, including fun activities along the way to support why I chose this topic!

Lesson #1:  Acute and Obtuse triangles

I start with explaining if both the hour and the minute hand on a clock read 3:15 (AM/PM is irrelevant), then the clock hand counting seconds actually ticks "backwards" to a certain number (i.e. 2, 1, 12 etc.)  Once it reaches, we draw a vertical/straight line down from it's tip, to 3:15.  I mention that

Lesson #2:  Sine, Cosine, Tangent

Here we explain 'SOH-CAH-TOA' for a triangle,


Lesson #3:  Problem solving in words

I would talk about tidal patterns (so high versus low), and explain how sinusoidal functions help navigators determine whether or not it is safe to dock their vessel.

My summative reflection of 342A  

Our course proved time and time again we as teachers must use a different lens when we communicate math with high school students.  It goes beyond that though; once we enter the profession, how can we prevent ourselves from becoming complicit with how things 

'were' within the old curriculum, and embrace the new? 
Most of the pedagogy I learned was useful, outlined below:

Readings:  I don't believe I answered most (if not all) of the blog posts sufficiently.  I made some interesting remarks, but they were off topic.

Activities:  The class we talked about the weight in students backpacks was something I never thought about before then.  Especially now how information is distributed online, do we ultimately need books anymore?

Discussions:  Sitting at hexagonal tables, our views on how to 'sub' divide different patterns of seating arrangement for students stood out with me.

Reflection on WPGA Math (Un) Fair:

I never attended West Point Grey, but I found the teachers' interest level in each and every student project really quite remarkable.  It showed me that the staff at that school really care for the child's success, and several times I heard comments like "well, how exactly is your game probability unfair?"  Alternately, what exactly makes your game fair?  The one-to-one relationship between teacher and children foster this idea that their game can be improved, and most of the time at all stations I felt as though the children invested a lot of time in crafting their game(s).

Many stations I attended however, were based on spinning a wheel.  The next fair that they host might include a sign-up sheet, so that there are not many derivatives on/of the same game.  I also believe some students could have a recap on how to properly tally, so that when their fair finished they would have some concrete evidence on whether or not the activity was truthfully biased or not.  The only other thing (which is really minor), but I would suggest to Alice for the next fair to make some view-able directory of where the rooms actually were.  Personally I didn't know the library was another space of activities until later on!