Unit Plan : Trigonometry of the Unit Circle. Precalculus 12

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

 

Name:                                   Jimena Grueso Tenorio

School, grade & course:        Point Grey Secondary School, Grade 12, Precalculus

 Topic of unit:                         Trigonometry of the Unit Circle; Angle Measure; Reference Angles; Trigonometric Ratios & Equations; Trigonometric Functions & Graphs (Sine, Cosine, Tangent); Applications of Periodic Functions

  

Preplanning:

 

·       Trigonometry is a foundational part of Precalculus 12 because it bridges algebraic thinking, geometry, and real-world modelling. ·       The BC curriculum includes this topic as preparation for Calculus, Physics, but also because trigonometric functions provide a powerful way to describe patterns, cycles, and relationships in the world like motion, sound, tides, seasons, and engineering designs. ·       Learning the unit circle deepens students’ understanding of angles as rotations, rather than static geometric shapes, and strengthens algebraic fluency through exact values and identities. ·       For multilingual learners, the visual and conceptual structure of the unit circle provides an accessible, language-light entry point into advanced mathematics. ·       I hope students leave this unit with an appreciation for mathematical coherence: how geometry, ratios, and graphs all interconnect. ·       The beauty lies in this unity, seeing that a circle, an angle, and a curve on a graph all tell the same story from different perspectives.   Methodology Notes: We will be using Building Thinking Classrooms environment.   Multilingual Learners. Point Grey has an average of 10% of international students mainly speaking Mandarin and Spanish.

Project Periodic Phenomena in the Real World: Modeling with Sine and Cosine  Students will investigate a real-world periodic phenomenon (e.g., tides, Ferris wheel motion, daylight hours, sound waves) and model it using a sine or cosine function. The project deepens conceptual understanding of amplitude, period, midline, and phase shift. It also develops mathematical communication skills and provides MLs with multiple modes of expression: visuals, data, graphs, and written or oral explanations.  Process and Timing: Day 1–2: Students select a phenomenon from a teacher-provided menu. MLs receive scaffolded templates with visuals and key vocabulary (amplitude, axis, peak, cycle). Day 3: Students collect data from websites, teacher datasets, or class measurements. They use Desmos or graphing calculators to visualize the shape. Day 4–5: Students determine parameters (A, B, C, D) and build a function that fits the data. Day 6–7: Students create a poster, slideshow, or video explanation. Day 8: Gallery walk presentations (supports MLs through multimodal output rather than exclusively written text). Assessment: Students will be evaluated on accuracy of the mathematical model: -          Clarity of explanation, -          Appropriate use of vocabulary, -         And the ability to justify parameter choices. Assessment includes a rubric with criteria on mathematical reasoning, communication, and representation. MLs receive alternative options for demonstrating understanding (verbal video explanation, bilingual labels, AI-supported vocabulary scaffolds with transparency about the tool).

Formative Assesment: ·       Warm-up problems, exit tickets, ·       Quick whiteboard checks at vertical erasable surfaces, ·       Desmos activities, ·       One on one interviews, and ·       Group problem solving.   Summative Assesment: ·       Unit test, ·       Quizzes ·       The periodic phenomena project, ·       And in-class performance tasks.   Observational : Mathematical communication, reasoning, and collaboration. MLs receive sentence stems, key-term glossaries, and visual supports during assessments. Where appropriate, MLs may provide oral explanations or Desmos graph annotations.   The focus will be on conceptual understanding, communication, and problem solving, with procedural accuracy on a side as byproduct of good learning habits.

Elements of your unit plan:

 

Lesson	Topic
1	Radians, Degrees & Angle Rotation (Intro to Unit Circle)
2	The Unit Circle: Coordinates & Exact Values History of this mathematics
3	Reference Angles & Special Triangles
4	Trigonometric Ratios on the Unit Circle
5	Solving Basic Trigonometric Equations
6	Sine Function: Characteristics & Transformations
7	Cosine Function: Characteristics & Transformations
8	Tangent Function & Asymptotes
9	Graphing Trigonometric Functions (Groups on Vertical Surfaces)
10	Modeling Real-World Periodic Phenomena
(11)	Trigonometric Identities (Intro)
(12)	Project Work & Review

 

Micro teaching Reflection -Linear Equations

The lesson ran smoothly, and our colleagues enjoyed the activities.

The most important feedback was to make sure we have clear objectives for our activities. I will take this to my lesson planning.

You can see our peers' feedback here: Peers feddback 

About how the Math Books position their readers

 

Reading the Article didn't help me to have a position between using or not textbooks for the class. Using textbooks in class is an option, and as a modern teacher, I am open to accommodating my class dynamic to the school's needs for the benefit of the students' progress.

Textbooks are one more tool, and nowadays they compete with all the digital resources we have available. As XXI math teachers, we should be able to integrate all the different media available to create engaging spaces that motivate and promote mathematical thinking.

What I like most about the article was finding a citation to one of Susan's publications about word problems:

     Gerofsky, S. (1996) ‘A linguistic and narrative view of word problems in mathematics education’, For the Learning of Mathematics 16(2), 36-45. 

 I read Susan's article and I found it clear and useful regarding the structure and the aims of word problems in math education.

In contrast, the article assigned for the class started with the description of a framework ( that I used to create the diagram in the photo), but then spoke vaguely about the relationships described in the framework. I would like to have read more about specific examples and the impact on the students' learning, I would like to have seen some data, and also some opinions of students and teachers through surveys.

Campbell's giant can

 My step-by-step thinking process

Given the size of the actual Campbell's Soup can (of normal size) and the height of the bike in the photo (my own medium-sized hybrid bike), what are the dimensions of the volunteer fire department's water tank? What is its volume? Does it hold enough water to put out an average house fire?

I started asking myself:

1.      What are the dimensions of a standard Campbell soup can? I would Google it

2.      Do I remember the formula to calculate the volume of a cylinder? I would Google it

3.      What are the dimensions (length and height) of Susan’s bike? I would Google it

4.      How can I use Susan’s bike to estimate the length and diameter of the water tank?

5.      How much water does an average house fire need? google it

 

I am so tempted to plug the picture into ChatGPT and ask for the volume of a water tank from the fire department in Hornby Island. I usually enjoy observing neural networks at work!

 

I also noticed my brain was asking questions around the piece of art that wouldn’t necessarily help me solve the problem:

-          What is the water tank made of? Why does it look crooked? Is it a visual effect?

-          Why are the tanks placed horizontally on the floor and not vertically at the height?

-          How far are these tanks from the firehouse? Do they need to pump the water?

-          Is this a good question to use for the “Thinking Building Classrooms”?

...to be continued. 

FLOW

     

I feel flow when I paint. But it doesn’t happen every time. I never really know when it will appear, so I keep going back to painting—always chasing that moment. Sometimes it comes easily; sometimes it doesn’t.

I’ve also felt that same sense of flow when teaching little kids. I became one of them, laughing, playing, learning, and we had an absolute blast.

During my short practicum, I had the privilege of witnessing flow in a math classroom. Let me tell you, you have to be there to truly feel it. By the third day, after reading "Building Thinking Classrooms", I finally understood why some describe it as a kind of “cult” in the best possible way. (Although, after checking the dictionary, I realized there’s really no “good” definition of that word!) So instead, I’d call it a community of BTC teachers.

It’s hard to explain unless you’ve experienced it yourself. But to answer the question, is flow possible in a math class? My answer is an enthusiastic yes!

I’m so excited for what’s ahead in my long practicum. I can’t wait to keep exploring how flow unfolds in the math classroom.

Arbitrary vs. Necesary

       

I feel motivated to identify those key awareness topics that I can use as a foundation for creating meaningful questions to help my students build conceptual understanding.

As I am going to work within a "Building Thinking Classrooms" framework during my long Practicum, Hewitt’s approach reinforces the importance of not simply providing students with properties or rules. Instead, the teacher should guide learning through carefully designed questions that promote thinking and awareness, allowing students to construct understanding through their own reasoning.

Another important takeaway is that once this process of thinking becomes habitual, it can be transferred to other areas such as problem-solving, critical thinking, and more. In this way, learners develop not only memory as a “power of the mind,” but also creativity, estimation, abstraction, and problem-solving skills.