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