UNIT PLANNING PLUS LESSONS - ASSIGNMENT PRE CALC 12

  

Teacher Candidate	Jimena Grueso Tenorio
School	Point Grey Secondary School
Grade	12
Course	Pre-Calculus
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 of this unit consist in being able to appreciate 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 by 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 ability to justify parameter choices.   Assessment includes 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).

 

 

Elements of unit plan:
Lesson	Topic
1	The Unit Circle: Radians, Degrees & Angle Rotation (Intro to Unit Circle) Indigenous perspectives and the Circle Across the cultures
2	The Unit Circle: Coordinates & Exact Values
3	Reference Angles & Special Triangles
4	Trigonometric Ratios on the Unit Circle History of this mathematics
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

 

Building Thinking Classroom Methodology

                                                                                    

 

Lesson Title:			1.    The Circle Across Cultures
T.C. Jimena Grueso Tenorio
OVERVIEW
Subject:	The Circle		Concepts/Themes/Topics: ●      Understanding Angles through movement ●      Angle rotation, Radians ●      Communication skills development ●      Indigenous perspectives ●      Integrate AI tools responsibly to support data interpretation and vocabulary acquisition.
Grade:	12
Date:	10/22/2025
Duration:	80 min
Big Ideas and Core Competencies:   -        Circular functions and trigonometry are used to model periodic phenomena. -        Angles and the unit circle provide tools for describing and analyzing rotation and periodic relationships. -        Mathematics is a human endeavour that reflects cultural practices, ways of knowing, and patterns in the natural world. Communication and Language Use mathematical vocabulary (rotate, radius, axis, coordinate, quadrant) and visual representations to explain angle measures and rotations. Collaborate in small groups and communicate reasoning at vertical surfaces. Thinking Apply reasoning to make sense of angle relationships on the unit circle. Use visual strategies to understand abstract mathematical concepts. Personal & Social Respect the cultural significance of circular forms in Indigenous traditions. Work collaboratively and support peers of different linguistic backgrounds.
Learner Profile: Students work effectively in random groups and whiteboards, communicating ideas openly and respectfully. They practice listening, building on others’ reasoning, and co-constructing understanding. They are comfortable with productive struggles and know that learning happens through trying, discussing, and revising strategies. MLL students who are international learners from Mandarin-speaking and Spanish-speaking backgrounds. Strong computation skills but varied English vocabulary for abstract concepts (rotation, radius, coordinate). Some learners may rely heavily on visual cues and gestures; others may prefer written bilingual explanations. Students may feel hesitant about speaking publicly in English, but excel in group-based, hands-on exploration. Instruction therefore emphasizes multimodal instruction: movement, visual support, and structured language scaffolds.
ATLS (Approaches to Learning Skills):   Thinking Skills: Transfer: connecting circle concepts to cultural and historical contexts. Critical thinking: deriving angle measures from rotation. Communication Skills:          Using sentence stems to express mathematical reasoning like comparative words (higher than, more likely, less common), causal connectives (because, since therefore), and support predictions or inference (might, suggests, indicates) Interpreting visual information and diagrams. Sellf Management Skills: Organizing mathematical ideas visually on whiteboards. Regulate emotions when challenged by practicing patience and perseverance. Social Skills Collaborating respectfully in mixed-language groups. Sharing interpretations across cultures
Curricular Content Objectives ·       The Unit circle as a representation of angles and rotations. ·       Positive and negative angle direction. ·       Key angles: 0, π/2, π, 3π/2. ·       The relationship between rotation and coordinate representation. ·       Cultural significance of circular forms in Indigenous cultures.
Materials/equipment needed:   Vertical whiteboards  Dry erase markers  Random group generator (cards, sticks, or digital tool) Projector Rope circle placed on floor (2–3 m diameter) images of Indigenous circular art and seasonal cycles (Sundance lodge, Mesoamerican calendars, canoe navigation tools). Angle prompt cards (e.g., “Rotate 225°”, “Find the coordinate at π/2”) Visual vocabulary cards (rotate, radius, axis, coordinate, quadrant) Bilingual vocabulary cards (English–Mandarin, English–Spanish)
Assessment: Formative: ·       Observation of group reasoning, ·       questioning, ·       Student participation in circle-walk activity, ·       for MLLs: a screen-recorded oral explanation.
Adaptation Specially for Mandarin and spanish		Students may work seated at desks if they have mobility or attention difficulties, with digital whiteboards or mini boards for participation.

 

LESSON COMPONENTS:
Intro (5 min)	(Warm-up): Students brainstorm where circles appear in human cultures. Structured Partner Talk Students receive sentence frames: “This circle represents ___ because… ” “I have used circles to____since…” Mixed-language pairs allow MLs to rehearse the language before sharing publicly.   Create the groups with the cards and have them write their names and answer on the board. Students work in random groups of 3 at vertical whiteboards. Teacher circulates, asking probing questions such as: - What do you notice? - Can you describe it in words or symbols?
Part 1 (5 mins)	(Presentation) – Indigenous perspective Present examples of how Coast Salish and other Indigenous groups use circular forms in weaving, navigation, and cosmology. Focus on continuity, cycles, and seasonal changes. Ask: 'Have you noticed any connections to periodic behaviour?
Part 2 (20 mins)	(Embodied Activity) Students physically walk the rope circle, marking 0, π/2, π, 3π/2 with their bodies. MLs benefit from movement-based meaning-making. Movement reduces linguistic load. AI-Supported Scaffold (Responsible Use) AI allowed only for vocabulary clarification (e.g., “Explain ‘quadrant’ in simple English”). Students must rewrite AI explanations in their own words using a teacher-provided template: “AI said: ____. I understand it as: ____.”
Part 3 (15 mins)	(Content Task) Groups receive one “angle card” and must determine its radian measure, draw it, and record its coordinates on the unit circle. Teacher tells only what is arbitrary (size of radius = 1) and students must derive what is necessary (coordinates).   Vocabulary & Language Scaffolds Provide a visual glossary at the beginning with words & icons: angle, rotation, radius, quadrant, clockwise, counterclockwise, origin, coordinate. Glossary includes examples in students’ home languages (teacher-created or AI-assisted). Teacher uses Total Physical Response (TPR) for movement words (e.g., “rotate,” “walk 90 degrees,” “turn half circle”). AI Support Station: MLs may ask AI for definitions, synonyms, or bilingual explanations, but must revise all text.
Part 4 (15 mins)	Consolidation Gather students and summarize what they found. Draw the unit circle with radious 1 unit on the cartesian plane. Relate the Arc Length and Angle measure in Radians in connection with the embodied activity. P () = (x,y) Ask what happen if we replace  with  ? Answer: P() = (-1,0)
Part 6 (5 min)	Check for Understanding (CFU) Quick sketch & identify one angle. Khanmigo / Khan Academy: guided practice for the unit circle graph. (The unit can be customized to mandarin and spanish)   https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb89:unit-circle/e/unit-circle

 

 

                                                                                    

 

Lesson Title:			5. Constructing The Unit Circle, Geometry Art
T.C. Jimena Grueso Tenorio
OVERVIEW
Subject:	The Circle		Concepts/Themes/Topics: -        Use reasoning to analyze and justify mathematical relationships. -        Represent mathematical ideas with art, visually and symbolically. -        Communicate mathematical thinking clearly using appropriate vocabulary and diagrams.
Grade:	12
Date:	12/21/2025
Duration:	80 min
Big Ideas and Core Competencies:   -        Mathematical structures as the circle, reveal patterns and relashionships that are logical and aesthetic.   Communication and Language    Represent and explain mathematical reasoning using diagrams, symbols, and mathematical language.   Thinking    Use spatial reasoning and logical deduction to derive coordinates of special angles.   Personal & Social-BTC    Collaborate respectfully in problem-solving communities and value multiple ways of knowing and expressing ideas.
Learner Profile: -        Students work effectively in random groups and whiteboards, communicating ideas openly and respectfully. -        Benefit from visual, step-by-step, and symbolic representations. -        They practice listening, building on others’ reasoning, and co-constructing understanding. -        They are comfortable with productive struggles and know that learning happens through trying, discussing, and revising strategies. -        MLL students who are international learners from Mandarin-speaking and Spanish-speaking backgrounds. -        More confident communicating through drawings, gestures, and peer discussion before whole-class sharing. -        Strong computation skills but varied English vocabulary for abstract concepts (rotation, radius, coordinate). -        Some learners may rely heavily on visual cues and gestures; others may prefer written bilingual explanations. -        Students may feel hesitant about speaking publicly in English, but excel in group-based, hands-on exploration.   Instruction therefore emphasizes: -        Multimodal instruction: movement, visual support, and structured language scaffolds. -        Low-language/high-reasoning tasks, visual scaffolds, and collaborative sense-making.
ATLS (Approaches to Learning Skills):   Thinking Skills: Applying geometric reasoning to derive trigonometric relationships.   Communication Skills: Using sentence stems to explain mathematical structure.   Sellf Management Skills:BTC Organizing work visually and managing task sequencing.   Social Skills Negotiating meaning in mixed-language groups.
Curricular Content Objectives Students will understand and apply: -        Unit circle construction -        Special angle triangles (30°–60°–90°, 45°–45°–90°) -        Exact trigonometric values -        Coordinate relationships on the unit circle
Materials/equipment needed:   Vertical whiteboards  Dry erase markers  Random group generator (cards, sticks, or digital tool) Projector 12”x18” Construction paper Compasses, rulers, string Colour acrylic markers, crayons or oil pastels (optional acrylic paint and bushes) Visual step by step construction cards Art images (mandalas, indigenous circular art) Vocabulary cards (English, mandarin, spanish)
Assessment: Formative: -        Teacher observation of reasoning at vertical surfaces -        Accuracy and clarity of constructed unit circles -        Oral explanations using sentence stems Success Criteria: -        Correct construction -        Accurate coordinates for special angles -        Logical justification -        Engagement in group reasoning
Adaptation Specially for Mandarin and spanish		-        Visual construction guides -        Colour coding for triangle sides and coordinates -        Sentence starters: -        “We know this triangle is ___ because…” -        “The coordinate must be ___ since…” -        Oral explanation allowed instead of written -        Extra processing time

 

LESSON COMPONENTS:
Intro (5 min)	(Warm-up): This or That Question , non curricular   https://youtu.be/VFbyGEZLMZw?si=YqRMI2FSzDCt-nok   Create the groups with the cards and have them write their names and answer on the board.
Part 1 (5 mins)	The Teacher shows mandalas and indigenous circular art
Part 2 (20 mins)	Students work in random groups of 3 at the tables with the paper, compass, ruler, acrylic.  Teacher circulates, asking probing questions such as: - What patterns can you see? -        How would you describe the patterns.
Part 3 (15 mins)
Part 4 (15 mins)	Consolidation Class discusses why coordinates are exact values. Explain the meaning of Symmetry. Discuss the aesthetics of mathematics
Part 6 (5 min)	Check for Understanding (CFU)   TBD- Pages from Math Links 12