Graphing Sine and Cosine Functions
Students graph sine and cosine functions, identifying amplitude, period, phase shift, and vertical shift.
Key Questions
- Analyze how changes in amplitude, period, phase shift, and vertical shift transform the basic sine and cosine graphs.
- Construct the equation of a sinusoidal function given its graph or key characteristics.
- Predict the behavior of real-world periodic phenomena using sinusoidal models.
Ontario Curriculum Expectations
About This Topic
Inclusive leadership in athletics focuses on creating environments where every participant, regardless of skill level, gender, or background, feels a sense of belonging. Grade 12 students explore different leadership styles, from servant leadership to transformational leadership, and how these styles impact team cohesion. They learn to modify games and activities to ensure everyone is challenged and included, which is a core component of the Ontario 'Living Skills' and 'Active Living' expectations.
This topic also addresses the importance of centering diverse perspectives, including Indigenous ways of knowing and the inclusion of students with disabilities. By focusing on the 'we' rather than the 'me,' students develop the emotional intelligence required for leadership in any field. This topic comes alive when students are tasked with designing and leading their own inclusive 'mini-tournaments' or practice sessions.
Active Learning Ideas
Inquiry Circle: The Inclusion Audit
Students observe a standard game and identify three barriers to participation (e.g., physical, social, or skill-based). They then brainstorm and test three 'modifications' (e.g., changing the ball size, adding a 'everyone must touch' rule) to make the game more inclusive.
Role Play: The Leadership Style Swap
During a drill, student leaders are assigned a specific style (e.g., 'The Encourager,' 'The Strategist,' or 'The Servant Leader'). Afterward, the group discusses which style made them feel most valued and why.
Think-Pair-Share: Defining a 'Good Leader'
Students individually list the traits of the best leader they've ever had. They pair up to find commonalities and then share one 'non-negotiable' trait for inclusive leadership with the whole class to create a 'Class Leadership Charter.'
Watch Out for These Misconceptions
Common MisconceptionThe best player is always the best leader.
What to Teach Instead
Leadership is about influence and empathy, not just skill. A great leader might be someone who organizes the team or supports a struggling peer. Role-playing different leadership styles helps students see that 'quiet' leadership is often more effective for team cohesion.
Common MisconceptionInclusion means 'making the game easy.'
What to Teach Instead
True inclusion means 'equity of challenge', where everyone is playing at their own 'edge.' Students need to learn how to modify games so they remain competitive while being accessible. The 'Inclusion Audit' helps them practice this balance.
Suggested Methodologies
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Frequently Asked Questions
How can I teach leadership to students who don't see themselves as 'leaders'?
How does Indigenous culture view leadership in sports?
What are some simple ways to modify games for inclusion?
How can active learning help students understand inclusive leadership?
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
unit plannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
rubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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