Verifying Trigonometric Identities
Students will use algebraic manipulation and fundamental identities to verify more complex trigonometric identities.
Key Questions
- Design a strategy to verify a complex trigonometric identity.
- Analyze common pitfalls and strategies when attempting to verify identities.
- Critique different approaches to verifying the same identity.
Common Core State Standards
About This Topic
The Plessy Era and Black Resistance covers the strategies for survival and progress developed by the African American community during the height of Jim Crow. This topic focuses on the intense debate between Booker T. Washington and W.E.B. Du Bois over the best path to racial equality. Students also examine the role of the Black church, the growth of Black-owned businesses, and the founding of the NAACP and the Niagara Movement.
For 11th graders, this topic is essential for recognizing that Black Americans were not passive victims of Jim Crow but active agents of change. It highlights the diversity of thought within the Black community and the long-term foundations of the modern Civil Rights Movement. Students grasp these complex ideological shifts faster through structured debates and collaborative investigations into the 'self-help' institutions of the era.
Active Learning Ideas
Formal Debate: Washington vs. Du Bois
Students take on the roles of supporters of both leaders. They debate whether 'industrial education' and economic self-help (Washington) or 'higher education' and political agitation (Du Bois) is the better strategy for the time.
Inquiry Circle: The Niagara Movement
Small groups research the founding of the Niagara Movement and its evolution into the NAACP. They must identify the specific goals of the organization and how they differed from the 'accommodationist' approach.
Think-Pair-Share: The 'Talented Tenth'
Students read Du Bois's essay on the 'Talented Tenth.' They work in pairs to discuss his idea that a small group of educated Black leaders would lead the race to equality, and the potential pros and cons of this elitist approach.
Watch Out for These Misconceptions
Common MisconceptionBooker T. Washington didn't care about civil rights.
What to Teach Instead
While he publicly advocated for economic focus, he secretly funded legal challenges to segregation. Peer-led analysis of his 'Atlanta Compromise' speech alongside his private actions helps students see the complexity of his strategy.
Common MisconceptionThe NAACP was the first organization to fight for Black rights.
What to Teach Instead
It was preceded by many other groups, including the Afro-American Council and the Niagara Movement. A 'genealogy of resistance' activity helps students see the continuous history of Black organizing.
Suggested Methodologies
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Frequently Asked Questions
What was the 'Atlanta Compromise'?
How did W.E.B. Du Bois's approach differ from Washington's?
What role did Black businesses play in the Jim Crow era?
How can active learning help students understand Black resistance?
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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