Volume of Cones
Learning and applying the formula for the volume of a cone.
Key Questions
- Explain the relationship between the volume of a cone and a cylinder with the same base and height.
- Construct solutions to problems involving the volume of cones.
- Predict how changes in radius or height impact the volume of a cone.
Common Core State Standards
About This Topic
The End of Reconstruction examines the period from 1870 to 1877, when Northern support for the rebuilding of the South faded, leading to the rise of Jim Crow laws. Students learn about the 'Compromise of 1877,' which ended federal military occupation of the South in exchange for a Republican presidency. The curriculum also covers the rise of the Ku Klux Klan and the systemic efforts to disenfranchise African American voters.
This topic is essential for understanding the long-term legacy of the Civil War and the roots of the 20th-century Civil Rights Movement. It explores the concept of a 'splendid failure', an era of great progress that was ultimately undone. Students grasp this concept faster through structured discussion and peer explanation, as they analyze the 'push and pull' of political interests that led to the abandonment of Reconstruction.
Active Learning Ideas
Simulation Game: The Compromise of 1877
Students act as political negotiators in the disputed election of 1876. They must decide whether to give the presidency to Hayes in exchange for removing troops from the South, experiencing the 'backroom deal' that ended Reconstruction.
Gallery Walk: The Rise of Jim Crow
Display examples of 'Black Codes' and early Jim Crow laws. Students use sticky notes to identify how each law was designed to bypass the 14th and 15th Amendments and maintain white supremacy.
Think-Pair-Share: Was Reconstruction a Success or Failure?
Students list three successes (e.g., schools, amendments) and three failures (e.g., violence, sharecropping). They discuss in pairs which side 'won' in the long run and share their conclusions with the class.
Watch Out for These Misconceptions
Common MisconceptionReconstruction ended because the South was 'rebuilt.'
What to Teach Instead
It ended because Northerners lost interest and political will, and because of a controversial presidential election. Peer discussion on 'political fatigue' helps students understand why the North walked away.
Common MisconceptionSharecropping was just a different kind of job.
What to Teach Instead
Sharecropping was often a 'cycle of debt' that kept formerly enslaved people tied to the land, almost like slavery. A 'sharecropping math' activity helps students see how the system was designed to keep workers poor.
Suggested Methodologies
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Frequently Asked Questions
What was the Compromise of 1877?
What were 'Black Codes'?
Why did the North lose interest in Reconstruction?
How can active learning help students understand the legacy of Reconstruction?
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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