Unpacked Content
Knowledge
Students know:
- Techniques to find the area and perimeter of parallelograms.
- Techniques to find the area of circles or polygons.
Skills
Students are able to:
- Accurately decompose circles, cylinders, pyramids, and cones into other geometric shapes.
- Explain and justify how the formulas for circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone may be created from the use of other geometric shapes.
Understanding
Students understand that:
- Geometric shapes may be decomposed into other shapes which may be useful in creating formulas.
- Geometric shapes may be divided into an infinite number of smaller geometric shapes, and the combination of those shapes maintain the area and volume of the original shape.
Vocabulary
- Dissection arguments
- Cavalieri's Principle
- Cylinder
- Pyramid
- Cone
- Ratio
- Circumference
- Parallelogram
- Limits
- Conjecture
- Cross-section
