Unpacked Content
Knowledge
Students know:
- Techniques to use dilations (including using dynamic geometry software) to create circles with arcs intercepted by same central angles.
- Techniques to find arc length.
- Formulas for area and circumference of a circle.
Skills
Students are able to:
- Reason from progressive examples using dynamic geometry software to form conjectures about relationships among arc length, central angles, and the radius.
- Use logical reasoning to justify (or deny) these conjectures and critique the reasoning presented by others.
- Interpret a sector as a portion of a circle, and use the ratio of the portion to the whole circle to create a formula for the area of a sector.
Understanding
Students understand that:
- Radians measure the ratio of the arc length to the radius for an intercepted arc.
- The ratio of the area of a sector to the area of a circle is proportional to the ratio of the central angle to a complete revolution.
Vocabulary
- Similarity
- Constant of proportionality
- Sector
- Arc
- Derive
- Arc length
- Radian measure
- Area of sector
- Central angle
- Dilation
