MA19.GDA.20

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.20
Derive and apply the formula for the length of an arc and the formula for the area of a sector.

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

Design by Adaptive Theme