- MAFS.912.G-C.2.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
|
Generated on 9/18/2025 at 4:08 PM |
The webpage this document was printed/exported from can be found at the following URL:
https://www.cpalms.org/PreviewAccessPoint/Preview/16179
https://www.cpalms.org/PreviewAccessPoint/Preview/16179
Apply the formula to the area of a sector (e.g., area of a slice of pie).
Clarifications:
Essential Understandings
Concrete:
- Identify a circle that would fit around a triangle using manipulatives.
- Identify a circle that would fit inside a triangle using manipulatives.
- Identify the circumcenter of the figure.
- Identify the incenter of the figure.
- Draw a circle that would fit around a triangle using manipulatives (compass).
- Draw a circle that would fit inside a triangle using manipulatives (compass).
- Understand the following concepts and vocabulary: inscribed, circumscribed, circle, triangle, compass, circumcenter, construction, equidistant, vertex and incenter.
- Identify inscribed circles using pictures or geometry software.
- Identify circumscribed circles using pictures or geometry software.
Access Point #: MAFS.912.G-C.2.AP.5c (Archived Access Point)
Access Point Standards
Visit the specific benchmark webpage to find related instructional resources.
Access Point Information
Number:
MAFS.912.G-C.2.AP.5c
Category:
Access Points
Date Adopted or Revised:
07/14
Cluster:
Find arc lengths and areas of sectors of circles. (Geometry - Additional Cluster) :
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Access Point Courses
- Foundational Skills in Mathematics 9-12 (#1200400): This course supports students who need additional instruction in foundational mathematics skills as it relates to core instruction. Instruction will use explicit, systematic, and sequential approaches to mathematics instruction addressing all strands including number sense & operations, algebraic reasoning, functions, geometric reasoning and data analysis & probability. Teachers will use the listed benchmarks that correspond to each students’ needs.
Effective instruction matches instruction to the need of the students in the group and provides multiple opportunities to practice the skill and receive feedback. The additional time allotted for this course is in addition to core instruction. The intervention includes materials and strategies designed to supplement core instruction.
- Geometry (#1206310): In Geometry, instructional time will emphasize five areas: (1) proving and applying relationships and theorems involving two-dimensional figures using Euclidean geometry and coordinate geometry; (2) establishing congruence and similarity using criteria from Euclidean geometry and using rigid transformations; (3) extending knowledge of geometric measurement to two-dimensional figures and three-dimensional figures; (4) creating and applying equations of circles in the coordinate plane and (5)developing an understanding of right triangle trigonometry.
All clarifications stated, whether general or specific to Geometry, are expectations for instruction of that benchmark.
Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
- Geometry Honors (#1206320): In Geometry Honors, instructional time will emphasize five areas: (1) proving and applying relationships and theorems involving two-dimensional figures using Euclidean geometry and coordinate geometry; (2) establishing congruence and similarity using criteria from Euclidean geometry and using rigid transformations; (3) extending knowledge of geometric measurement to two-dimensional figures and three-dimensional figures; (4) creating and applying equations of circles in the coordinate plane and (5) developing an understanding of right triangle trigonometry.
All clarifications stated, whether general or specific to Geometry Honors, are expectations for instruction of that benchmark.
Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
- Geometry for Credit Recovery (#1206315): In Geometry for Credit Recovery, instructional time will emphasize six areas: (1) proving and applying relationships and theorems involving two-dimensional figures using Euclidean geometry and coordinate geometry; (2) establishing congruence and similarity using criteria from Euclidean geometry and using rigid transformations; (3) extending knowledge of geometric measurement to two-dimensional figures and three-dimensional figures; (4) creating and applying equations of circles in the coordinate plane and (5) developing an understanding of right triangle trigonometry.
All clarifications stated, whether general or specific to Geometry, are expectations for instruction of that benchmark.
Curricular content for all subjects must integrate critical-thinking, problem-solving, and workforce-literacy skills; communication, reading, and writing skills; mathematics skills; collaboration skills; contextual and applied-learning skills; technology-literacy skills; information and media-literacy skills; and civic-engagement skills.
Credit Recovery courses are credit bearing courses with specific content requirements defined by state academic standards (SAS). Students enrolled in a Credit Recovery course must have previously attempted the corresponding course (and/or End-of-Course assessment) since the course requirements for the Credit Recovery course are exactly the same as the previously attempted corresponding course. For example, Geometry (1206310) and Geometry for Credit Recovery (1206315) have identical content requirements. It is important to note that Credit Recovery courses are not bound by Section 1003.436(1)(a), Florida Statutes, requiring a minimum of 135 hours of bona fide instruction (120 hours in a school/district implementing block scheduling) in a designed course of study that contains student performance standards, since the students have previously attempted successful completion of the corresponding course. Additionally, Credit Recovery courses should ONLY be used for credit recovery, grade forgiveness, or remediation for students needing to prepare for an End-of-Course assessment retake.
- Access Geometry (#7912065): Access Courses:
Access courses are for students with the most significant cognitive disabilities. Access courses are designed to provide students access to grade-level general curriculum. Access points are alternate academic achievement standards included in access courses that target the salient content of Florida’s standards. Access points are intentionally designed to academically challenge students with the most significant cognitive disabilities.