Secondary Mathematics II
Educational Links
Strand: GEOMETRY - Circles (G.C)
Understand and apply theorems about circles
(Standard G.C.1-4). Find arc lengths and areas of sectors of circles. Use this as a basis for introducing the radian as a unit of measure. It is not intended that it be applied to the development of circular trigonometry in this course
(Standard G.C.5).
Standard G.C.4
Construct a tangent line from a point outside a given circle to the circle.
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Inscribing and Circumscribing Right Triangles
This lesson unit is intended to help educators assess how well students are able to use geometric properties to solve problems.
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Module 7: Circles from a Geometric Perspective - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 7, Circles: A Geometric Perspective, is composed of four learning cycles. In the first learning cycle, students use rotations and perpendicular bisectors to find the center of a circle. The second learning cycle in Module 7 builds on the circle relationships that students have learned so far in the module to develop a formula for the perimeter and area of a regular polygon. The third learning cycle addresses relationships among central angles, radii, arcs, and sectors. Students calculate arc length and the area of a sector. The final learning cycle in Module 7 is an intuitive approach to volume of prisms, pyramids, and cylinders.
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Module 7: Circles from a Geometric Perspective - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 7, Circles: A Geometric Perspective, is composed of four learning cycles. In the first learning cycle, students use rotations and perpendicular bisectors to find the center of a circle. The second learning cycle in Module 7 builds on the circle relationships that students have learned so far in the module to develop a formula for the perimeter and area of a regular polygon. The third learning cycle addresses relationships among central angles, radii, arcs, and sectors. Students calculate arc length and the area of a sector. The final learning cycle in Module 7 is an intuitive approach to volume of prisms, pyramids, and cylinders.
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Student Task: Circles in Triangles
In this task, the students have to find the radius of circles inscribed in various sizes of right triangle.
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Student Task: Temple Geometry
During the Edo period (1603-1867) of Japanese history, geometrical puzzles were hung in the holy temples as offerings to the gods and as challenges to worshippers. Here is one such problem for students to investigate.
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Tangent to a circle from a point
This task is designed to allow students to construct a tangent line from a point outside a given circle to the circle.
http://www.uen.org - in partnership with Utah State Board of Education
(USBE) and Utah System of Higher Education
(USHE). Send questions or comments to USBE
Specialist -
Lindsey
Henderson
and see the Mathematics - Secondary website. For
general questions about Utah's Core Standards contact the Director
-
Jennifer
Throndsen.
These materials have been produced by and for the teachers of the
State of Utah. Copies of these materials may be freely reproduced
for teacher and classroom use. When distributing these materials,
credit should be given to Utah State Board of Education. These
materials may not be published, in whole or part, or in any other
format, without the written permission of the Utah State Board of
Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah
84114-4200.