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Module 2 builds on students' previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Algebra
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
08/15/2014
Unrestricted Use
CC BY
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Reference Sheet for students with definitions and formulas used when looking at circles from a geometric perspective.

Subject:
Mathematics
Material Type:
Diagram/Illustration
Student Guide
Unit of Study
Author:
Kristine Evans
11/24/2020
Conditional Remix & Share Permitted
CC BY-SA
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Subject:
Mathematics
Material Type:
Lesson Plan
Author:
Mindy Branson
04/23/2018
Educational Use
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In this video segment you’ll discover how using concentric circles can help you determine how much paint is needed to cover the deck of a carousel.

Subject:
Geometry
Mathematics
Material Type:
Lesson
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media Common Core Collection
Author:
New York Network
WNET
05/13/2010
Educational Use
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Using circumference, this segment measures the total distant traveled by two carousel riders after the carousel has rotated 10 times.

Subject:
Geometry
Mathematics
Material Type:
Lesson
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media Common Core Collection
Author:
New York Network
WNET
05/13/2010
Unrestricted Use
CC BY
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The purpose of this task is to strengthen students' understanding of area. It could be assigned in class to individuals or small groups or given as a homework exercise to generate interesting discussions the following day. The relatively high levels of complexity and technical demand enhance its instructional value.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
05/01/2012
Only Sharing Permitted
CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to: use the Pythagorean theorem to derive the equation of a circle; and translate between the geometric features of circles and their equations.

Subject:
Geometry
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
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This lesson unit is intended to help teachers assess how well students are able to: translate between the equations of circles and their geometric features; and sketch a circle from its equation.

Subject:
Geometry
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Unrestricted Use
CC BY
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This resource is an ordered outline for teachers who need guidance on what to cover for the geometry portion of the GED math test. Downloadable links are embedded in the outline as well as emphasis suggestions. The outline lists concepts to cover in a logical order for success on the geometry portion of the GED.

Subject:
Mathematics
Material Type:
Homework/Assignment
Syllabus
Teaching/Learning Strategy
04/25/2018
Conditional Remix & Share Permitted
CC BY-NC-SA
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This site teaches the Geometry of Circles to High Schoolers through a series of 1084 questions and interactive activities aligned to 9 Common Core mathematics skills.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Interactive
Provider:
Provider Set:
01/09/2015
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This geometry lesson shows that that an inscribed angle is half of a central angle that subtends the same arc. [Geometry playlist: Lesson 24 of 31]

Subject:
Geometry
Mathematics
Material Type:
Lecture
Provider:
Provider Set:
Author:
Salman Khan
02/20/2011
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CC BY-NC-ND
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This lesson unit is intended to help teachers assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties: solving problems by determining the lengths of the sides in right triangles; and finding the measurements of shapes by decomposing complex shapes into simpler ones. The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

Subject:
Geometry
Mathematics
Material Type:
Assessment
Lesson Plan
Provider:
Shell Center for Mathematical Education
Provider Set:
Mathematics Assessment Project (MAP)
04/26/2013
Educational Use
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finding the relationships between segments in circles; chord-chord, tangent-tangent, and secant-tangent.

Subject:
Geometry
Mathematics
Material Type:
Lecture
Author:
Math With Mark
11/23/2016
Conditional Remix & Share Permitted
CC BY-NC-SA
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CK-12's Texas Instruments Geometry Student Edition Flexbook is a useful collection of exercises intended to enrich a student's understanding of basic geometric principles.

Subject:
Geometry
Mathematics
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Jordan, Lori
12/14/2010
Unrestricted Use
CC BY
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Student-facing 7th grade math resources. Covers scale drawings, proportion, percentages, probability, expressions, and geometry.

Subject:
Mathematics
Material Type:
Unit of Study
Provider:
Open Up Resources
05/21/2019
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In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the Angle-Angle criterion for similar triangles.  The module begins with the definition of dilation, properties of dilations, and compositions of dilations.  One overarching goal of this module is to replace the common idea of same shape, different sizes with a definition of similarity that can be applied to geometric shapes that are not polygons, such as ellipses and circles.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Geometry
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
10/17/2013
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CC BY-NC-SA
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In this classic hands-on activity, learners estimate the length of a molecule by floating a fatty acid (oleic acid) on water. This lab asks learners to record measurements and make calculations related to volume, diameter, area, and height. Learners also convert meters into nanometers. Includes teacher and student worksheets but lacks in depth procedure information. The author suggests educators search the web for more complete lab instructions.

Subject:
Chemistry
Physical Science
Material Type:
Activity/Lab
Provider:
Exploratorium
Author:
Eric Muller
The Exploratorium
11/07/2007
Unrestricted Use
CC BY
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This task shows how to inscribe a circle in a triangle using angle bisectors. A companion task, ``Inscribing a circle in a triangle II'' stresses the auxiliary remarkable fact that comes out of this task, namely that the three angle bisectors of triangle ABC all meet in the point O.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
01/21/2013
Unrestricted Use
CC BY
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This task is primarily for instructive purposes but can be used for assessment as well. Parts (a) and (b) are good applications of geometric constructions using a compass and could be used for assessment purposes but the process is a bit long since there are six triangles which need to be constructed.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
08/21/2012
Unrestricted Use
CC BY
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This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.

Subject:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics