This task provides an opportunity to model a concrete situation with mathematics. …
This task provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function. When the task is complete, new insight is shed on the ``Seven Circles I'' problem which initiated this investigation as is noted at the end of the solution.
This task is inspired by the derivation of the volume formula for …
This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a Ňdouble-naped coneÓ with vertex at the center of the sphere and bases equal to the bases of the cylinder.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This lesson unit is intended to help you assess how well students …
This lesson unit is intended to help you assess how well students working with square numbers are able to: choose an appropriate, systematic way to collect and organize data, examining the data for patterns; describe and explain findings clearly and effectively; generalize using numerical, geometrical, graphical and/or algebraic structure; and explain why certain results are possible/impossible, moving towards a proof.
How does a lens form an image? See how light rays are …
How does a lens form an image? See how light rays are refracted by a lens. Watch how the image changes when you adjust the focal length of the lens, move the object, move the lens, or move the screen.
This task presents students with some creative geometric ways to represent the …
This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal.
In this lesson, students will how to name angles, measure and classify …
In this lesson, students will how to name angles, measure and classify angles, identify congruent angles, and how to find angle measures using Angle Addition Postulate.
CK-12's Basic Geometry FlexBook is designed to present students with geometric principles …
CK-12's Basic Geometry FlexBook is designed to present students with geometric principles in a simpler, more graphics-oriented course. Students will explore geometry at a slower pace with an emphasis placed on visual aids and approachability.
The Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem …
The Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem solving for teaching CK-12's Basic Geometry Student Edition. The solution and assessment guides are available upon request.
CK-12 Foundation's Geometry FlexBook is a clear presentation of the essentials of …
CK-12 Foundation's Geometry FlexBook is a clear presentation of the essentials of geometry for the high school student. Topics include: Proof, Congruent Triangles, Quadrilaterals, Similarity, Perimeter & Area, Volume, and Transformations.
Module 1 embodies critical changes in Geometry as outlined by the Common …
Module 1 embodies critical changes in Geometry as outlined by the Common Core. The heart of the module is the study of transformations and the role transformations play in defining congruence. The topic of transformations is introduced in a primarily experiential manner in Grade 8 and is formalized in Grade 10 with the use of precise language. The need for clear use of language is emphasized through vocabulary, the process of writing steps to perform constructions, and ultimately as part of the proof-writing process.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
Just as rigid motions are used to define congruence in Module 1, …
Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2. To be able to discuss similarity, students must first have a clear understanding of how dilations behave. This is done in two parts, by studying how dilations yield scale drawings and reasoning why the properties of dilations must be true. Once dilations are clearly established, similarity transformations are defined and length and angle relationships are examined, yielding triangle similarity criteria. An in-depth look at similarity within right triangles follows, and finally the module ends with a study of right triangle trigonometry.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
Module 3, Extending to Three Dimensions, builds on students understanding of congruence …
Module 3, Extending to Three Dimensions, builds on students understanding of congruence in Module 1 and similarity in Module 2 to prove volume formulas for solids. The student materials consist of the student pages for each lesson in Module 3. The copy ready materials are a collection of the module assessments, lesson exit tickets and fluency exercises from the teacher materials.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
In this module, students explore and experience the utility of analyzing algebra …
In this module, students explore and experience the utility of analyzing algebra and geometry challenges through the framework of coordinates. The module opens with a modeling challenge, one that reoccurs throughout the lessons, to use coordinate geometry to program the motion of a robot that is bound within a certain polygonal region of the planethe room in which it sits. To set the stage for complex work in analytic geometry (computing coordinates of points of intersection of lines and line segments or the coordinates of points that divide given segments in specific length ratios, and so on), students will describe the region via systems of algebraic inequalities and work to constrain the robot motion along line segments within the region.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
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