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 asects of the task and its potential use. Here are the first few lines of the commentary for this task: A square is inscribed in a circle which is inscribed in a square as shown below. Note that the vertices of the inner square meet the midpoints of the o...

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 asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below is a picture of rectangle $ABCD$ with diagonal $AC$. Draw the image of triangle $ACD$ when it is rotated $180^\circ$ about vertex $D$. Call $A'$ ...

Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the preimage to the image.

Describe a possible sequence of rigid transformations between two congruent figures.

Students will create an interactive Powerpoint game where they will create real world problems that are used as clues to move on to the next level. Problems include all 8th grade math standards.

An interactive applet and associated web page that demonstrate the concept of congruent angles. Three angles are shown which always remain congruent as you drag any defining point on any angle. They all change together. This is designed to demonstrate that the angles are considered congruent even if they are in different orientations and the line segments making them up are different lengths. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate the congruence of polygons. The applet presents nine polygons that are in fact congruent, but don't look it because they are reflected and rotated in various ways. If you click on one, it rotates and flips as needed, then slides over the top of another to show it is congruent. The web page describes how to determine if two polygons are congruent. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This task is designed to give students insight into the effects of translations, rotations, and reflections on geometric figures in the context of showing that two figures are congruent.

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

An interactive applet and associated web page that demonstrate the concept of congruent triangles. Applets show that triangles a re congruent if the are the same, rotated, or reflected. In each case the user can drag one triangle and see how another triangle changes to remain congruent to it. The web page describes all this and has links to other related pages. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b).

In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.

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

This lesson unit is intended to help you assess how students reason about geometry and, in particular, how well they are able to: use facts about the angle sum and exterior angles of triangles to calculate missing angles; apply angle theorems to parallel lines cut by a transversal; interpret geometrical diagrams using mathematical properties to identify similarity of triangles.

This lesson unit is intended to help you assess how well students are able to: interpret a situation and represent the variables mathematically; select appropriate mathematical methods; interpret and evaluate the data generated; and communicate their reasoning clearly.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

En este módulo, los estudiantes aprenden sobre traducciones, reflexiones y rotaciones en el avión y, lo que es más importante, cómo usarlas para definir con precisión el concepto de congruencia. A lo largo del tema A, sobre las definiciones y propiedades de los movimientos rígidos básicos, los estudiantes verifican experimentalmente sus propiedades básicas y, cuando son factibles, profundicen su comprensión de estas propiedades utilizando el razonamiento. Todas las lecciones del tema B demuestran a los estudiantes la capacidad de secuenciar varias combinaciones de movimientos rígidos mientras mantienen las propiedades básicas de los movimientos rígidos individuales. Los estudiantes aprenden que la congruencia es solo una secuencia de movimientos rígidos básicos en el Tema C, y el Tema D comienza el aprendizaje del Teorema Pitagórico.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the concept of congruence. Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these properties using reasoning. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while maintaining the basic properties of individual rigid motions. Students learn that congruence is just a sequence of basic rigid motions in Topic C, and Topic D begins the learning of Pythagorean Theorem.

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

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.  Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

This lesson unit is intended to help teachers assess how well students are able to: use the area of right triangles to deduce the areas of other shapes; use dissection methods for finding areas; organize an investigation systematically and collect data; deduce a generalizable method for finding lengths and areas (The Pythagorean Theorem.)

The goal of this task is to give students experience applying and reasoning about reflections of geometric figures using their growing understanding of the properties of rigid motions. In the case of reflecting a rectangle over a diagonal, the reflected image is still a rectangle and it shares two vertices with the original rectangle.

This lesson unit is intended to help teachers assess how well students are able to: recognize and visualize transformations of 2D shapes; and translate, reflect and rotate shapes, and combine these transformations. It also aims to encourage discussion on some common misconceptions about transformations.

This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence. As an instructional task, it can help students build up their understanding of the relationship between rigid motions and congruence.

Learn how and when the Eastern Shoshone came to Wyoming, what are the Shoshone values, and what are the people of the Eastern Shoshone like? In the accompanying lessons plans (found in the Support Materials), students will gain an understanding of the Fort Bridger Treaty of 1868 including its importance to the state of Wyoming and the Eastern Shoshone Tribe in 1868 and today. The American Bison, or Buffalo as preferred by most tribes, has a significant existence among the Native American people. For thousands of years, the great American Buffalo roamed the Great Plains, migrating from north to south, searching for areas on which to thrive. The Shoshone people depended on the buffalo for many things that included food, clothing, and shelter. Every part of the buffalo was used and provided for the people.

LEARNING OBJECTIVES:

Students will study (Highlight, paraphrase and report) the Treaty of 1868 between the Eastern Shoshone Tribe and the United States Government.
Students will learn about the Eastern Shoshone people through the use of research and technology.
Students will understand that the history of the Shoshone people in the Wind River Mountains dates back thousands of years.
Students will understand that the circle of life continues in a perpetual cycle and is passed on through oral tradition. These stories often taught a lesson to young people.
Students will understand the indigenous perspective of interconnectedness. Students will understand how bison populations were devastated by western expansion.
Students will learn how to construct, read, compare and analyze different population graphs.
Students will understand how the diets of the Shoshone people varied depending on the areas in which they lived.
Students will acquire knowledge of the Wind River Reservation communities and be able to identify these locations on a map.
Students will be able to further describe how their culture has shaped them.
Students will be able to define the concept of culture.
Students will be able to explain some of the attributes of culture.