Mathematics Grade 8
Educational Links

Strand: GEOMETRY (8.G)

Understand congruence and similarity using physical models, transparencies, or geometry software (Standards 8.G.1-5). Understand and apply the Pythagorean Theorem and its converse (Standards 8.G.6-8). Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres (Standard 8.G.9).

Standard 8.G.1

Verify experimentally the properties of rotations, reflections, and translations:

• 3D Transmographer
  This lesson contains an applet that allows students to explore translations, reflections, and rotations.
• A Scaled Curve
  The goal of this task is to motivate and prepare students for the formal definition of dilations and similarity transformations. While these notions are typically applied to triangles and quadrilaterals, having students engage with the concepts in a context where they don't have as much training (these more "random" curves) lead students to focus more on the properties of the transformations than the properties of the figure.
• Chapter 9 - Mathematical Foundation (UMSMP)
  This is Chapter 9 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Transformations, Congruence and Similarity.
• Chapter 9 - Student Workbook (UMSMP)
  This is Chapter 9 of the Utah Middle School Math: Grade 8 student workbook. It focuses on these topics: Transformations, Congruence and Similarity.
• Geometry (8.G) - 8th Grade Core Guide
  The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 8 Geometry.
• Grade 8 Math Module 2: The Concept of Congruence (EngageNY)
  In this Grade 8 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.
• Grade 8 Unit 1: Transformations, Congruence, and Similarity (Georgia Standards)
  In this unit students will develop the concept of transformations and the effects that each type of transformation has on an object; explore the relationship between the original figure and its image in regards to their corresponding parts being moved an equal distance which leads to concept of congruence of figures; learn to describe transformations with both words and numbers; relate rigid motions to the concept of symmetry and to use them to prove congruence or similarity of two figures; physically manipulate figures to discover properties of similar and congruent figures; and focus on the sum of the angles of a triangle and use it to find the measures of angles formed by transversals (especially with parallel lines), find the measures of exterior angles of triangles, and to informally prove congruence.
• Identifying Unknown Transformations
  This applet allows the student to drag a shape and then observe the changes to its behavior. They then determine whether the alteration is due to reflection, a rotation, or a translation/slide transformation.
• Is this a rectangle?
  The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle.
• Origami Silver Rectangle
  The purpose of this task is to apply geometry in order analyze the shape of a rectangle obtained by folding paper. The central geometric ideas involved are reflections (used to model the paper folds), analysis of angles in triangles, and the Pythagorean Theorem.
• Partitioning a Hexagon
  The purpose of this task is for students to find a way to decompose a regular hexagon into congruent figures. This is meant as an instructional task that gives students some practice working with transformations.
• Reflecting a rectangle over a diagonal
  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.
• Reflection
  In this animated video from UEN (Utah Education Network) students learn about one type of movement for geometric shapes - reflection. In the accompanying activity students demonstrate understanding by creating a geometric figure on a plane and then reflecting it into another quadrant. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Reflections, Rotations, and Translations
  The goal of this task is to use technology to visualize what happens to angles and side lengths of a polygon (a triangle in this case) after a reflection, rotation, or translation.
• Rotation
  In this animated Math Shorts video from the Utah Education Network, learn about rotation, which describes how a geometric shape turns around a point, called the center of rotation. In the accompanying classroom activity, students are given two rotations from a handout and work in pairs to try to determine whether one figure is a rotation of the other figure around the given point. Note: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Same Size, Same Shape?
  The purpose of the task is to help students transition from the informal notion of congruence as "same size, same shape" that they learn in elementary school and begin to develop a definition of congruence in terms of rigid transformations.
• Student Task: Short Tasks - Geometry
  A set of short tasks for grades 7 & 8 dealing with geometry.
• Translations, Reflections, and Rotations
  Students are introduced to the concepts of translation, reflection and rotation in this lesson plan.

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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.