Navigating through geometry in grades 6-8
Series: Navigations series.
Grades: 6 7 8
Edition: CD-ROM: Macintosh/Windows version.
Publisher: National Council of Teachers of Mathematics (NCTM)
Coordinate systems. Curriculum. Deductive reasoning. Geometry. Inductive reasoning. Instructional issues. Process skills. Shapes. Spatial sense. Symmetry. Teaching methods. Transformations. Visualization.
Lessons and activities.
This book with CD-ROM, part of the NAVIGATIONS series, is written to help teachers introduce geometric concepts to students in grades 6-8. The NAVIGATIONS series, designed as a curriculum supplement, extends the National Council of Teachers of Mathematics' Principles and Standards for School Mathematics into classroom practice. Each book in the series addresses one content standard in one of four grade bands (preK to 2, 3 to 5, 6 to 8, and 9 to 12). All books contain background information about the development of mathematical thinking and complete lesson plans with activities to engage, explore, and extend student understanding. Lesson plans include goals for student accomplishment and questions to stimulate students' thinking about mathematics. The accompanying CDs contain grade-band-specific professional development readings and applets for interactive student exploration of concepts.
This book's geometry lessons emphasize geometric thinking and are designed to help students make the transition from empirically-based, inductive reasoning to the deductive use of rules and abstract thinking. In addition, students learn to use multiple representations and transformations as tools for analysis. In one lesson, students explore dilations as a method for creating similar figures in coordinate space. Students draw an irregular pentagon and a triangle on a coordinate plane. Students identify the coordinates of each vertex, multiply the coordinates by 2, and plot the new vertices on the plane. The activity is repeated with the factor one-half. Discussion questions and extensions are included. The accompanying CD contains five applets including software for coordinate geometry and transformation explorations. Using the applets students can also spin and slice polyhedra and sort shapes using Venn diagrams. (Author/JRS)
Table of Contents:
About this book
1. Characteristics and properties of shapes
Geodee's sorting scheme
Exploring similar figures
Using Venn diagrams to reason about shapes
Midsegments of triangles
Reasoning about the Pythagorean theorem
2. Coordinate geometry and other representational systems
Constructing geometric figures in coordinate space
Exploring lines, midpoints, and triangles using coordinate geometry
Similarity and the coordinate plane
Exploring the slopes of parallel and perpendicular lines
3. Transformations and symmetry
Reflection of images
Translations, reflections, and rotations
Using scale factors
Explorations with lines of symmetry
Understanding types of symmetry
Rotational symmetry and regular polygons
Drawing figures with symmetry
4. Visualization, spatial reasoning, and geometric modeling
Exploring shapes with tangrams
Logos and geometric properties
Cross sections of three-dimensional shapes
I took a trip on a train
Constructing three-dimensional figures
Looking back and looking ahead
Blackline masters and solutions
Table of standards and expectations, geometry, preK-12
Coordinate geometry tool
I took a trip on a train
Spinning and slicing polyhedra
Blackline masters and templates
Isometric dot paper
Nets of polyhedra
Readings and supplemental materials
National Council of Teachers of Mathematics, Inc. (NCTM)
1906 Association Drive
Reston VA 20191
Fax: (703) 476-2970
Description: 1 text (paperback) and 1 CD-ROM (Macintosh/Windows)
National Council of Teachers of Mathematics (NCTM)
Terms governing use and reproduction: Permission to photocopy limited materials from Navigating through geometry in grades 3-5 is granted for educational purposes. Blackline masters from the CD-ROM may be downloaded and reproduced for classroom distribution; applets may be used in one classroom at a time.
|Authors: David K Pugalee; Jeffrey Frykholm; Art Johnson; Hannah Slovin; Carol Malloy; Ron Preston.|
Windows--IBM or compatible PC; Adobe Acrobat Reader; an Internet browser such as Netscape or Internet Explorer 5.x or above; specific requirements not listed in materials on hand.
Macintosh--Macintosh; Adobe Acrobat Reader; an Internet browser such as Netscape or Internet Explorer 5.x or above; specific requirements not listed in materials on hand.
1 text (viii, 128 pages : illustrations ; 28 cm.)
1 CD-ROM (Macintosh/Windows : color ; 4.75 in.)
Record Created: 03/12/2003 Last Modified: 08/23/2005