Navigating through geometry in grades 6-8 Series: Navigations series. Grades: 6 7 8 ENC#: ENC-026884 Edition: CD-ROM: Macintosh/Windows version. Publisher: National Council of Teachers of Mathematics (NCTM) Date: 2002 Ordering Information

Subjects:

Mathematics Coordinate systems. Curriculum. Deductive reasoning. Geometry. Inductive reasoning. Instructional issues. Process skills. Shapes. Spatial sense. Symmetry. Teaching methods. Transformations. Visualization.

Resource Type:
Lessons and activities.

Abstract:
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:
[Text:]
About this book
Introduction
1. Characteristics and properties of shapes
     Geodee's sorting scheme
     Exploring triangles
     Exploring similar figures
     Dilating 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
     Isometric explorations
     Cross sections of three-dimensional shapes
     I took a trip on a train
     Constructing three-dimensional figures
     Minimizing perimeter
     Indirect measurement
     The race
Looking back and looking ahead
Appendix
     Blackline masters and solutions
     References

[CD-ROM:]
Introduction
Table of standards and expectations, geometry, preK-12
Applet activities
     Coordinate geometry tool
     I took a trip on a train
     Shape sorter
     Spinning and slicing polyhedra
     Transformation tools
Blackline masters and templates
     Blackline masters
     Grid paper
     Isometric dot paper
     Nets of polyhedra
     Tangrams
Readings and supplemental materials

Vendor: National Council of Teachers of Mathematics, Inc. (NCTM) 1906 Association Drive Reston VA 20191 orders@nctm.org (703) 620-9840 (800) 235-7566 Fax: (703) 476-2970 http://www.nctm.org

Pricing Information:

Description: 1 text (paperback) and 1 CD-ROM (Macintosh/Windows)

Cost: $31.95

ISBN: 978-0-87353-513-7

Order#: 12174

Publisher:
National Council of Teachers of Mathematics (NCTM)

Notes:
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.

Contributor(s):

Authors: David K Pugalee; Jeffrey Frykholm; Art Johnson; Hannah Slovin; Carol Malloy; Ron Preston.

Equipment:
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.

Specifications:
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