Pre-Geometry Brain Teasers

Transcription

1 Pre-Geometry Author: Sylvia J. Connolly Introduction Geometry is the study of space. Space exists in the third dimension. This is the dimension in which we live. There is length, width, and depth to our reality. Twodimensional space exists only in the mind length and width (no depth). Onedimensional space also exists in the mind a line that has direction but no thickness. No dimension is almost impossible to imagine, but it is a point having no measurements. All dimensions other than the third have to be imagined. Students who have vivid imaginations are wonderful candidates to learn geometry. If you have students who like to draw and are visually inclined, geometry should be fun for them. The whole organization of geometry is similar to the rules of a game. You cannot play the game unless you know the rules. Learning the rules makes you a better game player. Geometry is the same way. Pre-Geometry will take the main rules of geometry and create problems that will reinforce the rules. This book is not meant to teach geometry but to supplement the textbook with activities that encourage students to expand their thinking. The exercises are also meant to be a springboard from which you as the teacher can think of other exercises that engage the class. Have the students use their previous work. Remind them that when one works in the business world, he or she often stores previous work for future reference. Teaching students to do the same is great training for the future. Contributing Author: Karen J. Goldfluss, M.S. Ed. Editor: Stephanie Buehler, M.P.W., M.A. Teacher Created Materials, Inc Industry Way Westminster, CA Teacher Created Materials, Inc. Made in U.S.A. ISBN Graphic Illustrator: James Edward Grace Cover Artist: Larry Bauer Chris Macabitas The classroom teacher may reproduce copies of materials in this book for classroom use only. The reproduction of any part for an entire school or school system is strictly prohibited. No part of this publication may be transmitted, stored, or recorded in any form without written permission from the publisher.

2 Table of Contents How to Use This Book Terms Used in Geometry Formulas Used in Geometry Tools Points in Geometry Teacher Pages: Points, Lines, and Patterns in Geometry Connecting Points Line Segments Using Friends Names Copying a Line Segment More Line Segments Simple Map Copying Perspective Pascal s Pattern Angles and Triangles Teacher Pages: Angles and Triangles Triangles from Points Naming Angles Angles Alphabet Angles Using Vectors Triangle Puzzler Euclid s Thinking Triangles Sides of a Triangle A Line and Point Postulate Pythagoras and the Right Triangle Circles Teacher Page: Circles Creating Circles Making a Clock Identifying Circle Terms Squaring Off a Circle Patterns Using a Circle Types of Circles Pi and Circumference Area of a Sector Finding Areas Within Areas #2218 Pre-Geometry 2 Teacher Created Materials, Inc.

3 Tables of Contents (cont.) Using Geometry Teacher Pages: Using Geometry Comparing in Geometry Congruence Similarity Facts About Similar Triangles Transformation Identifying Symmetry Symmetry By Reflection Symmetry By Translation Symmetry By Rotation Tessellations Designing Geometric Quilt Block Patterns Measuring Surface Area Measuring Distance Dream Catchers Pie Charts Tangrams How Many Diagonals? Square Versus Rectangle Indirectly Measuring an Object Solid Geometry Teacher Page: Solid Geometry Polyhedra A Closer Look at Polyhedra Polyhedron Patterns Finding Volume Teacher Created Materials, Inc. 3 #2218 Pre-Geometry

4 How to Use This Book The brain teaser exercises in this book require little preparation for the student or teacher. Each exercise begins with a set of student directions. Where necessary, teacher directions and/or solutions are provided on pages marked Teacher Page at the beginning of each section. As your students work through exercises in this book, keep the following information in mind. 1. Read the directions. Take some time and think about how this relates to all of geometry. If students do the exercises differently from the way in which you or I would do them, don t mark them incorrect. Try to figure out how they thought this out. Try to understand how they think. 2. When making lines, use a sharp pencil and a straight edge. Don t use the side of a book or a card. 3. Geometry is related to art. Some of your students will create beautiful patterns that you will want to display. Make certain that everyone is encouraged to participate in a classroom display. Note: Where possible, metric conversions have been provided. If metric measurement is not given, add or substitute the metric conversion information before reproducing a page. The tools needed include the following: sharp pencil protractor calculator colored pencils or pens compass straight edge with measure #2218 Pre-Geometry 4 Teacher Created Materials, Inc.

5 Alphabet Angles Directions: Many capital letters are made entirely of line segments and angles. The angles for each of these letters are indicated below. On separate paper, make an enlarged set of these letters. (Your letters should be large enough for you to measure the angles.) Use a protractor to measure the angles. Then, in the box, write the total number of degrees for each letter. A = E = F = H = I = K = L = M = N = T = V = W = X = Y = Z = Now create 10 words from these letters. Write the correct number of degrees for the inside angles of each letter in the word, add these, and write the total for each word. An example is provided. Example: IT = = Teacher Created Materials, Inc. 27 #2218 Pre-Geometry

6 Sides of a Triangle Directons: Measure the sides of these triangles (in centimeters) to see if you can discover another of Euclid s theorems. Write it on the lines provided. 1. C 2. F A B D E side AB side AC side CB side DE side DF side FE 3. H 4. L I G J K side GI side GH side HI side JK side JL side LK O R Q M N side MN side MO side ON side PQ side PR side RQ P Teacher Created Materials, Inc. 33 #2218 Pre-Geometry