Groovy Geometry: Games and Activities That Make Math Easy and Fun

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  • G R O O V YG E O M E T RY

    G a m e s a n d A c t i v i t i e s T h a t M a k e M a t h E a s y a n d F u n

    L y n e t t e L o n g

    J o h n W i l e y & S o n s , I n c .

    M a g i c a l M a t h

  • G R O O V YG E O M E T RY

  • A l s o i n t h e M a g i c a l M a t h s e r i e s

    Dazzling Division

    Delightful Decimals and Perfect Percents

    Fabulous Fractions

    Marvelous Multiplication

    Measurement Mania

  • G R O O V YG E O M E T RY

    G a m e s a n d A c t i v i t i e s T h a t M a k e M a t h E a s y a n d F u n

    L y n e t t e L o n g

    J o h n W i l e y & S o n s , I n c .

    M a g i c a l M a t h

  • This book is printed on acid-free paper.

    Copyright 2003 by Lynette Long. All rights reservedIllustrations copyright 2003 by Tina Cash-Walsh

    Published by John Wiley & Sons, Inc., Hoboken, New JerseyPublished simultaneously in Canada

    Design and production by Navta Associates, Inc.

    No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or byany means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permittedunder Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permissionof the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright ClearanceCenter, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web atwww.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Depart-ment, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008,email: permcoordinator@wiley.com.

    The publisher and the author have made every reasonable effort to ensure that the experiments and activitiesin this book are safe when conducted as instructed but assume no responsibility for any damage caused or sus-tained while performing the experiments or activities in the book. Parents, guardians, and/or teachers shouldsupervise young readers who undertake the experiments and activities in this book.

    For general information about our other products and services, please contact our Customer Care Departmentwithin the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002.

    Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our Web site atwww.wiley.com.

    Library of Congress Cataloging-in-Publication Data:

    Long, Lynette.Groovy geometry : games and activities that make math easy and fun / Lynette Long.

    p. cm.Includes index.ISBN 0-471-21059-5 (pbk. : alk. paper)

    1. GeometryStudy and teaching (Elementary)Activity programs. 2. Games inmathematics education. I. Title.

    QA462.2.G34 L36 2003372.7dc21 2002068996

    Printed in the United States of America

    10 9 8 7 6 5 4 3 2 1

  • v

    C o n t e n t s

    I . T h e M a g i c o f G e o m e t r y 1

    I I . A n g l e s 31 Measure Up 52 Draw It! 83 Name Game 114 Angle Pairs 135 Color by Angles 156 Perpendicular Numbers 187 Right-Angle Scavenger Hunt 20

    I I I . Tr i a n g l e s 2 38 Triangle Collage 259 Triangle Memory 2710 Triangle Angles 2911 Outside the Triangle 3112 Triangle Area 3513 Two the Same 3914 How Tall? 4215 Perfect Squares 4516 Pythagorean Proof 49

    I V. Q u a d r i l a t e r a l s 5 317 Crazy about Quadrilaterals 5518 Quadrilateral Angles 5819 String Shapes 6120 Doubt It! 6221 Rectangle Race 64

  • vi

    22 Parallelogram Presto Change-O 6623 Pattern Blocks 6824 Shape Storybook 71

    V. C i r c l e s 7 325 Around and Around 7526 Finding Pi 7727 Bicycle Odometer 8028 Circle Area 8129 Pizza Party 8330 Central Angles 86

    V I . S o l i d s 8 931 Solid Shapes 9132 Cereal Surfaces 9433 Cylinder Surfaces 9534 Cube Construction 9735 Volume of a Cylinder 9936 Building Blocks 101

    V I I . O d d s a n d E n d s 1 0 337 Shape Comparison 10538 Bulls Eye 10739 Mystery Picture 11040 Number Symmetry 112

    G e o m e t r y M a s t e r C e r t i f i c a t e 1 1 5I n d e x 1 1 7

  • 1

    I

    T H E M A G I C O FG E O M E T RY

    Geometry is the study ofpoints, lines, angles,and shapes, and their rela-tionships and properties.It sounds like a lot toknow, but much of it isalready in your head.Geometry is all aroundus. If people didnt thinkabout geometry, theywouldnt be able to buildgreat structures such as the pyr-amids, or even simple things thatlie flat such as a table.

  • 2

    Geometry can be easily learned by experimenting and having fun withthings you can find around the house. You can learn most of the principlesof geometry using cereal boxes, soda cans, plates, string, magazines, andother common household objects. So get ready to have a great time explor-ing the world of geometry.

    20

    circumference

    angle

    s90

    30 circle60

    90

    4560

    180

    20

    squaredegrees

    circumference

    angle

    s90

    30 i l60

    6

    6

    45

    Geometry starts with the concepts of lines,

    points, rays, and planes. You probably

    already have a pretty good idea of what

    lines and points are, but in geometry these

    terms have a more specific meaning than in

    everyday life. Here are some words and

    definitions youll need to know:

    Plane: a flat surface that extends infinitely in alldirections

    Point: a location on a plane

    Line: a straight path of points that goes on indefinitely

    Line segment: all of the points on a linebetween two specific end points

    Ray: all of the points on a line going out fromone end point indefinitely in one direction

    Plane geometry: the study of two-dimensional figures

    Solid geometry: the study of three-dimensional figures

    SOME KEY TERMS TO KNOW

  • 3

    I I

    A N G L E S

    A n angle is formed by the meeting of two rays at the same end point.The point where the two rays meet is called the angles vertex. Therays are called the sides of the angle.

    Angles are everywhere. When you bend your arm, your elbow becomesthe vertex of the angle formed by the two parts of your arm. When two

    streets cross each other, they form angles. Here are someexamples of angles:

    Angles are measured indegrees. If an angle is lessthan 90 degrees, it is calledan acute angle. If it isexactly 90 degrees, it iscalled a right angle. Andif it is more than 90degrees, it is called anobtuse angle.

  • 4

    In this section, youll practice measuring and creating different angles,learn the relationship between some interesting angle pairs, discover therelationship between the angles formed when two parallel lines are inter-sected by another line, practice recognizing right angles and perpendicularlines, and more.

    Along the way, youll measure angles around your house, have an angle-drawing competition, play a game of matching angle pairs, create numbersusing only perpendicular lines, and go on a right-angle scavenger hunt.These activities will teach you more than you can imagine about angles, sowhy not get started?

    20

    ang 90

    30 circle60

    90

    4560

    180

    squaredegrees

    circumference

    angle

    s90

    60

    6

    45

    Angles can be identified by labeling a point

    on each ray and the point that is the vertex.

    For example, the angle

    can be written as angle ABC or angle CBA

    (note that the vertex point always goes in the

    middle). You can also write this angle using

    an angle symbol as ABC or CBA.

  • 1Measure Up

    5

    Angles are measured in degrees using a protractor.If youve never used one, dont worry. Its easy and fun. You just align the bottom marking of the protractor with oneray of the angle you want to measure. The vertex of the angleshould be seen through the hole in the protractor. Next, readthe number on the protractor nearest to where the second raycrosses. Your protractor has two sets of numbers. The one youuse depends on the starting direction of the angle. You need tofigure out which set of numbers has the first ray starting atzero, then count up from there to find the right number. Trythis activity to practice measuring angles with a protractor.

    M AT E R I A L S

    protractorpencilpaper

    scissorscardboard

    rulerpaper brad

  • Procedure1. Look around any

    room in your housefor lines that meetat cornersforexample, tables,picture frames,blocks, books, clockhands, and so on.

    2. Use the protractorto measure some ofthe angles createdby the things in the room.

    3. Write down the name of the thing and the angle on a piece of paper.

    4. When youve measured at least six things, look at your list of measure-ments. What is the most common angle measurement on your list?

    6

  • 5. Cut out two strips from the cardboard that are about 1 inch (2.5 cm) 8inches (20 cm). Use a ruler to draw a ray down the middle of each strip.Connect the strips of cardboard at the end points of the two rays usingthe paper brad.

    6. Use the cardboard rays to make different angles and measure the angleswith your protractor.

    7

  • 2Draw It!

    8

    Try this game to practice drawing angles of different measures.

    Game Preparation1. Cut each sheet of paper into eight small pieces.

    2. Write one of the following measurements on each small piece of paper:

    10 degrees

    15 degrees

    20 degrees

    30 degrees

    40 degrees

    45 degrees

    50 degrees

    65 degrees

    75 degrees

    90 degrees

    100 degrees

    120 degrees

    135 degrees

    145 degrees

    160 degrees

    170 degrees

    M AT E R I A L S

    2 or more playersscissorspencilpaperbowlruler

    protractordie

  • 3. Fold the pieces of paper so that you cant see the measurements and placethem in the bowl.

    Game Rules1. Player 1 reaches into the bowl and picks a piece of paper. Player 1 reads

    the number of degrees out loud and tries to draw an angle with thismeasure using only a pencil and a ruler.

    2. Player 2, using a protractor, measures the angle drawn and writes themeasure of the angle inside the angle.

    3. Player 2 finds the difference between the measure of the angle as notedon the paper and the actual measure of the angle drawn.

    4. Player 1 rolls a single die. If the difference between the measure of theangle drawn and the measure on the piece of paper is less than the num-ber rolled, then Player 1 earns 1 point.

    EXAMPLEPlayer 1 is supposed to draw a 30-degree angle, but when Player 2measures it using a protractor, the angle is actually 34 degrees. Thedifference between these two measures is 4 degrees (34 30 = 4).Player 1 rolls a 5 on the die. Player 1 earns 1 point, since the differ-ence of 4 degrees is less than the number rolled, which is 5.

    5. Player 2 selects a piece of paper from the bowl, reads the number ofdegrees out loud, and tries to draw an angle with that measure. Player 1measures the angle drawn with a protractor and writes the measure.Player 2 rolls the die to determine if his or her drawing is accurate enoughto earn a point.

    6. The first player to earn 3 points wins the game.

    9

  • 10

    90

    4560

    80squaregrees

    circumferenceles

    90

    45

    sdegreesCreate new slips of paper and write new angle

    measures on them. Make the angles measure

    between 0 and 360 degrees. Play the game again

    using these new measures.

  • 3Name Game

    11

    Play this fast-paced game to practice identifying acute, right,and obtuse angles (see pages 34 for definitions and examples).

    Game PreparationWrite one of the following degree measurements on each of the index cards:

    M AT E R I A L S

    2 playerspencil

    16 index cards

    10 degrees

    20 degrees

    30 degrees

    40 degrees

    50 degrees

    60 degrees

    70 degrees

    80 degrees

    90 degrees

    100 degrees

    110 degrees

    120 degrees

    130 degrees

    140 degrees

    150 degrees

    160 degrees

  • Game Rules1. Deal eight cards to each player.

    2. Both players put their cards facedown in a stack in front of them.

    3. Players turn over their top cards at the same time and put them downfaceup next to each other.

    4. Each player calls out at the same time whether his or her angle is acute,right, or obtuse. An obtuse angle beats a right or an acute angle, and aright angle beats an acute angle. The winner gets to keep both cards. If theangles are both acute or both obtuse, then the largest angle wins. If theangles are both right, then the winner of the next round gets to keep thecards. If a player calls out the wrong type of angle, then he or she losesthe round no matter what angle is showing on the card.

    5. When all the cards have been played, the player with the most cards is thewinner.

    12

  • 4Angle Pairs

    13

    Angles also have different names that refer to special relation-ships that some angles have with other angles. These pairs ofangles are called vertical, complementary, and supplementary.Vertical angles are opposite angles that are formed when twolines intersect. They have the same measurement. For exam-ple, if the original angle is 31 degrees, the vertical angle is 31 degrees. Complementary angles are angleswhose measurements add up to 90 degrees.For example, if the original angle is 12degrees, the complementary angle meas-ures 78 degrees (90 12 = 78). Sup-plementary angles are angles whosemeasurements add up to 180 degrees.For example, if the original angle is 25 degrees, the sup-plementary angle measures 155 degrees (180 25 = 155). Playthis game to practice computing the measures of complementary, supplementary, and vertical angles.

    Game Preparation1. Write the words vertical angles on five index cards. Write the words comple-

    mentary angles on five index cards. Write the words supplementary angles onfive index cards.

    Game Rules1. Shuffle the cards and deal each player seven cards. There should be one

    card left over. Place this card facedown in the center of the table.

    M AT E R I A L S

    2 playerspencil

    15 index cardsdice

  • 2. Player 1 rolls the dice and uses the numbers rolled to form a two-digitnumber. The larger number rolled is the tens place and the smaller num-ber rolled is the ones place. For example, if a 6 and a 4 are rolled, thenumber rolled is 64. This is the number of your original angle.

    3. Players each select one of their index cards and place it faceup on thetable. If the cards are the same, Player 2 turns over another card until heor she gets a different type of angle card.

    4. Players compute the value of the type of angle named on their cards fromthe original angle. The player with the larger angle wins both cards.

    EXAMPLEThe number rolled is 55. Player 1 selected a vertical angle card. Thevertical angle of an angle that measures 55 degrees is an angle thatmeasures 55 degrees. Player 2 selected a complementary anglecard. The complementary angle of an angle that measures 55degrees is 35 degrees (90 55 = 35). Player 1 wins both cards,since 55 degrees is greater than 35 degrees.

    5. Players take turns rolling the dice and calculating the angles until thecards have run out. The winner is the player with the most cards at theend of the game.

    14

  • 5Color by Angles

    15

    Parallel lines are lines on the same planethat will never intersect. Atransversal is a line thatintersects two parallel lines.When two parallel lines arecut by a transversal,they form eightangles. The angles canbe named according totheir position.

    Angles between the two parallel lines areinterior angles.

    Angles 3, 4, 5, and 6 are interior angles

    Angles outside the parallel lines are exteriorangles.

    Angles 1, 2, 7, and 8 are exterior angles

    Angles on opposite sides of th...

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