long lynette groovy geometry games and activiti

Magical Math GROOVY GEOMETRY Games and Activities That Make Math Easy and Fun Lynette Long John Wiley & Sons, Inc Also in the Magical Math series Dazzling Division Delightful Decimals and Perfect Percents Fabulous Fractions Marvelous Multiplication Measurement Mania This book is printed on acid-free paper Copyright © 2003 by Lynette Long All rights reserved Illustrations copyright © 2003 by Tina Cash-Walsh Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published 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 by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, 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 activities in this book are safe when conducted as instructed but assume no responsibility for any damage caused or sustained while performing the experiments or activities in the book Parents, guardians, and/or teachers should supervise 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 Department within 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 at www.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) Geometry—Study and teaching (Elementary)—Activity programs Games in mathematics education I Title QA462.2.G34 L36 2003 372.7—dc21 2002068996 Printed in the United States of America 10 Contents I The Magic of Geometry II Angles Measure Up Draw It! Name Game Angle Pairs Color by Angles Perpendicular Numbers Right-Angle Scavenger Hunt 11 13 15 18 20 I I I Tr i a n g l e s 23 10 11 12 13 14 15 16 25 27 29 31 35 39 42 45 49 Triangle Collage Triangle Memory Triangle Angles Outside the Triangle Triangle Area Two the Same How Tall? Perfect Squares Pythagorean Proof I V Q u a d r i l a t e r a l s 17 18 19 20 21 Crazy about Quadrilaterals Quadrilateral Angles String Shapes Doubt It! Rectangle Race 53 55 58 61 62 64 v 22 Parallelogram Presto Change-O 23 Pattern Blocks 24 Shape Storybook V C i r c l e s 73 25 26 27 28 29 30 75 77 80 81 83 86 Around and Around Finding Pi Bicycle Odometer Circle Area Pizza Party Central Angles VI Solids 31 32 33 34 35 36 Solid Shapes Cereal Surfaces Cylinder Surfaces Cube Construction Volume of a Cylinder Building Blocks VII Odds and Ends 37 38 39 40 Shape Comparison Bull’s Eye Mystery Picture Number Symmetry Geometry Master Certificate Index vi 66 68 71 89 91 94 95 97 99 101 103 105 107 110 112 115 117 I THE MAGIC OF GEOMETRY G eometry is the study of points, lines, angles, and shapes, and their relationships and properties It sounds like a lot to know, but much of it is already in your head Geometry is all around us If people didn’t think about geometry, they wouldn’t be able to build great structures such as the pyramids, or even simple things that lie flat such as a table Geometry can be easily learned by experimenting and having fun with things you can find around the house You can learn most of the principles of geometry using cereal boxes, soda cans, plates, string, magazines, and other common household objects So get ready to have a great time exploring the world of geometry SOME KEY TERMS s e l g TO KNOW Geometry starts with the concepts of lines, circumference an 90 points, rays, and planes You probably already have a pretty good idea of what 60 lines and points are, but in geometry these 20 30 terms have a more specific meaning than in circle everyday life Here are some words and 180 definitions you’ll need to know: Plane: a flat surface that extends infinitely in all directions 45 90 square Point: a location on a plane deg ree Line: a straight path of points that goes on indefinitely s 60 Line segment: all of the points on a line between two specific end points 45 Ray: all of the points on a line going out from one end point indefinitely incircumference one direction s e l g an 90 Plane geometry: the study of twodimensional figures 60 Solid geometry: the study of threedimensional figures 30 20 i l II ANGLES 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 angle’s vertex The rays are called the sides of the angle Angles are everywhere When you bend your arm, your elbow becomes the vertex of the angle formed by the two parts of your arm When two streets cross each other, they form angles Here are some examples of angles: Angles are measured in degrees If an angle is less than 90 degrees, it is called an acute angle If it is exactly 90 degrees, it is called a right angle And if it is more than 90 degrees, it is called an obtuse angle g n a 90 Angles can be identified by labeling a point 60 on each ray and the point that is the vertex 30 For example, the angle 20 circle 180 deg 45 90 square ree s 60 45 can be written as angle ABC or angle CBA (note that the vertex point always goes in the s e l g circumference middle) You can also write this angle using an 90 an angle symbol as ∠ABC or ∠CBA 60 In this section, you’ll practice measuring and creating different angles, learn the relationship between some interesting angle pairs, discover the relationship between the angles formed when two parallel lines are intersected by another line, practice recognizing right angles and perpendicular lines, and more Along the way, you’ll measure angles around your house, have an angledrawing competition, play a game of matching angle pairs, create numbers using only perpendicular lines, and go on a right-angle scavenger hunt These activities will teach you more than you can imagine about angles, so why not get started? A rectangle with sides that are and inches long A rectangle with sides that are and inches long A rectangle with sides that are and inches long A rectangle with sides that are and inches long A circle with a radius of inches A circle with a radius of inches A parallelogram with a height of inches and a length of inches A parallelogram with a height of inches and a length of inches A parallelogram with a height of inch and a length of inches A parallelogram with a height of inches and a length of inches Game Rules Players place all the cards facedown on the center of the table Each player picks up one card Each player calculates the area of the figure on his or her card The player with the card that has the smallest area wins both cards If both cards have the same area, the cards are replaced and the players each pick a new card When there are no more cards on the table, the player with the most cards wins the game If the game ends in a tie, the player who won the card with the smallest area wins the game 106 38 Bull’s Eye Have you ever played Battleship? Plotting coordinate points on a graph is a lot like playing that game In this activity, you will learn how to plot coordinate points and use them to play a game of Bull’s Eye M AT E R I A L S players sheets of graph paper pencils Game Preparation Players first draw a straight horizontal line across the middle of the graph paper Label the center point on the line From the right of that point, label each point where a vertical line intersects your horizontal line 1, 2, 3, and so on, up to 10 To the left of the 0, label each point where a vertical line intersects your horizontal line –1, –2, –3, and so on, up to –10 Players draw a vertical line across the paper that intersects the point on the horizontal line at a right angle Label the points above the horizontal line 1, 2, 3, and so on, up to 10 Label the points below the horizontal line –1, –2, –3, and so on, up to –10 The two lines you made on the graph paper are called coordinate axes The horizontal line is the x-axis, and the vertical line is the y-axis 107 Game Rules Players each draw a square with sides boxes long on their coordinate axis Players each draw a square with sides boxes long inside the square with 5-box-long sides Players shade the center box of their squares Players should not let the other see the location of their bull’s eye 108 Players take turns calling out coordinate points, such as (3, 3), (–2, 1), etc., while the other player looks for that point on his or her graph If a player’s point lies on the outer square, the other player says, “warm.” If a player’s point lies on the inner square, the other player says, “hot.” If a player’s point lands on the small center square, the other player says, “bull’s eye,” and that player wins the game 109 39 Mystery Picture Find coordinate points to draw a mystery picture M AT E R I A L S pencil graph paper Procedure Draw a set of coordinate axes on graph paper and graph the following points Connect the points as you graph them (0, 0) (0, 6) (4, 4) (–1, 7) (4, 6) (–3, 7) (3, 7) (–4, 6) (1, 7) (–4, 4) What did you just draw using the connect-the-points method? 110 Graph and connect each of these pairs of points Connect (–3, 0) and (3, 0) Connect (–3,0) and (2, –3) Connect (–2, –3) and (3, 0) Connect (0, 2) and (–2, –3) Connect (0, 2) and (2, –3) What did you just draw using the straight-line method? deg r 90 80 square 90 ees your name in block letters using coordinate squ deg points Write 60 ree s and the straight-line method 45 Write your name in script using coordinate points and the connect-the-points method ng les circumference 45 s 111 40 Number Symmetry Symmetry is the property of some geometrical shapes whose parts look like mirror images of one another when the shape is split in half A line of symmetry is the line around which the shape is symmetrical Symmetry can be horizontal, vertical, or both Try this activity to find out if numerals are symmetrical M AT E R I A L S paper marker small hand mirror pencil Procedure Use the marker to write the numerals from to on paper Make the numerals about inches tall Place the mirror vertically down the center of the zero so that you can see the other half of the zero in the mirror You are conducting a vertical symmetry test Look in the mirror Is a complete zero formed by the combination of the half zero on the paper and the half zero in the reflection? If it is, then a zero has vertical symmetry Enter the word yes in a chart like the one on page 113 112 Place the mirror horizontally across the center of the zero to conduct a horizontal symmetry test Look in the mirror Is a zero formed in the reflection? If it is, then a zero has horizontal symmetry Enter the word yes in your chart Perform both the horizontal and the vertical symmetry test on each numeral from to Enter the results in your chart Numeral Vertical Symmetry Horizontal Symmetry Which numerals have horizontal symmetry? Which numerals have vertical symmetry? Which numerals have both vertical and horizontal symmetry? 113 9square 80 90 gre 1.eDraw from A to Z d onea sheet ofsqu s all the capital letters gre 60 es paper Use a mirror to test the vertical and horizontal symmetry of these letters Draw a chart and enter the 45 results in the chart 45 s circumference e Test the lowercase letters for horizontal and vertical gl symmetry s e 90 l g an Some symmetrical figures have more than two lines 60 of symmetry Draw some different shapes, such as tri- 20 angles and snowflakes, and cut them out Fold the 30 paper circle in as many ways as you can to get mirror 180 images What shape has the most lines of symmetry? 114 c GEOMETRY MASTER CERTIFICATE Now that you’ve mastered all the geometry facts, problems, and games in this book, you are officially certified as a geometry master! Make a photocopy of this certificate, write your name on the copy, and hang it on the wall 115 Index acute angles, 3, acute triangles, 25–26 alternate angles, 15–17 angles acute, 3, alternate, 15–17 complementary, supplementary, and vertical, 13–14, 17 corresponding, 16–17 definition of, drawing, 8–10 exterior, 15–17, 31–34 identifying, interior, 15–17, 34 measuring, 5–7 naming, 11–12 obtuse, 3, of circles, 86–87 of quadrilaterals, 58–60 pairs of, 13–14 parallel lines, transversal, and, 15–17 right, 3, 4, 18, 20–21 area definition of, 35 of circle, 81–82, 83–85 of parallelogram, 66–67 of rectangle, 35, 64–65 of shapes, comparing, 105–106 of square, 62–63 of triangle, 35–38 See also surface area axes, coordinate, 107 calculating area of circle, 83–85 circumference with pi, 80 measures of angles, 13–14 volume of cube, 97–98 volume of cylinder, 99–100 See also measuring circles area of, 81–82, 83–85 central angles of, 86–87 creating perfect, 75–76 parts of, 73 pi and, 77–79 circumference definition of, 75 finding, 77–79, 80 complementary angles, 13–14 computing See calculating cones creating, 91–93 definition of, 90 congruent triangles, 39–41 coordinate axes, 107 coordinate points drawing picture with, 110–111 plotting on graph, 107–109 corresponding angles, 16–17 cubes creating, 91–93 definition of, 90 volume of, 97–98 cylinders creating, 91–93 definition of, 90 surface area of, 95–96 volume of, 99–100 decagons, 71–72 diameter definition of, 75 measuring, 77–79 117 drawing angles, 8–10 picture with coordinate points, 110–111 remote, 34 isosceles triangles, 25–26 kites, 55–57 edge, 89 equilateral triangles, 25–26 exterior angles measuring, 15–17 of triangle, 31–34 face, 89 formulas area of circle, 83–85 area of triangle, 38 games Angle Pairs, 13–14 Bull’s Eye, 107–109 Crazy about Quadrilaterals, 55–57 Draw It!, 8–10 Name Game, 11–12 Rectangle Race, 64–65 Right-Angle Scavenger Hunt, 20–21 Shape Comparison, 105–106 Triangle Memory, 27–28 geometry definition of, learning, Geometry Master Certificate, 115 graphs drawing picture with coordinate points, 110–111 plotting coordinate points on, 107–109 heptagons, 23, 71–72 hexagons, 23, 71–72 horizontal symmetry, 112–114 hypotenuse, 45 interior angles measuring, 15–17 118 INDEX legs, 45 line of symmetry, 112–114 line segments, lines definition of, perpendicular, 18–19 measuring angles, 5–7 area of triangle, 35–38 diameter, 77–79 exterior angles, 15–17, 31–34 perimeter of quadrilateral, 61 surface area, 94, 95–96 See also calculating naming angles, 11–12 nonagons, 71–72 obtuse angles, 3, obtuse triangles, 25–26 octagons, 71–72 origin, 75 parallel lines, 15 parallelograms changing into rectangles, 66–67 definition of, 55 matching, 55–57 pentagons angles of, 60 creating, 71–72 definition of, 23 perfect squares, 45–48 perimeter, 61 perpendicular lines, 18–19 pi calculating circumference with, 80 finding, 77–79 plane geometry, planes, points definition of, plotting on graph, 107–109, 110–111 polygons definition of, 23–24 types of, 71–72 See also triangles polyhedrons, 89–90 prisms, 90 proportion, 42 protractor, using, 5–7 pyramids creating, 91–93 definition of, 90 Pythagorean theorem perfect squares, 45–48 proving, 49–51 quadrilaterals angles of, 58–60 definition of, 53 perimeter of, 61 types of, 55–57 See also rectangles; squares radius, 75 rays, 2, rectangles area of, 35, 64–65 changing parallelograms into, 66–67 definition of, 55–57 rectangular solids creating, 91–93 surface area of, 94 volume of, 101–102 remote interior angles, 34 rhombuses definition of, 55 making patterns with, 68–70 matching, 55–57 right angles definition of, 3, finding, 20–21 perpendicular lines and, 18 right triangles, 25–26 scalene triangles, 25–26 shapes, comparing area of, 105–106 similar triangles, 42–44 solid geometry, solids creating, 91–93 types of, 89–90 See also surface area spheres creating, 91–93 definition of, 90 squares area of, 62–63 definition of, 55–57 perfect, 45–48 rhombuses compared to, 68 squaring, 45 supplementary angles, 13–14, 17 surface area cylinder, 95–96 rectangular solid, 94 symmetry, 112–114 transversals, 15 trapezoids making patterns with, 68–70 matching, 55–57 INDEX 119 triangles acute, 25–26 area of, 35–38 congruent, 39–41 equilateral, 25–26 exterior angles of, 31–34 hypotenuse of, 45 isosceles, 25–26 matching, 27–28 obtuse, 25–26 Pythagorean theorem and, 45–48 right, 25–26 scalene, 25–26 similar, 42–44 sum of angles of, 29–30 types of, 24, 25–26 120 INDEX vertex/vertices of angle, of parallelogram, 66 of solid, 89 vertical angles, 13–14 vertical symmetry, 112–114 volume of cube, 97–98 of cylinder, 99–100 of rectangular solid, 101–102 x-axis, 107 y-axis, 107 [...]... angles Angles 3, 4, 5, and 6 are interior angles Angles outside the parallel lines are exterior angles Angles 1, 2, 7, and 8 are exterior angles Angles on opposite sides of the transversal that have the same measurement are alternate angles Angles 3 and 6 are alternate interior angles Angles 4 and 5 are alternate interior angles 15 Angles 1 and 8 are alternate exterior angles Angles 2 and 7 are alternate... Fold the pieces of paper so that you can’t see the measurements and place them in the bowl Game Rules 1 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 this measure using only a pencil and a ruler 2 Player 2, using a protractor, measures the angle drawn and writes the measure of the angle inside the angle 3 Player... the center of the table 13 2 Player 1 rolls the dice and uses the numbers rolled to form a two-digit number The larger number rolled is the tens place and the smaller number rolled is the ones place For example, if a 6 and a 4 are rolled, the number 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 the table If the cards are the... loud, and tries to draw an angle with that measure Player 1 measures the angle drawn with a protractor and writes the measure Player 2 rolls the die to determine if his or her drawing is accurate enough to earn a point 6 The first player to earn 3 points wins the game 9 gre 90 Ces 80 square reate new slips of paper and write new angle 60 de gre measures on them Make the angles measure e between 0 and. .. 7 are alternate exterior angles Angles on the same side of the transversal that have the same measurement are corresponding angles Angles 1 and 5 are corresponding angles Angles 2 and 6 are corresponding angles Angles 3 and 7 are corresponding angles Angles 4 and 8 are corresponding angles Try this activity to see the relationship between the angles formed when two parallel lines are intersected by... cards and place them in a brown paper bag Game Rules 1 Each player reaches into the bag and selects an index card 2 Players each have 10 minutes to go into the room they selected and make a list on paper of as many right angles as they can find (Hint: you can use a corner of your index card as a right-angle tester.) 20 3 After 10 minutes, players read their lists to each other The player with the longest... heptagons (with seven sides), and many more 23 Polygons with three sides are some of the most interesting figures in geometry You probably know that these figures are called triangles But triangles are not as simple as they first appear There are many types of triangles Many of them are named after the types of angles they contain, such as acute, obtuse, and right There are also scalene and isosceles triangles... isosceles triangles In this section, you’ll learn about many of the different kinds of triangles, the exterior and interior angles in a triangle, congruent triangles, and the Pythagorean theorem Along the way, you’ll make a triangle collage, play triangle memory, put together a triangle puzzle, and use triangles to figure out the heights of objects Triangles are fascinating So let’s get started! 24 8 Triangle... Procedure 1 Look around any room in your house for lines that meet at corners—for example, tables, picture frames, blocks, books, clock hands, and so on 2 Use the protractor to measure some of the angles created by the things in the room 3 Write down the name of the thing and the angle on a piece of paper 4 When you’ve measured at least six things, look at your list of measurements What is the most common... 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 down faceup 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 a right angle beats an acute angle The winner gets to keep both cards If the angles are both acute or both