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
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email:
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
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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. Geometry—Study and teaching (Elementary)—Activity programs. 2. Games in
mathematics education. I. Title.
QA462.2.G34 L36 2003
372.7—dc21

2002068996

Printed in the United States of America
10

9

8

7

6

5

4

3

2

1


Contents
I. The Magic of Geometry
II. Angles
1
2
3
4
5
6
7

Measure Up
Draw It!

Name Game
Angle Pairs
Color by Angles
Perpendicular Numbers
Right-Angle Scavenger Hunt

1
3
5
8
11
13
15
18
20

I I I . Tr i a n g l e s

23

8
9
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.

1


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

6

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

2

20
i

l

6


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.

3


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

6

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?

4


1

Measure Up
Angles are measured in degrees using a protractor.
If you’ve never used one, don’t worry. It’s easy and fun.
You just align the bottom marking of the protractor with one
ray of the angle you want to measure. The vertex of the angle
should be seen through the hole in the protractor. Next, read
the number on the protractor nearest to where the second ray
crosses. Your protractor has two sets of numbers. The one you
use depends on the starting direction of the angle. You need to

figure out which set of numbers has the first ray starting at
zero, then count up from there to find the right number. Try
this activity to practice measuring angles with a protractor.

M AT E R I A L S
protractor
pencil
paper
scissors
cardboard
ruler
paper brad

5


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 angle measurement on your list?

6


5. Cut out two strips from the cardboard that are about 1 inch (2.5 cm) × 8
inches (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 using
the paper brad.

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

7


2

Draw It!
M AT E R I A L S

Try this game to practice
drawing angles of different measures.

2 or more
players
scissors
pencil
paper
bowl

ruler
protractor
die

Game Preparation
1. Cut each sheet of paper into eight small pieces.
2. Write one of the following measurements on each small piece of paper:
10 degrees

50 degrees

135 degrees

15 degrees

65 degrees

145 degrees

20 degrees

75 degrees

160 degrees

30 degrees

90 degrees

170 degrees

40 degrees

100 degrees

45 degrees

120 degrees
8


3. 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 2 finds the difference between the measure of the angle as noted
on the paper and the actual measure of the angle drawn.
4. Player 1 rolls a single die. If the difference between the measure of the
angle drawn and the measure on the piece of paper is less than the number rolled, then Player 1 earns 1 point.

E XAMPLE
Player 1 is supposed to draw a 30-degree angle, but when Player 2
measures it using a protractor, the angle is actually 34 degrees. The
difference 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 difference 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 of
degrees out 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 360 degrees. Play the game again

45

using these new measures.

les

10

9s0

circumference

s

45


3

Name Game
Play this fast-paced game to practice identifying acute, right,
and obtuse angles (see pages 3–4 for definitions and
examples).

M AT E R I A L S
2 players
pencil
16 index cards

Game Preparation
Write one of the following degree measurements on each of the index cards:
10 degrees

70 degrees

130 degrees

20 degrees

80 degrees

140 degrees

30 degrees

90 degrees

150 degrees

40 degrees

100 degrees

160 degrees

50 degrees

110 degrees

60 degrees

120 degrees
11


Game Rules
1. 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 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 obtuse, then the largest angle wins. If the
angles are both right, then the winner of the next round gets to keep the
cards. If a player calls out the wrong type of angle, then he or she loses
the 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 the
winner.

12


4

Angle Pairs
Angles also have different names that refer to special relationships that some angles have with other angles. These pairs of
angles are called vertical, complementary, and supplementary.

Vertical angles are opposite angles that are formed when two
lines intersect. They have the same measurement. For example, if the original angle is 31 degrees, the vertical angle is
31 degrees. Complementary angles are angles
whose measurements add up to 90 degrees.
For example, if the original angle is 12
degrees, the complementary angle measures 78 degrees (90 – 12 = 78). Supplementary angles are angles whose
measurements add up to 180 degrees.
For example, if the original angle is 25 degrees, the supplementary angle measures 155 degrees (180 – 25 = 155). Play
this game to practice computing the measures of complementary,
supplementary, and vertical angles.

M AT E R I A L S
2 players
pencil
15 index cards
dice

Game Preparation
1. Write the words vertical angles on five index cards. Write the words complementary angles on five index cards. Write the words supplementary angles on
five index cards.

Game Rules
1. 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.
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 same, Player 2 turns over another card until he
or she gets a different type of angle card.
4. Players compute the value of the type of angle named on their cards from
the original angle. The player with the larger angle wins both cards.

E XAMPLE
The number rolled is 55. Player 1 selected a vertical angle card. The
vertical angle of an angle that measures 55 degrees is an angle that
measures 55 degrees. Player 2 selected a complementary angle
card. The complementary angle of an angle that measures 55
degrees 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 the
cards have run out. The winner is the player with the most cards at the
end of the game.

14


5

Color by Angles
Parallel lines are lines on the same plane
that will never intersect. A
transversal is a line that
intersects two parallel lines.
When two parallel lines are
cut by a transversal,
they form eight

angles. The angles can
be named according to
their position.

M AT E R I A L S
ruler
pencil
paper
crayons or
colored pencils
protractor

Angles between the two parallel lines are
interior 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 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 a transversal.
Procedure
1. Using a ruler, draw two parallel lines on a piece of paper.
2. Using a ruler, draw a transversal across the lines.
3. Label the eight angles 1, 2, 3, 4, 5, 6, 7, and 8, as in the illustration on
page 15.
4. Using a protractor, measure each of the angles. Write the measures on a
separate piece of paper.
Angle 1 =
Angle 2 =
Angle 3 =
Angle 4 =
Angle 5 =
Angle 6 =
Angle 7 =
Angle 8 =
5. Use crayons or colored pencils to color the space inside all the angles
with the same measure one color. How many different colors did you
use?
16


6. Add any two angles with different measures. What is the sum of these two
angles?

A

ny two different angles in the figure will be supplementary angles,

which means they will always add up
to 180 degrees.

gre

0
9square

80

esind the alternate interior

F

60

and exterior angles and the

corresponding angles in the
45
picture you colored.

s
e
l

g

circumference

17


6

Perpendicular
Numbers

A right angle is an angle of 90 degrees. Two lines that meet
in a right angle are called perpendicular lines. Try this activity to form numbers using only perpendicular lines.

Procedure
1. Using a highlighter, copy the following diagram on
a piece a paper. Make each of the line segments as
long as one of your toothpicks.

18

M AT E R I A L S
highlighter
paper
toothpicks


2. Use your toothpicks to cover each of the seven segments. You have made
the number 8 using only perpendicular lines.

3. Now see if you can use the toothpicks to make all the numbers from 0
to 9 using only perpendicular lines. (Hint: use the highlighted lines from
the number 8 figure as a base from which to create the rest of the
numbers.)
4. How many right angles can you find in each number?

90

80

square

gre
e

Ucan make versions 60
of all the lets

se the toothpicks to see if you

d

ters of the alphabet.
45

s

19