delightful decimals and perfect percents, games and activities that make math easy and fun - long

Like fractions, decimals are numbers that sent part of a whole, but unlike fractions, decimals don’t use a fraction bar.Instead they use a decimal point.. Write one of the following phra

DECIMALS AND PERFECT PERCENTS: Games and Activities That Make Math

Easy and Fun

D E L I G H T F U L

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

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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 tained 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.

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to the grocery store, you’ll

find the cost of

every-thing expressed in

deci-mals The weight of the

meat is also expressed in

decimals And if there is

a sale on meat, it might

be expressed as a

per-cent If you want to

suc-ceed at math and really

understand the world you live

in, you have to get to know

deci-mals and percents

But what are decimals? Like fractions, decimals are numbers that sent part of a whole, but unlike fractions, decimals don’t use a fraction bar.Instead they use a decimal point Everything to the right of the decimalpoint is less than zero, and everything to the left of the decimal point isgreater than zero One thing that makes decimals easy to work with is that,unlike fractions, you don’t have to find a common denominator to add orsubtract them.

repre-You will use decimals and percents every day of your life So you might aswell start practicing Begin with the fun activities in this book and you’llsoon be a master of decimals and percents Then you can proudly displaythe decimals and percents master certificate at the back of this book

I I

In this section, you’ll learn all the basic facts

about decimals You’ll learn how to read a

decimal and write one, how to change a

decimal to a percent, and, of course, how to

change a fraction to a decimal and a

deci-mal to a fraction Last but not least, you’ll

learn what a repeating decimal is

While learning, you’ll solve a

decimal dot-to-dot, check

out the stats of your

Fractions, decimals, and percents express parts of wholes In

fact, you can use fractions, decimals, and percents to describe

parts of just about anything The statements “3⁄5 of Americans

prefer chocolate ice cream over vanilla,” “0.6 of Americans

prefer chocolate ice cream over vanilla,” and “60% of

Ameri-cans prefer chocolate ice cream over vanilla” all mean the

same thing Which version you use depends partly on

convention (what other people do in the same situation)

and partly on practicality (it’s easier to say “two-thirds”

than “0.666666666 ”) In this game, you’ll compete

with friends to find examples of fractions, decimals, and

Game Preparation

1 Each player should fold a piece of white paper into eight sections Write

one of the following fractions at the top of each section:

2 Each player should fold a second piece of white paper into eight sections.

Write one of the following decimals in each section:

3 Each player should fold a third sheet of white paper into eight sections.

Write one of the following percents in each section

Game Rules

1 Each player should take a stack of newspapers Players have 30 minutes to

look through the newspapers and to cut out and glue on their sheets

examples of any of the listed fractions, decimals, and percents

2 After the 30 minutes are

up, players should

count the numbers of

fractions, decimals, and

percents on their sheets

The player who has the

most wins the scavenger

examples of fractions, decimals,

or percents?

What section of the newspapercontained the most examples of frac-tions, decimals, and percents?

Name That Place!

The value of a numeral depends on its place in the number.

Look at any number As you move to the left, every place is 10

times larger than the previous place As you move to the right,

every place is one-tenth the place on its left Here are the

values of common places: millions, hundred-thousands,

ten-thousands, hundreds, tens, ones, (DECIMAL POINT)

tenths, hundredths, thousandths, ten-thousandths,

hundred-thousandths, millionths Notice that the

decimal point separates the numerals

that are greater than one from the

numerals that are less than one.

Learn the value of decimal

num-bers with this fast-paced game.

MAT E R I A L S

2 players

10 index cards pencil die stopwatch or watch with second hand

Game Rules

1 Shuffle the index cards and turn them facedown in front of player 1.

2 Player 1 rolls the die The number rolled is the Name That Place!

number

3 Player 2 starts the stopwatch and gives player 1 one minute to Name That

Place! on the entire stack of 10 cards.

4 Player 1 turns over the top card He or she looks at the decimal on the

top card and names the place in which the rolled number appears in the

place in the card

Example: If the number on the card is 123.456 and the rolled number

is 6, then the player shouts “Thousandths!.” If the rolled number is 5,

the player shouts “Hundredths!.” If the rolled number is 4, the player

shouts “Tenths!” and so on

5 Player 1 turns over the rest of the cards one by one and repeats step 4 for

each card Note: The rolled number stays the same through each player’s

turn Each player only rolls the die once

6 If player 1 names all 10 place values correctly, he or she wins one point.

7 If a player names a place value incorrectly, he or she loses the rest of his

or her turn

8 After player 1’s turn is over, the index cards are shuffled and placed

face-down in front of player 2

9 Player 2 rolls the die to get a new Name That Place! number Player 2

now has one minute to see if he or she can Name That Place! for the

same 10 index cards If player 2 is successful, he or she earns one point

Player 1 sets the timer for this turn

Draw a chart like this one Enter your decimal numbers into the

chart and use the top row of the chart to help you read them

DECIMAL Thousands Hundreds Tens Ones POINT Tenths Hundredths Thousandths

You can draw a decimal line and learn

more about place value.

Procedure

1 Use the ruler to draw

a 10-inch line on a piece

of paper

2 Mark the line at 1-inch intervals.

3 Label the decimal line by placing a “0” at one end of the line and a “1” at

the other end of the line This entire line represents one whole number,

5 Make a mark halfway between each two decimal numbers Label these

1.135 Add the following decimal numbers

to your decimal line:

Practice moving a decimal point and

reading decimal numbers.

Game Preparation

1 Write one of the following phrases

on each index card:

Move the decimal point two places to the right

Move the decimal point two places to the right

Move the decimal point two places to the left

4

Roving Decimal Points

Move the decimal point three places to the right.

Move the decimal point three places to the left

Keep the decimal point in the same place

Keep the decimal point in the same place

2 Remove the face cards (kings, queens, and jacks) from a deck of playing

cards These picture cards will be used to represent zeros

Game Rules

1 Shuffle the index cards and place them facedown on the table.

2 Shuffle the numbered playing cards and place them facedown on the

table

3 Turn over the top three playing cards Place them in a row on the table.

Using the penny as a decimal point, place the decimal point to the right

of all three cards Read this number Aces are the same as ones

4 Turn over the top index card Move the decimal point (penny) according

to the direction on the card Use the picture cards as zeros to fill in any

empty spaces What is the new decimal number?

5 Continue to turn over the top index card Keep moving the decimal point

(penny) according to the directions on each card Use the picture cards aszeros to fill in any empty spaces Read each new number out loud Keepplaying until you’ve gone

through all the index cards

6 Put your first three playing cards

aside Take out three more cards

from the deck Reshuffle the

index cards and play again! What

is the largest number you

cre-ated? What is the smallest

num-ber you created?

1.135 Play the game again, this

time starting with five ing cards and with the pennytwo places in from the right

play-Read the decimal point as “AND.” If the decimal is less than one,

put a zero in the ones place Don’t forget to name that place,

whether it’s tenths, hundredths, or thousandths

Examples:

1.23 is read as one and twenty-three hundredths

0.007 is read as zero and seven-thousandths

Improve your understanding of decimals while

solving a dot-to-dot picture puzzle.

Procedure

1 Use a copy machine to copy

the dot-to-dot puzzle

2 Starting at 0.0, connect

the dots in order

from the smallest

decimal to the

largest

5

Decimal Dot-to-Dot

MAT E R I A L S

paper pencil

Compare the decimals first by the numbers in the tenths place,

then by the numbers in the hundredths place, then by the

numbers in the thousandths

1.135 Create your own decimal

dot-to-dot Make a list of decimals

Place them in order from the est to the largest Think of a pictureand arrange a series of dots on apiece of paper to make that picturewhen they are connected Label thedots with the decimals so that theycan be connected in the correctorder

small-To change a decimal to a fraction, use the numerals of the

decimal to form the numerator (number above the fraction

bar) of the fraction The denominator (the number below the

fraction bar) of the fraction is always a multiple of ten, such

as 10, 100, 1000, and so on You can tell which multiple of

ten by looking at the place value of the numeral

farthest to the right in the decimal (Here’s

another way to find the denominator: it

should contain the same number of

zeros as there are numerals to the right

of the decimal.) Once the decimal is

con-verted to a fraction, reduce it to the lowest

common denominator (See the Tips and Tricks

box for a reminder about how to reduce fractions.)

To change 0.4 to a fraction, place 4 in the numerator Since 0.4 has the

4 in the tenths place, use 10 for the denominator Write it as the fraction

4⁄10 Reduce 4⁄10to2⁄5

To change 0.55 to a fraction, place 55 in the numerator Since 0.55

means fifty-five hundredths, the denominator is 100 Write it as the

frac-tion55⁄100 Reduce 55⁄100 to11⁄20

Play this game with some friends to practice converting decimals to

fractions and reducing them.

6

Dynamite Decimal Reduction

MAT E R I A L S

2 or more players deck of playing cards

EXAMPLE

Game Preparation

1 Remove all the tens and face cards (kings, queens, and jacks) from a deck

of playing cards

2 Separate the remaining red cards from the remaining black cards (Save

the black cards for the Brain Stretcher section.)

Game Rules

1 Shuffle the red cards and place them facedown in the center of the table.

2 Player 1 turns over the top card and places it face up in the center of the

table The red card represents a decimal fraction in tenths For example,

the three of hearts or the three of diamonds represents 0.3 (three-tenths)

The six of hearts or the six of diamonds represents 0.6 (six-tenths)

3 Both players change the decimal to a fraction and reduce it to the smallest

fraction possible The first player to shout out the smallest correct fraction

wins the card For example, if the 5 of diamonds is turned over, the first

player to shout out “One-half!” wins the card If the ace of hearts is

turned over, the first player to shout out “One-tenth!” wins the card

Remember that aces are the same as ones

4 The player who gets the most cards wins the game.

S UPER R EDUCING D ECIMALS

Play the game the same way except this time use the black cards to represent

the hundredths place in each decimal fraction Pick up both a black card

and a red card from the top of each pile The number on the red card

becomes the number in the tenths place and the number on the black

To reduce a fraction to lowest terms, divide the numerator and denominator

by the same number (If you cannot find a number that will divide evenlyinto both the numerator and denominator, the fraction is in lowest terms.)

To change a fraction to a decimal, divide the numerator by

the denominator Practice changing fractions to decimals

while you study the statistics of your favorite baseball team.

Procedure

1 Log on to the Internet Go to the website www.mlb.com If you don’t

have a computer with Internet access, look in the sports section of your

7

Batting It In

MAT E R I A L S

computer with Internet access or

a newspaper with sports statistics pencil paper calculator

3 Copy the chart shown here onto your sheet of paper.

4 Write the names of the players on your team and their positions in the

chart

5 Copy the numbers from the AB column (which stands for at bats) onto

your chart This is the number of times the player was at bat

6 Copy the numbers from the H column (which stands for hits) onto your

chart This is the number of times the player got a hit A hit is a single,double, triple, or home run

7 AVG stands for the player’s batting average Find each player’s batting

average by dividing the number of hits by the number of at bats Use thecalculator for help Enter the averages in the chart

AVG = H⁄AB

Does your answer match the answer found on the Internet or in thenewspaper under AVG?

8 Copy the numbers from the HR column (which stands for home runs)

onto your chart This is the number of home runs each player got

Players and Positions AB H AVG HR HR AVG

9 Now compute each player’s HR AVG (home run average) by dividing the

number of home runs (HR) by the number of at bats (AB) Use the

cal-culator for help Enter the results in the chart

HR AVG = HR⁄AB

10 Who has the highest average on the team? Who has the highest HR

age on the team? What positions do the players with the highest

1.135 Use the website to look up league leaders (players with

the highest batting average or the most home runs)

Game Rules

1 Shuffle the index cards and deal each player half the cards Each player

should place his or her cards facedown in front of himself or herself

2 Player 1 turns over his or her top card and places it in the center of the

table

3 Player 2 turns over his or her top card and places it on top of player 1’s

card Players take turns adding cards face up to the center of the stack

4 When two consecutive cards have the same value, players slap the stack of

cards The first player to slap the stack of cards wins the entire stack

Remember the idea is to match up fractions and decimals that have the

same values

5 If a player slaps the stack of cards when the two top cards do not have the

same value, the other player wins the stack of cards

6 Continue until one player wins all the cards.

game, you’ll not only become a champion at Slap Match, you’ll

always be able to change these fractions to their decimals and back

again, just like that!

Decimals Forever

A repeating decimal is a decimal in which the same numeral

or series of numerals repeats forever Here’s a game that will

help you learn to recognize repeating decimals.

Game Preparation

1 Remove all of the face cards (kings, queens, and jacks)

from a deck of playing cards

2 Give each person a piece of paper and a pencil.

Game Rules

1 Shuffle the cards and place them facedown in the

center of the table

2 Player 1 rolls the die The number rolled is the numerator of the fraction.

3 Payer 2 turns over the top card The number on the card is the

denomina-tor of the fraction

4 Both players convert the fraction to a decimal by dividing the numerator

by the denominator Players may use paper and pencil to do their

calcu-lating

5 If the decimal is a repeating decimal, players yell “Repeating!” and tap the

card The first player to tap the card wins the top card and all the cards

under it

6 Player 2 turns over the next card and both players use this as the next

denominator with the same numerator Repeat steps 4 and 5

MAT E R I A L S

2 players deck of playing cards

2 sheets of paper

2 pencils die

7 Continue going through the stack of cards one by one When all the cards

are gone, the player with the most cards wins the round

8 Player 2 rolls the die to find a new numerator Player 1 shuffles the cards

and places them facedown in the center of the table Player 1 turns over

the top card and players start the next round

9 The first player to win three rounds wins the game.

.3333

3 1.000

To indicate a repeating decimal, put a bar over the number or

I I I

Now that you know decimal basics, it is time

to learn how to add and subtract

decimals You’ll learn how to add and subtract

decimal numbers and decimal

numbers that are greater

than one And, of course,

you’ll learn how to subtract

a decimal from a whole

number, which is always a

tricky feat Along the way,

you’ll figure out all the

combinations of change

that make a dollar, go on a

shopping spree, compare

the costs of sending a

package, and play lots of

fun games

To add decimals together, you first match up the decimal

points, then add the two numbers as you would add any

two numbers Remember to start adding on the right and

carry to the left In this activity you will convert coins

to their decimal equivalents and find different

ways to add these decimals so that they

make one dollar

Game Preparation

Every coin in the American

monetary system actually

repre-sents part of one whole dollar For

example, 25 cents is the same as 0.25 of a dollar

Dollars are written as whole numbers and the coins

are written as decimals Here is how to write the

deci-mal equivalent of each coin

W

W LIB ER LIB E R

W

W LIB ER LIB E R

W

W LIB ER LIB E R

W

W LIB E

W

W LIB ER LIB E R

W

W LIB ER LIB E R

W

W LIB ER LIB E R

W

W LIB E

W

W LIB ER LIB E R

To add the values of two coins together, you can just add their decimalvalues For example, to add two quarters, just add 0.25 and 0.25 Keep thedecimal point in the same place and be sure to include it in your answer.

0.25+0.250.50Twenty-five cents plus twenty-five cents equals fifty cents

To add a quarter, a nickel, and a dime, convert them to their decimal ues, line up the decimal points, and add the numbers

val-0.250.05+0.100.40

If you have a quarter, a nickel, and a dime, you have forty cents

How much are two quarters, three dimes, and four nickels worth?

Add the decimal values of the coins to find out

0.250.250.100.100.100.050.050.05+0.051.00

If you have two quarters, three dimes, and four nickels, you have one lar! Note that the 1 was carried over to the ones place

dol-Game Rules

1 There are many different ways you can make $1 using nickels, dimes,

quarters, and half-dollars Think of as many combinations as you can and

write them down Check your addition by adding the values of the coins

on a calculator

2 Answer the following questions Try to answer them first without a

calcu-lator, then check your math

• You can make a dollar with just nickels How many nickels do you

• There is only one way to make a dollar using only quarters and dimes

Can you figure out what it is?

• There are nine different ways to make a dollar using both nickels and

dimes Can you figure them all out?

• There are eleven ways to

make a dollar when one of

the coins is a half-dollar

What are they?

• There are only two different

ways to make a dollar using

at least one of each coin

What are they?

pennies, nickels, dimes,quarters, and half-dollars? Howmany different ways can you

To add decimals and whole numbers, put the decimals

in a vertical column one on top of the other Be sure

to line up the decimal points In the answer, place the decimal

point directly underneath the other decimal

points Play this game to practice adding

decimals and whole numbers.

Game Preparation

1 Remove all the 10s and face cards (kings, queens, and jacks) from the

deck of playing cards Remember that aces are the same as ones

2 Give each player two pennies.

Game Rules

1 Shuffle the playing cards and place them facedown in the center of the

table

2 Deal each player four cards Each player places his or her cards facedown

in two rows with two cards in each row Each player places a penny to

the right of each set of two cards The pennies represent the decimal

points

11

Dazzling Decimal Addition

MAT E R I A L S

IN GO D WE TRUST INGOD WE TRUST LIBERTY 2000

IN GO D WE TRUST

IN GOD WE TRUST LIBERTY 2000

IN GO D WE TRUST

IN GOD WE TRUST LIBERTY 2000

IN GO D WE TRUST

IN GOD WE TRUST LIBERTY 2000

2 or more players deck of playing cards

4 pennies pencils paper

3 One player says “Go” and both players turn over their cards Players

move all red cards to the right of the decimal point All black cards stay

to the left of the decimal point

4 Both players add their decimal numbers and write their answers on a

sheet of paper

5 The first player to add his or her two numbers together correctly wins

the round

6 The used cards are discarded and the dealer deals each player six new

cards Each player places his or her cards facedown in two rows of three

cards each Each player places a decimal point (penny) to the right of

each set of three cards

7 One player says “Go” and both players turn over their cards Players

move all red cards to the right of the decimal point All black cards stay

to the left of the decimal point

8 Both players add their decimal numbers and write their answers on a

sheet of paper

9 The first player to add his or her two numbers together correctly wins

the round

10 The used cards are discarded and the dealer deals each player eight new

cards Each player places his or her cards facedown in two rows of four

cards each Each player places a penny to the right of each set of four

cards

11 One player says “Go” and both players turn over their cards Players

move all red cards to the right of the decimal point All black cards stay

to the left of the decimal point

Subtracting decimals is easy To subtract one decimal from

another decimal, just line up the decimal points and subtract

as you would any two numbers Start at the right

and move to the left In the answer, place

the decimal point right under the

other decimal points If one

deci-mal is shorter than the

other, put zeros at the

end to make both

numbers the

same length

$7.50–2.25

EXAMPLE

0.5 – 0.32 = 0.50–0.320.18