Customized Activity Book

Transcription

Customized Activity Book
For
HALEY LYNCH
Kid’s College is an online program that diagnoses a student’s mastery of essential skills in reading,
language arts and mathematics. Once diagnosed, the student is provided instructional practice on
any foundational skills not mastered at earlier grade levels, then quickly brought up to the
instructional skills at their current grade level.
The online video games within Kid’s College both motivate and offer an incentive for students to stay
on task and perform more accurately. Student performance is continually monitored, providing
teachers, parents and administrators with snapshots of each student’s progress.
Based on the results of a recent assessment in Kid’s College, this customized Activity Book
has been generated to boost your student's performance in skill strands that need
improvement.
Mathematics:
Operations with W hole Numbers
The following section of this customized textbook includes material from these skill areas:
Skill Description
2465:apply order of operations to solve problems
2.3 Illustrate general properties of operations.
2497:solve addition problems with whole numbers
5.1.spi.4 add, subtract, multiply, and divide whole numbers (multipliers and divisors no more than
two-digits).
2507:apply rules to determine divisibility
2511:solve division problems with whole numbers with and without remainders
two-digits).
2515:solve multiplication problems with whole numbers
two-digits).
2519:solve problems with ratios
2520:solve subtraction problems with decimals
5.1.spi.8 add, subtract, and multiply decimals;
2521:solve subtraction problems with fractions
5.1.spi.12 add and subtract commonly used fractions.
2522:solve subtraction problems with integers
2523:solve subtraction problems with whole numbers
two-digits).
6416:determine operations and order of operations for whole number problems
Page 2
Choosing the Operation
After the problem is identified and carefully read, find out what operations are needed.
Watch for word clues that give a hint at the operation.
5,958,000 people visit an emergency
T he words h o w m an y
fe w e r suggest that
subtraction is the operation
for this problem.
room for stomach pain each year.
2,867,000 visit an emergency room for
head pain. How many fewer visitors
are seeking help for head pain?
I
n the United States, there is one doctor
for approximately every 365 people.
T he words o n e h un dre d
tim e s as m an y suggest
I
n M ozambique, there is one doctor for
about one hundred times as many
that multiplication is the
operation for this problem.
people. About how many patients are
there per doctor in M ozambique?
Choosing the Ord er of Operations
M any problems call for more than one operation.
S ometimes, it mak es a difference which operation is done first.
L ook carefully at the problem before you decide the order of the operations.
An orangutan weighed 5 times as much as a 15kg gibbon.
A chimpanzee weighed 25 kg less than the orangutan.
A gorilla weighed twice as much as the orangutan.
W hat is the total weight of all these animals?
F irst: . . . Multiply 5 and 1 5 to find the orangutan’s weight:
S econd: . . . . . . . Subtract 2 5 from the orangutan’s weight:
T hird: . . . . . . . . . . . Multiply the orangutan’s weight by 2 :
F ourth: . . . . . . . . . . . . . . . . . . . . . . . . Add all four weights:
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Page 3
193
Get Sharp: Approaches to Problems
A d d ition
Addition is the combining of two or more numbers or amounts.
52 + 10 0 + 1,0 0 0 + 640 = 1,792
ad d end s
su m
T he symbol for addition is
+
T he word used for addition
is plus .
T he numbers being combined
are adde n ds .
T he number resulting from addition
is a s um .
Each
year
in
the
U.S.,
about
5,100,000 people go to hospital
emergency rooms with pains in
the stomach. About 2,500,000
visit the emergency room with
head
pain. Another
4,500,000
go with chest pains.
76
Get Sharp: Addition
Page 4
A d d ition w ith Carry ing ( or R enam
ing)
When addition results in a sum greater than 9 in any place,
any amount over 10 is carrie d to the nex t place.
In the ones place of this ex ample, 8 +
8 = 16.
T he 6 is written in the one s place, and the rest of the amount (1 ten)
is carrie d over to the te ns place. T hat ex tra ten is added to the other tens
in the column. R e n am in g and re g ro upin g are other terms used
for this process.
In the ex ample, 8 + 5 eq uals 13.
S ince these digits are in the tens place,
the sum of these digits has a value of 13 tens.
T he amount of 1 3 tens is re n am e d as 3 te ns a nd 1 h u ndr e d.
T he 3 is written in the te ns place, and the 1 (value of 1 0 0 )
is added to the other amounts in the h u ndr e ds column.
S everal addends lined up
beneath each other
form a column.
T his is called
co lum n additio n .
17
88
42
90
5
+ 66
30 8
Page 5
77
Get Sharp: Addition
Add & Subtract Whole Numbers
EN GUARD!
Fencing was one of the events at the first Modern Olympic Games in 1896, but it began
around 4000 B.C. Fencers use various types of swords: the foil, which weighs about 500
grams; the épée, which weighs 770 grams; and the sabre, which weighs 500 grams. When the
director of the bout calls “en guard,” the competitors take a ready position. They begin the
“bout” when the director gives the “fence” command.
Try your skill in this bout
with addition and subtraction.
1.
47
9
+
10.
2.
3.
–
4.
1 2.
+
5.
1 3.
89
24
+
–
11 .
179
761
+
6.
+
234
78
+
864
342
229
6 44
–
8 1 49
28 8 9
8000
505
1 4.
333
222
–
7.
712
5 42
+
15.
30 ,0 6 8
+ 9 5 ,5 8 1
6161
40 9 9
1 0 ,0 0 0
– 7108
16.
–
8.
–
9.
–
666
47 7
973
45 8
7 40 0
42
Olympic Fact
Fencers began to wear white uniforms because
ink from the end of the weapon would leave a
spot when a hit was made. The ink showed up
well on the white. This practice is not followed
anymore, but fencers still wear the white
uniforms. Some fencers would dip their uniforms
in vinegar so the mark would not show.
Name
© 2000 by Incentive Publications, Inc., Nashville, TN.
2 39 6
Answer Copyright
key page
26, unit 239
Page
The BASIC/Not Boring Fifth Grade Book
Whole Number O p eration s
THE BI
G WI
NNERS
The Modern Olympic Games began in 1896, 100 years before
the S ummer Games in Atlanta. S ince then, thousands of medals
have been given to hard-working athletes. The gold medal for
first place is the most priz ed award! A silver medal is given for
second place, and a bronz e medal is given for third place. A
new design for the medals is created for each Olympic Games.
S olve the problems below with the information from the chart
of top medal-winning countries.
1. Total medals won by the top 5 countries = _ _ _ _ _ _ _ _ _ _
2. Germany’s medals + Canada’s = _ _ _ _ _ _ _ _ _ _
3. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ won about 3 times as many as Cuba.
4. Great Britain won _ _ _ _ _ _ _ _ _ _ fewer medals than the U .S .
5. This country won 211 fewer medals than Japan. _ _ _ _ _ _ _ _
6. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ won about 4 times as many as Greece.
7. The Netherlands won _ _ _ _ _ _ _ _ fewer medals than France.
8. Belgium and D enmark together won _ _ _ _ _ _ _ _ _ _ medals.
9. S witz erland won _ _ _ _ _ _ _ _ _ _ fewer medals than Germany.
10. The top 10 winners had a total of _ _ _ _ _ _ _ _ _ _ medals.
11. Before the 1996 Olympics, S pain had a total of
46 medals. H ow many did S pain win in 1996? _ _ _ _ _ _ _ _ _
12. Before the 1996 Olympics, the U nited S tates
had a total of 1,910 medals. H ow many did
the U nited S tates win in 1996? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Olympic Fact
The gold medal is not really made
of gold. It is made mostly of silver,
but it must contain at least six
grams of pure gold.
Name
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 26, unit 240
2 4 07
Page
Copyright © 2000 by Incentive Publications, Inc., Nashville, TN.
D iv id in g a N u m b e r b y Its e lf
A N Y
number divided by itself yields
D iv id in g a N u m b e r b y O n e
1!
yields that number
65 ÷ 65 = 1
No matter HO W
number divided by 1
A N Y
.
95 ÷ 1 = 95
BI
G the number is,
the quotient is still O NE.
999,999,999 ÷ 999,999,999 = 1
70 0 ,0 0 0 ÷ 1 = 70 0 ,0 0 0
D ivisibility
A number is div is ible by another number if the q uotient of the two numbers is a whole number.
(5 0 is divisible by 5 because the q uotient is a whole number, 1 0 .)
A number is div is ible by 2 if the last digit is 0 , 2 , 4 , 6 , or 8 .
A number is div is ible by 3 if the sum of its digits is divisible by 3 .
A number is div is ible by 4 if the last two digits are divisible by 4 .
A number is div is ible by 5 if the last digit is 0 or 5 .
A number is div is ible by 6 if the number is divisible by both 2 and 3 .
A number is div is ible by 8 if the last three digits are divisible by 8 .
A number is div is ible by 9 if the sum of its digits is divisible by 9 .
A number is div is ible by 1 0 if the last digit is 0 .
84
Get Sharp: D iv ision
Page 8
D ivision w ith One- D igit D ivisors
S te p 1 : D oe s 5 g o into 7 ? (y e s —1 tim e )
Write the 1 above the 7 .
M ultiply 1 x 5 . Write the product under the 7 .
S ubtract 7 – 5 ( = 2 ).
B ring the nex t digit (9 ) down nex t to the 2 .
S te p 2 : D oe s 5 g o into 2 9 ? (y e s —5 tim e s )
M ultiply 5 x 5 . Write the product under 2 9 .
S ubtract 2 9 – 2 5 ( = 4 ).
B ring the nex t digit (7 ) down nex t to the 4 .
S te p 3 : D oe s 5 g o into 4 7 ? (y e s —9 tim e s )
M ultiply 9 x 5 . Write the product under 4 7 .
S ubtract 4 7 – 4 5 ( = 2 ).
Write the remainder (2 ) nex t to the q uotient.
D ivision w ith M u ltiples of T en
36,0 0 0 ÷ 10 0 =
S te p 1 :
P lace a decimal point
after the dividend:
S te p 2 :
M ove the decimal point
one place to the left
for each z ero in the divisor:
36,0 0 0 .
360 .0 0
(The decimal point was moved
2 places because 100 has 2 zeros.)
S te p 3 :
D rop any z eros to the
right of the decimal point:
36,0 0 0 ÷ 10 0 = 360
Page 9
85
D ivision w ith L arger D ivisors
When the divisor has more than one digit, division problems can get very trick y.
H ere are some steps to help you handle this process without feeling baffled.
S te p 1 : D oe s 3 2 g o into 1 ? (no)
S te p 2 : D oe s 3 2 g o into 1 1 ? (no)
S te p 3 : D oe s 3 2 g o into 1 1 8? (y e s )
R ound 3 2 to the closest 1 0 . (3 0 )
E stimate the number of 3 0 s in 1 1 8 . (about 3 )
Write 3 above the 8 of 1 1 8 .
M ultiply 3 x 3 2 . Write the product under 1 1 8 .
S ubtract 1 1 8 – 9 6 (= 2 2 ).
B ring down the nex t digit (4 ) beside the 2 2 .
S te p 4 : D oe s 3 2 g o into 2 2 4 ? (y e s )
R ound 3 2 to 3 0 again.
E stimate the number of 3 0 s in 2 2 4 . (about 7 )
Write 7 above the 4 of 1 ,1 8 4 .
M ultiply 7 x 3 2 . Write the product under the 2 2 4 .
S ubtract 2 2 4 – 2 2 4 (= 0 ).
B ring down the nex t digit (8 ) beside the 0 .
S te p 5 : D oe s 3 4 g o into 8? (no)
Write 0 above the 8 of 1 1 ,8 4 8 .
M ultiply 0 x 3 2 . Write the product under 8 .
S ubtract 8 – 0 (= 8 ).
8 is smaller than the divisor, 3 2 . T herefore, 8 is the remainder.
Write the remainder beside the q uotient.
86
Page 10
D iv ide Whole Numbers
F
ANSBYTHE THOUS
ANDS
When a country hosts the Olympic Games, they spend many months and a lot of money
getting ready. Most countries try to use sports arenas and areas that they already have, but
many new buildings and venues must be built for all the events and the spectators. U sually a
country builds a new Olympic S tadium. The stadium in Atlanta was built to hold 85,000 fans.
If the 8 5,000 se ats in Atlanta we re arrang e d in 50 e q ual se ctions, how m any se ats
would the re be in e ach se ction? To find the answe r, you would ne e d to div ide 8 5,000
by 50. U se div ision to find the answe rs to the se p roble m s.
1. Aq uatic Center— swim events
14,000 seats ÷ 20 sections = _ _ _ _ _ _ _ _ _ _ _ _
2. Georgia World Congress— fencing, judo
7,500 seats ÷ 25 sections = _ _ _ _ _ _ _ _ _ _ _ _
3. Georgia Tech Coliseum— box ing
9,500 seats ÷ 10 sections = _ _ _ _ _ _ _ _ _ _ _ _
4. Nagano’s H ockey Arena— hockey
10,000 seats ÷ 50 sections = _ _ _ _ _ _ _ _ _ _ _ _
5. White R ing— speed skating
7,300 seats ÷
5 sections = _ _ _ _ _ _ _ _ _ _ _ _
6. Nagano Olympic S tadium
50,000 seats ÷ 50 sections = _ _ _ _ _ _ _ _ _ _ _ _
7. Atlanta Olympic S tadium
85,000 seats ÷ 50 sections = _ _ _ _ _ _ _ _ _ _ _ _
8. Clark U niversity S tadium— field hockey
9. Georgia D ome— basketball
10. Omni Coliseum— baseball
11. 9 8190
12. 3 1227
5,000 seats ÷ 25 sections = _ _ _ _ _ _ _ _ _ _ _ _
32,000 seats ÷
8 sections = _ _ _ _ _ _ _ _ _ _ _ _
52,000 seats ÷ 40 sections = _ _ _ _ _ _ _ _ _ _ _ _
13. 6 9 5 3 4
14. 8 46,328
Olympic Fact
Atlanta spent $500
million on new
buildings for the
1996 O lympics.
The O lympic Stadium
cost $209 million.
Name
Answer The
key
page 26, unit 244
2 4 4 11 Copyright © 2000 by Incentive Publications, Inc., Nashville, TN.
Page
M u ltiplic ation
M u ltip lic a tion is repeated addition. When you multiply, you are adding the same number over and
over again.
Y ou can add 6 + 6 + 6 + 6 + 6 + 6 + 6 to get 4 2 .
O r, you can multiply 6 x 7 and get 4 2 .
6 x 7 means seven groups of six .
6
x7
42
f ac tors
prod u c t
111
x 4
444
3,333 x 3 = 9,999
f ac tor
f ac tor
prod u c t
M u ltip ly in g b y O n e
A N Y
number multiplied by one has
a product the same as the number!
65 x 1 = 65
999,999 x 1 = 999,999
M u ltip ly in g b y Z e ro
A N Y
number multiplied by zero
is
0!
65 x 0 = 0
N o m a t t e r H O W B IG t h e n u m b e r
is , t h e p r o d u c t is s t ill Z E R O .
0 x 999,999,999,999 = 0
80
Get Sharp: Mu ltiplication
Page 12
M u ltiplic ation w ith R enam ing
S ometimes you will need to r e na m e (or regroup) numbers to complete a multiplication task . H ere’s how
it work s.
S te p 1 : M u ltip ly th e one s . 6 x 9 = 5 4 one s .
R ename the 5 4 ones as 5 tens and 4 ones.
Write the 5 above the tens column, and the 4 in the ones
place in the product.
S te p 2 : M u ltip ly th e te ns : 6 x 3 = 1 8.
Add the 5 tens. 1 8 + 5 = 2 3 tens.
R ename the 2 3 tens as 2 hundreds and 3 tens.
Write the 2 above the hundreds column, and the 3 in the
tens place in the product.
S te p 3 : M u ltip ly th e h u ndr e ds : 6 x 8 = 4 8 h u ndr e ds .
Add the 2 hundreds: 4 8 + 2 = 5 0 hundreds
R ename the 5 0 hundreds as 5 thousands and 0 hundreds.
Write the 0 in the hundreds place, and the 5 in the
thousands place in the product.
M u ltiplic ation w ith M u ltiples of T en
30 x 80 0 =
S te p 1 :
S te p 2 :
S te p 3 :
D rop the z eros and
rewrite the problem as a
basic multiplication fact.
F ind the product.
At the end of the product,
write the same number
of z eros you dropped.
3x8
3 x 8 = 24
Page 13
24,0 0 0
81
M u ltiplic ation by L arger N u m bers
S te p 1 : M u ltip ly b y one s .
M u ltip ly 7 x 8 (7 x 8 = 5 6 one s )
R ename the 5 6 ones as 5 tens and 6 ones.
M u ltip ly 7 x 6 (7 x 6 = 4 2 te ns ).
Add the 5 tens. (4 2 + 5 = 4 7 tens)
M u ltip ly 7 x 3 (7 x 3 = 2 1 h u ndr e ds ).
Add the 4 hundreds. (2 1 + 4 = 2 5 hundreds)
R ename the 2 5 hundreds as 2 thousands
and 5 hundreds.
S te p 2 : M u ltip ly b y te ns .
M u ltip ly 5 x 8 (5 x 8 = 4 0 te ns )
M u ltip ly 5 x 6 (5 x 6 = 3 0 h u ndr e ds ).
Add the 4 hundreds. (3 0 + 4 = 3 4 hundreds)
R ename the 3 4 hundreds as 3 thousands
and 4 hundreds.
M u ltip ly 5 x 3 (5 x 3 = 1 5 th ou s a nds ).
Add the 3 thousands (1 5 + 3 = 1 8 thousands).
R ename the 1 8 thousands as 1 ten thousand
and 8 thousands.
S te p 3 : M u ltip ly b y h u ndr e ds .
M u ltip ly 2 x 8 (2 x 8 = 1 6 h u ndr e ds )
R ename the 1 6 hundreds as 1 thousand
and 6 hundreds.
M u ltip ly 2 x 6 (2 x 6 = 1 2 th ou s a nds ).
Add the 1 thousand. (1 2 + 1 = 1 3 thousand)
R ename the 1 3 thousands as 1 ten thousand
and 3 thousands.
M u ltip ly 2 x 3 (2 x 3 = 6 te n th ou s a nds ).
Add the 1 ten thousand. (6 + 1 = 7 ten thousands.)
S te p 4 : Add th e c olu m ns .
82
Page 14
M ultip ly Whole Numbers
MAYTHE BES
TS
AI
L
OR WI
N
Y achting has been an Olympic sport since the 1896 games in Athens. U nfortunately, the yachting
races had to be canceled at those games! The weather was just too bad. In each racing class, all
the yachts must have the same design. This way, the best sailor wins the race, not the best boat!
Solv e the m ultip lication p roble m s in the p uz z le . U se the color code to find the color
for e ach se ction. If you g e t the answe rs rig ht, the colore d p icture will show you one
kind of yacht use d
in O lym p ic racing .
COLORCODE
Red
66,16
Hot Pink
5 4, 5 6 , 8 4,
7 2, 41 0
Purple
42, 8 0
W hite
25 , 7 5
DarkBlue
36 , 440 , 6 0 ,
8 9 1 , 11 0
Bright Green
44, 6 5 , 9 0 ,
1 0 8 , 1 26
Olympic Fact
Competitors sail 1 race each day of the
competition. The crew throws out their
worst race. All the other scores are
added together. The lowest score wins!
Orange
9 6 , 49 , 30
Yellow
1 2, 48 , 32
Brown
1 20 , 8 1
Name
2 4 315
Answer Copyright
key page
26, unit 243
Page
R atio
A r a tio is a comparison between two numbers or
amounts. R atios are used to compare all k inds of things,
such as age, prices, weights, times, or distances.
T erm s of a R atio
T he numbers in a ratio are called te r m s .
In the ratio of spiders to rats above,
the terms are 12 and 6.
T he 12 is the first term and the 6 is the second term.
Watch the order of the terms carefully.
T he above ratio 12 : 6 is the ratio of spiders to rats.
W h a t is th e r a tio of r a ts to s p ide r s ?
T he terms get reversed!
6 .
T he ratio is 6 : 12 o r 12
—
(P ay close attention to the o rde r of terms! If y ou chang e
the order, the meaning of the ratio is entirely different.)
10 6
Get Sharp: R atio
Page 16
R ed u c ing R atios to L ow est T erm s
R atios are reduced in the same way that fractions are reduced.
6
1
— . T his can be reduced to — .
T he ratio of r a ts to s p ide r s is 12
2
6
1
T he ratio of r a ts to tota l c r e a tu r e s is 24
— . T his can be reduced to — .
4
Changing F rac tions to W hole N u m ber R atios
Y ou can change a fraction ratio to a whole number ratio.
2
T he ratio of s p ide r s to r a ts is 12
— , reduced to — .
6
1
S o you can say, th e re are 2 s pide rs fo r e v e ry rat, or 2 to 1 .
E q u ivalent R atios
E q u iv a le nt r a tios are ratios that name the same value.
When reduced to lowest terms, eq uivalent ratios will be the same.
7:5 6 is eq uivalent to 4:3 2
7
1 .
5—6 in lowest terms is —
8
4
1 .
3—2 in lowest terms is —
8
U sing E q u ivalent R atios to F ind M issing N u m bers
When you k now the ratio, you can use eq uivalent ratios to find missing q uantities.
O n this camping trip, there are 60 mosquitoes in the 15 tents. Every tent has the same number
of mosquitoes. How many mosquitoes are in 1 tent?
S te p 1 :
Write the ratio.
60
15
S te p 2 :
S te p 3 :
60
F ind a ratio eq uivalent to 1 5 .
S ince the q uestion ask s how
many mosq uitoes in 1 tent,
the second term of the second
ratio must be 1 . T o get 1 in
60
this ratio ( 1 5 ), you must
divide the denominator by 1 5 .
60 ÷ 15
15 ÷ 15
=
D ivide the 6 0
by 1 5 also.
Write this as
the first term
in the new ratio.
4
1
4 m osq u itoes in 1 tent!
Page 17
10 7
Get Sharp: R atio
Operations w ith D ec im als
A d d ing & S u btrac ting D ec im als
S te p 1 : L ine up the decimal points of both numbers
in the problem.
S te p 2 : Add or subtract just as with whole numbers.
S te p 3 : Align the decimal point in the sum or difference with
decimal points in the numbers above.
M u ltiply ing D ec im als
S te p 1 : M ultiply as you would with whole numbers.
Multiply 2 .65 x 3 9 .6 to g e t 1 0 4 ,9 4 0 .
S te p 2 : C ount the number of places to the right of the
decimal point in both factors (total).
C o un t th e n um be r o f place s to th e rig h t o f th e de cim al
po in t: 2 .65 h as 2 ; 3 9 .6 h as 1 , fo r a to tal o f 3 .
S te p 3 : C ount over from the right end of the product that
same number of places.
I n th e pro duct, co un t 3 place s back w ard fro m th e rig h t.
S te p 4 : Insert the decimal point.
P lace th e de cim al po in t be tw e e n th e 4 an d th e 9 .
Q uillayute ’s an n ual pre cipitatio n is abo ut 1 0 4 .9 4 in ch e s .
112
Get Sharp: D ecimal C on cepts
Page 18
Operations w ith M oney
O perations with money are just lik e operations with decimals, because money amounts are decimals.
A d d ition
S u btrac tion
L ine up the decimal points carefully in both
addends. Align the decimal point in the sum
(answer) with the numbers above it.
L ine up the decimal points carefully in both
numbers. T hen, align the decimal point in the
difference (answer) with the numbers above it.
O n the opening weekend of a new
All that popcorn and candy made kids
superhero movie, kids in our city
really thirsty. They spent $20,554.25
spent $53,850.50 on movie tickets.
on drinks at the movie.
Those same kids spent $29,282.35
How much more did they spend on
on candy and popcorn at the movies.
candy and popcorn than on drinks?
How much did they spend all together?
M u ltiplic ation
D ivision
M ultiply as with whole numbers. T ally the
total number of places to the right of the
decimal point. C ount the same number of
places from the right in the product.
M ove the decimal point in the divisor to mak e it
a whole number. M ove the decimal point in the
dividend the same number of places. Align the
decimal point in the q uotient with the decimal point
in the dividend. D ivide as with whole numbers.
Anna paid the train fare for herself and
four friends when they went into the city
M ax, a great moviegoer, spent a total of
to see a movie. The roundtrip fare
$37.60 on movie tickets last month. O n the
was $5.25 for each rider.
average, how much did he spend each week?
How much did Anna spend?
Page 19
115
Get Sharp: Mon ey
A d d ing & S u btrac ting F rac tions
H ow to A d d & S u btrac t L ik e F rac tions
S te p 1 : If the fractions have lik e denominators, just add or subtract the numerators.
(D enominators stay the same.)
S te p 2 : R educe sums or differences to lowest terms.
H ow to A d d & S u btrac t U nlik e F rac tions
S te p 1 : F ind the L C M for all denominators and change the fractions to lik e fractions.
S te p 2 : Add or subtract the numerators. (D enominators stay the same.)
H ow to A d d & S u btrac t M ixed N u m erals
S te p 1 : C hange all mix ed numerals to improper fractions.
S te p 2 : F ind the L C M for all the denominators and change the fractions to lik e fractions.
S te p 3 : Add or subtract the numerators. (D enominators stay the same.)
Page 20
10 3
Get Sharp: O peration s w ith F raction s
Operations w ith Integers
T he sum of two positive integers is a positive integer.
1
2
—
+—
3 = 3
5 + 10 0 = 10 5
0 .5 + 1.3 = 1.8
1
—
3
T he sum of 2 negative integers is a negative integer.
–5 + –8 = –13
–8.5 + –2 = –10 .5
2 + –—
1 = –—
3
–—
4
4
4
T he sum of a positive integer and a negative integer
has the sign of the number with the greater absolute value.
10 0 + –6 0 = 40
–30 .5 + 10 = –20 .5
4 + –—
7
3
—
8
8 =–—
8
T o subtract an integer, add its positive.
–6 – ( –3) = –6 + 3 = –3
10 – ( – 4) = 10 + 4 = 14
12 – ( –14) = 12 + 14 = 26
80 – 3 = 80 + –3 = 77
17 6
Get Sharp: In tegers
Page 21
T he product of two positive integers is a p os itiv e integer.
7 x 10 = 70
0 .3 x 6 = 1.8
1
1
—
2 x 3 = 1—
2
T he product of two negative integers is a p os itiv e integer.
–5 x –0 .5 = 2.5
–10 x –20 = 20 0
1 x–—
1 =—
1
–—
4
2
8
T he product of a positive and a negative integer is a ne g a tiv e integer.
10 0 x –6 = –6 0 0
–0 .2 x 16 = –32
6 x –6 = –36
T he q uotient of two positive integers is a p os itiv e inte g e r .
15 ÷ 5 = 3
6 70 ÷ 10 0 = 6 .7
5 0 ÷ 5 = 10
T he q uotient of two negative integers is a p os itiv e inte g e r .
–80 ÷ –10 = 8
–12 ÷ –0 .5 = 24
–45 0 0 ÷ – 9 = 5 0 0
T he q uotient of a positive and a negative integer
is a ne g a tiv e inte g e r .
– 5 6 0 ÷ 8 = –70
–25 .5 ÷ 0 .5 = –5 1
810 ÷ –9 0 = –8
Page 22
17 7
Get Sharp: In tegers
In teg ers
TEMPERATURE COUNTS
The temperature really does matter for ski races. S now conditions
change with temperature changes, and this can affect the skiers’
speed and control. As a result, racers, coaches, and Olympic officials
pay a lot of attention to the thermometer.
U se this the rm om e te r as a num be r line to he lp you solv e the se
p roble m s with inte g e rs. R e m e m be r, inte g e rs are a se t of p ositiv e and ne g ativ e num be rs.
1. At 5 o’clock in the morning, the temperature at the
top of the race course was – 13°. By 10:00 A.M.,
it was + 12°. H ow much had the temperature risen? _ _ _ _ _ _ _ _ _ _
2. The temperature rose from + 12° to + 23° by noon.
H ow much did the temperature change? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
3. In the afternoon, the temperature fell rapidly
from + 23° to -1°. H ow much change is this? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
4. By 7:00 P.M., the temperature was – 9°. H ow much
had the temperature changed from 10:00 A.M.? _ _ _ _ _ _ _ _ _ _ _ _ _ _
5. It continued to get colder. By midnight, the
temperature was 35° colder than it had been
at noon. What was the midnight temperature? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
6. If the temperature rose 12° between midnight
and 6:00 A.M. the nex t morning, what was
the temperature at 6:00 A.M.? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
F inish the se p roble m s.
7.
30 – 41 = _ _ _ _ _ _ _ _
11.
– 12 + – 4 = _ _ _ _ _ _ _ _
8. – 10 + 15 = _ _ _ _ _ _ _ _
12. 40 + – 6 + – 10 = _ _ _ _ _ _ _ _
9.
5 + – 7 = ________
13. – 10 + – 5 + 15 = _ _ _ _ _ _ _ _
10.
– 9 + 4 = ________
14.
20 + 3 + – 6 = _ _ _ _ _ _ _ _
Name
2 6123
Answer Copyright
key page
28, unit 261
Page
S u btrac tion
S u b tr a c tion is the operation of finding a missing addend
(or, the tak ing away of one number or amount from another).
T he symbol for subtraction is
–
T he word used for addition is m
in us .
T he number being subtracted from is the m
in ue n d.
T he number being subtracted is the s ubtrah e n d.
78
Get Sharp: Su btraction
Page 24
S u btrac tion w ith B orrow ing ( or R enam
ing)
S ometimes a digit in the minuend is smaller than the digit of the same place in the subtrahend. When this
happens, it is necessary to bo rro w from the nex t place to the left.
B o rro w in g is the same as re n am in g . It means ex changing a ten to mak e a number in the ones place
la r g e r than the digit in the subtrahend. (O R , it might mean ex changing a hundred for 1 0 tens, or a
thousand for 1 0 hundreds, etc.)
Addition & Subtraction
Are Relatives!
Addition and subtraction are
opposite (
inverse)operations.
9 + 7 = 16
16 – 9 = 7
and 16 – 7 = 9
An addition problem can be
checked with subtraction.
8,222
+ 9,666
17,888
17,888
– 9,666
8,222
A subtraction problem can be
checked with addition.
50 ,0 0 0
–
50 0
49, 50 0
49,50 0
+
50 0
50 , 0 0 0
In this ex ample, 8 is too
large to subtract from 5 . S o,
one of the tens is bo rro w e d
o r re n am e d as 1 0 ones.
N ow there are 1 5 ones.
8 can be subtracted from 1 5 .
T hat leaves only 2 tens.
(S ee the 2 written above the
tens place.)
In this, the 8 in the tens
place is smaller than the 9
in the tens place. S o, one of
the hundreds is bo rro w e d o r
re n am e d as 1 0 tens.
N ow there are 1 8 tens.
9 can easily be subtracted
from 1 8 .
T his leaves only 6 hundreds.
(S ee the 6 written above the
hundreds place.)
Page 25
79
Get Sharp: Su btraction
Better Grades & Higher Test Scores / MATH
43
Page 26
Get Set: Probem-Solving Skills
44
Get Se:-Problem-Solving Skills
Page 27
45
Page 28
Get Set: Probem-Solving Skills
90
Get Sharp : O p erations
Page 29
193
Page 30
Get Sharp : Ap p roaching Problems
C hoose C orrect O p eration
BUMPS
,BRUI
S
ES
,&BREAKS
The Blue Berg H ockey Team never makes it through a game without some injuries. It looks
as if Bruiser is out of the game for a while! H elp the team solve some of their injury problems
by deciding what operation is needed for each one. (S ome may need more than one.) Write
A (add ), S (su b trac t), M (m u ltip ly ), or D (div ide) nex t to each problem. Then use a separate
piece of paper to find the answers.
_ _ _ _ _ _ _ 1. The cost of
hospital trips for the Blue
Bergs averages $ 125,000 a
season. If the season is five
months long, what is the
average monthly hospital cost
for the season? _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ 3. Pierre, the
goalie, lost an average of 27
minutes per game because of
bloody noses. H ow many
games did he play in if he
lost 135 minutes total for his
nosebleeds? _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ 2 . The Blue Bergs
had a total of 396 teeth intact
when they started the season.
They lost 45 of them. H ow
many teeth did the team have
left at the end of the season?
_______
_ _ _ _ _ _ _ 4 . E ach defensive
player bumped his shins and
bruised his nose a total of 26
times in each game period.
There are 3 game periods and
2 defensive players. At this
rate, how many bumps and
bruises will they get in the
entire game? _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ 5. In one season,
12 of the 130 total injuries
were broken bones and torn
ligaments, 53 were broken or
lost teeth, and 30 were black
eyes. The rest were bumps
and bruises. H ow many were
bumps and bruises? _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ 6. Two team
members got food poisoning
the morning of the big game.
Twice that many had colds
and couldn’t play. Three
more were on crutches. If
there are 18 players on the
team, how many were left to
play the game? _ _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ 7. D uring one game, a referee called minor penalties on Big Bruno and Biffo for
roughing. Five more players got minor penalties for tripping and 3 more for high sticking. If a
minor penalty is 2 minutes in the penalty box , how many total minutes did the team spend in
the penalty box during the game? _ _ _ _ _ _ _ _
_ _ _ _ _ _ _ 8 . In one game alone, there were these injuries: one player had a hockey stick
broken over his head, two guys got in a bloody fist fight, and five more got cut by skates to
the cheek. All of them had to take time out from the game. H ow many players got called
off the ice for injuries? _ _ _ _ _ _ _ _
Name
2 1731
Answer Copyright
key page
25, unit 217
Page
C hoose O p eration s
TOURI
S
TATTRACTI
ONS
Two million people attended the 1996 Olympics. They bought tickets; watched events; traveled
to different venues; toured Atlanta; lived in hotels, tents, campers, and homes; and bought a lot
of food and souvenirs.
De cide which op e ration you should use to solv e e ach of the se p roble m s about O lym p ic
tourists. W rite the op e ration ( add, subtract, m ultip ly, or div ide ) afte r e ach p roble m .
The n solv e the p roble m .
1. Tickets for the kayaking race cost $ 27. The ticket office
counted $ 29,403 for this event. H ow many tickets were sold?
O p e ration _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Answe r _ _ _ _ _ _ _ _ _ _ _ _ _ _
2. If hot dogs sold for $ 2.00 in the Olympic Park and 986,443 hot
dogs were sold, how much money was collected?
3. 26,000 bus and limo drivers were hired for the Olympics.
If 35 worked every day, how many worked at one time?
4. One family drove 243.33 km from their home to Atlanta for
the games. They went home by a route 21.7 km longer. H ow
long was their trip home?
5. In Nagano, 10,000 people could attend a hockey game at once. Of these, 15 had “standing
room only” tickets. H ow many fans had to stand?
O p e ration _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Answe r _ _ _ _ _ _ _ _ _ _
6. Brielle’s family bought 18 Olympic basketballs as
souvenirs to take home to friends. They spent
$ 412.20. H ow much did each ball cost?
7. Not all sports fans can get to the Olympics, so they
are televised around the world. TV rights cost
$ 2,500,000 in 1968. In 1992, they cost 120 times that
much. H ow much did the 1992 rights cost?
8. In Nagano, tickets for good seats at the Opening
Ceremony cost $ 350. In Atlanta, the tickets cost $ 636.
H ow much did Joanna’s family of 4 pay to go to both?
O p e rations _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ & _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Answe r _ _ _ _ _ _ _ _ _ _ _ _ _ _
Name
Answer The
key
page 26, unit 246
2 4 632
Page
Mathematics:
Fractions
The fol
l
owing section ofthis customized textbook incl
udes materialfrom these skil
lareas:
Skill Description
2299:understand concepts ofrate and rate ofchange
2.4 Anal
yze change in various contexts.
5.2.spi.8 extend rate charts to sol
ve real
-worl
d probl
ems.
2443:Fractions
5.1.spi.11 compare and order fractions using the appropriate symbol(<,>,=);
2445:rel
ate fractions to decimal
s
2446:represent fractions in equival
ent forms
5.1.spi.2 connect symbol
icrepresentations ofproper and improper fractions to model
s ofproper
and improper fractions;
5.1.spi.13 generate equival
ent forms ofcommonl
y used fractions, decimal
s, and percents (e.g.,
1/10, 1/4, 1/2, 3/4);
2495:sol
ve addition and subtraction probl
ems with fractions
5.1.spi.12 add and subtract commonl
y used fractions.
2509:sol
ve division probl
ems with fractions
2513:sol
ve mul
tipl
ication probl
ems with fractions
5.1.spi.14 mul
tipl
y a fraction by a mul
tipl
e ofits denominator (denominator l
ess than or equalto
10)(3)
Page 33
R ates
A r a te is a ratio that compares q uantities of different units.
R ed u c ing R ates to F ind Q u antities
S ince you k now the ratio (rate), you can find the cost
by reducing the ratio to lowest terms.
D ivide both terms of the ratio by 4 . (Y ou use 4 because the
second term of the new ratio must be 1 , so you must use the
number that will yield a q uotient of 1 when it goes into 4 .)
It c o s ts $ 3 .2 0 p e r p o u n d !
U sing E q u ivalent R atios to F ind Other R ates
S ince you k now the ratio (rate), you can find other costs
by writing eq uivalent ratios.
M ultiply both terms of the ratio by 5 .
(Y ou use 5 because the second term of the new ratio
must be 2 0 , so you must choose the number that will
yield a product of 2 0 when multiplied by 4 .)
It c o s ts $ 64.00 p e r 2 0 p o u n d s !
10 8
Get Sharp: R ates
Page 34
T im e Z ones
As E arth turns, the sun shines on different parts of the sphere at different times. B ecause of this, we have
divided E arth into several time z ones.
T he line of 0 ° longitude (the P rime M eridian) goes through G reenwich, E ngland. E arth’s time z ones are
all related to the time in G reenwich, called G reenwich time. F rom G reenwich, an hour is subtracted as
you travel west through each time z one. As you travel east from G reenwich, an hour is added to the time.
It
it
it
it
it
it
it
is
is
is
is
is
is
is
7 a .m . ( 5 t im e z o n e s w e s t )
1 p .m . ( 1 t im e z o n e e a s t )
3 p .m . ( 3 t im e z o n e s e a s t )
in
in
in
in
in
in
in
N e w Y o r k C it y , N Y
L o s A n g e le s , C A
A n c h o ra g e ,A K
Pa r is , F r a n c e
M o s c o w , R u s s ia
H ong Kong
To ky o ,J a p a n
a n d . . . it is m id n ig h t ( 12 t im e z o n e s e a s t o r w e s t )
o n t h e In t e r n a t io n a l D a t e L in e ( 180 ° E o r W lo n g it u d e )
M easu ring R ate
R a te
is a measure of an amount compared to something else. O ften it is an amount compared to time.
R ate can tell how far something moves or how often something occurs over a certain period of time, such
as a second, minute, hour, week , year, and so on. S peed is described as a rate.
1 8 6 ,2 8 2 ,3 9 7 miles per second (mps)
speed of light
6 6 miles per hour (mph)
speed a sailfish can swim
6 5 k ilometers per hour (k ph)
speed a mallard duck can fly
1 2 miles per hour (mph)
speed of a running rabbit
1 1 .6 k ilometers per hour (k ph)
speed a honeybee can fly
0 .0 3 miles per hour (mph)
speed a snail can crawl
2 6 1 .8 miles per hour (mph)
speed of J apan’s fast N oz omi 5 0 0 train
2 6 pounds per year
amount of chocolate eaten by average S wiss person
4 8 gallons per year
amount of soda pop drunk by average American
Page 35
14 9
Get Sharp: Measu remen t
F rac tions
A fr a c tion is any number written in the form of
a
b
F raction comes from the L atin word fractio, meaning brok en parts.
F ractio n means part o f a s e t or part o f a w h o le . A fraction is written in a
way that compares two numbers or amounts.
P roper & Im proper F rac tions
In a p r op e r fr a c tion,
the numerator is smaller
than the denominator.
7
8
11
12
2
3
14
20
3
10 0
6
9
2
9
reads s e v e n -e ig h th s
reads e le v e n -tw e lfth s
reads tw o -th irds
reads fo urte e n -tw e n tie th s
reads th re e -h un dre dth s
reads s ix -n in th s
96
Get Sharp: F raction C on cepts
In an im p r op e r fr a c tion, the numerator
is larg er than the denominator.
T he value of the fraction is always eq ual to
or g reater than one.
12
7
R ead ing and W riting F rac tions
A f r a c t io n is a ls o a w a y o f
w r it in g a d iv is io n p r o b le m .
3
24
m eans
3 ÷ 24
( t h r e e d iv id e d b y t w e n t y - f o u r )
Page 36
Solv e P roblems w ith D ecimals
“
FI
GURI
NG”OUT DECI
MAL
S
Tamara is working on perfecting her figures for a skating competition. They must be precise
for the judges. Numbers with decimals can be tricky, too. Y ou can practice decimals by
finding the decimal number in Jenny’s figure 8 that matches the problem. Circle each one
with the correct color.
_ _ _ _ _ _ 1. one-tenth more than 7 R E D
_ _ _ _ _ _ 2. five-hundredths more than 6.3 BL U E
_ _ _ _ _ _ 3. the difference between 10.8 and 10.2 PINK
_ _ _ _ _ _ 4. one hundred plus twelve-hundredths BL ACK
_ _ _ _ _ _ 5. 3 tenths more than 6 hundredths Y E L L OW
_ _ _ _ _ _ 6. 0.05 plus 0.04 PU R PL E
_ _ _ _ _ _ 7. 9 tenths less than ten TAN
_ _ _ _ _ _ 8. two-tenths more than 14 OR ANGE
_ _ _ _ _ _ 9. 5 hundredths more than 2 BR OWN
_ _ _ _ _ _ 10. one-tenth less than one TAN
_ _ _ _ _ _ 11. two-tenths plus four-hundredths S IL V E R
_ _ _ _ _ _ 12. 9 tenths plus 9 hundredths GR E E N
_ _ _ _ _ _ 13. ten plus twelve-hundredths R E D
_ _ _ _ _ _ 14. eight-hundredths more than eight BL U E
_ _ _ _ _ _ 15. one-tenth less than ten GR E E N
_ _ _ _ _ _ 16. two-tenths less than nine PINK
_ _ _ _ _ _ 17. ten less than 12.4 PU R PL E
_ _ _ _ _ _ 18. 0.004 more than 0.005 R E D
_ _ _ _ _ _ 19. ten less than 10.22 OR ANGE
_ _ _ _ _ _ 20. 0.6 more than three Y E L L OW
_ _ _ _ _ _ 21. two-tenths more than 0.3 BL U E
_ _ _ _ _ _ 22. 5 tenths less than fifty-one GR E E N
_ _ _ _ _ _ 23. five-tenths less than 21 S IL V E R
_ _ _ _ _ _ 24. one hundred plus two-tenths PU R PL E
Name
2 1537
Answer Copyright
key page
25, unit 215
Page
F raction s as P arts of Sets
WATCHTHATPUCK!
These fans are gathered for an ex citing, high-speed ice hockey game.
All the action in the game is focused on a little rubber disc that moves
so fast that often it is hard to tell where it is and which team has it! An
ex citing Olympic moment for the U nited S tates was in 1980 when the
U .S . team defeated Finland to win its first gold medal in 20 years.
Olympic Fact
The 1998 W inter
O lympics in Japan were
the first G ames that
permitted women to
compete in ice hockey.
P ay atte ntion to the se fans to p ractice your fraction-hunting skills. W rite a fraction to
fill e ach blank.
1. _ _ _ _ _ _ of the fans are holding balloons.
11. _ _ _ _ _ _ of the fans are wearing earmuffs.
2. _ _ _ _ _ _ of the fans are holding flags.
12. _ _ _ _ _ _ of the fans are wearing hats.
3. _ _ _ _ _ _ of the flags have words on them.
13. _ _ _ _ _ _ of the shoes and boots have laces.
4. _ _ _ _ _ _ of the flags are black.
5. _ _ _ _ _ _ of the flags have no words.
14. _ _ _ _ _ _ of the hands are wearing mittens
or gloves.
6. _ _ _ _ _ _ of the fans are holding cups.
15. _ _ _ _ _ _ of the fans are wearing scarves.
7. _ _ _ _ _ _ of the cups have 2 straws.
16. _ _ _ _ _ _ of the fans are hatless.
8. _ _ _ _ _ _ of the cups have no straws.
17. _ _ _ _ _ _ of the hats have feathers.
9. _ _ _ _ _ _ of the fans are wearing boots.
18. _ _ _ _ _ _ of the fans have mustaches.
10. _ _ _ _ _ _ of the shoes and boots have black
on them.
19. _ _ _ _ _ _ of the balloons are held by the
girl with pigtails.
Name
Answer The
key
page 27, unit 248
2 4 8 38
Page
C omp are & O rder F raction s
OVER THE NET
Olympic Fact
In beach volleyball,
each team has only
two players.
They play barefoot
in the sand.
Beach volleyball began in the 1940s on the beaches of California.
It was played for fun at first, but now it is a serious professional
sport. It did not gain a place at the Olympic Games until 1996,
when the U .S . men’s teams won the gold and silver medals.
C om p are e ach se t of fractions be low to se e which is g re ate r. C ircle the larg e st
fraction. If the fractions are e q ual, circle the m both!
2
4
1.
1
4
2.
5
7
3
7
3.
2
7
4.
5.
1
3
5
8
9.
2
3
10.
2
4
1
3
1
6
6.
3
4
7.
4
8
7
9
5
6
1
3
7
8
8.
11
12
2
10
11.
2
5
4
10
5
6
1
5
12.
2
10
R e write the fractions in orde r from sm alle st to larg e st.
1
2
13.
2
5
1
4
__________________
14.
3
18
5
6
2
3
__________________
15.
2
5
6
7
5
9
__________________
Name
2 4 9 39
Answer Copyright
key page
27, unit 249
Page
C omp are F raction s
L
OS
T!
Badminton may seem like a rather easy sport where you just hit the “birdie” around at a slow
pace. Actually, it is the world’s fastest racket sport. The “birdies” are really called shuttlecocks, and
they travel as fast as 200 miles per hour. Players must be very q uick, strong, and agile to compete.
P e te has g otte n se p arate d from the badm inton te am on the
way to the com p e tition. To he lp him join his te am m ate s,
com p are the fractions in e ach box . C olor the box e s that hav e
the corre ct sig n ( < , > , or = ) be twe e n the fractions. If you do
this corre ctly, you will hav e colore d a p ath for P e te .
8
2
=
12 3
11 5
<3
6
2
5
>
3
4
3
4
2
4
5
= 10
6
3
=
8
4
4
5
7
< 10
2
9
2
5
5
> 10
8
4
12
=6
7
4
6
3
2
3
7
1
=
16 4
20 4
=
25 5
=
7 14
=
12 24
0
2
<
3
6
>
1
2
=
4
6
=
0
4
Name
Answer The
key
page 27, unit 250
2 5040 Copyright © 2000 by Incentive Publications, Inc., Nashville, TN.
Page
Imp rop er F raction s & M ix ed Numerals
THE L
ONGES
TJ
UMPS
It sounds pretty hard! An athlete runs down a short path and jumps as far as possible, landing
into a pit of sand. A measurement is taken from the beginning of the jump to the impression
the body leaves in the sand. If the athlete falls backward from where the feet land, the
measurement will be shorter than desired!
H e re are som e m e asure m e nts of long jum p s from athle te s of all ag e s. The y are
writte n as im p rop e r fractions. C hang e the m into m ix e d num e rals.
Olympic Fact
U.S. track and field athlete Jackie
Joyner-Kersee won the gold medal in
1988 with a jump of 24 ft 3 12 in.
U.S. jumper Carl Lewis won the gold
medal in the long jump at the last four
O lympic G ames:1984, 1988, 1992, & 1996.
1. Carl
57
2
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
9. James
49
4
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
2. L utz
57
6
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
10. R andy
109
4
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
3. Jackie
97
4
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
11. Tatyana
71
3
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
4. H eike
47
2
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
12. Mary
63
4
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
5. Amber
32
5
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
13. Bob
165
6
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
6. Y vette
85
8
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
14. Albert
129
12
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
7. Arnie
88
3
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
15. Jenny
101
4
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
8. E llery
83
4
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
16. Tommy
14
3
feet = _ _ _ _ _ _ _ _ _ _ _ _ _ _
Name
Answer The
key
page 27, unit 252
2 52 41
Page
Imp rop er F raction s & M ix ed Numerals
GETTI
NG TO VENUES
A venue is a place where one of the Olympic events is held. There are many venues at each
Olympic Games. These Olympic athletes are trying to get to their proper venues, but their
paths are blocked. R emove the obstacles along the paths by changing each improper fraction
to its correct mix ed numeral.
Olympic Fact
There were 27 different venues at
the 1996 games. Some were many miles
away. Canoeing and kayaking events
took place on the O coee River in
Tennessee, 150 miles from Atlanta.
Name
2 5342
Answer Copyright
key page
27, unit 253
Page
F rac tions & D ec im als
H ow to W rite a F rac tion as a D ec im al
S te p 1 : D ivide the numerator by the denominator.
S te p 2 : Write a z ero to hold the ones place
(if there is no number in that place).
7 = 0 .875
8
H ow to W rite a D ec im al as a F rac tion
S te p 1 : R emove the decimal point and write the number as
the numerator. T he denominator is 1 0 or a multiple
of 1 0 , depending what place the last digit of the
decimal occupied. F or instance, in 0 .0 4 4 , the last
digit is a thousandth.
S te p 2 : R educe the fraction to lowest terms.
44
11
10 0 0 reduced to lowest terms is 250 .
116
Get Sharp: F raction s & D ecimals
Page 43
Solv e P roblems w ith P ercen t & F raction s
HANG TEN PERCENT
The surf’s up at S hark Beach! One hundred surfers showed up on S aturday to “hang ten” for
the awesome waves. If a surfer is “hanging ten percent”— what would that mean? S ee if you
can figure it out!
Choose the correct percentage from the waves below to match the fraction in each problem.
Write the answer on the line. S ome answers may be used more than once.
R em em b er: To w rite a frac tion as a p erc ent, y ou hav e to w rite an eq u iv alent
20 = 20% !
frac tion w ith a denom inator of 100. For ex am p le: 51 = 100
____%
____%
____%
____%
____%
____%
____%
1.
2.
3.
4.
5.
6.
7.
3 of the surfers fell off their boards.
4
1 can hang ten.
10
1 forgot their sunscreen.
5
9 are afraid of sharks.
10
1 wear sunglasses at all times.
4
8 wax their own boards.
10
1 have been stung by jellyfish.
2
____%
____%
____%
____%
____%
____%
____%
____%
____%
____%
____%
____%
____%
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
4
10 have sand in their swimsuits.
1
2 0 have never seen a shark.
6
2 0 saw a shark today.
55
100 have had surfing injuries.
3
2 0 are very sunburned.
27 learned to surf very young.
30
9 forgot to eat breakfast.
12
10
100 are over 50 years old.
4
16 did not fall today.
3
10 never had a surfing lesson.
2 got smashed by the last wave.
5
4 are high school students.
5
11 have on wet suits today.
22
Name
Answer The
key
page 25, unit 220
2 2 044 Copyright © 2000 by Incentive Publications, Inc., Nashville, TN.
Page
F raction s & D ecimals
OVER THE TOP
Pole vaulters sprint along a short track with a long, flex ible pole. Then they plant the pole
and soar upside down over another pole that might be almost 20 feet high. The goal is to
make it over the top without knocking off that pole! At the 1996 Olympics, Jean Galfione
from France won the gold medal with a jump over a pole that was 19 feet, 5 inches high!
If a p ole v aulte r m ake s it ov e r the top 6 tim e s out of 7 trie s, a fraction ( 67 ) can show
his succe ss rate . The fraction can be chang e d to a de cim al score . ( Div ide 6 by 7. The
de cim al is 0.8 6.) F ind the de cim al to m atch e ach fraction that shows how the se p ole
v aulte rs are doing at the ir p ractice . R ound to the ne are st hundre dth.
Athlete
Fraction
Decimal
1 . M ax im
14
18
________
2 . J av ier
16
20
________
3 . Serg ei
20
27
________
4 . Wolfg an g
13
18
________
5 . F rederick
20
26
________
6 . Q uin on
13
16
________
7 . P hilip p e
21
28
________
8 . William
16
22
________
9 . C harles
15
21
________
9
12
________
1 0 . G rig ori
Name
2 59 45
Answer Copyright
key page
28, unit 259
Page
E q u ivalent F rac tions
E q u iv a le nt fr a c tions are two or more fractions that represent the same amount.
H ow to F orm E q u ivalent F rac tions
3 =
4
56 =
72
Ste p 1 : M ultiply or divide both the numerator and the denominator
by the same nonz ero number.
Ste p 2 : Write the new fraction.
3x2 = 6
4x2
8
56 ÷ 8 = 7
72 ÷ 8
9
H ow to T ell E q u ivalent F rac tions
Ste p 1 : C ross multiply.
Ste p 2 : C ompare the
two products.
Ste p 3 : If the products are eq ual, the fractions
are eq uivalent. O therwise they are not.
2
5
4
10
2 x 10 = 20
5 x 4 = 20
2 0 = 2 0, s o
th e fr a c tio n s a r e e q u iv a le n t
7
9
4
5
7 x 5 = 35
9 x 4 = 36
3 5 =/ 3 6, s o
th e fr a c tio n s a r e n o t e q u iv a le n t
Page 46
99
Get Sharp: F raction C on cepts
E q uiv alen t F raction s
WI
NTER OL
YMPI
CTRI
VI
A
D o you know the name of the most difficult ice-skating jump ever landed in Olympic
competition? D o you know what is the oldest game played on ice? D o you know how fast
downhill skiers might travel? D o you know how many people fit on a luge sled? D o you
know the length of the longest cross-country ski race?
F ind the answe rs to the se and othe r triv ia q ue stions while you p ractice ide ntifying
e q uiv ale nt fractions. In e ach p roble m , two of the fractions are e q uiv ale nt. The
fraction that is not e q uiv ale nt g iv e s the answe r to the triv ia q ue stion! C ircle the
non-e q uiv ale nt fraction in e ach p roble m .
1. L uge sleds can reach
speeds over
A.
B.
C.
16
18
8
9
5
9
150 mph
300 mph
80 mph
B.
C.
2
3
1
5
6
9
curling
A.
B.
C.
B.
A.
ice bowling
B.
200 mph
C.
80 mph
40 mph
B.
C.
A.
B.
C.
3
5
4
7
8
14
1992
1984
1998
7
8
9
12
28
32
ice skate
V iking ship
snowshoe
7. People have been using
skis for
A.
4. The number of competitors riding each luge
sled is
1
3
7
21
5
8
6. The speedskating rink in
L illehammer in 1994 was
shaped like a
ice hockey
3. D ownhill racers travel at
speeds of up to
4
5
7
9
12
15
A.
C.
2. The oldest game played
on ice is
A.
5. The first Olympics that
included snowboarding
was in
1
11
2
12
1
6
A.
3 or 4
B.
4 or 5
C.
3
4
6
7
18
21
B.
1
2
5
11
C.
2
4
A.
9000 years
200 years
100 years
8. H ow far can ski jumpers
fly?
1 or 2
9. The biathlon combines
skating & skiing
cross-country
skiing & rifle
shooting
luge & bobsled
10. The most difficult iceskating jump landed in
Olympic competition
(as of 1997) was
about 600 feet
A.
about 1 mile
B.
about 2000 feet
C.
1
4
2
8
2
6
the q uadruple lutz
the triple flip
the triple ax le
Name
2 5147
Answer Copyright
key page
27, unit 251
Page
Add & Subtract F raction s
THE #1S
PORT
In ancient versions of soccer, players tossed the ball around in the air,
bouncing it off their hands and heads. Today, only the goalie is allowed
to touch the ball with his or her hands while it is in play on the field.
S occer was the first team sport to be included in the Olympics. At every
Olympic Games, it draws some of the biggest crowds. In Barcelona,
S pain, the mainly S panish crowd was thrilled to see the S panish team win the gold medal!
L ook on the socce r fie ld for the answe r to e ach p roble m . C ircle the corre ct answe r
with the color shown ne x t to the p roble m . Answe rs m ust be in lowe st te rm s.
1. GR E E N:
2
3
+
1
6
= _________
8. PINK :
1
2
+
2
22
= _________
2. R E D :
5
10
–
1
5
= _________
9. R E D :
20
30
–
2
6
= _________
3. BL U E :
5
12
–
1
3
= _________
10. BL U E :
1
9
+
2
3
–
1
3
= _________
4. Y E L L OW:
3
4
–
5
8
= _________
11. PU R PL E :
2
9
+
8
9
–
1
3
= _________
5. PU R PL E :
1
4
+
4
16
= _________
12. GR E E N:
4
7
+
1
3
= _________
6. BR OWN:
10
25
+
2
5
= _________
13. OR ANGE :
11
14
–
3
7
+
1
7
= _________
7. OR ANGE :
11
12
–
3
4
= _________
14. BR OWN:
1
6
+
3
4
–
1
8
= _________
Name
Answer The
key
page 27, unit 254
2 54 48
Page
D ivid ing F rac tions
H ow to D ivid e F rac tions
S te p 1 : Invert (flip over) the second fraction (the divisor fraction).
S te p 2 : C hange the problem into a multiplication problem.
S te p 3 : M ultiply the fractions.
S te p 4 : R educe the q uotient fraction to lowest terms.
H ow to D ivid e a W hole N u m ber by a F rac tion
( or a F rac tion by a W hole N u m ber)
S te p 1 : C hange the whole number into an improper fraction
with the whole number as the numerator and 1 as the denominator.
S te p 2 : P roceed with the instructions for dividing fractions.
S te p 3 : C hange any improper fractions in the q uotient to mix ed numerals,
and reduce to lowest terms.
H ow to D ivid e M ixed N u m bers
S te p 1 : C hange any mix ed numbers into improper fractions.
S te p 2 : P roceed with the instructions for dividing fractions.
S te p 3 : C hange any improper fractions in the q uotient to mix ed numerals, and reduce to lowest terms.
Page 49
10 5
D iv ide F raction s
THROUGHWI
L
D WATERS
In the Olympic kayaking events, kayakers race through wild, foaming water (called whitewater). They must get down the river through a series of gates safely and fast! S ome of the
gates req uire them to paddle upstream against the raging waters! Of course, sometimes the
kayaks flip, but the athletes are good at turning right side up again.
To div ide fractions, you ne e d to do som e flip p ing , too! The se cond num be r in the
p roble m m ust be turne d up side down. The n, you m ultip ly the two fractions to g e t the
answe r to the div ision p roble m !
3 ÷ 7 = 3 x 10 = 30 = 6
5
10
5
7
35
7
F lip the se cond fraction in all the se p roble m s to find the rig ht answe rs.
1.
3
4
÷
7
8
= _________________________
2.
4
7
÷
1
2
= _________________________
9.
1
6
÷
2
3
= _________________________
3.
9
11
÷
2
3
= _________________________
10.
4
5
÷
1
9
= _________________________
4.
2
3
÷
1
5
= _________________________
11.
5
12
÷
1
3
= _________________________
5.
1
30
÷
2
20
= _________________________
12.
8
9
÷
3
4
= _________________________
6.
2
9
÷
4
5
= _________________________
13.
1
6
÷
2
5
= _________________________
7.
7
8
÷
5
6
= _________________________
14.
3
4
÷
3
4
= _________________________
8.
10
11
÷
11
10
= _________________________
15.
2
5
÷
5
2
= _________________________
Name
2 5550
Answer Copyright
key page
27, unit 255
Page
M u ltiply ing F rac tions
H ow to M u ltiply F rac tions
S te p 1 : M ultiply the numerators; this product is the new numerator.
S te p 2 : M ultiply the denominators; this product is the new denominator.
S te p 3 : R educe the product fraction to lowest terms.
H ow to M u ltiply a F rac tion
by a W hole N u m ber
S te p 1 : M ultiply the numerator by the whole number.
S te p 2 : Write this product as the numerator
in the answer.
S te p 3 : Write the original denominator in the answer.
S te p 4 : C hange the improper fraction
into a mix ed numeral, and
reduce to lowest terms.
H ow to M u ltiply M ixed N u m bers
S te p 1 : C hange all mix ed numerals to improper fractions.
S te p 2 : M ultiply the numerators; this product is the new numerator.
S te p 3 : M ultiply the denominators; this product is the new denominator.
S te p 4 : C hange the improper fraction into a mix ed numeral,
and reduce to lowest terms.
10 4
Page 51
Mathematics:
Geometry
The fol
l
lareas:
Skill Description
2301:estimate angl
e measures
2318:use coordinate graphs to pl
ot and name ordered pairs
0506.5.2 :Represent data using ordered pairs in the first quadrant ofthe coordinate system.
2321:draw and discuss transformations
3.3 Appl
y transformations and use symmetry to anal
yze mathematicalsituations.
5.3.spi.4 use spatialreasoning to predict the resul
t ofsl
iding, fl
ipping, or turning a twodimensionalshape;
2324:identify and construct congruent figures
2326:identify and construct symmetricalfigures
3.3 Appl
y transformations and use symmetry to anal
yze mathematicalsituations.
5.3.spi.2 identify l
ines ofsymmetry in two-dimensionalgeometricfigures.
2331:understand the properties ofpl
ane geometricalfigures
2337:identify and describe basicproperties ofcommon pl
ane geometricfigures and their
corresponding parts
3.1 Anal
yze characteristics and properties oftwo-and three-dimensionalshapes.
5.3.spi.3 identify two-or three-dimensionalshapes given defining attributes;
5.3.spi.6 cl
assify geometricfigures using properties;
2338:identify and describe basicproperties ofcommon sol
id geometricfigures and their
corresponding parts
3.1 Anal
yze characteristics and properties oftwo-and three-dimensionalshapes.
5.3.spi.3 identify two-or three-dimensionalshapes given defining attributes;
5.3.spi.6 cl
assify geometricfigures using properties;
Page 52
A ngles
An a
ng le
is a figure formed by two rays with a connecting e ndp oint.
T his endpoint is called a v e r te x .
Angles come in many siz es.
Angles are classified by their measurements.
T he unit of measurement for an angle is a de g r e e .
Ap
r otr a c tor
is used to measure angles.
12 4
Get Sharp: Plan e Geometry
Page 53
A ngle R elationships
Angles have some very curious and interesting
relationships with one another. M ak e sure you can
k eep all these relationships straight!
C ong r u e nt Ang le s
Angles that have the same measure are congruent.
∠ C D F and ∠ FD E are congruent because
they both measure 4 5 ° .
Write ∠ C D F ≅ ∠ FD E
C om p le m e nta r y Ang le s
When the sum of two angles is 9 0 ° , the angles
are complementary.
∠ GHJ and ∠ J HI are complementary.
S u p p le m e nta r y Ang le s
When the sum of two angles is 1 8 0 ° , they are
supplementary.
∠ K L N and ∠ N L M are supplementary.
Adja c e nt Ang le s
When angles have a common vertex and a
common edge (or leg), they are adjacent.
∠ O P R and ∠ R P Q are adjacent.
V e r tic a l Ang le s
When two lines intersect, vertical angles are
formed. T hese are the angles that are opposite
each other at the vertex .
T wo pairs are formed ↔
↔
by the intersection of S T and U V .
T hese pairs are: ∠ S W U and ∠ V W T
∠ S W V and ∠ U W T
Page 54
12 5
G raphing on a Coord inate P lane
A c oor dina te p la ne is formed by two lines, called a x e s ,
drawn perpendicular to each other to form a grid. An or de r e d
p a ir of numbers (such as 5 , 4 ) can be graphed as a point on a
coordinate plane. T he pair of numbers gives the c oor dina te s
(location) of the point.
T he h or iz onta l line is the x -a x is .
T he v e r tic a l line is the y -a x is .
T he two ax es meet at a point called the or ig in.
Fou r q u a dr a nts , or sections, are formed when two ax es cross.
T his coordinate graph (grid) below shows one q uadrant.
O n this graph, all the numbers along the x - and y - a x e s
are positive integers.
T o graph an ordered pair (5 , 4 ), start at the origin. M ove 5 units along the x -ax is. T hen move 4 units
along the y-ax is. D raw a point. O n this graph, (5 , 4 ) gives the coordinates of point B.
O ther coordinates:
A (3 ,0 )
C (1 ,5 )
18 8
Get Sharp: C oordin ate Graphin g
D (0 ,7 )
E (6 ,6 )
Page 55
F (8 ,7 )
G (7 ,2 )
H (3 ,7 )
I (4 ,5 )
G raphing in T w o Q u ad rants
T he coordinate graph (grid) below shows two of the four q uadrants that are formed when two
perpendicular ax es intersect.
O n this graph, the numbers along the x -a x is are positive integers to the right of z ero
and negative numbers to the left of z ero. O nly the positive portion of the y -a x is is shown.
Page 56
18 9
G raphing in F ou r Q u ad rants
T he coordinate graph (grid) below shows all four of the q uadrants that are formed when two
perpendicular ax es intersect.
O n this graph, the numbers along the x -a x is are positive integers to the right of z ero and negative
numbers to the left of z ero. T he numbers along the y -a x is are positive integers above z ero and negative
integers below z ero.
190
Page 57
F in d L ocation s on a C oordin ate G rid
DOZENSOFDANCERS
D ancers around the world try to set records for the longest or fastest dance, or for the dance
with the most people. The biggest tap dance, with 6,654 dancers, took place in New Y ork
City. The longest line dance had 5,502 dancers. The longest dancing dragon was made up of
2,431 people.
These dancers are making their line around a coordinate grid. Write the coordinates of each
dancer on the grid. Write coordinates like this: (x , y).
A. _ _ _ _ _ _ _
B. _ _ _ _ _ _ _
C. _ _ _ _ _ _ _
D . _______
E . _______
F. _ _ _ _ _ _ _
G. _ _ _ _ _ _ _
H . _______
I. _ _ _ _ _ _ _
J. _ _ _ _ _ _ _
K . _______
L. _______
M. _ _ _ _ _ _ _
N. _ _ _ _ _ _ _
O. _ _ _ _ _ _ _
P. _ _ _ _ _ _ _
Q . _______
Name
2 8 358
Answer Copyright
key page
30, unit 283
Page
T essellations, T ransf orm ations, & S y m m etry
Page 59
133
R ecog n iz e T ran sformation s of P lan e F ig ures
OUTOFORDER
The sports storage room is a mess. Pieces of eq uipment have been tossed
around carelessly. Custodian George has to put things back in order.
L ook at each pair of items. Tell whether the second item in each pair
is a slide, flip, or turn of the first item. Write S , F, or T beside each
pair. (S ome pairs may have more than one label!)
D raw a slide (translation) of this figure:
D raw a turn (rotation) of this figure:
D raw a flip (reflection) of this figure:
D raw a turn (rotation) of this figure:
Name
2 69 60
Answer Copyright
key page
29, unit 269
Page
Congru ent & S im ilar F igu res
C ong r u e nt fig u r e s
are figures that have the same siz e and shape. E ach angle in one figure
has a corresponding angle of the same measure. E ach side in one figure has a corresponding side
of the same length.
S im ila r fig u r e s
have congruent corresponding angles, but the corresponding sides are not
necessarily congruent.
C ong r u e nt Ang le s
T wo angles are congruent when they have
the same measure. Angle Y is congruent to
angle B because they have the same measure.
Write: ∠ ABC ≅ ∠ XY Z
C ong r u e nt Tr ia ng le s
T hese triangles are congruent. (T hey have the same
siz e and shape.) T he corresponding angles are congruent.
(T hey have the same measure.) T he corresponding sides
are congruent. (T hey have the same length.) N otice how
the angles and sides are mark ed alik e to show the
congruence.
Write: ∆C D E ≅ ∆FGH
O th e r C ong r u e nt P oly g ons
T hese two polygons are congruent.
F or each side and angle in figure M N O P Q ,
there is a corresponding congruent side or angle
in figure S TU V W .
Write: M N O P Q ≅ S TU V W
S im ila r Fig u r e s
T he angles in figure A are congruent with corresponding angles
in figure Z . T he lengths of the sides, however, are different.
F igure A is similar to figure Z.
F igure F is similar to figure G.
Write: A ∼ Z
F∼G
132
Page 61
Iden tify Sy mmetrical F ig ures
MI
RROR I
MAGES
Jenna often practices her dance moves in front of a mirror.
S he hopes the reflection shows a perfect performance.
In a symmetrical figure, each half is a perfect reflection of
the other.
L ook at the figures below. Color the ones that are
symmetrical. U se a ruler to draw the line of symmetry in
each symmetrical figure.
Complete figures I, J, and K to make them symmetrical.
The line of symmetry is already given for you.
Name
Answer The
key
page 29, unit 268
2 68 62
Page
P oly gons
A p oly g on is a plane figure formed by joining three or more
straight line segments at their endpoints.
T he line segments are called s ide s .
E ach endpoint where sides join is a v e r te x .
P oly g ons a r e na m e d
b y th e nu m b e r of s ide s .
12 8
Page 63
T riangles
A tr ia ng le is a three-sided plane figure.
B ut not all triangles are the same!
Page 64
12 9
Q u ad rilaterals
A q u a dr ila te r a l is a polygon that has four sides and four vertices.
D on’t be confused by the different k inds of q uadrilaterals.
A p a r a lle log r a m is a q uadrilateral
that has parallel line segments
in both pairs of opposite sides.
O pposite internal angles are congruent.
O pposite sides are congruent.
A r e c ta ng le is a parallelogram
that has four right angles.
A s q u a r e is a rectangle that has sides
of eq ual length and four right angles.
A sq uare is a parallelogram.
A r h om b u s is a parallelogram that
has four sides of eq ual length.
A rhombus does not necessarily have
four right angles.
A tr a p e z oid is a q uadrilateral that
has only one pair of parallel sides.
An is os c e le s tr a p e z oid is a trapez oid
that has congruent nonparallel sides
and congruent base angles.
130
Page 65
Circ les
A c ir c le is the set of all the points in a plane that are the same distance from a particular point.
T hat given point is the center of the circle (N ).
T he dia m e te r is a chord that passes through the center
of the circle. T he diameter is twice the length of a radius.
—
—
E x amples: Q T and M K are diameters.
T he r a diu s is any line
segment from the center to a
point on the circumference of
the circle.
— — —
— —
N Q , N H are radii.
E x amples: N M , N T, N K ,
T he c ir c u m fe r e nc e is the
distance around the outside
edge of the circle.
T he circumference of a
circle is the length of its
diameter multiplied by π
(pi, which is approx imately
eq ual to 3 .14 ).
A ta ng e nt is a line
that touches the edge of
a circle at one point but
does not pass into or
through the circle.
—
E x ample: V W touches
the circle at point X.
A c e ntr a l a ng le is
an angle formed by two
radii of a circle.
E x ample: ∠ TN K and
∠ HN M are central angles.
A c h or d is a line segment
joining two points on the circle.
—
—
E x ample: Q J and Q T are chords.
An a r c is any part of the
circle or any section of the
line segment that forms the
outside edge of the circle.
E x ample: H to T is an arc.
Page 66
131
Iden tify P oin ts, L in es, An g les, R ay s, & P lan es
S
I
GNSFROM THE CROWD
The rowdy crowd is getting ready for the opening football game of the season between the
Ashland Griz z lies and the Crescent City Cougars.
D raw a line from each label to match the correct sign.
Name
Answer The
key
page 28, unit 262
2 62 67 Copyright © 2000 by Incentive Publications, Inc., Nashville, TN.
Page
Iden tify P lan e F ig ures
A PL
ANE MES
S
Coach Jackson teaches math when he is not coaching volleyball. H e had some great posters
ready for his geometry lesson today, but, as usual, he forgot to close the window. A huge wind
blew his stuff all over the floor.
Get the definition posters back together with the math terms in time for class. D raw a line from
each math term to its matching poster.
Name
2 6368
Answer Copyright
key page
28, unit 263
Page
Iden tify K in ds of P oly g on s
THE GREATS
HAPE MATCHUP
All the parents of the basketball players have come to watch the first home game. They’re all
holding up numbered cards with symbols to match the names of their kids on the team.
S earch the cards to match the parents and players. Write the number of each card on the
correct player.
Name
Answer The
key
page 28, unit 266
2 6669 Copyright © 2000 by Incentive Publications, Inc., Nashville, TN.
Page
Iden tify K in ds of Q uadrilaterals
KEEPI
NG BUS
Y
Ashley never stops being active in sports! As soon as one
season is over, she starts something new. S o, she has
many labels: athlete, basketball player, volleyball player,
tennis player, gymnast, pitcher, and swimmer.
Q uadrilaterals are like that, too. They have many
labels.
All q uadrilaterals have four sides. But a four-sided figure
can show up in many “uniforms” or different “looks.”
Which figures match each description? (There may be
more than one.)
1. All angles are right angles,
but all sides are not eq ual. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
2. Only one pair of
opposite sides is parallel. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
3. A rectangle with
all sides eq ual _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
4. A figure with two pairs
of opposite sides parallel _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
5. A parallelogram with all
sides the same length _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
6. All sides are eq ual, but all angles may not be eq ual. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Write (T) TR U E or (F) FAL S E nex t to each statement.
_____
1. All sq uares are rectangles.
_____
6. A sq uare is a rectangle.
_____
2. All rectangles are q uadrilaterals.
_____
7. All sq uares are rhombuses.
_____
3. No rhombuses are trapez oids.
_____
8. A trapez oid is a q uadrilateral.
_____
4. R ectangles have no right angles.
_____
9. All parallelograms are rectangles.
_____
5. A rectangle is a sq uare.
_ _ _ _ _ 10. All rhombuses are sq uares.
Name
2 6770
Answer Copyright
key page
29, unit 267
Page
S pac e F igu res
S p a c e fig u r e s
are geometric figures with three dimensions (length, width, and height).
M ost space figures have fa c e s (sides that are polygons), v e r tic e s (points where more than two sides meet),
and e dg e s (lines along which two sides meet). M ost also have a b a s e . (T he base is one of the faces.)
A p oly h e dr on is a space figure with faces that are polygons.
A p r is m has two
congruent polygonal bases.
A prism is named for
the shape of its base.
A c u b e is a rectangular prism
with six sq uare, congruent faces.
(T he faces are all ex actly the same siz e
and shape.)
A p y r a m id has a polygonal base.
All other faces meet at a single vertex .
A pyramid is named for
the shape of its base.
T he base is the face
opposite the vertex .
A c one has a circular base.
O pposite the base, the curved face meets
at a single vertex .
134
Get Sharp: Space Geometry
Page 71
A c y linde r has two congruent
circular bases. A curved face
joins the two bases.
A s p h e r e is a space figure with curved edges.
E very point on the edge is an eq ual distance
from the center in all four directions.
A sphere has no base and no polygonal sides.
F ig u r e
S hape
ofB ase
cube
N um ber of N um ber of N um ber of
fa c e s (F
V e r tic e s (V ) E d g e s (E )
square
6
8
12
rectangle
6
8
12
triangle
5
6
9
pentagon
7
10
15
octagonal prism
octagon
10
16
24
triangular pyramid
triangle
4
4
6
rectangular pyramid
rectangle
5
5
8
hexagonal pyramid
hexagon
7
7
12
rectangular prism
triangular prism
pentagonal prism
Page 72
135
Get Sharp: Space Geometry
Mathematics:
Probability
The fol
l
lareas:
Skill Description
2552:cal
cul
ate the probabil
ity ofan outcome or event
2553:compare experimentalresul
ts to theoreticalprobabil
ity
2555:determine possibl
e outcomes, combinations, and permutations
Page 73
Ou tc om es & E vents
An ou
tc om e
is the result of an action or ex periment.
If you spin this spinner, there are four possible outcomes:
re d, blue , ye llo w , or g re e n .
If you flip a coin, the number of possible outcomes
is two: h e ads or tails .
If you toss one die, the number of possible outcomes
is six : a 1 , 2 , 3 , 4 , 5 , or 6.
An e v e nt is a particular outcome or set of outcomes.
If you spin this spinner once, the number of possible
outcomes is 8 , but the number of times that 1 5 is a
possible outcome is 3 .
F or this spinner, some events are m or e lik e ly to happen
than others. F or instance, the event of stopping on 1 5 is
certainly more lik ely than stopping on 6 .
P robability of an event =
the nu m ber of possible events
the total nu m ber of possible ou tc om es
T he probability of stopping on 1 5 is written this way: P ( 15) =
T he probability of stopping on 8 is written this way: P ( 8) =
16 4
Get Sharp: Probability
Page 74
number of 15s
total possible outcomes
number of 8s
total possible outcomes
=
3
8
=
2
8
Ou tc om es of T w o A c tions
When tw o actions happen, the possible outcomes can be shown in a table.
Tw o c oins a r e tos s e d . . .
T he table shows the four possible outcomes.
What is the probability that both coins will land
with heads facing up?
T o find the probability, use this formula:
P robability ( of an event) =
the nu m ber of possible events
the total nu m ber of possible ou tc om es
1 P (H , T ) = —
2
P (H , H ) = —
4
4
Tw o dic e a r e tos s e d . . .
T he table shows the 3 6 possible outcomes.
1
P( 6 , 6 ) = —
36
6 (o r
P( b o t h t h e s a m e ) = —
36
2 (o r
P( a 3 a n d a 4) = —
36
1)
—
6
1 )
—
18
J ojo s p ins b oth s p inne r s onc e . . .
T he table shows the 1 2 possible outcomes.
1
P( 8, g ) = —
12
2 or —
1
P( 4, n o t g ) = —
12
6
Page 75
16 5
F in d P robability of an E v en t
PI
GGYBANKPROBABI
L
I
TI
ES
It has taken Ove Nordstrom forty years to build his record-setting collection of piggy banks.
H e now has 3,575 pig-shaped containers that hold money!
This piggy bank has seven coins inside:
A. If you shake one coin out, what is
the probability (chance) that it will
be a q uarter?
1. P (Q ) = _ _ _ _ _ _ _
2. What is the chance
it will be a penny?
P (P) = _ _ _ _ _ _ _
3. P (D ) = _ _ _ _ _ _ _
4. P (N) = _ _ _ _ _ _ _
B. A piggy bank has these coins:
6 dimes, 3 q uarters, 3 nickels,
2 pennies. S hake out one coin.
C. A piggy bank has these coins:
7 pennies, 4 dimes, 5 nickels.
S hake out one coin.
1. P (D ) = _ _ _ _ _ _ _
1. P (not a dime) = _ _ _ _ _ _ _
2. P (Q ) = _ _ _ _ _ _ _
2. P (N) = _ _ _ _ _ _ _
3. P (N) = _ _ _ _ _ _ _
3. P (P) = _ _ _ _ _ _ _
4. P (not a dime) = _ _ _ _ _ _ _
4. P (D ) = _ _ _ _ _ _ _
5. P (not a q uarter) = _ _ _ _ _ _ _
5. P (N or D ) = _ _ _ _ _ _ _
6. P (D or N) = _ _ _ _ _ _ _
6. P (Q uarter) = _ _ _ _ _ _ _
7. P (Q or a P) = _ _ _ _ _ _ _
7. P (D or P) = _ _ _ _ _ _ _
Name
Answer The
key
page 30, unit 284
2 8 4 76
Page
L
OTS&L
OTSOFL
I
TTER
One day a huge number of collectors gathered to pick up litter in one place. There were
50,405 people that worked to pick up litter on the California coast. This set a record for the
most litter collectors.
This bag of litter contains 10 old shoes (S ), 5 banana peels (BP), 5 burned out light bulbs
(L B), and 10 candy wrappers (CW).
If you reach in and grab the first piece of
litter you touch, what is the probability
(chance) that it will be a . . . .
1. P (S ) = _ _ _ _ _ _ _
2. P (BP) = _ _ _ _ _ _ _
3. P (L B) = _ _ _ _ _ _ _
4. P (CW) = _ _ _ _ _ _ _
Another bag of litter contains
6 soda pop cans (S P)
4 cracker box es (CB)
8 mittens (M)
2 hats (H )
If you reach in and grab the first piece of
litter you touch, what is the probability
(chance) that it will be a . . .
5. P (S or CW) = _ _ _ _ _ _ _
6. P (not a CW) = _ _ _ _ _ _ _
7. P (not a BP) = _ _ _ _ _ _ _
8. P (BP or L B) = _ _ _ _ _ _ _
9. P (not a S ) = _ _ _ _ _ _ _
10. P (not a L B) = _ _ _ _ _ _ _
11. P (S P) = _ _ _ _ _ _ _
12. P (CB) = _ _ _ _ _ _ _
13. P (M) = _ _ _ _ _ _ _
14. P (H ) = _ _ _ _ _ _ _
15. P (M or H ) = _ _ _ _ _ _ _
16. P (not M) = _ _ _ _ _ _ _
Name
2 8 577
Answer Copyright
key page
30, unit 285
Page
WAL
KI
NG T
AL
LFOR NEW RECORDS
The longest walk on stilts covered 3,008 miles. Joe Bowen walked from California to
K entucky in 1980. The tallest stilts ever used for a walk were over 40 feet tall. Travis Wolf
walked 26 steps on these in 1988.
The spinner is a guide for kids doing a stilt race. The spinner tells them how many steps to
take on each turn.
L ook at the spinner to answer these probability problems.
1. H ow many different outcomes are there
for ONE spin? _ _ _ _ _ _ _
What is the probability for each outcome
below with ONE spin?
2. P (6 steps forward) = _ _ _ _ _ _ _
rd
wa
r
o
F
ep s
t
s
6
F or
w
6 st ard
ep s
3. P (5 steps forward) = _ _ _ _ _ _ _
F or
w
5 st ard
ep s
ard
kw
B ac ste p
1
F or
w
4 st ard
ep s
rd
wa
r
o
F
ep
1 st
4. P (1 step forward) = _ _ _ _ _ _ _
5. P (2 steps forward) = _ _ _ _ _ _ _
6. P (4 steps forward) = _ _ _ _ _ _ _
7. P (steps forward) = _ _ _ _ _ _ _
8. P (steps backward) = _ _ _ _ _ _ _
9. P (1 step in either direction) = _ _ _ _ _ _ _
10. P (3 steps forward) = _ _ _ _ _ _ _
rd
wa
F or te p s
2 s
F or
w
4 st ard
ep s
11. P (less than 5 steps forward) = _ _ _ _ _ _ _
12. P (more than 2 steps forward) = _ _ _ _ _ _ _
13. P (more than 2 steps backward) = _ _ _ _ _ _ _
14. P (5 or 6 steps forward) = _ _ _ _ _ _ _
Name
Answer The
key
page 30, unit 286
2 8 678
Page
F in d O dds of an E v en t
WI
L
LTHERE BE L
I
GHT?
S ix hundred thousand lightbulbs would give off a lot of light. This is how many bulbs the
world’s greatest collector of lightbulbs has gathered. H ugh H icks has been keeping lightbulbs
since childhood. Is it possible that they all still work?
Out of 10 lightbulbs, 4 are burned out. If you choose a bulb, what is the chance that it will be
4.
burned out? Y ou know that the probability of choosing a burned-out bulb is 10
There is another way to talk about such choices. This is to describe odds in favor of an
event and odds against an event.
number burned out
4
“Odds in favor” are written like this:
or
.
number not burned out
6
The odds in favor of getting a burned-out lightbulb are
4
or 4 to 6.
6
The odds against getting a burned-out lightbulb are 6 to 4 or
6
4 .
1. 8 lightbulbs; 3 are burned out
a. odds in favor of choosing a burned-out bulb = _ _ _ _ _ _ _
b. odds against choosing a burned-out bulb = _ _ _ _ _ _ _
4. 11 lightbulbs; 1 is burned out
Name
2 8 779
Answer Copyright
key page
30, unit 287
Page
F in d P robability of T w o E v en ts
THE BI
GGES
TDROP
,CONT.
U se the table you finished on page 288 to help you solve these probability problems.
The problems ask about the probability for different outcomes when the tightrope walkers
tossed two dice to decide who would walk the rope first.
1. P (1, 3) = _ _ _ _ _ _ _
11. P (two numbers ≥ 4) = _ _ _ _ _ _ _
2. P (3, 3) = _ _ _ _ _ _ _
12. P (two numbers < 4) = _ _ _ _ _ _ _
3. P (5, 6) = _ _ _ _ _ _ _
13. P (two numbers < 6) = _ _ _ _ _ _ _
4. P (6, 7) = _ _ _ _ _ _ _
14. P (two odd numbers) = _ _ _ _ _ _ _
5. P (two of same number) = _ _ _ _ _ _ _
15. P (no ones) = _ _ _ _ _ _ _
6. P (a 4 and a 3) = _ _ _ _ _ _ _
16. P (4, 6) = _ _ _ _ _ _ _
7. P (2 even numbers) = _ _ _ _ _ _ _
17. P (two numbers < 3) = _ _ _ _ _ _ _
8. P (an odd and even number) = _ _ _ _ _ _ _
18. P (a sum of 8) = _ _ _ _ _ _ _
9. P (a sum of 2) = _ _ _ _ _ _ _
19. P (a sum of 10) = _ _ _ _ _ _ _
10. P (a sum of 4) = _ _ _ _ _ _ _
20. P (a sum of 11) = _ _ _ _ _ _ _
The longest tightrope walk
lasted 205 days. An
amaz ing performer, Jorge
Ojeda-Guz man, spent all
this time dancing and
walking and balancing a
chair on the tightrope that
was 35 feet above the
ground. Y ou can imagine
how much fun this was for
the spectators!
U se with page 288.
Name
2 8 9 80
Answer Copyright
key page
30, unit 289
Page
U se R an dom Samp lin g to M ak e P robability P rediction s
A PUZZL
I
NG RECORD
The largest jigsaw puz z le on record that was successfully finished was
43,924 pieces. Imagine how long it took to put this one together!
Patricia wants to figure out how many puz z le pieces of each color are in
this bag of 1200 pieces. S he does not have time to count all the pieces,
but she can estimate the number of pieces by taking a sample.
S he draws 5 puz z le pieces and records the colors. S he puts the pieces
back and draws another sample of 5. Patricia does this 4 times.
Out of her 20 samples, she has found:
2 white
10 red
4 purple
4 black
1. In her sample, what was the probability of white? _ _ _ _ _ _ _
2. What was the probability of red? _ _ _ _ _ _ _
3. What was the probability of purple? _ _ _ _ _ _ _
4. What was the probability of black? _ _ _ _ _ _ _
5. Can you use these probability fractions to predict
the number of each color in the whole bag of 1200?
a. white = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
b. red = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
c. purple = _ _ _ _ _ _ _ _ _ _ _ _ _ _
d. black = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
6. A bag of snack bars contains 500 bars.
A sample of 50 gives these results:
20 chocolate
25 strawberry
5 apple
Predict the total number of each flavor
in the bag of 500.
a. chocolate = _ _ _ _ _ _ _
b. strawberry = _ _ _ _ _ _ _
c. apple = _ _ _ _ _ _ _
Name
2 9 181
Answer Copyright
key page
30, unit 291
Page
P robability of Ind epend ent E vents
E vents are inde p e nde nt when the outcome of one event is not affected by the outcome of the other.
F or instance, if a coin is flipped and one die is tossed, the outcome of the coin toss will not affect the
outcome of the toss of the die.
T o find the probability of two independent events, multiply the probability of one event by the probability
of the other.
P ( event A ) x P ( event B )
or
P (A ) x P (B )
2 x—
2=—
4 =—
2
P( r e d s h ir t a n d je a n s ) = P( R ) x P( J ) = —
6 5 30 15
2 x—
1 =—
2 =—
1
P( b lu e s h ir t a n d g r e y p a n t s ) = P( B ) x P( G ) = —
6 5 30
15
1 x—
1 =—
1
P( s t r ip e d s h ir t a n d k h a k is ) = P( S ) x P( K ) = —
6 5 30
1 x—
3 =—
3 =—
1
P( w h it e s h ir t a n d n o t je a n s ) = P( W ) x P( n o t J ) = —
6 5 30 10
16 6
Page 82
P robability of D epend ent E vents
E vents are de p e nde nt when the outcome of one event
is affected by the outcome of a previous event.
For instance, Ben buys a gumball from a machine that contains 12 j
umbo balls.
The machine has 3 blue, 4 white, 2 red, and 3 pink. He puts in his quarter and the
first gumball comes out. He puts in a second quarter. The probability of the color of
the second gumball will be affected by the color of the first gumball.
The probability of one event (
B)happening, given that another event (
A)has
already taken place, is written like this:
P (B | A )
and reads the probability
of B given A .
Use this formula for the probability of two dependent events:
P ( A and B ) = P ( A ) x P ( B | A )
B en’s first gumball is blue . What is the
probability that th e s e co n d o n e will be w h ite ?
P( B a n d W ) = P( B ) x P( W | B )
3 x—
4
= —
12 11
1
12 = —
=—
132 11
What is the probability that bo th will be re d?
P( R a n d R ) = P( R ) x P( R | R )
2
1
=—
12 x —
11
1
2 = —
=—
132 66
Page 83
16 7
T ree D iagram s
A tr e e dia g r a m is an interesting and helpful visual tool for figuring probability.
All the possible outcomes for independent events can be shown on a tree diagram.
Angie got to lunch late.
There were 3 sandwiches left:
2 turkey and 1 roast beef.
There were 2 cookies left:1 chocolate and 1 peanut butter.
All cookies and sandwiches were wrapped, but had no
labels. Angie took one sandwich and one cookie.
The tree diagram shows the possible outcomes
for Angie’
s choices.
T = turk e y s an dw ich
R = ro as t be e f s an dw ich
16 8
Page 84
C = ch o co late co o k ie
P = pe an ut butte r co o k ie
D escribe O utcomes of T w o E v en ts
THE BI
GGES
TDROP
The highest tightrope walk on record was set by a Frenchman in 1989. Michel Menin walked
high above the countryside in France at 10,335 feet in the air. This is the biggest drop on
record. Fortunately, Michel did not drop off the rope!
In one tightrope contest, the competitors rolled two dice to see who would walk the rope
first. The person with the highest number was the starter.
When you roll two dice, what are all the possible outcomes of the two events? It is helpful to
put the outcomes on a chart. Finish the chart to show all the possibilities.
U se the chart to help solve the probability problems on page 289.
(1, 1)
Name
Answer The
key
page 30, unit 288
Page
Iden tify C ombin ation s of Sets Within a Set
CAREFUL
L
YBAL
ANCED EGGS
It is q uite a trick to balance one egg on the edge of a table or ledge. Imagine how difficult it
must be to balance 210 eggs at the same time. This is the record for egg balancing by one
person. It was set by K enneth E pperson of Georgia, in 1990.
A. When egg balancer E gbert gets ready to practice, he takes several eggs out of his egg
bag. Today his bag contains eggs of four colors: red, blue, green, and white.
E gbert chooses two eggs. There are an eq ual number of all the colors in the bag. What
different color combinations are possible for E gbert to choose? (The order of the colors
does not matter; for instance, red and b lu e is the same combination as b lu e and red.)
U se the table to show the
different combinations.
B. If there are five colors— red, blue, pink,
orange, and white— what combinations of
two eggs could E gbert possibly choose?
U se the table to show the
different combinations.
Name
Answer The
key
page 30, unit 290
2 9 086
Page
U se P robability C on cep ts to Solv e P roblems
BARROW RACI
NG FOR DOL
L
ARS
The shortest time on record for racing a wheelbarrow one mile is 4 minutes, 48.51 seconds.
This record was set in S outh Africa in 1987.
The wheelbarrow racers are hoping to win some priz es. E ach race has two competitors. When the
race is over, each competitor chooses an envelope. They combine their winnings.
The envelopes contain $ 10, $ 20, $ 50, and $ 100 bills. E very racer has an eq ual chance of
getting any of the envelopes.
1. H ow many different possible totals are there? _ _ _ _ _ _ _ Write them on the table.
2. Could Will and Wilma win $ 100 between the two of them? _ _ _ _ _ _ _
3. Could they win $ 250 after one race? _ _ _ _ _ _ _
4. Could they win $ 50 total? _ _ _ _ _ _ _
5. Could they win $ 70 total? _ _ _ _ _ _ _
6. What is the probability of winning $ 200? _ _ _ _ _ _ _
Name
Answer The
key
page 30, unit 292
Page

Customized Activity Book

Transcription

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