1. science
2. mathematics
3. algebra

Customized Study Guide
For
MATDELINE PHILLIPS
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:
Fractions
The following section of this customized textbook includes material from these skill areas:
Skill Description
2299: understand concepts of rate and rate of change
5.RP.1: Use ratio and rate reasoning to solve real-world and mathem problems, e.g., by
reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or
equations. NOTE; This is an extension standard from the 6th grade standard 6.RP.3.
2443: Fractions
5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by
replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum
or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.
(In general, a/b + c/d = (ad + bc)/bd.)
2445: relate fractions to decimals
5.NF.8: Use decimal notation for fractions with denominators 10 or 100. NOTE: This is a
reinforcement standard from the 4th grade standard 4.NF.6.
2446: represent fractions in equivalent forms
5.NF.4.a: Interpret the product (a/b) x q as a parts of a partition of q into b equal parts;
equivalently, as the result of a sequence of operations a x q ÷ b.
2495: solve addition and subtraction problems with fractions
5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same
whole, including cases of unlike denominators,e.g., by using visual fraction models or equations
to represent the problem. Use benchmark fractions and number sense of fractions to estimate
mentally and assess the reasonableness of answers.
Page 2
2509: solve division problems with fractions
5.NF.7.c: Solve real world problems involving division of unit fractions by non-zero whole numbers
and division of whole numbers by unit fractions, e.g., by using visual fraction models and
equations to represent the problem.
5.NF.7.b: Interpret division of a whole number by a unit fraction, and compute such quotients.
5.NF.7.a: Interpret division of a unit fraction by a non-zero whole number, and compute such
quotients.
5.NF.7: Apply and extend previous understandings of division to divide unit fractions by whole
numbers and whole numbers by unit fractions.1
2513: solve multiplication problems with fractions
5.NF.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g.,
by using visual fraction models or equations to represent the problem.
5.NF.5.b: Explaining why multiplying a given number by a fraction greater than 1 results in a
product greater than the given number (recognizing multiplication by whole numbers greater than
1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results
in a product smaller than the given number; and relating the principle of fraction equivalence a/b =
(nxa)/(nxb) to the effect of multiplying a/b by 1.
5.NF.5.a: Comparing the size of a product to the size of one factor on the basis of the size of the
other factor, without performing the indicated multiplication.
5.NF.5: Interpret multiplication as scaling (resizing)
5.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole
number by a fraction.
Page 3
Rates
A rate is a ratio that compares quantities of different units.
Reducing Rates to Find Quantities
Since you know the ratio (rate), you can find the cost
by reducing the ratio to lowest terms.
Divide both terms of the ratio by 4. (You use 4 because the
second term of the new ratio must be 1, so you must use the
number that will yield a quotient of 1 when it goes into 4.)
It costs $ 3.20 per pound!
Using Equivalent Ratios to Find Other Rates
Since you know the ratio (rate), you can find other costs
by writing equivalent ratios.
Multiply both terms of the ratio by 5.
(You use 5 because the second term of the new ratio
must be 20, so you must choose the number that will
yield a product of 20 when multiplied by 4.)
It costs $ 64.00 per 20 pounds!
108
Get Sharp: Rates
Page 4
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Time Zones
As Earth turns, the sun shines on different parts of the sphere at different times. Because of this, we have
divided Earth into several time zones.
The line of 0° longitude (the Prime Meridian) goes through Greenwich, England. Earth’s time zones are
all related to the time in Greenwich, called Greenwich time. From Greenwich, an hour is subtracted as
you travel west through each time zone. As you travel east from Greenwich, an hour is added to the time.
It is 7 a.m. (5 time zones west)
it is 4 a.m. (8 time zones west)
it is 3 a.m. (9 time zones west)
it is 1 p.m. (1 time zone east)
it is 3 p.m. (3 time zones east)
it is 8 p.m. (8 time zones east)
it is 9 p.m. (9 time zones east)
in New York City, NY
in Los Angeles, CA
in Anchorage, AK
in Paris, France
in Moscow, Russia
in Hong Kong
in Tokyo, Japan
and . . . it is midnight (12 time zones east or west)
on the International Date Line (180° E or W longitude)
Measuring Rate
Rate is a measure of an amount compared to something else. Often it is an amount compared to time.
Rate 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. Speed is described as a rate.
186,282,397 miles per second (mps)
speed of light
66 miles per hour (mph)
speed a sailfish can swim
65 kilometers per hour (kph)
speed a mallard duck can fly
12 miles per hour (mph)
speed of a running rabbit
11.6 kilometers per hour (kph)
speed a honeybee can fly
0.03 miles per hour (mph)
speed a snail can crawl
261.8 miles per hour (mph)
speed of Japan’s fast Nozomi 500 train
26 pounds per year
amount of chocolate eaten by average Swiss person
48 gallons per year
amount of soda pop drunk by average American
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Page 5
Get Sharp: Measurement
149
Fractions
A fraction is any number written in the form of
a
b
Fraction comes from the Latin word fractio, meaning broken parts.
Fraction means part of a set or part of a whole. A fraction is written in a
way that compares two numbers or amounts.
Proper & Improper Fractions
In a proper fraction,
the numerator is smaller
than the denominator.
7
8
11
12
2
3
14
20
3
100
6
9
96
2
9
reads seven-eighths
reads eleven-twelfths
reads two-thirds
reads fourteen-twentieths
reads three-hundredths
reads six-ninths
Get Sharp: Fraction Concepts
In an improper fraction, the numerator
is larger than the denominator.
The value of the fraction is always equal to
or greater than one.
12
7
Reading and Writing Fractions
A fraction is also a way of
writing a division problem.
3
24
means
3 ÷ 24
(three divided by twenty-four)
Page 6
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Solve Problems with Decimals
“FIGURING” OUT DECIMALS
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. You 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 RED
______ 2. five-hundredths more than 6.3 BLUE
______ 3. the difference between 10.8 and 10.2 PINK
______ 4. one hundred plus twelve-hundredths BLACK
______ 5. 3 tenths more than 6 hundredths YELLOW
______ 6. 0.05 plus 0.04 PURPLE
______ 7. 9 tenths less than ten TAN
______ 8. two-tenths more than 14 ORANGE
______ 9. 5 hundredths more than 2 BROWN
______ 10. one-tenth less than one TAN
______ 11. two-tenths plus four-hundredths SILVER
______ 12. 9 tenths plus 9 hundredths GREEN
______ 13. ten plus twelve-hundredths RED
______ 14. eight-hundredths more than eight BLUE
______ 15. one-tenth less than ten GREEN
______ 16. two-tenths less than nine PINK
______ 17. ten less than 12.4 PURPLE
______ 18. 0.004 more than 0.005 RED
______ 19. ten less than 10.22 ORANGE
______ 20. 0.6 more than three YELLOW
______ 21. two-tenths more than 0.3 BLUE
______ 22. 5 tenths less than fifty-one GREEN
______ 23. five-tenths less than 21 SILVER
______ 24. one hundred plus two-tenths PURPLE
Name
©2000 by Incentive Publications, Inc., Nashville, TN.
215 7
Answer Copyright
key page
25, unit 215
Page
The BASIC/Not Boring Fifth Grade Book
Fractions as Parts of Sets
WATCH THAT PUCK!
These fans are gathered for an exciting, 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
exciting Olympic moment for the United States was in 1980 when the
U.S. team defeated Finland to win its first gold medal in 20 years.
Olympic Fact
The 1998 Winter
Olympics in Japan were
the first Games that
permitted women to
compete in ice hockey.
Pay attention to these fans to practice your fraction-hunting skills. Write a fraction to
fill each 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
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 27, unit 248
248 8
Page
Copyright ©2000 by Incentive Publications, Inc., Nashville, TN.
Compare & Order Fractions
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.
Compare each set of fractions below to see which is greater. Circle the largest
fraction. If the fractions are equal, circle them 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
Rewrite the fractions in order from smallest to largest.
1
2
13.
2
5
1
4
__________________
14.
3
18
5
6
2
3
__________________
15.
2
5
6
7
5
9
__________________
Name
©2000 by Incentive Publications, Inc., Nashville, TN.
249 9
Answer Copyright
key page
27, unit 249
Page
The BASIC/Not Boring Fifth Grade Book
Compare Fractions
LOST !
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 quick, strong, and agile to compete.
Pete has gotten separated from the badminton team on the
way to the competition. To help him join his teammates,
compare the fractions in each box. Color the boxes that have
the correct sign ( <, >, or = ) between the fractions. If you do
this correctly, you will have colored a path for Pete.
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
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 27, unit 250
25010
Page
Copyright ©2000 by Incentive Publications, Inc., Nashville, TN.
Improper Fractions & Mixed Numerals
THE LONGEST JUMPS
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!
Here are some measurements of long jumps from athletes of all ages. They are
written as improper fractions. Change them into mixed numerals.
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
Olympic Games: 1984, 1988, 1992, & 1996.
1. Carl
57
2
feet = ______________
9. James
49
4
feet = ______________
2. Lutz
57
6
feet = ______________
10. Randy
109
4
feet = ______________
3. Jackie
97
4
feet = ______________
11. Tatyana
71
3
feet = ______________
4. Heike
47
2
feet = ______________
12. Mary
63
4
feet = ______________
5. Amber
32
5
feet = ______________
13. Bob
165
6
feet = ______________
6. Yvette
85
8
feet = ______________
14. Albert
129
12
feet = ______________
7. Arnie
88
3
feet = ______________
15. Jenny
101
4
feet = ______________
8. Ellery
83
4
feet = ______________
16. Tommy
14
3
feet = ______________
Name
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 27, unit 252
25211
Page
Copyright ©2000 by Incentive Publications, Inc., Nashville, TN.
Improper Fractions & Mixed Numerals
GETTING 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. Remove the obstacles along the paths by changing each improper fraction
to its correct mixed 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 Ocoee River in
Tennessee, 150 miles from Atlanta.
Name
©2000 by Incentive Publications, Inc., Nashville, TN.
25312
Answer Copyright
key page
27, unit 253
Page
The BASIC/Not Boring Fifth Grade Book
Fractions & Decimals
How to Write a Fraction as a Decimal
Step 1: Divide the numerator by the denominator.
Step 2: Write a zero to hold the ones place
(if there is no number in that place).
7 = 0.875
8
How to Write a Decimal as a Fraction
Step 1: Remove the decimal point and write the number as
the numerator. The denominator is 10 or a multiple
of 10, depending what place the last digit of the
decimal occupied. For instance, in 0.044, the last
digit is a thousandth.
Step 2: Reduce the fraction to lowest terms.
44
1000
116
Get Sharp: Fractions & Decimals
Page 13
11
reduced to lowest terms is 250
.
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Solve Problems with Percent & Fractions
HANG TEN PERCENT
The surf’s up at Shark Beach! One hundred surfers showed up on Saturday to “hang ten” for
the awesome waves. If a surfer is “hanging ten percent”—what would that mean? See 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. Some answers may be used more than once.
Remember: To write a fraction as a percent, you have to write an equivalent
20 = 20%!
fraction with a denominator of 100. For example: 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
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 25, unit 220
22014
Page
Copyright ©2000 by Incentive Publications, Inc., Nashville, TN.
Fractions & Decimals
OVER THE TOP
Pole vaulters sprint along a short track with a long, flexible 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 pole vaulter makes it over the top 6 times out of 7 tries, a fraction ( 67 ) can show
his success rate. The fraction can be changed to a decimal score. (Divide 6 by 7. The
decimal is 0.86.) Find the decimal to match each fraction that shows how these pole
vaulters are doing at their practice. Round to the nearest hundredth.
Athlete
Fraction
Decimal
1. Maxim
14
18
________
2. Javier
16
20
________
3. Sergei
20
27
________
4. Wolfgang
13
18
________
5. Frederick
20
26
________
6. Quinon
13
16
________
7. Philippe
21
28
________
8. William
16
22
________
9. Charles
15
21
________
9
12
________
10. Grigori
Name
©2000 by Incentive Publications, Inc., Nashville, TN.
25915
Answer Copyright
key page
28, unit 259
Page
The BASIC/Not Boring Fifth Grade Book
Equivalent Fractions
Equivalent fractions are two or more fractions that represent the same amount.
How to Form Equivalent Fractions
Step 1: Multiply or divide both the numerator and the denominator
by the same nonzero number.
Step 2: Write the new fraction.
3 =
4
56 =
72
3x2 = 6
4x2
8
56 ÷ 8 = 7
72 ÷ 8
9
How to Tell Equivalent Fractions
Step 1: Cross multiply.
Step 2: Compare the
two products.
Step 3: If the products are equal, the fractions
are equivalent. Otherwise they are not.
2
5
4
10
2 x 10 = 20
5 x 4 = 20
20 = 20, so the fractions are equivalent
7
9
4
5
7 x 5 = 35
9 x 4 = 36
35 =/ 36, so the fractions are not equivalent
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Page 16
Get Sharp: Fraction Concepts
99
Equivalent Fractions
WINTER OLYMPIC TRIVIA
Do you know the name of the most difficult ice-skating jump ever landed in Olympic
competition? Do you know what is the oldest game played on ice? Do you know how fast
downhill skiers might travel? Do you know how many people fit on a luge sled? Do you
know the length of the longest cross-country ski race?
Find the answers to these and other trivia questions while you practice identifying
equivalent fractions. In each problem, two of the fractions are equivalent. The
fraction that is not equivalent gives the answer to the trivia question! Circle the
non-equivalent fraction in each problem.
1. Luge 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
Viking 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
Lillehammer in 1994 was
shaped like a
ice hockey
3. Downhill 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. How 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 quadruple lutz
the triple flip
the triple axle
Name
©2000 by Incentive Publications, Inc., Nashville, TN.
25117
Answer Copyright
key page
27, unit 251
Page
The BASIC/Not Boring Fifth Grade Book
Adding & Subtracting Fractions
How to Add & Subtract Like Fractions
Step 1: If the fractions have like denominators, just add or subtract the numerators.
(Denominators stay the same.)
Step 2: Reduce sums or differences to lowest terms.
How to Add & Subtract Unlike Fractions
Step 1: Find the LCM for all denominators and change the fractions to like fractions.
Step 2: Add or subtract the numerators. (Denominators stay the same.)
Step 3: Reduce sums or differences to lowest terms.
How to Add & Subtract Mixed Numerals
Step 1: Change all mixed numerals to improper fractions.
Step 2: Find the LCM for all the denominators and change the fractions to like fractions.
Step 3: Add or subtract the numerators. (Denominators stay the same.)
Step 4: Reduce sums or differences to lowest terms.
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Page 18
Get Sharp: Operations with Fractions
103
Add & Subtract Fractions
THE #1 SPORT
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.
Soccer was the first team sport to be included in the Olympics. At every
Olympic Games, it draws some of the biggest crowds. In Barcelona,
Spain, the mainly Spanish crowd was thrilled to see the Spanish team win the gold medal!
Look on the soccer field for the answer to each problem. Circle the correct answer
with the color shown next to the problem. Answers must be in lowest terms.
1. GREEN:
2
3
+
1
6
= _________
8. PINK:
1
2
+
2
22
= _________
2. RED:
5
10
–
1
5
= _________
9. RED:
20
30
–
2
6
= _________
3. BLUE:
5
12
–
1
3
= _________
10. BLUE:
1
9
+
2
3
–
1
3
= _________
4. YELLOW:
3
4
–
5
8
= _________
11. PURPLE:
2
9
+
8
9
–
1
3
= _________
5. PURPLE:
1
4
+
4
16
= _________
12. GREEN:
4
7
+
1
3
= _________
6. BROWN:
10
25
+
2
5
= _________
13. ORANGE:
11
14
–
3
7
+
1
7
= _________
7. ORANGE:
11
12
–
3
4
= _________
14. BROWN:
1
6
+
3
4
–
1
8
= _________
Name
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 27, unit 254
25419
Page
Copyright ©2000 by Incentive Publications, Inc., Nashville, TN.
Dividing Fractions
How to Divide Fractions
Step 1: Invert (flip over) the second fraction (the divisor fraction).
Step 2: Change the problem into a multiplication problem.
Step 3: Multiply the fractions.
Step 4: Reduce the quotient fraction to lowest terms.
How to Divide a Whole Number by a Fraction
(or a Fraction by a Whole Number)
Step 1: Change the whole number into an improper fraction
with the whole number as the numerator and 1 as the denominator.
Step 2: Proceed with the instructions for dividing fractions.
Step 3: Change any improper fractions in the quotient to mixed numerals,
and reduce to lowest terms.
How to Divide Mixed Numbers
Step 1: Change any mixed numbers into improper fractions.
Step 2: Proceed with the instructions for dividing fractions.
Step 3: Change any improper fractions in the quotient to mixed numerals, and reduce to lowest terms.
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Page 20
Get Sharp: Operations with Fractions
105
Divide Fractions
THROUGH WILD 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! Some of the
gates require 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 divide fractions, you need to do some flipping, too! The second number in the
problem must be turned upside down. Then, you multiply the two fractions to get the
answer to the division problem!
3 ÷ 7 = 3 x 10 = 30 = 6
5
10
5
7
35
7
Flip the second fraction in all these problems to find the right answers.
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
©2000 by Incentive Publications, Inc., Nashville, TN.
25521
Answer Copyright
key page
27, unit 255
Page
The BASIC/Not Boring Fifth Grade Book
Multiplying Fractions
How to Multiply Fractions
Step 1: Multiply the numerators; this product is the new numerator.
Step 2: Multiply the denominators; this product is the new denominator.
Step 3: Reduce the product fraction to lowest terms.
How to Multiply a Fraction
by a Whole Number
Step 1: Multiply the numerator by the whole number.
Step 2: Write this product as the numerator
in the answer.
Step 3: Write the original denominator in the answer.
Step 4: Change the improper fraction
into a mixed numeral, and
reduce to lowest terms.
How to Multiply Mixed Numbers
Step 1: Change all mixed numerals to improper fractions.
Step 2: Multiply the numerators; this product is the new numerator.
Step 3: Multiply the denominators; this product is the new denominator.
Step 4: Change the improper fraction into a mixed numeral,
and reduce to lowest terms.
104
Get Sharp: Operations with Fractions
Page 22
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Mathematics:
Decimals
The following section of this customized textbook includes material from these skill areas:
Skill Description
2435: order decimals
5.NBT.3.a: Read and write decimals to thousandths using base-ten numerals, number names,
and expanded form, e.g., 347.392 = 3 x 100 + 4 x10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x
(1/1000).
2436: read decimals
5.NBT.3.a: Read and write decimals to thousandths using base-ten numerals, number names,
and expanded form, e.g., 347.392 = 3 x 100 + 4 x10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x
(1/1000).
2437: Decimals
5.NBT.3.b: Compare two decimals to thousandths based on meanings of the digits in each place,
using >, =, and < symbols to record the results of comparisons.
5.NBT.3.a: Read and write decimals to thousandths using base-ten numerals, number names,
and expanded form, e.g., 347.392 = 3 x 100 + 4 x10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x
(1/1000).
5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by
powers of 10, and explain patterns in the placement of the decimal point when a decimal is
multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
2439: round decimals
5.NBT.4: Use place value understanding to round decimals to any place.
Page 23
2494: solve addition problems with decimals
5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or
drawings and strategies based on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written method and explain the
reasoning used.
5.NBT.3.a: Read and write decimals to thousandths using base-ten numerals, number names,
and expanded form, e.g., 347.392 = 3 x 100 + 4 x10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x
(1/1000).
2508: solve division problems with decimals
5.NBT.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or
drawings and strategies based on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written method and explain the
reasoning used.
Page 24
Comparing & Ordering Numbers
Lots of problems and mathematical operations require you to compare numbers to each other. Whenever
you need to put numbers in order, you must compare the numbers and the amounts they represent.
Compare numbers by paying careful attention to place value. Also, it is important to pay attention to signs
for positive and negative numbers.
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Page 25
Get Sharp: Number Relationships
73
Decimals
Some decimal numerals:
The set of decimals includes all numbers in a base ten system.
The term decimal, however, is often used to describe numbers
that use a decimal point to show an amount between two whole
numbers. A mixed decimal numeral is one that includes a
whole number and digits to the right of the decimal point.
0.706
–18.5
10.0505
–6.07
127.3
Place Value in Decimals
Learn these places.
tenths
hundredths
thousandths
ten thousandths hundred thousandths
5.12345
5.1............................. reads five and one tenth.
5.12......................... reads five and twelve hundredths.
5.123 .................... reads five and one hundred twenty-three thousandths.
5.1234 ................ reads five and one thousand two hundred thirty-four ten thousandths.
5.12345 ............ reads five and twelve thousand three hundred forty-five hundred thousandths.
Rounding Decimals
To round a mixed numeral to a whole number, look at the first digit to the right of the decimal point.
If it is 5 or greater, round up to the next whole number.
If it is less than 5, round down to the whole number written.
31.482 rounds (down) to 31.
15.677 rounds (up) to 16.
72
Get Sharp: Number Concepts
Page 26
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Place Value in Decimals
Places to the right of the ones place show decimals.
A decimal point separates the ones place from the tenths place.
The chart below shows the first six places to the right of the decimal point.
tens
1
ones
tenths
hundredths
thousandths
5.
5
1.
ten
thousandths
hundred
thousandths
1
2
3
0.
0
0
7
1
0.
1
5
0
5
5
2.
0
0
0
8
6
millionths
6
Reading & Writing Decimals
Read the whole number first. Then, read the entire number to the right
of the decimal point, adding the label from the place of the last digit.
5.5
1.123
reads five and five tenths
reads one and one hundred twenty-three thousandths
0.0071
reads seventy-one ten thousandths
0.15055
reads fifteen thousand fifty-five hundred thousandths
12.000866
reads twelve and eight hundred sixty-six millionths
Rounding Decimals
Decimals are rounded in the same way as whole numbers.
If a digit is 5 or greater, round up to the next highest value in the place
to the left. If the digit is 4 or less, round down.
0.005 rounded to the nearest hundred is 0.01
0.63 rounded to the nearest tenth is 0.6
5.068 rounded to the nearest tenth is 5.1
5.068 rounded to the nearest hundredth is 5.07
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Page 27
Get Sharp: Decimal Concepts
111
Decimals
A decimal is a way of writing a fractional number that has
a denominator of 10 or a multiple of 10.
Decimals are written using a
decimal point. The decimal point is
placed to the right of the ones place.
1 = .1
10
1 = .01
100
1 = .001
1000
1
= .0001
10,000
Terminating Decimals
A terminating decimal is a decimal number that ends.
When a quotient for a divided fraction eventually shows a
remainder of zero, the decimal terminates.
5
When 8
is divided, the result is a terminating decimal.
Repeating Decimals
A repeating decimal is a decimal that has one or more
digits that repeat indefinitely. The quotient for a divided
fraction never results in a remainder of zero, and one or more
of the final digits keep repeating. A repeating decimal is
indicated by a bar written above the numbers that repeat.
When 31 is divided, the result is a repeating decimal: 0.33
Mixed Decimal Numbers
Mixed decimal numbers combine whole numbers and decimals.
A mixed number has digits
on both sides of the decimal point.
110
Get Sharp: Decimal Concepts
Page 28
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Round Decimals
A HUGE OBSTACLE COURSE
So many obstacles! A runner in the steeplechase race has to run 3,000 meters and jump over 28
hurdles and 7 water jumps. See if you can get past all the obstacles in this steeplechase course.
At each jump, round the decimal as the directions tell you. If you get them
all correct, you will have successfully completed this steeplechase course.
The real Olympic course will be a lot harder than this!
Olympic Fact
Larissa Latynina, a gymnast from the
USSR, holds the record for the most
medals won ever—18. She also won 9
gold medals—the most ever for a woman.
Name
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 28, unit 256
25629
Page
Copyright ©2000 by Incentive Publications, Inc., Nashville, TN.
Operations with Decimals
Adding & Subtracting Decimals
Step 1: Line up the decimal points of both numbers
in the problem.
Step 2: Add or subtract just as with whole numbers.
Step 3: Align the decimal point in the sum or difference with
decimal points in the numbers above.
Multiplying Decimals
Step 1: Multiply as you would with whole numbers.
Multiply 2.65 x 39.6 to get 104,940.
Step 2: Count the number of places to the right of the
decimal point in both factors (total).
Count the number of places to the right of the decimal
point: 2.65 has 2; 39.6 has 1, for a total of 3.
Step 3: Count over from the right end of the product that
same number of places.
In the product, count 3 places backward from the right.
Step 4: Insert the decimal point.
Place the decimal point between the 4 and the 9.
Quillayute’s annual precipitation is about 104.94 inches.
112
Get Sharp: Decimal Concepts
Page 30
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Add Decimals
WHO WEARS THE MEDALS?
In the Olympics, the individual
all-around championship is the
highest achievement a gymnast
can achieve. Most gymnasts
dream of winning this gold
medal. Gymnasts must compete
in four events. Their scores from
all four events are totaled to see
who has the highest score.
Add up the scores for all these
gymnasts. Then rank them in
order from first to last.
Who won the Gold? _______________ Silver? _______________ Bronze? _______________
Name
©2000 by Incentive Publications, Inc., Nashville, TN.
25731
Answer Copyright
key page
28, unit 257
Page
The BASIC/Not Boring Fifth Grade Book
Dividing a Decimal by a Whole Number
Step 1: Place the decimal point in the quotient
directly above the decimal point in the dividend.
Step 2: Divide as you would with whole numbers.
Step 3: Add zeros where necessary to hold places.
Dividing a Decimal by a Decimal
Step 1: Move the decimal point to the right to write the
divisor as a whole number. Count the number of
places you must move the decimal point.
Step 2: Move the decimal point in the dividend the same
number of places to the right.
Step 3: Divide as you would with whole numbers.
Step 4: Align the decimal point in the quotient with the
decimal point in the dividend.
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Page 32
Get Sharp: Decimal Concepts
113
Multiply & Divide Decimals
WHAT’S THE COST?
Sonja Henie was eleven years old when she entered her first Olympic Games in 1924. Even
though this young figure skater finished last, she did not give up. She came back three more
times and won the gold medal every time! She was known for her interesting, graceful movements and her fancy costumes. Those fancy costumes and other supplies add up to a lot of
expense for a skater! You can be sure that they are all more expensive today than they were in
Sonja Henie’s time! Practice your decimal skills to find the costs for these skating items. Use
scrap paper to solve the problems.
______ 1. One skater paid $108.00 for
36 fancy jewels to sew on her
costume. What did each
jewel cost?
______ 6. If Jill’s skating tights cost $53.60
for 8 pair, how much will 4 pair
cost?
______ 2. Laces for her skates were 5 pair
for $13.00. What does one pair
cost?
______ 7. The coach’s fees are $45.00 per
hour. Jill trains with her coach 8
hours each week. How much per
week does this cost Jill?
______ 3. A pair of skate blades costs
$189.00. A pair of skate boots
costs 4 times that much. How
much are the skates and blades
all together?
______ 8. Last year, Scott paid $800 in entry
fees for 6 competitions. If each
fee was the same, about how
much did each competition cost
him to enter?
______ 4. If a skater’s vitamins for one
month cost $17.50, how much
does one year’s supply cost?
______ 9. If Kristi’s new skates cost $695
and she buys 3 pair each year,
how much would she spend in a
year on skates?
______ 5. Every practice session at Kurt’s
rink costs $5.00. Kurt goes to 4
sessions a day, 6 days a week.
How much does he spend each
week on ice time?
______ 10. If Paul spent $322.00 on moleskin
and cream for blisters last year,
how much did it cost him per
month to take care of blisters?
______ 11. Jenni’s newest costume cost twice
as much as her last one. This one
was $286. How much did the last
one cost?
______ 12. Todd’s skating partner drinks hot
chocolate twice a day at the rink.
The hot chocolate costs $1.25,
and they skated 290 days last
year. How much did she spend
on hot chocolate all year?
Name
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 28, unit 258
25833
Page
Copyright ©2000 by Incentive Publications, Inc., Nashville, TN.
Mathematics:
Pre Algebra and Algebra Concepts
The following section of this customized textbook includes material from these skill areas:
Skill Description
2280: select from and use number sentences to represent real-life situations
5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical
expressions without evaluating them.
2281: understand and use algebraic language appropriately
5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate
expressions with these symbols.
2282: understand the use of variables to represent unknowns
5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical
expressions without evaluating them.
2283: Algebra Concepts
5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate
expressions with these symbols.
2287: translate mathematical relationships into symbolic and verbal notation
5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical
expressions without evaluating them.
2449: compare integers
5.NBT.3.a: Read and write decimals to thousandths using base-ten numerals, number names,
and expanded form, e.g., 347.392 = 3 x 100 + 4 x10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x
(1/1000).
2466: apply substitution to solve problems
5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical
expressions without evaluating them.
Page 34
Subtraction
Subtraction is the operation of finding a missing addend
(or, the taking away of one number or amount from another).
The symbol for subtraction is
–
The word used for addition is minus.
The number being subtracted from is the minuend.
The number being subtracted is the subtrahend.
78
Get Sharp: Subtraction
Page 35
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Write Equations to Solve Problems
SINK THAT BASKET
The Panthers and the Warriors are big rivals. This game is the big one! The championship is at
stake. To solve these problems about the teams and the game, change each problem into an
equation. Read the problem, write an equation, and then solve the equation to find the answer.
1. The Warriors scored 42 two-point baskets and 7 three-pointers.
What was their final score?
_________________________________________________________
2. In this game and the last two games, the Panthers scored the exact
same number of points. The total of all these was 216. What was
their score for each game?
_________________________________________________________
3. To get to the game, the Panthers traveled 195 miles less than the
Warriors, who traveled 400 miles. How far did the Panthers travel
to the game?
_________________________________________________________
4. The Warriors bought 96 pairs of court shoes at the beginning of the
season. They had to buy 28 more a month later to replace the ones
that had worn out. How many did they not have to replace?
_________________________________________________________
5. A typical player breathes seven quarts of air a minute while sitting
on the bench and 20 times that much per minute while playing a
strenuous game. How many quarts per minute would that be?
_________________________________________________________
6. There were 155 more Panther fans than Warrior fans at the game.
There were 2,224 Warrior fans. Among all of the fans, 350 had to
stand. How many fans had seats?
_________________________________________________________
7. The concession stand took in $4,500 at the game. Of that, $1,850
was for food, and $570 was for souvenirs. The rest was for drinks.
How much was spent on drinks?
_________________________________________________________
8. Player Sarah Peters dribbled the basketball a total distance of
4,788.5 feet. Her sister Denise dribbled it half that far. How far did
Denise dribble the ball?
_________________________________________________________
Name
©2000 by Incentive Publications, Inc., Nashville, TN.
20936
Answer Copyright
key page
24, unit 209
Page
The BASIC/Not Boring Fifth Grade Book
Find More Than One Solution
GRIDIRON SOLUTIONS
A gridiron is another name for a football field. The aim of a football game is to score more
points than the other team by crossing the opponent’s goal line with the ball. Points are
scored in many ways. The chart under the goalpost below shows the ways to score points.
Notice that extra points with kicks, runs, or passes can only occur after a touchdown!
If the Grizzlies scored 30 points in a game, they might have collected these points in a few
different ways. Here are a few:
5 TD = 30 points
10 FG = 30 points
3 TD + 3 XK + 3 FG = 30 points
4 TD + 3 XK + 1 FG = 30 points
3 FG + 3 TD + 1 XRP + 1 XK = 30 points
1 S + 3 TD + 2 XRP + 2 FG = 30 points
TD = touchdown = 6 points
XK = (kick) extra point after
touchdown = 1 point
XRP = (run or pass) extra point
after touchdown = 2 points
FG = field goal = 3 points
S = safety = 2 points
Write 3 or more equations to show how the Grizzlies might have scored their points in
each game described.
2. The Grizzlies won the second game
49 to 18.
1. The first game of the season ended
with a 16 to 16 tie.
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
Use with page 231.
Name
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 26, unit 230
23037
Page
Copyright ©2000 by Incentive Publications, Inc., Nashville, TN.
Find More Than One Solution
GRIDIRON SOLUTIONS,
cont.
Write 3 or more different equations to show how the Grizzlies might have scored their points
in each game described.
3. In the game against the Cougars, the
toughest game of the season, the Grizzlies
scored 37 points.
_____________________________________
_____________________________________
_____________________________________
4. Oh, oh! The only loss of the season came
to the Vikings. The Grizzlies lost in a close
one: 21 to 20.
_____________________________________
_____________________________________
_____________________________________
5.
The homecoming game was a great victory.
The Grizzlies won 56 to 18.
________________________________________
________________________________________
________________________________________
6.
The final game of the season ended in another
tie. The score was 29 to 29.
________________________________________
________________________________________
________________________________________
Use with page 230.
Name
©2000 by Incentive Publications, Inc., Nashville, TN.
23138
Answer Copyright
key page
26, unit 231
Page
The BASIC/Not Boring Fifth Grade Book
Know Your Mathematical Symbols
$
¢
Ø
{}
%
dollars
cents
empty set
empty set
percent
≠ pi (3.14159)
°
degrees
F Fahrenheit
C centigrade
. point
√— square root
∩ arc
÷ divide
—
| — divide
+ add
– subtract
x multiply
•
multiply
∪ union of sets
∩ intersection of sets
= is equal to
32
Get Set: Math Tools
=/
≈
<
>
≥
≤
=
∼
≅
≅/
+4
–4
↔
—
→
∠
m∠
Δ
⊥
//
63
Page 39
is not equal to
is equivalent to
is less than
is greater than
is greater than or equal to
is less than or equal to
is approximately equal to
is similar to
is congruent to
is not congruent to
positive integer
negative integer
line
line segment
ray
angle
measure of an angle
triangle
is perpendicular to
is parallel to
6 to the 3rd power
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Absolute Value — the distance of a number from zero on a number line
Axes — the two perpendicular number lines in a coordinate plane
that intersect at 0
Coefficient — the number value in a mathematical expression
In the expression 8x, 8 is the coefficient of x.
Coordinate Plane — a grid on a plane with two perpendicular lines of axes
Coordinates — a pair of numbers that give the location of a point on a plane
Coincide — the intersection of two lines in more than one point
Collinear Points — points that lie on the same line
Coordinate — a number paired to a point
Coordinates — a pair of numbers paired with a point
Coordinate Plane — a grid on a plane with two perpendicular number lines (axes)
Cube Numeration — a number raised to the third power (83)
Equation — a mathematical sentence which states that two expressions are equal
7 x 9 + 3 + (4 x 5) = 86
Equivalent Equations — equations that have the same solution
Evaluate — to substitute a number for each variable in an expression and
simplify the expression
Function — a set of ordered pairs (x, y) where for each value of x, there is only
one value of y
Inequality — a number sentence showing that two numerals or two groups of
numerals stand for different amounts or numbers
The signs < (is less than), > (is greater than),
/ (is not equal to) show inequality.
and =
7 + 5 < 17 – 3
Integers — the set of numbers greater than and less than zero
negative integers — the set of integers less than zero
positive integers — the set of integers greater than zero
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Page 40
Get Sharp: Math Terms
231
Linear Equation — an equation whose graph is a straight line
Open Sentence — a number sentence with a variable
Opposites — two numbers on a number line that are the same distance from 0
on each side
Opposite Property — a property that states that if the sum of two numbers is 0,
then each number is the opposite of the other
– 4 + 4 = 0; – 4 and 4 are opposites
Ordered Pair — a pair of numbers in a certain order
with the order being of significance
Radical Sign — the square root symbol
Rational Numbers — a number that can be written
as the quotient of two numbers
(A terminating or repeating decimal is rational.)
Real Numbers — any number that is a positive number, a negative number, or 0
Reciprocals — two numbers whose product is one
1
—
3
3 are reciprocals because —
1 x
and —
1
3
3
—
1
= 1.
Replacement Set — a set of numbers that could replace a variable in a number sentence
Solution Set — the set of possible solutions for a number sentence
Square Root — a number that yields a given product when multiplied by itself
The square root of 25 is 5 because 5 x 5 = 25
Scientific Notation — a number expressed as a decimal number (usually with an absolute value
less than 10) multiplied by a power of 10
4.53 x 103 = 4,530
Solution — the number that replaces a variable to complete an equation
Variable — a symbol in a number sentence that could be replaced by a number
In 3 + 9x = 903, x is the variable.
X-Axis — the horizontal number line on a coordinate grid
Y-Axis — the vertical number line on a coordinate grid
232
Get Sharp: Math Terms
Page 41
Better Grades & Higher Test Scores / MATH gr. 4–6
Copyright ©2005 by Incentive Publications, Inc., Nashville, TN.
Choose Correct Equation
WILD WHITEWATER WHIRL
Kayakers will have a much better chance of getting down wild rivers safely if they choose the
best path. You’ll have a better chance of solving math problems correctly if you can find the
equation that best fits the problem. Circle the correct equation and solve each problem. If you
get them right, you’ll help Will find the right path down the river.
1. Will puts his kayak in at the dam. The first
set of rapids is 3 miles downstream, the next
is 4 miles farther, and the next is 2 12 miles
farther. He gets out 2 miles after the third set.
How many miles has he paddled? _________
a. 3 + 4 = n
b. n = 3 + 4 + 2 12
c. 3 + 4 + 2 12 + 2 = n
d. 3 x 2 x 2 x 2 12 = n
2. It takes 6 hours to drive to Raging River
without stopping. If Wanda and Will
stop twice for 12 hour each time and
once for a 1-hour lunch, how long will
their trip take? ____________
a. n = 6 + 12 + 12
b. n = 6 + 12 – 12 + 1
c. 6 + 12 + 12 + 1 = n
d. 6 – 12 – 12 – 1 = n
3. Will and his 12 teammates each have a
helmet, paddle, wetsuit, and splashskirt to
carry in their kayaks. How many items of
gear do they have in all? ____________
a. 12 x 4 = n
b. n = 4 x 13
c. 12 + 4 = n
d. 1 + 1 + 1 + 1 + 12 = n
4. This summer Will entered 17 whitewater
rodeos. This was 9 more than last year.
How many rodeos did he enter last year?
____________
a. 17 + 9 = n
b. n = 17 x 9
c. n = 17 – 9
d. 17 ÷ 9 = n
5. The Whitewater club has 24 members
with kayaks. If each car-top rack holds 4
kayaks, how many cars will they need to
travel? ____________
a. n = 24 ÷ 4
b. n = 24 x 4
c. 24 + 4 = n
d. 24 – 4 = n
6. Will got dunked 5 times. Wanda got dunked
3 times. Wayne got dunked twice the
number of times that Will and Wanda did.
How many times did Wayne go in? ______
a. n = 2 (5 + 3)
b. n = 2 + 8 + 3
c. 2 x 5 + 3 = n
d. 5 + 3 + 2 x 5 = n
Name
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 24, unit 208
20842
Page
Copyright ©2000 by Incentive Publications, Inc., Nashville, TN.
Mathematical Expressions
A
mathematical expression
is a phrase or statement that uses symbols instead of words.
Terms are the numbers and variables in an expression.
5n – 7y + 3b has three terms: 5n, 7y, and 3b.
A variable is a number represented by a letter in an expression.
In 12x, the variable is x. In 145b, the variable is b.
A coefficient is the number before the letter in an expression with a variable.
In 12x, the coefficient is 12. In –70g, the coefficient is –70.
178
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Equations
A variable is a part of many equations.
A variable is a quantity that is represented by a letter because it is unknown.
Example:
20x = 80
x is the variable
An equation is solved when you find the value of the variable.
The value of the variable is called the solution.
Example:
In 20n = 80, n = 4
4 is the solution
Reading and Writing Equations
b=r+8
Bob (b) is 8 years older than Rachael (r).
m = 3c
Michael’s running time in the race (m)
was triple the time that Charlie had (c)
Sam’s socks (s) have 3 more than twice
the number of holes as Abby’s socks (a).
s = 2a + 3
Zeke (z) spent one-fourth the amount of money
that Al (a) and Dana (d) spent together.
z=
On Saturday (s), Todd rode his bike
6 miles farther than on Wednesday (w).
180
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1 (a + d)
—
4
w+6=s
OR s = w + 6
Page 44
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Properties
THE RIGHT PROPERTIES
Hockey players have some special properties—the equipment they need to wear on the ice.
Without the right stuff, they wouldn’t be able to play the game very well (or very safely)!
Their equipment certainly helps them with problems on the ice.
Math operations have properties that you need
to use for solving math problems. Review
these properties. Then decide which ones are
used in the problems below. Write the name
of the property below each problem.
Zero Property of Addition
Zero Property of Subtraction
Zero Property of Multiplication
Property of One
Opposites Property of Addition
Commutative Property of Addition
Commutative Property of Multiplication
7. 53 + 17 = 17 + 53
1. 8 x 4 = 32 and 4 x 8 = 32
_________________________________
_________________________________
8. 666 – 0 = 666
2. 8633 x 1 = 8633
_________________________________
_________________________________
9. 25 + 10 = 35 and 35 – 10 = 25
3. 99 x 0 = 0
_________________________________
_________________________________
4. 110 x 55 = 6050 and 55 x 110 = 6050
10. 1700 + 0 = 1700
_________________________________
_________________________________
5. 1 x 99 = 99
11. 7401 x 15 = 15 x 7401
_________________________________
_________________________________
6. 6 x 8 = 8 x 6
12. 77 x 0 = 0
_________________________________
_________________________________
Name
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24745
Answer Copyright
key page
26, unit 247
Page
The BASIC/Not Boring Fifth Grade Book
Explain Problem Solutions
SUBMERGED SOLUTIONS
Often when you solve a problem, all that shows on paper is the answer. The way that you
solved the problem is not shown. It is submerged in your mind, but no one else can see it.
Sometimes, you don’t even stop to think about what you did to solve the problem.
When you solve these underwater problems (on pages 234 and 235), pay attention to how you
go about getting the answer. Solve each problem, write your answer, and then explain how you
found the solution. You may draw diagrams or pictures as a part of your explanation.
1. A school of barracudas swam past Samantha. She saw
twice as many lobsters as barracudas, and three more
angelfish than lobsters. She saw 25 angelfish. How many
barracudas did she see?
___________________
How did you solve this problem?
__________________________________________________
__________________________________________________
__________________________________________________
__________________________________________________
2. Scuba diver Samantha got to the sunken ship before Seth,
but not before Tabitha and Josiah. Dara got to the ship
before Josiah, but after Tabitha. Who got to the ship last?
___________________
How did you solve this problem?
__________________________________________________
__________________________________________________
__________________________________________________
__________________________________________________
Use with page 235.
Name
BASIC/Not Boring Fifth Grade Book
Answer The
key
page 26, unit 234
23446
Page
Copyright ©2000 by Incentive Publications, Inc., Nashville, TN.
Explain Problem Solutions
3. Josiah spent $280 on new scuba gear. Then he bought a new underwater camera
for $112 and an underwater watch for $56. Since he made some money from the
sale of his old gear, he only had to come up with $362 for the new gear. How much
did he get from the sale of the old gear? ____________
How did you solve this problem?
_________________________________________________________________________
_________________________________________________________________________
4. The divers fed the fish half of the food in a cube-shaped container. Each side of the
cube measured 12 inches. If the container was full to start with, what is the volume
of food given to the fish? ____________
How did you solve this problem?
_________________________________________________________________________
_________________________________________________________________________
*Challenge!*
5. Tabitha and Dara have been diving a number of years that is half of the age of
Dara. Dara is 3 years older than Tabitha. The total of their ages is 33.
How old is Tabitha? ____________ How old is Dara? ____________
How long have they been diving? ____________
How did you solve this problem?
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
Use with page 234.
Name
©2000 by Incentive Publications, Inc., Nashville, TN.
23547
Answer Copyright
key page
26, unit 235
Page
The BASIC/Not Boring Fifth Grade Book
To compare integers, picture their location on a number line.
–12 > –15
–20 < 2
1.7 > –7
–13 < –9 < 5 reads like this:
–9 is between –13 and 5, or
–9 is greater than –13 and less than 5
To order integers, start with the number
with the least value, and write numbers in
order of increasing value, up to the
number with the greatest value.
In order from least to greatest,
these numbers read:
–6, –—12 , –0.03, 0.8, 1.5
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175
Integers
TEMPERATURE COUNTS
The temperature really does matter for ski races. Snow 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.
Use this thermometer as a number line to help you solve these
problems with integers. Remember, integers are a set of positive and negative numbers.
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°. How much had the temperature risen? __________
2. The temperature rose from +12° to + 23° by noon.
How much did the temperature change? ___________________
3. In the afternoon, the temperature fell rapidly
from +23° to -1°. How much change is this? ________________
4. By 7:00 P.M., the temperature was – 9°. How 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 next morning, what was
the temperature at 6:00 A.M.? ______________________________
Finish these problems.
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
©2000 by Incentive Publications, Inc., Nashville, TN.
26149
Answer Copyright
key page
28, unit 261
Page
The BASIC/Not Boring Fifth Grade Book
Problem-Solving Strategies
A problem-solving strategy is a method for approaching and solving a problem. There are many different
ways to solve problems. Different strategies fit well with different kinds of problems.
One of the skills involved in sharp problem solving is being able to choose a good strategy. Here are
some strategies to have among your list of tools for attacking problems. (See pages 196–206).
Guess & Check
Sometimes the best strategy for solving a problem is to make a
smart guess. After you make a careful guess, if it is possible, you
can count or calculate to see if your guess was right.
The Guess & Check strategy is a good one for a problem where
you can see a quantity, but it is too large, complex, or far away to
count accurately and easily. Use it for this problem.
The Problem:
How many candy worms are in this jar?
Trial & Error
For some problems, the best strategy is to try different solutions
until you find one that works.
Trial & Error is a good strategy for those tricky age problems.
The Problem:
Tracy is twice Lacy’s age.
Six years ago, Tracy was
eight times Lacy’s age.
In seven years, Lacy will be
2
—
3 of Tracy’s age.
How old is Lacy?
196
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