ALGEBRA
Hope Martin
ALGEBRA
Hope Martin
iii
Table of Contents
States of the Union
1–35
Famous Firsts
36–69
Discoveries, Inventions, and
Notable Accomplishments
70–103
Happy Birthday to You
104–148
Historical Highlights
149–180
Glossary
181–184
Daily Warm-Ups: Algebra
iii
Table of Contents
States of the Union
1–35
Famous Firsts
36–69
Discoveries, Inventions, and
Notable Accomplishments
70–103
Happy Birthday to You
104–148
Historical Highlights
149–180
Glossary
181–184
States of the Union
T h e g r o w t h o f t h e U n i t e d S t a t e s took place over the course of 172 years. Delaware
was the first of the colonies to join the Union (December 7, 1787), and Hawaii became the 50th
state (August 21, 1959).
The mathematics puzzles in this chapter help celebrate the nation we are today. When you solve the
mathematical clues, you learn the year that each state became a part of the United States of
America. You can also explore the correlation between the dates colonies and territories became
states, life in colonial times, pioneer exploration, and the growth of the western part of the United
States. And, when you investigate mathematics within the framework of history, you view math in
context, and it begins to make sense.
States of the Union
T h e g r o w t h o f t h e U n i t e d S t a t e s took place over the course of 172 years. Delaware
was the first of the colonies to join the Union (December 7, 1787), and Hawaii became the 50th
state (August 21, 1959).
The mathematics puzzles in this chapter help celebrate the nation we are today. When you solve the
mathematical clues, you learn the year that each state became a part of the United States of
America. You can also explore the correlation between the dates colonies and territories became
states, life in colonial times, pioneer exploration, and the growth of the western part of the United
States. And, when you investigate mathematics within the framework of history, you view math in
context, and it begins to make sense.
T h e C o n s t i t u t i o n of the United States was adopted
by a Convention of States on September 17 of this year. Solve the
puzzle to find the year.
:A
lge
bra
• My hundreds and units digits are the sixth prime number.
Da il
yW
arm
U
ps
• The two digit number formed by my thousands and tens digits is
equal to x in x = 32.
2
• The sum of all of my digits is equal to 52 – 2.
What year am I?
1
©
20
03
J. W
r
eston
Walch, Publishe
T h e C o n s t i t u t i o n of the United States was adopted
by a Convention of States on September 17 of this year. Solve the
puzzle to find the year.
:A
lge
bra
• My hundreds and units digits are the sixth prime number.
Da il
yW
arm
U
ps
• The two digit number formed by my thousands and tens digits is
equal to x in x = 32.
2
• The sum of all of my digits is equal to 52 – 2.
What year am I?
1
©
20
03
J. W
r
eston
Walch, Publishe
D e l a w a r e , P e n n s y l v a n i a , and New Jersey were
the first three colonies to enter the Union. They all became states
in the month of December of the same year. Solve this puzzle to
learn the year.
=3.
ily
3
--- x
7
Da
• My hundreds and units digits are the same
number, and each is the solution to this equation:
W
• My tens digit is equal to 23.
m
ar
• The sum of all of my digits is equal to 33 – 22.
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
-U
ps
:A
lgeb
ra
:A
lgeb
ra
__________
Units
2
u
,P
lch
© 20
03 J. Weston Wa
er
sh
bli
D e l a w a r e , P e n n s y l v a n i a , and New Jersey were
the first three colonies to enter the Union. They all became states
in the month of December of the same year. Solve this puzzle to
learn the year.
=3.
W
• My tens digit is equal to 23.
ily
3
--- x
7
Da
• My hundreds and units digits are the same
number, and each is the solution to this equation:
What year am I?
__________
Thousands
2
u
,P
lch
© 20
03 J. Weston Wa
er
sh
bli
__________
Hundreds
m
ar
• The sum of all of my digits is equal to 33 – 22.
__________
Tens
__________
Units
-U
ps
Famous Firsts
W e a r e a l l f a s c i n a t e d by the first of anything—the first person to climb a mountain, the
first minority to be elected to office, even the first telephone operator! These puzzles take us back in
time to contemplate those explorers, scientists, entrepreneurs, and others who have changed history
by being the first of something. By solving these puzzles, you learn the year that the famous first
occurred while you practice algebra skills.
Famous Firsts
W e a r e a l l f a s c i n a t e d by the first of anything—the first person to climb a mountain, the
first minority to be elected to office, even the first telephone operator! These puzzles take us back in
time to contemplate those explorers, scientists, entrepreneurs, and others who have changed history
by being the first of something. By solving these puzzles, you learn the year that the famous first
occurred while you practice algebra skills.
I n t h i s y e ar,
the first women to become FBI agents
completed their training in Quantico, Virginia. The new agents
were Susan Roley and Joanne Pierce. Solve this puzzle to learn
the year.
Da
• The two-digit number formed by my tens and units digits is
equal to the complement of an 18° angle.
ily
W
• My hundreds digit increased by 6 is equal to 15.
m
ar
• The sum of all of my digits is equal to |–9 – 10|.
-U
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
ps
:A
lgeb
ra
:A
lgeb
ra
__________
Units
36
u
,P
lch
© 20
03 J. Weston Wa
er
sh
bli
I n t h i s y e ar,
the first women to become FBI agents
completed their training in Quantico, Virginia. The new agents
were Susan Roley and Joanne Pierce. Solve this puzzle to learn
the year.
Da
• The two-digit number formed by my tens and units digits is
equal to the complement of an 18° angle.
ily
W
• My hundreds digit increased by 6 is equal to 15.
What year am I?
__________
Thousands
36
u
,P
lch
© 20
03 J. Weston Wa
er
sh
bli
__________
Hundreds
__________
Tens
m
ar
• The sum of all of my digits is equal to |–9 – 10|.
__________
Units
-U
ps
On January 5
of this year, the first junior high school
was opened in the United States. Solve this puzzle to learn the year.
:A
lge
bra
• The two-digit number formed by my tens and units digits is equal
to the sum of the first four counting numbers.
Da il
yW
arm
-U
ps
• My hundreds digit is equal to the value of n in this equation:
2
--- n + 4 = n + 1.
3
• The sum of all of my digits is the same as the number of players
each team has on a football field.
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
__________
Units
37
©
20
03
J. W
r
eston
Walch, Publishe
On January 5
of this year, the first junior high school
was opened in the United States. Solve this puzzle to learn the year.
:A
lge
bra
• The two-digit number formed by my tens and units digits is equal
to the sum of the first four counting numbers.
Da il
yW
arm
-U
ps
• My hundreds digit is equal to the value of n in this equation:
2
--- n + 4 = n + 1.
3
• The sum of all of my digits is the same as the number of players
each team has on a football field.
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
__________
Units
37
©
20
03
J. W
r
eston
Walch, Publishe
Nellie Tayloe Ross
became the first woman to be
elected a governor in the United States. She took the oath of office
on January 5 of this year. The state was Wyoming.
ily
W
m
ar
• The two-digit number formed by my tens and units digits is the
2
value of t in this equation: --5- t = 10.
Da
• The product of my tens and units digits is equal to the sum of my
hundreds and thousands digits.
• The sum of all of my digits is equal to the value of c in this
equation: –5.73c = –97.41.
-U
ps
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
:A
lgeb
ra
:A
lgeb
ra
__________
Units
38
u
,P
lch
© 20
03 J. Weston Wa
er
sh
bli
Nellie Tayloe Ross
became the first woman to be
elected a governor in the United States. She took the oath of office
on January 5 of this year. The state was Wyoming.
W
What year am I?
__________
Thousands
38
u
,P
lch
© 20
03 J. Weston Wa
er
sh
bli
__________
Hundreds
__________
Tens
m
ar
• The sum of all of my digits is equal to the value of c in this
equation: –5.73c = –97.41.
ily
• The two-digit number formed by my tens and units digits is the
2
value of t in this equation: --5- t = 10.
Da
• The product of my tens and units digits is equal to the sum of my
hundreds and thousands digits.
__________
Units
-U
ps
Discoveries, Inventions, and Notable Accomplishments
L o o k i n g a t a t i m e l i n e of the history of humankind, one might consider the changes that
have come to pass during the 20th century as nothing less than amazing. My grandmother was born
before there were automobiles, my mother was born before there were airplanes, and I was born before
there were jet airplanes or men on the moon. In three generations, we have gone from the horse
and buggy era to an International Space Station that orbits the earth! This section will look at the
discoveries, inventions, and other notable accomplishments that have changed our world. When you
solve each of these puzzles, you learn the year each of these accomplishments occurred and, maybe,
that learning math can be quite interesting.
Discoveries, Inventions, and Notable Accomplishments
L o o k i n g a t a t i m e l i n e of the history of humankind, one might consider the changes that
have come to pass during the 20th century as nothing less than amazing. My grandmother was born
before there were automobiles, my mother was born before there were airplanes, and I was born before
there were jet airplanes or men on the moon. In three generations, we have gone from the horse
and buggy era to an International Space Station that orbits the earth! This section will look at the
discoveries, inventions, and other notable accomplishments that have changed our world. When you
solve each of these puzzles, you learn the year each of these accomplishments occurred and, maybe,
that learning math can be quite interesting.
I n t h i s y e ar,
:A
lge
bra
Ruth Handler, the co-founder of Mattel
toys, introduced her invention, the Barbie® doll. She named the
doll after her daughter, Barbara. The first doll sold for only $3.00.
To learn the year this doll was invented, just solve this puzzle.
yW
Da il
arm
-U
ps
• My hundreds, tens, and units digits form a palindrome whose
sum is 23.
• My tens digit is 50% of the sum of my thousands and hundreds
digits.
• The sum of my digits is equal to 33 – 3.
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
__________
Units
83
©
20
03
J. W
r
eston
Walch, Publishe
I n t h i s y e ar,
:A
lge
bra
Ruth Handler, the co-founder of Mattel
toys, introduced her invention, the Barbie® doll. She named the
doll after her daughter, Barbara. The first doll sold for only $3.00.
To learn the year this doll was invented, just solve this puzzle.
yW
Da il
arm
-U
ps
• My hundreds, tens, and units digits form a palindrome whose
sum is 23.
• My tens digit is 50% of the sum of my thousands and hundreds
digits.
• The sum of my digits is equal to 33 – 3.
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
__________
Units
83
©
20
03
J. W
r
eston
Walch, Publishe
Unhappy with
ily
W
• The two-digit number formed by my tens and units digits has the
same value as the Roman numeral L.
Da
cloth diapers that leaked and had to be
washed, Marion Donovan invented the disposable diaper in this
year. When companies thought her product would be too expensive
to produce, she went into business for herself. A few years later, she
sold her business for $1 million. Solve this puzzle to learn the year.
m
ar
• My hundreds digit is 1 less than twice my tens digit.
-U
• The sum of all of my digits is equal to the sum of the first five
counting numbers.
ps
:A
lgeb
ra
:A
lgeb
ra
What year am I?
__________
Thousands
84
u
,P
lch
© 20
03 J. Weston Wa
__________
Hundreds
__________
Tens
__________
Units
er
sh
bli
Unhappy with
ily
W
• The two-digit number formed by my tens and units digits has the
same value as the Roman numeral L.
Da
cloth diapers that leaked and had to be
washed, Marion Donovan invented the disposable diaper in this
year. When companies thought her product would be too expensive
to produce, she went into business for herself. A few years later, she
sold her business for $1 million. Solve this puzzle to learn the year.
• The sum of all of my digits is equal to the sum of the first five
counting numbers.
What year am I?
__________
Thousands
84
u
,P
lch
© 20
03 J. Weston Wa
er
sh
bli
__________
Hundreds
__________
Tens
m
ar
• My hundreds digit is 1 less than twice my tens digit.
__________
Units
-U
ps
Happy Birthday to You
T h e p u z z l e s i n t h i s s e c t i o n all relate to the birthdays of famous (and sometimes not-sofamous) people. Because many of these people will be familiar to you, you may analyze the clues by
focusing on the historical context rather than on the isolated mathematics problem. It is possible you will
think, “That answer doesn’t make sense—this person had to be born in the 1900s!” This is a good thing!
When you start to look at mathematics as a “sense-making” experience, you begin to understand the
power of mathematics, and you learn to be real problem-solvers.
Happy Birthday to You
T h e p u z z l e s i n t h i s s e c t i o n all relate to the birthdays of famous (and sometimes not-sofamous) people. Because many of these people will be familiar to you, you may analyze the clues by
focusing on the historical context rather than on the isolated mathematics problem. It is possible you will
think, “That answer doesn’t make sense—this person had to be born in the 1900s!” This is a good thing!
When you start to look at mathematics as a “sense-making” experience, you begin to understand the
power of mathematics, and you learn to be real problem-solvers.
On March 2
of this year, author and illustrator Dr. Seuss
(Theodor Seuss Geisel) was born in Springfield, Massachusetts.
(Can you think of some of his popular books?)
Da
• The two-digit number formed by my hundreds and tens digits is
equal to the number of degrees in one of the interior angles of a
square.
ily
W
• My units digit is the missing number in this sequence:
1, __, 9, 16, 25, 36.
ar
m
• The sum of all of my digits is equal to 25 × 4 + 16 .
-U
ps
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
:A
lgeb
ra
:A
lgeb
ra
__________
Units
118
u
,P
lch
© 20
03 J. Weston Wa
er
sh
bli
On March 2
of this year, author and illustrator Dr. Seuss
(Theodor Seuss Geisel) was born in Springfield, Massachusetts.
(Can you think of some of his popular books?)
ily
W
• The sum of all of my digits is equal to 25 × 4 + 16 .
What year am I?
__________
Thousands
118
u
,P
lch
© 20
03 J. Weston Wa
er
sh
bli
__________
Hundreds
__________
Tens
m
ar
• My units digit is the missing number in this sequence:
1, __, 9, 16, 25, 36.
Da
• The two-digit number formed by my hundreds and tens digits is
equal to the number of degrees in one of the interior angles of a
square.
__________
Units
-U
ps
:A
lge
bra
On March 6
yW
Da il
arm
-U
ps
of this year, painter and sculptor Michelangelo
(Buonarroti) was born in the town of Caprese, Tuscany. He is famous
for his painting of the Sistene Chapel in Rome and his statue of
David (which is located in Florence). Solve this puzzle to learn the
year.
• The two-digit number formed by my hundreds and tens digits is
equal to f(9) for the function f(x) = 5x + 2.
• My units digit is the value of x in this equation: –6x – (–10) = –4x.
• The sum of all of my digits is the smaller of three consecutive odd
integers whose sum is 57.
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
__________
Units
119
©
20
03
J. W
r
eston
Walch, Publishe
:A
lge
bra
On March 6
yW
Da il
arm
-U
ps
of this year, painter and sculptor Michelangelo
(Buonarroti) was born in the town of Caprese, Tuscany. He is famous
for his painting of the Sistene Chapel in Rome and his statue of
David (which is located in Florence). Solve this puzzle to learn the
year.
• The two-digit number formed by my hundreds and tens digits is
equal to f(9) for the function f(x) = 5x + 2.
• My units digit is the value of x in this equation: –6x – (–10) = –4x.
• The sum of all of my digits is the smaller of three consecutive odd
integers whose sum is 57.
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
__________
Units
119
©
20
03
J. W
r
eston
Walch, Publishe
Historical Highlights
F r o m t h e f i r s t e l e c t i o n for president of the United States to the first radio broadcast of
The Lone Ranger, these puzzles encourage you to explore history from a mathematical perspective.
Exponents, square roots, number patterns, and more are used to help you find, among other
things, the year of the highest recorded wind speed or the last time M*A*S*H was seen
on television.
You will again be using context clues to help you solve these puzzles. Relating historical events to
abstract mathematics clues can help take the mystery out of the problem.
Historical Highlights
F r o m t h e f i r s t e l e c t i o n for president of the United States to the first radio broadcast of
The Lone Ranger, these puzzles encourage you to explore history from a mathematical perspective.
Exponents, square roots, number patterns, and more are used to help you find, among other
things, the year of the highest recorded wind speed or the last time M*A*S*H was seen
on television.
You will again be using context clues to help you solve these puzzles. Relating historical events to
abstract mathematics clues can help take the mystery out of the problem.
On January 7
:A
lge
bra
of this year, the first presidential election
was held in the United States. To learn the year, solve this puzzle.
Da il
yW
arm
-U
ps
• My hundreds, tens, and units digits are consecutive integers whose
sum is 24.
132°
140°
• The sum of all of my digits
r
is equal to r.
63°
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
__________
Units
149
©
20
03
J. W
r
eston
Walch, Publishe
On January 7
:A
lge
bra
of this year, the first presidential election
was held in the United States. To learn the year, solve this puzzle.
Da il
yW
arm
-U
ps
• My hundreds, tens, and units digits are consecutive integers whose
sum is 24.
132°
140°
• The sum of all of my digits
r
is equal to r.
63°
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
__________
Units
149
©
20
03
J. W
r
eston
Walch, Publishe
On January 11
of this year, Chicago schools were closed in
the wake of record-breaking –26°F temperatures. Learn the year by
solving this puzzle.
:A
lge
bra
• 3 less than the sum of my units digit and 5 is 4.
Da il
yW
arm
-U
ps
• My tens digit is 1 less than my hundreds digit; their sum is 17.
• The sum of all of my digits is equal to the sum of the first five
even numbers.
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
__________
Units
151
©
20
03
J. W
r
eston
Walch, Publishe
On January 11
of this year, Chicago schools were closed in
the wake of record-breaking –26°F temperatures. Learn the year by
solving this puzzle.
:A
lge
bra
• 3 less than the sum of my units digit and 5 is 4.
Da il
yW
arm
-U
ps
• My tens digit is 1 less than my hundreds digit; their sum is 17.
• The sum of all of my digits is equal to the sum of the first five
even numbers.
What year am I?
__________
Thousands
__________
Hundreds
__________
Tens
__________
Units
151
©
20
03
J. W
r
eston
Walch, Publishe