Dia Michels
The founder and president of Platypus
Media, an independent press in
Washington, DC, whose goal is to
create and distribute materials that
promote family life by educating
grown-ups about infant development
and by teaching children about the
world around them. She is an awardwinning science writer who has written
or edited over a dozen books for adults
and children. She has spoken at
national and international conferences
for such groups as American
Association for the Advancement of
Science, national Association of
Biology Teachers, La Leche League
International, Smithsonian Institution,
and the Museum of Science. She can be
reached at [email protected].
Nathan Levy
is the author of Stories with Holes,
Whose Clues? and Nathan Levy’s 100
intriguing Questions. A gifted
educator, Nathan worked directly
with children, teachers, and parents in
his 35 years as a teacher and principal.
He has developed unique teaching
strategies that encouraged the love of
learning. He has also mentored more
than 30 current principals and
superintendents, as well as helped to
train thousands of teachers and
parents in better ways to help children
learn. He can be reached at
[email protected].
101 Things Everyone Should Know
About Science
“…encourages a lifetime of curiosity about the world
around us!”
Ages 8-12, 8.5” x 5.5”, 160 pages; $9.95
Science affects everything—yet so many of us wish we understood
it better. Using an accessible question-and- answer format, 101
Things Everyone Should Know About Science expands every
reader’s knowledge. Key concepts in biology, chemistry, physics,
earth, and general science are explored and demystified by an
award-winning science writer and a seasoned educational trainer.
Endorsed by science organizations and educators, this book is
perfect for kids, grown-ups, and anyone interested in gaining a
better understanding of how science impacts everyday life.
Sample Questions!
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Name some characteristics of all mammals
What are the three states of water?
What mineral is found in a saline solution?
What do we use calories to measure?
What happens over time when iron is exposed to oxygen?
At the same pressure, which is more dense—hot air or
cold air?
How does a semiconductor work?
Why is it colder an hour after sunrise than it is at sunrise
itself?
What is a hypothesis?
How can you use a lemon to light a light bulb?
Answers:
1. All mammals have backbones, are warm-blooded, have
hair or fur, and drink their mother’s milk when they are
born. All mammals are vertebrates, which means they have
backbones, unlike worms or insects. They are also able to
maintain a constant body temperature, which is called being warm-blooded. Mammals have hair
or fur at some point in their lives, and the females produce milk for their young through
mammary glands. Mammals have large brains with modified skulls, complex teeth, and three ear
bones. Their skulls have adapted over time to support their elaborate chewing muscles, and to
better contain their large brains. Scientists believe that mammalian ear bones (the malleus, incus,
and stapes) evolved from bones that were no longer needed, such as a bone to support gills. There
are three orders of mammals: monotremes (egg-layers), marsupials (pouched mammals), and
placentals (which account for the majority of mammals, including humans).
2. Liquid, solid, and gas.
Water exists in three states. We use the liquid state most often in our daily activities, for drinking,
washing things, and cooking. Liquids do not hold a shape, but they maintain the same volume. In
humans, liquid water makes up about 70 percent of our bodies. Ice, snow, and frost are frozen
water. Water’s freezing temperature—the highest temperature at which water will become
solid—is 32°F (0°C). Water vapor is water in its gaseous state. Until it reappears as a liquid or
solid, it is invisible. Water evaporates into the air from bodies of water and from plant and animal
respiration. Water vapor is an important regulator of the earth’s heat. Without it, and other socalled greenhouse gases, our planet would be very hot by day and very cold at night. A gas doesn’t
hold its shape or maintain its volume. For example, if you pour one liter of water from a watering
can into a bucket, it’s still one liter. If you take one liter of water vapor and release it into a twoliter bottle, it will spread out to fill the entire bottle. At sea level, water vaporizes at 212°F (100°C).
3. Salt.
Minerals (like salt) are natural compounds formed through geological processes. Saline is the
term used to describe something, including a solution, that contains salt. The chemical name for
salt is sodium chloride. Oceans are huge saline solutions, containing about 3.5 percent salt. Salt is
also found in some rivers, lakes, and seas (e.g., the Dead Sea and Great Salt Lake). There are
natural salt beds that are thought to have come from the salt water of evaporated ancient seas.
Salt manufacturers obtain salt either from these beds or by evaporating seawater. People have
used salt as a seasoning and to preserve food supplies since ancient times. It was even used as
money, in the form of salt cakes, by the Hebrews and other societies during Biblical times. There
are references in the Christian Bible to salt and its value (e.g., “any man worth his salt.”) In Roman
times, salt was an important item of trade and was used as money as well. Roman soldiers
received part of their pay in salt, and newborn babies were rubbed with salt to promote good
health. To compare a person to the “salt of the earth” is to say that they are valuable and have
worth. Before refrigeration, rubbing salt into meat was the only way to preserve it. Salt is an
excellent cleaning agent, drives away ants, is an effective antiseptic, and is used in skin
treatments. Solutions of salts in water are called electrolytes. Both electrolytes and molten salts
conduct electricity. Electrolytes also help the kidneys retain proper fluid levels and help balance
the amounts of acids and bases in our bodies. They also help the cells in our bodies maintain a
proper “voltage” so that the nerve cells can communicate with each other via electrical signals.
Electrolyte drinks containing sodium and potassium salts are used to replenish the body’s water
and electrolyte levels after water loss. Excessive water loss, resulting in dehydration, can be
caused by exercise, diarrhea, vomiting, starvation, or surgery.
4. Energy.
We use calories to measure heat or energy. Scientists define the small calorie, or gram calorie (c),
as the amount of heat it takes to raise the temperature of one gram of water 1°C. The large calorie,
or kilocalorie (C), is equal to 1,000 small calories and is used to measure the amount of energy
produced by the food we eat. Some items we consume have no calories, like water, coffee, or
artificially-sweetened drinks, and provide us with no energy—although coffee and some diet
sodas contain caffeine, which can create the illusion of energy. Other foods, such as cake and
doughnuts, have lots of calories, but they provide little energy since they are very low in nutrients.
These are known as empty calories. Any extra calories we consume beyond what is needed for our
daily activities are stored by the body as fat.
5. It rusts.
Rust is the common name for a very common compound, iron oxide. For iron (chemical symbol
Fe) to become iron oxide, three things are required: iron, water, and oxygen. Iron oxide, (Fe2O3)
is so common because iron readily combines with oxygen (so readily, in fact, that pure iron is only
rarely found in nature). Iron or steel rusting is an example of corrosion, an electrochemical
process. Water speeds the process because it allows for the formation of hydroxide (OH-) ions.
The rust that forms is much weaker than iron; when iron becomes severely rusted, it will crumble
away. To prevent rusting (or the oxidation of iron), rustproof paint can be applied—a common
occurrence on the Golden Gate Bridge in San Francisco. In other applications, nickel and
chromium are added to iron to bind together the atoms and prevent them from rusting.
6. Cold air.
Cold air is more dense than warm air. Air is made up of nitrogen, oxygen, and other molecules
that are moving around at incredible speeds, colliding with each other and all other objects. The
higher the temperature is, the faster the molecules move. As the air is heated, the molecules
speed up and push harder against their surroundings and each other. If the volume of the area is
not fixed, this increases the space between the molecules, making the air less dense. For example,
when the air in a hot-air balloon is heated, it expands (molecules speed up and spread apart).
Now less dense than the surrounding air, the balloon rises. When the heater is turned off, the air
in the balloon cools, the molecules slow down and move closer together, and the balloon
descends.
7. By conducting electric impulses in a controlled fashion. Semiconductors have had a
monumental impact on our society. You find semiconductors inside most microprocessor chips—
the heart of any normal computer. Anything that’s computerized or uses radio waves depends on
semiconductors. Semiconductors, often created with silicon, allow the
transmission and control of electric impulses in microscopic circuits. The smallness of these
circuits has led to portable technology that could not have been built with the previous
technology of vacuum tubes. For example, the computing power of a modern laptop computer
would have required a large building full of power-hungry equipment and a large
maintenance staff were it not for semiconductor technology. A diode is the simplest possible
semiconductor device, and is therefore an excellent beginning point if you want to understand
how semiconductors work. A diode allows current to flow in one direction but not the other. You
may have seen turnstiles at a stadium that let people go through in only one
direction. A diode is a one-way turnstile for electrons. Most diodes are made from silicon. You can
change the behavior of silicon and turn it into a conductor by mixing a small amount of an
impurity into the silicon crystal. A minute amount of an impurity turns a silicon crystal into a
viable, but not great, conductor—hence the name “semiconductor.”
8. Because the planet continues losing heat after sunrise. We think the minimum
temperature should occur at sunrise because the earth has been cooling down all night. The
temperature drops throughout the night because of two processes. The earth no longer receives
energy from the sun, and the earth radiates energy to space. Overnight, the balance is strongly
negative, and the earth loses heat. At sunrise, solar energy again arrives, but the heat loss due to
radiation to space dominates until about an hour after sunrise. At that time, incoming solar
radiation increases enough to overcome the radiational heat loss.
9. A proposed explanation for why something happens. In common usage today, a hypothesis
(which is Greek for assumption) is a provisional idea whose merit must be evaluated. Science
happens in many ways. In some instances, a scientist observes a phenomenon—such as, food left
at room temperature spoils more rapidly than food kept cool—and then develops a hypothesis for
why. Other times, scientists set out to answer a question—such as, will mice be healthier if they
eat vegetables or chocolate. Whether the hypothesis comes from an intellectual pursuit or an
observation, the job of scientists is to perform tests in order to validate or negate their ideas.
Through rigorous testing, scientists can help us learn what is speculation and what is real.
10. Turn the lemon into a battery. A lemon can be used like a battery by placing a copper penny
and a steel paper clip (or a zinc-coated nail) into slits cut into the lemon skin, then connecting
the penny and clip with a small piece of wire. The two different metals react with the acid in the
lemon juice and cause electrons to travel from the negative terminal (the steel or zinc) to the
positive terminal (the penny). An electric potential is created when the different metals are
immersed in the lemon, and you can measure this with a voltmeter. One lemon alone will
probably not produce enough power to light a bulb, but if you link four or more lemons together
in a circuit by connecting the negative terminal of one lemon to the positive terminal of the next,
and so on, you may get enough electricity to light an LED bulb, or some other small device.
101 Things Everyone Should
Know About Math
“A wonderful book for making complex math
topics enjoyable!”
Ages 11-15, 8.5” x 5.5”, 208 pages; $9.95
Math is a critical part of our everyday lives. The second title in the
award-winning “101 Things Everyone Should Know” series helps
you understand how you use math dozens of times––every day.
With entertaining, real-life connections in sports, travel, food,
hobbies and more, math concepts are simplified and explained.
You’ll even learn some fun trivia and math history! Using an
engaging question-and-answer format, 101 Things Everyone Should
Know About Math is perfect for kids, parents, educators, and
anyone interested in the difference between an Olympic event
score of 9.0 and a Richter scale score of 9.0.
Sample Questions!
1. Following Orders
Solve the following: 7 x 3 + 2 ÷ 4 – 22 x (6 – 1)2
2.
There and Back Again
Zach lives a mile from school. It takes him 15 minutes to ride
his bike to school, but only 5 minutes to ride home (There’s a
lesson on motivation here, but that’s beside the point). What
is Zach’s average speed?
A. 4 miles per hour
B. 6 miles per hour
C. 8 miles per hour
D. 12 miles per hour
Marc Zev
is an engineer who
has published in the fields of Structural
Mechanics and Information Technology.
He is founder and president of the
Foundation for Innovative Learning, a nonprofit dedicated to enhancing the problemsolving abilities of children and adults. He
also owns Pensive Products, which creates
educational tools, such as Math Flaps, a
manipulative specifically designed to teach
division. He lives in Chatsworth, California
with his wife, two sons, four finches and
dog. He can be reached at
[email protected].
Kevin Segal
has a Bachelor's in
Pure Mathematics and a Master's in
Applied Mathematics, both from California
State University, Fullerton. He also
completed four years of post-graduate
studies in Applied Mathematics at UCLA.
An Associate of the Society of Actuaries, he
now works as a "charismatic number
cruncher." He lives in Chatsworth,
California with his wife, daughter, and son.
He can be reached at
[email protected].
Nathan Levy
is the author of
Stories with Holes, Whose Clues? and
Nathan Levy’s 100 intriguing Questions. A
gifted educator, Nathan worked directly
with children, teachers, and parents in his
35 years as a teacher and principal. He has
developed unique teaching strategies that
encouraged the love of learning. He has
also mentored more than 30 current
principals and superintendents, as well as
helped to train thousands of teachers and
parents in better ways to help children
learn. He can be reached at
[email protected].
3. Team Player
Daniel plays soccer on a team in the local BES (“Busy Every Saturday”) soccer league. There
are 10 players on his team. At any one time, eight players are on the field. The coach always
chooses his players randomly. What percent of the time does Daniel not play?
4. Sprockets
Bob has a new mountain bike with three sprockets in the front and six sprockets in the back.
Each sprocket, front and back, is a different size. Bob can use each possible combination of
sprockets to make a “gear.” Each gear gives him an advantage in speed or in riding up and
down hills. How man different “gears” does the bike have?
5. Steve, Steve, Steve, Mary and Steve
Five friends, Steve, Steve, Steve, Mary and Steve go to a baseball game. One of them catches a
foul ball. What are the odds that it was a Steve?
a) 5 to 1 in favor
c) 4 to 1 in favor
b) 1 to 5 in favor
d) 1 to 4 in favor
6. Triple Doubles
In Monopoly, you roll two dice and move the number of spaces equal to the sum of the dice. If
you roll doubles, you get to roll again. However, if you roll 3 doubles in a
row, you go directly to jail, do not pass Go and do not collect $200. What are the chances of
this happening?
a) 1 in 6
c) 1 in 216
b) 1 in 36
d) 1 in a million
7. Chuck the Woodchuck
Giles notices an advertisement in the newspaper for an in-store discount of 50% off
Woodchuck Chuckin’ Wood. This is good news for Giles, who knows precisely how much
wood his woodchuck Chuck chucks, since his woodchuck can chuck wood.
At the store, Giles notes that Chuck’s favorite flavor of Chuckin’ Wood (maple, of course) has
a coupon for an additional 50% off the lowest marked price. The cashier says that 50% + 50%
= 100%, so the bag is free. Is the cashier correct?
8. Father of Algebra
Who is considered the father of algebra?
a) Muhammad ibn Musa al-Khwarizmi
b) Euclid of Alexandria
c) Gottfried Wilhelm Leibniz
d) Leonhard Euler
9. Proof Positive
True or false: the following proves that 1=2:
Suppose a = b
Multiply both sides by b
Subtract a2 from both sides
Factor both sides
Cancel (b – a) from both sides
Substitute a for b, since a = b
Divide both sides by a
ab = b2
ab - a2 = b2 - a2
a(b – a) = (b + a) (b – a)
a=b+a
a = a + a or a = 2a
1=2
10. Flip a Coin
When your friend is bored, he has a habit of flipping a coin into the air, catching it and calling
out whether it landed on heads or tails. Today, he is bored. You have heard him call out
“Heads, tails, tails, heads, heads, heads.” He then says to you, “I just flipped three heads in a
row. What is the chance that my next flip will be heads?” Is it…
a) 25%
c) 75%
b) 50%
d) 100%
Answers:
1. The answer is: -78.5
NEED A CLUE? The key to this problem is to understand what calculations to do first. That is
called the “order of operations”. In arithmetic and algebra, certain rules are used for the order in
which the operations in expressions are to be evaluated. These precedence rules (which are just
conventions, not mathematical facts) are also used in many programming languages and by most
modern calculators.
The order of operations is: 1. parentheses 2. exponents (to the power of) and roots (square root,
cube root, etc) 3. multiplication and division (from left to right) 4. addition and subtraction (from
left to right) and it works as follows:
1. Do all the calculations inside of parentheses first. If there are parentheses inside
parentheses, do the inner most set first. So, (1 + (3 x 2)) would be solved as (1 + (3 x 2)) = (1
+ 6) = 7.
2. Resolve all the expressions with exponents, that includes “to the power of” and roots
(e.g. square root, cube root, etc.) as well. If there are expressions that are nested (one
inside the other) do the innermost first. So, √43 = √64 = 8
3. Perform all the multiplication and divisions. In math multiplication and division are
basically two ways of looking at the same thing. So, when performing this step, just move
through the equation from left to right and perform the divisions and multiplications in
the order in which you find them.
The right way: 2 x 10 ÷ 4 x 3 = 20 ÷ 4 x 3 = 5 x 3 = 15
The wrong way: 2 x 10 ÷ 4 x 3 = 20 ÷ 4 x 3 = 20 ÷12 = 5/3
4. Perform all the subtractions and additions. In math subtraction and addition are also
two ways at looking at the same thing. So, when performing this step, just move through
the equation from left to right and perform the additions and subtractions in the order in
which you find them.
The right way: 2 - 10 + 4 - 3 = -8 + 4 - 3 = -4 - 3 = -7
The wrong way: 2 - 10 + 4 - 3 = 2 - 14 - 3 = -12 - 3 = -15
In this case,
7 x 3 + 2 ÷ 4 – 22 x (6 – 1)2 = 7 x 3 + 2 ÷ 4 – 22 x 52 =
7 x 3 +2 ÷ 4 – 4 x 25 = 21 +1/2 - 100 = -78.5
2. The answer is: B, 6 miles per hour
Distance is given in miles, and we want to know Zach’s rate in miles per hour, or miles/hour.
If it takes Zach 15 minutes to go one mile to school and 5 minutes to come home, it takes Zach a
total of 20 minutes to go 2 miles.
That means Zach’s average rate is: r = 2 miles/20 minutes = 2 miles/(1/3) hour = 6 miles per hour.
3. The answer is: 20%.
An easy way to calculate this is to note that, all things being equal, two of the 10 players will be
sitting out at any given time, so everyone will sit 2/10 (or 20%) of the time. Another way to solve
this problem is to figure out how many different combinations of players can be fielded—and
then determine how many include Daniel. Choosing at random, there are 10 players that the
coach can pick for the first person to sit out, and nine choices remaining for the second
person to sit out. That would be 90 choices for players to sit out. However, it doesn’t matter
whether a player is picked first or second to sit out. To take that into account, we need
to divide by the number of ways two players can be chosen (2). Therefore, we get 90/2 = 45
possible ways for two players to sit on the bench.
Next, we need to figure out how many of those ways include Daniel. There are nine combinations
of Daniel and one other player sitting out. So out of 45 possible choices, 9 include Daniel. 9/45
reduces to 1/5, or 20%.
4. The answer is: 18
This question is asking how many different ways you can combine the three sprockets in front
with the six sprockets in back. You find this by multiplying the number of front sprockets with
the number of rear sprockets: 3 x 6 = 18.
5. The answer is C, 4 to 1
There are five friends, and four are named Steve, so the probability of a Steve catching the ball is
4/5 or 80%. However, the question asked for the odds. The fraction 4/5 tells us that out of five
catches, a Steve is expected to catch the ball four times and, therefore, not catch the ball one time.
In other words, the odds of a ball being caught by a Steve is four for every one ball not caught by a
Steve. That’s odds of 4 to 1 in favor of a Steve.
6. The answer is: C, 1 in 216
NEED A CLUE? First, determine the chances of rolling doubles on the first roll.
There are six outcomes possible for each die, making a total of 36 possible outcomes. There are six
ways to roll doubles (1-1, 2-2, 3-3, 4-4, 5-5, and 6-6). Six in 36 is the same as 1/6. The same holds
true on the second and third rolls. Since the rolls don’t influence each other (the dice have no
recollection of what was rolled each time), we need to multiply the results of each separate roll
together. When we do, we get: 1/6 x 1/6 x 1/6 = 1/216 , or 1 in 216.
7. The answer is: No
Giles, being exceptionally honest, corrects the cashier and explains that he should not get the
Chuckin’ Wood for free. He should get 75% off.
Here’s why:
• The first discount is 50%, so the price becomes 50% of the original price.
• The second discount is against the discounted price or 50% of 50%, or 25% of the original price.
• So, the total discount of the original price is 50% + 25% = 75%.
8. The answer is: A
NEED A CLUE? The source of the world “algebra” is an Arabic word: al-jabr
The word “algebra” comes from the title of Muhammad ibn Musa al-Khwarizmi book, Hisab aljabr w’almuqabala, written around the year 830 BCE. The title translates to “Calculation by
Restoration and Reduction.” Besides other important advances, al-Khwarizmi was among the first
to use zero as a number. This probably seems simple, since you already know about zero, but
imagine if you didn’t! He’s also immortalized in another way: the word “algorithm” is derived
from his name.
Euclid is the “father of geometry.” He was a Greek mathematician who lived in Alexandria, Egypt
between about 325 and 265 BCE. His most popular work, Elements, is still widely-used today.
Gottfried Wilhelm Leibniz (1646-1716) was a German polymath (someone who excels in multiple
fields). Leibniz is famous not just for his work in mathematics, but also for his contributions to
philosophy, biology, medicine, geology, politics, psychology, theology and law. One of Leibniz’s
claims to fame is his invention of calculus.
Sure, Isaac Newton usually gets the credit, but Leibniz invented calculus independently, and it is
Leibniz’s notation that is still used. He even developed the binary system, the foundation of
virtually all modern computer architectures.
Leonhard Euler (pronounced “Oiler”) (1707-1783) was a Swiss mathematician and physicist. He
created much of the terminology and notation for mathematics, including the notations for
square root and pi. According to the Guinness Book of World Records, he holds the record for
mathematical authorship. His collected works fill 60 to 80 volumes. Euler is so famous that his
picture is on money in Switzerland.
9. The answer is: False
When we cancel factors, we are actually dividing by that factor. If a = b, then b – a = 0. We can’t
divide by zero so the proof is false. So just what is a proof? A proof is a logical way of proving
something is true. It starts with a hypothesis. It proceeds, step by step, based on what we know to
be true (called “theorems”) and what we assume to be true (called “axioms”). If every step of the
argument is true, then the conclusion must also be true. Another way to use a proof is instead of
proving something to be true, we can assume it’s false and see if we can arrive at a contradiction.
10. The answer is: B, 50%
Coins do not have memory. The probability of flipping a coin heads-side up (or tails-side up for
that matter) never changes, regardless of the number of previous flips. There is always a 50-50
chance of the coin landing on heads.
On the other hand, suppose you have a bag filled with 100 marbles where 99 are black and 1 is
white. The likelihood of drawing a white marble would change with every draw, assuming that
any marble drawn is not put back in the bag.
One Minute Mysteries: 65 More Short
Mysteries You Solve With Science!
“These brainteasers are science magic!”
Ages 8-12, 8.5” x 5.5”, 180 Pages, $9.95
The mysteries are back! One Minute Mysteries: 65 More Short
Mysteries You Solve With Science! continues the fun. These
mysteries have a clever twist—you have to be a super sleuth,
tapping into your science wisdom and critical thinking skills
to solve them. Each story takes just one minute to read and
challenges your knowledge in a variety of science disciplines.
These brainteasers keep you engaged and eager to learn
more! Written by the same father-daughter team that
brought you the award-winning 65 Short Mysteries You Solve
With Math!, this entertaining and educational book is great
for kids, grown-ups, educators and anyone who loves good
mysteries, good science, or both!
Eric Yoder
is a writer and editor who has been
published in a variety of magazines,
newspapers, newsletters and online
publications on science, government,
law, business, sports and other topics.
He has written, contributed to or
edited numerous books, mainly in the
areas of employee benefits and
financial planning. A reporter at The
Washington Post who also does
freelance writing and editing, he was a
member of the Advisory Committee for
Science, Naturally’s 101 Things Everyone
Should Know About Science. He and his
wife, Patti, have two daughters, Natalie
and Valerie. He can be reached at
[email protected].
Sample Questions and Answers!
1. Tanks A Lot
When Giselle and Camilla finally got the aquarium they had wanted
in their room, their mother reminded them that they had promised
to take good care of the fish.
“You need to replace a third of the water every week,” she said as
they set up the tank. “And once a month, put the fish in another
container, clean everything and put in all new water.”
“That sounds like two equal jobs,” Giselle said when the girls were
alone later. “One person changes a third of the water every week and
the other does the complete change once a month. Doesn’t matter to
me. Take your pick.”
“I’ll change a third of the water every week,” Camilla said.
“Deal,” Giselle said.
“And I’ll do it the easy way,” Camilla added.
“What do you mean?” Giselle asked.
“I won’t have to take out old water,” Camilla said. “I’ll just leave the
top off the tank. Over a week, about that much will evaporate. Then
all I’ll need to do is put in the fresh water.”
“That’s not fair!” Giselle said.
“Sorry, we had a deal,” Camilla said.
“I mean it’s not fair to the fish,” Giselle said.
“What do you mean, not fair to the fish?” Camilla asked.
Answers: “The point of changing water is that you’re
taking out some of the old water that has gotten dirty from
Natalie Yoder
is a high-school student whose favorite
subjects are math, science and English.
A sports enthusiast, she participates in
gymnastics, field hockey, soccer and
diving. She also enjoys reading,
writing, playing the clarinet, playing
with the family beagle, Trevor, and
listening to music. She loved helping to
create and shape these science
mysteries. She is hoping to work in
advertising after college. She can be
reached at
[email protected].
uneaten food and from the fish living in the water,” Giselle said.
“If you just let water evaporate, the dirty stuff stays in the water left behind and it’s even
worse for the fish because it’s more concentrated.”
“Okay, I’ll take out old water,” Camilla said. “We’ve been asking for these fish for a long
time and we should take care of them the right way.”
2. Time for a Change
Ivan’s father had bought new smoke detectors six months earlier, putting one on each level of
their house: one in the laundry room downstairs, one in the sunroom on the main level and one
in the upstairs hall between the bedrooms. The smoke detectors sent wireless signals to an alarm
system.
Ivan’s father had asked him to replace the batteries and looked surprised when Ivan brought the
smoke detectors to him where he was working at his tool bench in the garage. That was where
they kept the fresh batteries.
“You didn’t have to take them off their bases,” his father said. “You could have just taken the new
batteries, opened each smoke detector where it was, and switched the batteries there.”
“Sorry, I guess I didn’t understand what you meant,” Ivan said. “Can’t we just change them here?”
“We’ll do that, but we have to put each smoke detector back in the same place or the alarm
system won’t work right,” his father said. “And they’re all the same, except that the color of one is
more faded than the others and one has some dark spots.”
“At least that tells us what we need to know, doesn’t it?” Ivan asked.
Answer: “This faded one must be the one from the sunroom, the brightest of the three
places,” Ivan said, setting aside the one with the lighter color. “And the dark spots on this
one are mildew, meaning it must have come from a damp, dark place—the laundry room.
That leaves the other one for the upstairs hall.”
3. Eggcellent Idea
“Mom, where are you?” Carol called as she unlocked the back door and entered the kitchen.
Three other equally sweaty and hungry girls followed her after playing a pick-up soccer game on
the field near Carol’s house. On the table, they saw a note from Carol’s mother.
It said, “Had to run an errand. Will be back around one. You and your friends can help yourself to
lunch. Eggs are in the fridge.”
“Mom boiled a dozen eggs this morning to make egg salad sandwiches. I know how to make
them,” Carol said as she opened the refrigerator.
Two identical egg cartons were inside.
“How do we know which dozen is hard-boiled?” Bianca asked. “If we crack one open and it’s still
raw, we’re wasting an egg and making a mess.”
“How about seeing if any are still warm?” Jade suggested. “Or still wet from being in the water?”
Carol brought out both egg containers and felt the eggs. All the eggs were cold and dry.
“That doesn’t help. They’re all the same. I think we have to guess,” she said.
“We don’t have to guess,” Lucy said.
All their heads turned toward her.
Answer: Lucy explained, “Spin the eggs here on the counter. They will spin differently.
The raw ones will spin more slowly than hard-boiled ones. That’s because the hard-boiled
eggs have been cooked solid, but the liquid inside of the raw egg will slow the egg down.
That’s how we will be able to tell which eggs are which.”
One Minute Mysteries: 65 Short
Mysteries You Solve With Science!
“For anyone who loves good science, good
mysteries or both!”
Ages 8-12, 8.5” x 5.5”, 176 pages; $9.95
Not an ordinary mystery book, One Minute Mysteries: 65 Short
Mysteries You Solve With Science! makes science fun. These short
mysteries have a clever twist—you have to tap into your science
wisdom to solve them. Each story, just one minute long,
challenges your knowledge in earth, space, life, physical, chemical
and general science. Exercise critical thinking skills with dozens of
science mysteries (solutions included) that will keep you
entertained—and eager to learn more! Written by a fatherdaughter team, this entertaining and educational book is great for
kids, grown-ups, educators and anyone who loves good mysteries,
good science, or both!
Sample Questions and Answers!
1. Bear Scare
At a one-week ski camp in mid-winter, three best friends
were in the same group—Carla, Sasha and Elizabeth. Today
their group was going on a treasure hunt for a bag of candy.
They had a map with names of the different ski trails and
clues that led them to the right ones. After going down
several trails and up some ski lifts, they found a tree
painted with an X. Also on the tree was a large scratch mark.
“X marks the spot,” Carla said. They took off their skis and dug in
the snow at the base of the tree. But there was only an empty box.
They skied down to the ski school, where they found
Leslie Coyle, their instructor. “We found the box, but there was no
candy in it,” Sasha said.
“I asked the workers to take out the prize because of the
bears,” Ms. Coyle said. “Bears can smell food even through
a box and we don’t want them going to the areas where
there are skiers.”
Eric Yoder
is a writer and editor who has been
published in a variety of magazines,
newspapers, newsletters and online
publications on science, government,
law, business, sports and other topics.
He has written, contributed to or
edited numerous books, mainly in the
areas of employee benefits and
financial planning. A reporter at The
Washington Post who also does
freelance writing and editing, he was a
member of the Advisory Committee for
Science, Naturally’s 101 Things Everyone
Should Know About Science. He and his
wife, Patti, have two daughters, Natalie
and Valerie. He can be reached at
[email protected].
Natalie Yoder
is a high-school student whose favorite
subjects are math, science and English.
A sports enthusiast, she participates in
gymnastics, field hockey, soccer and
diving. She also enjoys reading,
writing, playing the clarinet, playing
with the family beagle, Trevor, and
listening to music. She loved helping to
create and shape these science
mysteries. She is hoping to work in
advertising after college. She can be
reached at
[email protected].
Elizabeth noticed a big bag of candy on Ms. Coyle’s desk.
“Stealer!” Elizabeth said, laughing. “You just wanted the candy for yourself. And I can prove it.”
“So, prove it,” Ms. Coyle laughed. “Are you saying there are no bears in this area? Or that bears
couldn’t smell candy through a box?”
Answer: “There are bears here—that’s what made the scratch
mark on the tree,” replied Elizabeth. “And bears probably could smell the candy through a
box. But it’s the middle of winter. Bears are hibernating now, so they wouldn’t be out roaming
around,” Elizabeth said as they all shared the candy.
2. A Question of Identity
“Watch out!” Samir yelled.
“What?” Maggie asked.
“Don’t step on it! Look!” Samir said.
“Eww, yuck!” Maggie said as she lifted her foot. On the ground lay something slimy, long and
skinny. They were outside walking alongside the playground during break time, and Samir had
spotted something dark in the grass just where Maggie was about to step. It was several inches
long, dark in color and about as big around as a pencil. It was also dead, and a little shriveled up,
so it was hard to tell exactly what it was. Their teacher heard them and came over.
“What’s wrong?” Miss Geong said.
“I almost stepped on a dead snake!” Maggie said. Miss Geong took a stick and poked at it. “It
could be a small snake, or maybe just a large worm,” she said.
“Whatever it is, let’s just leave it here,” Maggie said.
“I can’t do that,” Miss Geong said. “If it’s a snake, there could be a whole lot more. I’ll have to tell
the principal to cancel all recesses until an expert comes.”
“No, we can figure this out ourselves,” Samir said. “Is it okay if we take a closer look at it?”
“Yes, since it’s dead,” Miss Geong said. “But how do you expect to tell what it is?”
Answer:
They picked up the dead, unknown thing with the stick, put it into a bag and
carried it into the science room. There Samir got a sharp knife and cut it open. “The
playground doesn’t have to be closed,” he said. “This cannot be a snake because a snake has a
backbone—it’s a vertebrate. Worms do not have backbones—they’re invertebrates. This does
not have a backbone, so it must be just a large worm.”
3. A Fishy Solution
“Man, a backyard fish pond is a lot more work than an aquarium!” Dennis said to his friend
Anders. Digging the hole for the pond was hard work, and then Dennis and his father had to set
up the liner, cover it with gravel and fill it with water. Now they were ready to get the fish and put
them in. Or so they thought. The man in the fish store had a warning. “Raccoons, skunks and
certain birds might treat your pond as a fast-food restaurant,” he said.
Dennis told that to Anders, who had come over to see how things were going. “That could be a
problem,” Anders said. “I’ve seen raccoons around, and sometimes you smell that a skunk has
been here. And there are a lot of crows.”
“That’s why I came up with the idea to put a cover on the pond,” Dennis said, showing Anders a
large sheet of clear plastic. “It had to be something that we could see through, but that would
discourage anything from getting at the fish. All I have to do is cut this to the shape of the pond
and lay it on top of the water. That way we’ll have no problems.”
“I’m not so sure about that. You might want to talk to the guy in the fish store again,” Anders said.
“You could be causing a bigger problem than you’re solving.”
“What do you mean?” Dennis asked.
Answer:
“Fish need oxygen to live, just like we do,” Anders said. “A lot of the oxygen that’s
in their water gets absorbed from the air. If you lay that plastic on top of the water, you’d be
cutting off their supply of oxygen and it could kill them.”
4. Freeze Fall
It was late winter, and the temperature had just fallen after several mild days. To make the walk
home from school even colder, it had rained earlier, and a chilly mist still hung in the air. Tom
and Evan glanced up at the flashing clock in front of the bank. It said “32°F, 0°C.”
They stopped in a candy store for a snack and to warm up before they continued on their way
home. Their shoes splashed through puddles as they headed toward the railroad bridge. The
bridge, several hundred yards long, had a narrow sidewalk next to train tracks, where the tracks
crossed the river far below. It could get scary crossing the bridge when a train was on it. But the
only way to avoid it was to take a different route that added ten minutes to the walk.
“I think we should go the long way,” Evan said. “The bridge is probably icy.”
“We haven’t seen any ice. These sidewalks are just wet,” Tom said.
A few moments later they were on the bridge. Tom’s foot slipped on a patch of ice and he fell.
“I told you so,” Evan said, teasing him.
“How did you know there would be ice here when there isn’t ice anywhere else?” Tom asked as
Evan helped him up.
Answer: “The Earth absorbs heat from the Sun and radiates that heat back out. Up until the
bridge, there is ground under the sidewalks. The ground provides some insulation and
keepsthe sidewalks above the freezing point, even though the air temperature itself is at the
freezing point,” Evan said. “But underneath the bridge there is just cold air without any
insulation, so the surface on the bridge freezes first.”
5. In Hot Water
Danielle and her family went to a hot-springs pool after a day that included ice skating on an
outdoor rink and a horse-drawn sleigh ride through the snow. They were staying at a resort hotel
that had hot springs. They checked out the spot where the water was bubbling out from the
ground, sending up wisps of steam. From there, the water flowed into a pool about the size of a
small swimming pool. The sign said the water in that pool was 105° F (41° C). The water flowed
down from there to another pool, where the temperature was 98° F (37° C).
They stayed in the 98° pool for about ten minutes and then went to the 105-degree pool. Danielle
enjoyed sitting right where the water was flowing in from spring. A man with a nametag that said
“Charlie” came over to where the water was coming out of the ground and dipped a little glass
container in the water. “What are you doing?” Danielle asked him.
“I’m just testing the chlorine level,” he said. Danielle had seen the lifeguards at the pool she
belonged to back home test for chlorine. But when the man walked away, she said to her father, “I
think you ought to tell the people who are in charge here about that man. I bet he doesn’t even
work here. Maybe he’s looking for a chance to steal somebody’s wallet.” “What makes you think
that?” her father asked.
Answer: “Since the water is coming right from the ground, there’s no chlorine in it,”
Danielle said. “Anyone who worked here would know that.” “That’s right,” her father said.
“Chlorine is found in water that has been treated for home use, and even more is added at
swimming pools to kill bacteria in the water. I’ll go talk to the manager.”
6. Taken with a Grain of Salt
One evening, the campers cooked their own meals with their cooking kits over open fires outside
the dining hall. Then, they brought the food inside where the tables were set up for dinner as
usual, and desserts were on a side table. Mark should have known better than to get up from the
table to get a dessert without taking his glass of water along, because when he got back to the
table, he saw that the glass had been moved. He couldn’t quite be sure, but he thought the salt
shaker had been moved too. And a couple of the guys looked like they were trying hard not to
laugh. “Did you guys put salt in my water?” Mark asked. “There’s only one way to find out,” Breon
said, picking up the glass and handing it to him. “Take a nice deep drink.”
“I bet I can find out without tasting even a drop of it,” Mark said. “Without anyone else tasting it
either. And without anyone telling me.”
“What do you want to bet?” Breon responded.
“Chores for the rest of the week,” Mark said. “If I win, you do mine. If you win, I do yours.” “You’re
on,” Breon said. “How are you going to prove it?”
Answer:
“I’ll take the glass out to the campfire, pour the water into my cooking pan and let
the water boil off,” Mark said. “If there’s salt in the water, it’s in solution now and we can’t see
it, but once I remove the water by boiling it off, any salt will stay behind in the pan.”
7. Needing a Lift
“Hey, watch out!” Karl said. “Oops, sorry!” Barry said. It was Earth Day, and as part of their
project, they were planting trees at the elementary-school playground. Karl and Barry each had
taken one handle of a wheelbarrow. In the wheelbarrow was a tree, its roots protected by a heavy
cloth sack full of dirt. As they crossed the playground toward the holes that had already been dug
for the trees, they struggled to control the wheelbarrow because of the weight.
As they got near the see-saw, Barry’s hand had slipped and he let go of his handle. The
wheelbarrow tipped over and the tree slid out onto the ground. The two of them tried to pick it
up, but it was too heavy. Alejandro and DeWayne came to help, but even the four of them
couldn’t lift the tree. “We’d better stop before we hurt ourselves,” Alejandro said.
“How about if we push it?” DeWayne suggested. They did manage to scoot it across the ground a
little. “That won’t work. Even if we could push it all the way to the hole, the sack would tear and
we’d ruin the roots,” Barry said.
“I have an idea,” Karl said. “Let’s hear it,” Barry said.
Answer:
“A see-saw is a lever,” Karl said. “Let’s adjust it so the side next to the tree is the
short end. Then we’ll push the root ball onto that end. Alejandro and DeWayne, you push
down on the long end, I’ll hold the tree steady and Barry can move the wheelbarrow
underneath it.” In a few moments, the tree was back in the wheelbarrow and on its way to
being planted.
8. Powerful Argument
Jeremy, Vishal and Aiden met in the extended-day room before school one day to assemble the
project they’d all been working on. It was a model of a city, showing how services such as water
and electricity are delivered. The model had miniature businesses and homes along streets,
with model-railroad telephone poles strung with thread to represent power lines, and air hoses
from a fish tank to represent water lines. They had put most of it together after school the day
before when they realized they had forgotten to make a power plant. Aiden had volunteered to do
that, and this morning he brought in a clay model of a building to use as the power plant for the
finishing touch. “You know, this doesn’t look much like a power plant,” Vishal said, examining it.
“It’s missing something . . . I know, it has no smokestacks!” “So what?” Aiden said.
“Power plants burn fuel to generate electricity. You burn coal, you need a smokestack. You burn
oil, you need a smokestack,” Vishal said.
“Well, it’s too late,” Aiden said. “I didn’t bring any more clay with me, and we have to turn this in
during first period.”
“There goes our grade,” Vishal grumbled. “Take it easy. I know how to fix this,” Jeremy said,
walking toward the cafeteria. He returned with some aluminum foil.
“What are you going to do with that?” Aiden asked.
Answer:
Jeremy folded the foil so it would fit on top of the roof of the model power plant.
“Now it’s a solar power plant, which means it gets energy from the Sun. Nothing gets burned,
so no smoke is made, and no smokestack is needed.”
9. Bird Watching
“It’s one o’clock. Time for my shift,” Mike said as he opened the gate into Garreth’s backyard.
For science class, Mike and Garreth were counting how many birds came to a feeder in two-hour
time spans in the morning, mid-day and evening. That Saturday morning, they set up a bird
feeder at Garreth’s house, which was next door to Mike’s, and sat in his yard from eight o’clock to
ten, counting the birds.
But there wasn’t enough to do for two people, so they decided that for the other two periods, each
would take one hour.
Mike sat down in the chair next to Garreth and looked at the fizzing drink on the ground next to
him. Garreth noticed Mike eyeing it and said, “I opened that thing at noon when I started and I’ve
been sitting here with it the whole time and forgot to drink it. Do you want me to go inside and
get you one?”
“No, thanks. How did the bird watching go?” Mike asked. Garreth showed him the sheet. There
were hardly any marks on it. “Well, you can see, not many birds came for lunch.”
Mike said, “You would have seen more if you had been sitting here the whole time like you say
you were.”
“What makes you think I wasn’t?” Garreth asked.
Answer: “If you opened that soda an hour ago at noon like you said, it would have gone flat
by now,” Mike said. “But it’s still fizzing, so you must have just opened it. That meant you
went in the house, and probably not just to get a soda. Which video game were you playing
rather than counting birds?”
10. Thrown a Curve
“No kidding, your coach taught you how to throw a curve ball?” Wayne asked.
“Yep,” Randy said.
Randy was a good athlete. He was quarterback for his football team in the fall, point guard for his
basketball team in the winter and pitcher for his baseball team in the spring.
“I thought you weren’t allowed to throw curve balls until you got older,” said Wayne.
“The rule actually is that you can only throw so many curve balls in a practice or a game,” Randy
said. “Because throwing too many can hurt your arm.” “Can you show me how?” Wayne asked.
They were standing in the school courtyard at break time after lunch. The problem was they
didn’t have a baseball, just a smooth ball about the size and weight of a baseball.
“Okay, you grip it like this,” Randy said, showing Wayne how to position his fingers. “When you
throw it, you snap your hand down to put topspin on it. Like this.” Randy threw the ball with a
downward snap of his wrist, but the ball just went straight. Wayne retrieved the ball after it
bounced off the brick wall and handed it back to Randy. “Try again,” Wayne said.
Randy did, snapping his wrist harder this time. But still the ball went straight.
After three more tries with the same result, Randy said, “The ball was really curving for me at
practice last night. What’s happening?”
Answer:
“At practice, you were using a real baseball, which has stitches that are above the
surface of the ball,” Wayne said. “The stitches are what grab into the air when you put topspin
on the ball by snapping your wrist. Because of the topspin, air is moved out of the way under
the ball, lowering the air pressure there, and more air is brought around to the top of the ball,
raising the air pressure there. The result is the ball curves down. It’s the same reason golf balls
have dimples—to grab the air. Except in golf, backspin is put on the ball and the dimples help
it go up. This ball is smooth, so you don’t get that effect.”
One Minute Mysteries: 65 Short Mysteries You
Solve With Math!
“Solve the greatest mystery of all… why you should
pay attention in math class!”
Ages 11-15, 8.5” x 5.5”, 176 pages; $9.95
These aren’t your ordinary mysteries! One Minute Mysteries: 65 Short
Mysteries You Solve With Math! challenges readers of all ages to become
super sleuths. These fun mysteries are each one minute long and have a
unique twist—you need to tap into your mathematical wisdom to solve
them. Plus, they will help you figure out the greatest mystery of all: why
you actually need the skills you learn in math class!
Written by the same father-daughter team who brought you the awardwinning One Minute Mysteries: 65 Short Mysteries You Solve With
Science!, this entertaining and educational book is easy to use at home, in
school, or in the car. This book is the perfect solution for any kid, parent,
or educator who loves good mysteries, good math, or both!
Sample Questions and Answers!
1. Heavy Toll
“A speeding ticket? What?” Suzy’s father said as he opened
the day’s mail.
“What’s the matter, Daddy?” Suzy asked.
“Well, Suzy, this ticket says that we were speeding on the toll road we
took when we were driving back from the state science fair last
weekend,” he explained.
As drivers entered the road they got a receipt showing the time and exit
number. The exit numbers were also mileage markers.
When they got off the road, drivers had to pay different amounts
depending on how far they went.
“Are you sure they’re right?” Suzy asked. “What does it say?”
“Well, it says that we got on at exit 64 at 12:13 p.m., then got off the road
at exit 148 at 1:33 p.m.,” he said. “And it says the speed limit was 55 miles
an hour—I thought it was 65. How can they know if we were speeding?”
he asked. “I didn’t see any police cars.”
“It’s too bad, but they’re right,” Suzy said.
“How do you know?” he asked.
Eric Yoder
is a writer and editor who has
been published in a variety of
magazines, newspapers,
newsletters and online
publications on science,
government, law, business,
sports and other topics. He has
written, contributed to or
edited numerous books,
mainly in the areas of
employee benefits and
financial planning. A reporter
at The Washington Post who
also does freelance writing and
editing, he was a member of
the Advisory Committee for
Science, Naturally’s 101 Things
Everyone Should Know About
Science. He and his wife, Patti,
have two daughters, Natalie
and Valerie. He can be reached
at [email protected].
Natalie Yoder
is a high-school student whose
favorite subjects are math,
science and English. A sports
enthusiast, she participates in
gymnastics, field hockey,
soccer and diving. She also
enjoys reading, writing, playing
the clarinet, playing with the
family beagle, Trevor, and
listening to music. She loved
helping to create and shape
these science mysteries. She is
hoping to work in advertising
after college. She can be
reached at
[email protected].
Answer:
“If we got on the road at 12:13 and got off at 1:33, that means we were on the road
for one hour and 20 minutes, or 80 minutes,” Suzy explained. “Since the exit numbers are
mileage markers, the distance between exits 64 and 148 is 84 miles—148 minus 64.
That means we went 84 miles in 80 minutes—that’s more than one mile per minute,
which is more than 60 miles per hour. So we were speeding, since the speed limit was 55
miles per hour.”
“To figure it out exactly,” she added, “84 miles divided by 80 minutes makes 1.05 miles per
minute. Multiplying 1.05 miles per minute by 60 minutes in an hour to get miles per hour
means we averaged 63 miles per hour.”
“Well, we were going less than that for some of the time,” her father said.
“Yes, but to average 63 miles an hour, we must have been going faster than that at other
times,” she said. “I hope that ticket isn’t too expensive.”
2. Pancake Mix-up
“Mooommm!” Meg yelled from the kitchen. “Can you please come down here?”
Meg’s family and two other families had rented a house at a ski resort for a long weekend. Each
family was going to cook and clean up for one of the three days. It was the morning of Meg’s
family’s day.
While Meg’s mother finished getting dressed, Meg went into the kitchen and started preparing
the pancake mix. They had brought individual-sized serving packages of mix. They also had
several boxes of cereal and bread to make toast, but everyone had said they wanted pancakes.
“I’ll be there in a minute, Meg. What’s the problem?” her mother called.
“I have everything ready to make the pancakes. But each of these packages needs two-thirds of a
cup of milk, and there’s no two-thirds measuring cup in this kitchen,” Meg called. “All they
have is a three-fourths measuring cup. Can I just estimate?”
“Not if you want the pancakes to be any good,” her mother replied.
“Never mind,” Meg said a moment later. “I have the solution.”
“What did you do?” her mother asked as she walked into the kitchen.
Answer:
“I did some math. It’s a question of least common multiples,” Meg told her
mother. “First, I figured out how many times you’d have to fill each kind of measure to reach a
whole number. With the three-fourths measuring cup, to reach a whole number you’d need to
use the measure four times. Four times three-fourths is twelve-fourths, which reduces to
three. So filling that measure four times gives us three cups of milk. “Each package of mix
required two-thirds of a cup of milk. If we had a two-thirds measuring cup, you would need to
fill it three times to get a whole number. Three times two-thirds is six-thirds, which reduces
to two. So, filling a two-third measuring cup three times would give us two cups of milk,” she
continued. “All I had to do then was find the least common multiple of three and two—the
smallest number that is a multiple of both. That’s six. Since I would need to fill the threefourths measuring cup four times to get three cups, I would need to fill it twice that many
times, eight times, to get six cups. I did that and put the milk in the bowl. And since three
fillings of a two-thirds measuring cup would give us two cups, to get six cups I would need
three times that many, or nine, to get the right amount of mix. So I added nine packages of
the mix. I hope everyone’s hungry!”
3. Cover Up
As a birthday present to her little sister Laura, Miranda had promised to paint the inside of the
family playhouse for her.
Years before, their father had painted the walls and floor pink, Miranda’s favorite color. But since
Laura was the one who mainly used it now, and her favorite color was blue, she wanted
the pink covered up.
Miranda measured the inside of the playhouse. The two longer sides were 10 feet long and 6 feet
high, and the ends were 6 feet long and 6 feet high. Above that was the inside of the roof, which
didn’t need to be painted. Her father warned her that covering up the pink would require two
coats of paint. Later at the hardware store, Laura chose a shade of blue that she liked.
“Okay, here’s a can that says it will cover 520 square feet,” Miranda said. “Each longer side of the
playhouse is 60 square feet—10 times 6—so together they would be twice that, or 120 square feet.
The ends are 36 square feet each—6 times 6—so together they would be twice that, or 72 square
feet. And 120 plus 72 is 192 square feet. Painting that twice means I need to cover 384 square feet
in total—two times 192. So a can that covers 520 square feet will be enough.”
Since she was paying for it out of her own money, Miranda didn’t want to buy too much.
“That’s enough to cover the walls, but don’t forget you have to paint the floor, too,” her father
said. “Oops! I didn’t measure the floor,” Miranda said.
“Should we drive back home to measure it?” Laura asked. “Or should you just buy an extra can of
paint to be sure you have enough?”
Answer:
“Neither,” Miranda said. “Since we know the two longer sides of the playhouse are
10 feet long and the ends are 6 feet long, the floor must be a 6 foot by 10 foot rectangle,
meaning its area is 60 square feet. Painting that twice means I have to cover another 120
square feet. So I need to cover 504 square feet—384 plus 120—in total. That means one can
will still be enough.”
4. Getting a Lift
Jada and Michelle’s school was closed for a winter teacher training day, so their parents decided
to take a day off from work to take the family skiing. They were glad to see when they got there
that there were no lines at the chair lifts.
The two girls were good skiers, so they headed to the part of the mountain with the black
diamond trails, the hardest ones. Three lifts started next to each other and ran up the mountain,
to a spot on the top leading to many different trails.
“Let’s try to get in as many runs as we can,” Jada said.
They looked at a sign to decide which lift to use. The Sheer Drop lift had four seats per chair and
its capacity was 1,200 skiers an hour. The Hang onto Your Hat lift was a two-seat lift with a
capacity of 800 skiers an hour. The White Cliffs lift was a three-seat lift that could move 900
skiers an hour. The sign said each had the same number of chairs.
“Where do you think should we go?” Michelle asked.
Answer:
“Sheer Drop. It moves the fastest—it carries 1,200 skiers an hour versus 900 and
800 for the other two,” Jada said. “It carries the most skiers but that doesn’t mean it moves
the fastest,” Michelle said. “Since there are no lines at the lifts, and all three lifts have the
same number of chairs and start and end next to each other, the question is how frequently a
lift drops off groups of skiers–in other words, how fast a chair gets from the bottom of the
mountain to the top. “Now, the Sheer Drop lift has four seats per chair and it has a capacity
of 1,200 skiers an hour, meaning it makes 300 drops an hour—1,200 divided by four,”
Michelle said. “And the White Cliffs lift is a three-seat lift that can drop off 900 skiers per
hour, meaning it also makes 300 drops per hour—900 divided by three. The Hang onto Your
Hat lift can drop off 800 skiers an hour and has two seats per chair, meaning it makes 400
drops an hour—800 divided by two. So the Hang onto Your Hat lift will get us to the top the
fastest.”
5. Chute in the Works
On Saturday morning, Caleb rode up the bike path to his friend Patrick’s house. That morning
Patrick was in his yard painting a model rocket. As much as Caleb loved bicycle riding— he had a
bike with a speedometer, lights, water bottle holder and other accessories—Patrick loved model
rockets. “Cool,” Caleb said, admiring his friend’s new rocket. “Maybe too cool to use,” Patrick said.
Patrick and his father belonged to a club that launched model rockets. Sometimes, though,
rockets crashed and broke apart because their parachutes didn’t open. The parachute for Patrick’s
new rocket was already attached to the nose cone.
“I’m worried about this parachute,” Patrick said. “The instructions say it should open when the
rocket hits 30 miles an hour on the descent. I’ve tried to test it, but I guess I can’t throw
the nose cone that fast.”
“I’ll take it on a ride down the bike path,” Caleb suggested. “Once I get going that fast, we’ll know
if it will open or not.” Caleb tried several times but could never get the parachute
to open. “Sorry, I can’t get this bicycle going more than about 20 miles
an hour,” Caleb said when he returned.
“I have an idea,” Patrick said. “And I wouldn’t suggest this if you weren’t a good enough biker to
handle it.” “What do you have in mind?” Caleb asked.
Answer:
“Once you get going on your bike, throw the nose cone forward,” Patrick said.
“The speed of the throw will be added to the speed of the bicycle. So if you’re riding at 20
miles an hour and you throw it at even just 10 miles an hour, it will be moving forward at 30
miles an hour, and you’ll see if it opens.” Caleb did just that. It was a little tricky since he had
to steer with only one hand and throw with the other, but it worked. The parachute opened.
“Now it’s time for lift-off!” Patrick said.
6. Ace of Clubs
Natalie and her father had been taking golf lessons. They were hitting the ball pretty well, so they
thought it was time to go out and play their first real round of golf.
On the first hole, they hit their drives down the fairway. “This marker says we’re 150 yards out
from the green, Daddy,” Natalie said when they reached his ball. “Okay, the instructor said 150
yards is how far I hit with a sixiron,” her father said, pulling out that club. He took a practice
swing that was interrupted when his hat flew off back toward the tee, making Natalie laugh.
He hit the shot the way he usually did, but it landed 30 yards short of the green. “I could have
sworn he told me I hit six-irons 150 yards,” he said.
The next hole ran parallel to that one, but going the other way. After their drives, Natalie’s father
was once again about 150 yards from the green. “Let’s see, the instructor said there’s about
a 15-yard difference in how far different clubs send the ball, and the lower the number of the club
the farther the ball goes. So if I hit the six-iron 120 yards like I did on the last hole, I’ll need to
use the longer club that will hit it 30 more yards. That means a four-iron,” he said.
“I wouldn’t do that if I were you, Daddy,” Natalie said.
“Why not?” he asked.
Answer:
“On the first hole you hit a shot that normally would travel about 150 yards,” she
said. “That shot was into the wind. You hit a good shot, but it still only went 120 yards. So, the
wind reduced the distance of your shot by 30 yards, or a fifth.
“On this hole, we’re going the opposite direction, meaning the wind is behind us. So the wind
will add about one-fifth to the distance of your shot. So hit the club that normally makes the
ball go about 120 yards, and let the wind push it.
Since you usually hit the six-iron 150 yards, and each higher numbered club sends the ball 15
yards less, you should use an eight-iron.”
7. Cutting Corners
“Who wants to take drinks to the older boys?” Brandon’s father asked.
Voices called out: “Me! No, me! Me! I want to!”
Many of the players on Brandon’s soccer team had older brothers on the team that had just
finished the first half of their game. Brandon’s team was going to play a game on the same field
afterward, and his father, the coach, suggested that the entire team come early to watch the older
kids play.
It was a hot day, so Brandon’s team was behind a corner of the field in the shade. One of the
parents had brought a case of sports drinks for both teams to share. The older team was going off
to the opposite corner of the field, where there was also shade.
“We don’t need everybody to go,” Brandon’s father said.
“Ali, Jacob, Christian, Luis and Brandon, how about you take an armload of bottles each?”
I might as well be polite and go around the outside of the field, Brandon said to himself. But then
he saw the others cutting across the middle.
“Race you!” Jacob called and they all started running as fast as they could. Brandon continued
around the outside of the field and got to the older team last.
“I know I’m faster than them,” Brandon said to his older brother Victor as they handed out the
drinks.
“How did they beat me?”
Answer:
Victor said, “You were running faster than them—I could see that—but they had
less distance to cover. A straight line is always the shortest distance between two points.”
8. Go Take a Hike
Carla and Amanda’s family was vacationing at a national park one summer and decided to take a
hike down from the top of a gorge to see the river below. A sign said:
Three trails lead from here to different points along the river.
The trails do not join each other, and each takes approximately two hours to walk. Riverside Trail:
Steepest. Plan on taking 30 minutes down, 1 1/2 hours back. Scenic Overlook Trail: Medium
steepness. Plan on taking 40 minutes down, 1 hour 20 minutes back. Forest Path: Most level. Plan
on taking 1 hour down, 1 hour back.
Caution: No water available on the trails. Do not drink water from the river or any streams along
the way. Please carry water and use it wisely.
They saw another family that had just finished a hike. “How was it?” Carla asked.
“It was great,” the other family’s mother said. “But take that warning about water seriously. We’d
used one-third of our water when we got to the bottom, and that was just right.”
“What trail did you take?” Amanda asked.
Answer:
“They took the Scenic Overlook Trail,” Carla said. “The Forest Path takes the
same amount of time to walk back as to walk down—one hour each way. When you reach
the bottom of that trail, you’ve walked one half of the total—one hour out of two hours.
The Riverside Trail takes three times as long to walk back as to walk down—90 minutes
back versus 30 minutes down. When you reach the bottom of that trail, you’ve walked one
quarter of the total—30 minutes out of 120. The Scenic Overlook Trail takes twice as long
to walk back as to walk down—80 minutes back versus 40 minutes down. So when you
reach the bottom of that trail, you’ve walked for one third of the total—40 minutes out of
120.”
9. Mixing it Up
“We will see you all next week at our next meeting!” said Mrs. Jackson. She was the leader of a
mother-daughter book club that met at the library. “Wait, one more thing. We need someone to
bring drinks. Anybody?”
“I will,” Denise said. “I can bring punch.” “You’re always bringing things. Let me help you,” Mary
said as they were walking out. “My mother has a great recipe for punch. It’s half seltzer and half
orange juice.”
“Alright,” Denise said. “I’ll bring the juice, and you bring the seltzer.”
At the next meeting, Mary left a two-liter bottle of seltzer on the table and noticed that Denise
had brought in a two-quart container of orange juice. Denise emptied both ingredients into
the punch bowl as Mary helped set up the chairs. Denise brought Mary a cup of the punch. “I
really like the way your mother’s punch tastes,” Denise said.
“I’m sure I’ll like it too,” Mary said, taking the cup. “But it won’t taste quite the same.”
“Why not?” Denise asked. “We followed the recipe.”
Answer:
“The ingredients were the same, but the amounts weren’t,” Mary said. “The recipe
calls for half seltzer and half juice. We had two liters of seltzer and two quarts of juice. Liters
and quarts are close in size, but they’re not the same. A quart is 32 fluid ounces, while a liter is
33.8 ounces. That’s 1.8 ounces more in each liter. Multiply that by two, because there are two
liters, and that means there are 3.6 ounces more seltzer than juice.” Mary tasted it. “Actually, I
like it better this way than the way my mom makes it. With more seltzer, the punch has more
punch.”
10. Coupon Rate
Arianna was at the mall doing some shopping with Haley’s family. Arianna had brought along $20,
which she’d saved from her allowance so she could buy her sister a sweater as a birthday
present. That morning she’d seen one advertised in the newspaper for $19.95. The newspaper also
had a $1 off coupon, which she’d cut out.
They found the sweaters soon enough, but Arianna realized that she’d forgotten there was a sales
tax of 5.5 percent. She was worried that she wouldn’t have enough money.
“Can I borrow some change?” she asked Haley as they stood in line. “I’ll pay you back when I get
home.” “Sure, but can I look at that coupon first?” Haley replied.
“Okay, but what good will that do?” Arianna asked.
Answer: “It’s a question of whether they take the value of the coupon off the price
before they charge the taxes or after,” Haley said. “That does make a difference.” She
opened the calculator application on her cell phone. “To find how much 5.5 percent tax
adds to $19.95, multiply 19.95 times 1.055. That comes to $21.04725, which we’ll round up to
$21.05. So if you subtract a $1 coupon off that, you’ll need another nickel. “But let’s say they
take the value of the coupon off first. Now you’re paying tax only on $18.95. Multiplying
18.95 times 1.055 is $19.99225. Even if the store rounds up, your $20 would be enough.” As
she looked at the coupon again, Arianna was happy to see that the taxes were charged
after the value of the coupon was deducted. She didn’t have to borrow anything from
Haley after all.
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