The post Paper by the Pound appeared first on Bedtime Math.

]]>You can find paper in so many things: books, magazines, birthday cards, gift wrap. Even cereal and pasta boxes are made of paper, except it’s thicker. So our friend Ruby W. asked, how much paper do we use, anyway? One site says that America alone uses 69 million tons of paper and paperboard every year. Just to imagine how huge that is: a ton is 2,000 pounds, about half the weight of a car. Most books weigh a lot less than a pound, and magazines use even less paper. So even 1 ton is a huge stack of paper. The good news is, we can recycle paper. A machine chews it up and mixes it with liquids, smushes it, then rolls it back out as new paper. Every recycled ton of paper saves between 15 and 17 trees, and the energy saved could heat your home for 6 months. So as much as we love paper, let’s try to recycle and save some trees.

*Wee ones:* Look around the room. How many things do you see that use paper? Count as many as you can!

*Little kids:* Recycling a 3-foot stack of newspaper saves 1 tree! Is that stack shorter or taller than you? *Bonus:* If starting in October you heat your house for 6 months with the saved energy from 1 ton of paper, until what month does the heat last?

*Big kids:* If you recycle 10 pounds of paper each month, how much do you save in 1 year? Count up by 10s! *Bonus:* If your family recycles 60 pounds total of paper and cardboard, and twice as much of it is cardboard as paper, how much of each do you recycle?

*The sky’s the limit:* Do these webpages’ numbers make sense? If every ton of paper uses 16 trees, how many trees does 70 million tons use? (You can round to 70, and hint if needed: 16 is 2 x 2 x 2 x 2.)

Answers:

*Wee ones:* Different for everyone…see if you can count them all!

*Little kids:* Again, different for everyone…find out your own height in feet. *Bonus:* Until the same day of the month in April.

*Big kids:* 120 pounds, which is almost 1/16 of a ton…so you’ve saved a tree! *Bonus:* 40 pounds of cardboard and 20 pounds of paper. The cardboard is like 2 more sets of paper, so you have 3 sets of paper that add up to 60.

*The sky’s the limit:* 1,120,000,000 trees (1 billion 120 million). We double to 140 million, 280 million, 560 million, and finally 1,120 million. Scientists say Earth has more than 3 trillion trees, or about 3,000 times this number…so it all could be possible.

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]]>The post A Good Way to Get Dizzy appeared first on Bedtime Math.

]]>When it comes to naming things, sometimes we get lazy. A shoe for horses — a horseshoe. A house up in a tree — a treehouse. And the ride that goes round and round and makes us merry — a merry-go-round. But that really is the perfect name for it. Merry-go-rounds, also called carousels, are all silly, and all different. They have different numbers of animals; some have 2 levels instead of 1; and they turn at different speeds. Sometimes the animals stand 3 side by side, so there’s an inner ring, a middle ring and an outside ring. Usually when they do this, the smaller kinds of animals (like rabbits and foxes) go in the innermost ring, with the biggest animals on the outside. Today is National Merry-Go-Round Day, so hop on a pink and purple horse and ride until you’re dizzy. Then try doing the math about it!

*Wee ones:* If a merry-go-round has horses, giraffes, zebras, lions, cows, and tigers, how many kinds of animals does it have?

*Little kids:* If you ride the horse, then the zebra, then the lion, then the horse again to repeat, what do you ride next? *Bonus:* If on 1 spin of the merry-go-round you go up 6 times and down 6 times, how many movements do you make?

*Big kids:* If your horse goes up and down 6 times as you go around once, how many times do you go up and down on 4 spins? *Bonus:* If the animals are in rows of 3, how many rows do you need if you want to give seats to at least 50 people?

Answers:

*Wee ones:* 6 kinds of animals.

*Little kids:* The zebra. *Bonus:* 12 movements.

*Big kids:* 24 times. *Bonus:* You need at least 17 rows, because 16 rows will give you only 48 seats.

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]]>The post How Many Houses? appeared first on Bedtime Math.

]]>Our friend Alan D-S. asked us a great question: how many buildings are there in the world? And he means everything from teepees to skyscrapers. Well, no one has made a nice neat list of buildings for the whole world. Some countries count them up, while others don’t; even inside the countries who do, it’s usually cities and towns who keep track. But we can use math to make a good guess. The more people stuffed into a town, the more buildings they need – except when it gets so high that lots of people live in one tall building. Out on farmland there might be just 1 building every square mile, but in New York City, one street block 1/20 of a mile wide might have 20 buildings crammed into it. If we run the numbers, we can find a guess at least for the U.S. Just remember that might not work everywhere: we’re pretty sure Antarctica has more penguins than buildings!

*Wee ones:* Look at your home from the outside. Is it taller than it is wide, or wider than its height?

*Little kids:* How many people live in the building you call home? Talk about it worth a grown-up! *Bonus:* If a building has 7 floors with 10 people living on each, how many people live there?

*Big kids:* If a square city block has 5 buildings on each edge, how many buildings are on the whole block? (Remember, the corner buildings each sit on 2 sides!) *Bonus:* If 100 people live in each, how many people is that?

*The sky’s the limit:* The U.S. covers about 3,800,000 square miles, and about 1/3 of it has no people. If 1,000,000 have 1 building each square mile, another 1,000,000 have 4 buildings each, and the last 500,000 average 30 buildings each, how many buildings do we have? See if you can remember all the parts!

Answers:

*Wee ones:* Different for everyone…an apartment building is taller than wide, but a house (like a ranch style) could be wider than tall.

*Little kids:* Different again…count just your family for a single-family home, but an apartment building will have many more. *Bonus:* 70 people.

*Big kids:* 16 buildings, since each side adds 4 new ones. Another take: 5 on a side means 2 corner buildings and 3 middle ones; you have 4 of those sets of 3 plus the 4 corners. *Bonus:* 1,600 people.

*The sky’s the limit:* 20 million buildings (1 + 4 + 15). That could be low, as one site says we have more than 5 million office buildings only. Also, New York City has about 860,000 buildings for 8 million people; our country has at least 40 times as many people, which would give us 34 million buildings for all of them.

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]]>The post Dog Day of Summer appeared first on Bedtime Math.

]]>Today is National Hot Dog Day — or at least some people say so. Other calendars say it’s July 14. Where we *do* agree, though, is that 1) hot dogs are tasty, and 2) they aren’t good for you. That doesn’t stop us from eating them, as the numbers show. The average American eats 50 hot dogs a year, coming to more than 15 billion a year for the whole country! We eat 150 million of them just on the Fourth of July. 7-Eleven stores sell more hot dogs than anyone else, selling 100 million a year. Even though Americans love hot dogs, the food wasn’t invented here. Its other name is the “frankfurter,” because the first ones were made in Frankfurt, Germany way back in 1484. And based on how many we eat here, we’re glad the hot dog came to America.

Answers:

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]]>The post Ducks of a Different Color appeared first on Bedtime Math.

]]>When you think of ducks, what color are they in your mind? Are they white with orange beaks, or brownish with green shiny heads, or fluffy gray ducklings? These ducks here are wearing a whole other set of colors. They’re called black-bellied whistling ducks, but we love their pink beaks and the funny white ring around their cute little eyes. Their tummies are hidden underwater, but you can probably guess that those feathers are black. This was Picture of the Day on Wikimedia last week, so we can see them very nicely here — but we can’t hear them. They say these ducks are super loud: as their name tells us, they whistle to call each other. The live in Texas and Louisiana, so if you visit there, keep an eye and an ear out for these feathered friends.

*Wee ones:* Can you count the ducks in the picture? How many do you see?

*Little kids:* If 3 of those ducks swim up ahead, how many are left behind? *Bonus:* How many ways could the ducks split up into equal groups (with more than one in each group)?

*Big kids:* If a line of 30 ducks swims along, and every 3rd duck whistles and every 4th duck quacks, which ducks do both? *Bonus:* How many ducks don’t make either sound?

Answers:

*Wee ones:* 8 ducks.

*Little kids:* 5 ducks. *Bonus:* 2 ways: 2 groups of 4 ducks, or 4 groups of 2 ducks.

*Big kids:* The 12^{th} and 24^{th} ducks. *Bonus:* 15 ducks. The 3^{rd}, 6^{th}, 9^{th}, …up to the 30^{th} duck whistle (10 of them), while the 4^{th}, 8^{th}, 16^{th}, 20^{th}, and 28^{th} quack (5 more), because we already counted the 12^{th} and 24^{th}.

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]]>The post Happy Birthday, Snooty! appeared first on Bedtime Math.

]]>We people aren’t the only lucky ones who get to celebrate birthdays. Today Snooty turns 68 years old. Snooty is a manatee, a funny-looking sea animal with a big snout (they’re cousins of the elephant). He’s the oldest living manatee in “captivity,” meaning people take care of him. In fact, he might be breaking the record for all manatees living in the ocean, too. Normally these big, lumpy ocean creatures don’t live past 60 years. But Snooty has a pretty easy life. He swims around his pool, poses for pictures, and eats a nice healthy 80 pounds of lettuce and veggies every day. It doesn’t sound exciting to us, but it’s working for him.

*Wee ones:* If Snooty munches lettuce, then swims, then munches, then swims, then munches…what do you think he does next?

*Little kids:* If Snooty is 68 years old today, what was his age yesterday? *Bonus:* How old will he turn 2 years from today?

*Big kids:* Manatees spend about 1/2 the day sleeping. How many hours is that? (Reminder if needed: a day has 24 hours.) *Bonus:* If Snooty spends 1/3 of the rest of his time eating, how much time does he have left for swimming?

*The sky’s the limit:* Snooty weighs 1,000 pounds. If we count up the lettuce he eats, starting with the 80 pounds today, on what date will he have eaten his weight in lettuce?

Answers:

*Wee ones:* He swims.

*Little kids:* 67 years old. *Bonus:* 70 years!

*Big kids:* 12 hours. *Bonus:* 8 hours, since he spends 4 hours eating (1/3 of 12).

*The sky’s the limit:* On August 2. He needs 12 1/2 batches of 80 to reach 1,000. He finishes the 1st batch on July 21, so each batch’s number is 20 less than the date. He’ll eat batch 11 on July 31, then batch 12 on August 1, totaling 960 pounds. He will eat the final 1/2 batch on August 2.

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]]>The post Tower of Water appeared first on Bedtime Math.

]]>When you turn on the faucet, have you ever wondered where that water comes from? Or why it sprays out so fast? Water comes from many places, but to make it to your house, it first has to be pumped up into a water tower. It’s just a giant tank high up off the ground. When the water comes back down, it pushes down on itself and rushes through the pipes underground. So our friends Elijah and Shane S. asked us, how much water does a water tower hold, and why are water towers so high off the ground? The higher they are, the farther the water has to fall and the faster it goes. Water towers come in all sizes, but each holds about 1 day’s worth of water needed for its town. It can be a million gallons or more — that’s 50 times as much as a swimming pool!

*Wee ones:* Hold a glass under a faucet, turn on the water, and count “1 alligator, 2 alligator…” until it’s full. How many seconds (alligators) did it take? Try again running it faster!

*Little kids:* If it takes 1 minute to fill a big bucket of water from your faucet, but 10 minutes to fill your bathtub, how much longer did the tub take? *Bonus:* If your tub holds 40 gallons, how would you count those up counting by 10s?

*Big kids:* Can you “spell” the number 1 million in digits? *Bonus:* A fire hydrant gushes water really fast: up to 1,500 gallons a minute or more! If your pool party starts 20 minutes from now and your pool needs 28,000 gallons, will that hydrant fill it in time?

Answers:

*Wee ones:* Different for everyone’s faucet…see what you get!

*Little kids:* 9 minutes more. *Bonus:* 10, 20, 30, 40.

*Big kids:* 1,000,000. *Bonus:* Yes! The hydrant will put out 30,000 gallons.

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]]>The post The Buck Moon Stops Here appeared first on Bedtime Math.

]]>Hey, there’s a Buck Moon tonight! That is, there’s a full moon, which happens when the Moon is on the opposite side of Earth from the Sun. That’s why we see the moon’s shiny side. The fun part is, each full moon of the year has its own special name based on the time of year. Native Americans long ago named the full moons to help track the passing seasons. The July full moon was named after bucks (male deer), since this is when they grow new antlers. June’s full moon is called the Strawberry Moon for strawberry-picking season. May’s is called the Pink Moon thanks to a weird pink moss that grows. To top it off, a rare “blue moon” — 2 full moons in the same calendar month — can also happen. If you want to know what month it is, maybe it’s easier just to check your calendar.

*Wee ones:* What shape does a full moon look like?

*Little kids:* The Worm Moon happens in March. What month comes after that? *Bonus:* We’ve had just 1 full moon each month this year. How many full moons have we had including tonight?

*Big kids:* Full moons are 29 1/2 days apart. What’s the latest July date we could have a full moon and get a 2nd one that month? *Bonus:* The August full moon, The Sturgeon Moon (a type of fish), will happen on August 18. How many calendar days is that from tonight’s (July 19)?

*The sky’s the limit:* The next blue moon is coming on January 31, 2018! How many more full moons after tonight’s will we have before then?

Answers:

*Wee ones:* A circle (in real life it’s a ball, or “sphere”).

*Little kids:* April. *Bonus:* 7 full moons.

*Big kids:* July 2 (early in the day), putting the blue moon on July 31. *Bonus:* 30 days later, since August 19 is 31 days later.

*The sky’s the limit:* 18 full moons. We’ll have 5 more in 2016, another 12 in 2017, and then that first January one in 2018.

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]]>The post 3, 2, 1, Blast-Off! appeared first on Bedtime Math.

]]>How high can you jump? And how high can you lift something heavy, like a bowling ball? It’s hard work to lift things, whether it’s a toy or your own body, because gravity keeps pulling everything down. And the hardest one is the rocket, the biggest object we hurl into the air. It takes lots of burning fuel to launch a rocket: The old space shuttle weighed only 165,000 pounds, but the fuel to fly it weighed over 4 *million* pounds! A rocket burns 45,000 gallons of liquid hydrogen and 17,000 gallons of liquid oxygen every minute…just to compare, a car holds only about 20 gallons in total. Today a SpaceX Falcon 9 blasted off from Kennedy Space Center to bring supplies to the International Space Station. We’ve heard it costs another $10,000 for every extra pound a rocket brings to them…hopefully the astronauts don’t need a bowling ball.

*Wee ones:* If you toss a bowling ball, a model rocket and a paper airplane, how many toys do you toss?

*Little kids:* The last 10 seconds before a launch are the most exciting! Can you count down from 10 to 1? *Bonus:* Which is more, 8 thousand pounds or 4 million pounds?

*Big kids:* Astronauts on the Space Station see a sunrise every 90 minutes! If they see one at 8:30 at “night,” when do they see the next? *Bonus:* It takes about 150 seconds for a rocket to break out of the Earth’s atmosphere (the layer of air around Earth), and 2 minutes to burn all its solid fuel. Which happens first? (Reminder if needed: A minute has 60 seconds.)

Answers:

*Wee ones:* 3 toys.

*Little kids:* 10, 9, 8, 7, 6, 5, 4, 3, 2, 1! *Bonus:* 4 million pounds, because a million is a lot, lot more than a thousand.

*Big kids:* At 10:00. *Bonus:* The fuel happens first, because 2 minutes equals just 120 seconds.

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]]>The post What Does the Dolphin Say? appeared first on Bedtime Math.

]]>Lots of animals love to make noise, as we talked about the other day. But one of the coolest might be the dolphin. Our fan Mia G. asked, how far does a dolphin’s sound travel? (and sent this awesome drawing!) It turns out dolphins make all kinds of sounds: clicks, squeaks, whistles, and creaking noises. Bottlenose dolphins make as many as 2,000 squeaks per second; the sounds bounce off objects, telling the dolphins how far away they are. This works best within 700 feet. Along with that, dolphins make clicking sounds to talk to each other, and every dolphin makes its own special whistle sound that is different from all others’ (like fingerprints on us humans). Now the trick is to figure out what they’re saying!

*Wee ones:* If there are 5 dolphins in a “pod” (group) and 1 dolphin has a baby, how many dolphins are there now?

*Little kids:* If you get to feed the dolphins every other day starting on Sunday, what other days that week do you feed them? *Bonus:* Dolphins can leap up to 15 feet in the air! How high above your head is that (if you’re standing at pool edge)? Find your height in feet!

*Big kids:* If 20 dolphins are dancing and every 3rd one is waving its left flipper, how many at most could be doing that? (You can pick which dolphin is the 1st waver.) *Bonus:* It takes about 20 seconds to sing the ABCs. How many squeaks can a dolphin make in that time at 2,000 squeaks a second?

*The sky’s the limit:* If a dolphin creaks twice, whistles 3 times, then clicks 4 times, then squeaks twice again to start the pattern again, what’s the 200th sound it makes?

Answers:

*Wee ones:* 6 dolphins.

*Little kids:* Tuesday, Thursday and Saturday. *Bonus:* Different for everyone…subtract your height in feet from 15.

*Big kids:* 7 dolphins, if the 1st or 2nd dolphin waves (if it starts with the 3rd, the 18th will be last and you’ll have only 6). *Bonus:* 40,000 squeaks.

*The sky’s the limit:* A creak. The dolphin makes sounds in sets of 9, so you can find the biggest multiple of 9 that’s less than 200, then count up. Cool trick: multiples of 9 have digits that always add up to 9 or a multiple of 9. 198 is the biggest multiple less than 200, so the 200th sound is 2 sounds into the next set, which is a creak. Another way to find it: we know 18 is a multiple, and so is 180, then 189 and 198.

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