The post Sleeping in the Ice Hotel appeared first on Bedtime Math.

]]>If your town is in the thick of winter and you’re feeling chilly, think about the people sleeping tonight in the Ice Hotel. Built every winter in Quebec, Canada, the Ice Hotel is exactly what it sounds like: a sparkling hotel totally made of ice and snow. The smooth, almost-clear blocks of ice gleam a faint blue, and are held together with 15,000 *tons* of packed snow. Even your bed is a block of ice, with a deerskin over it to make it comfy (we’ve tried it). It’s less than 30 degrees F inside the hotel, since of course there’s no heat. So you sleep on that deerskin in a subzero sleeping bag — and just in your underwear, to avoid sweaty, chilly PJs. There are also Ice Hotels in Norway, Sweden and Switzerland. So if you’ve wondered what it’s like to stay in an igloo, you have several freezing cold places you can try.

*Wee ones:* If you’ve visited 2 of the Ice Hotels, then visit 1 more, have you visited all of them?

*Little kids:* If your bed is a layer of 6 blocks topped by a layer of 4 bigger blocks, how many blocks did they need to “make” your bed? *Bonus:* If they build the Ice Hotel in December and it finally melts in March, during how many months can you stay there?

*Big kids:* If an ice block takes up 3 cubic feet of space, but the fluffy snow they melted to make it took up 6 times as much space, how many cubic feet of snow made that block? *Bonus:* If the wall of your hotel room is 9 ice blocks wide and 9 block layers high, how many blocks are in that wall?

*The sky’s the limit:* At the Ice Hotel, even drinks are served in “glasses” made of ice. If you need 2 cups of water to make a small ice glass and 3 cups to make a large one, how many glasses can you make from 60 cups of water, if you make the same number of each size?

Answers:

*Wee ones:* No, because you’ve seen 3 and there are 4.

*Little kids:* 10 blocks. *Bonus:* 4 months.

*Big kids:* 18 cubic feet of snow. *Bonus:* 81 blocks.

*The sky’s the limit:* 12 glasses of each size. Each pair of small-and-large uses 5 cups water total, so 60 cups will let you make 12 sets.

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]]>The post Stacking Lego to the Sky appeared first on Bedtime Math.

]]>Lego, those colorful, clicking, bumpy toy bricks, lets you make just about anything you can think up. And if you have enough bricks, you can really go big. So our friends Mikey and Mateo C. asked, how many would it take to reach the top of the Empire State Building? Well, to start we need to know its height. For a long time it was the tallest building in the world, from 1931 until the first World Trade Center went up in 1970. Now we have to decide whether to count just the building itself, which is 1,250 feet, or to the top of its antenna, which stands 1,454 feet high. Let’s go with the whole shebang for fun. Lego bricks are 9.6 millimeters thick, just shy of 1 centimeter (a bit less than 1/2 inch). So 1,000 Legos are 9.6 meters tall, or 31 1/2 feet – and that’s only 2 or 3 floors! Let’s find out how much Lego we need to build to the sky.

*Wee ones:* If you stack red, green, blue, yellow, and white Lego pieces, how many colors is that?

*Little kids:* If you’re stacking a 10-brick chunk and you have 8 bricks so far, how many more bricks do you need? *Bonus:* If you speed things up by stacking 100-brick chunks up to 900 bricks, what numbers do you say to count up by 100s?

*Big kids:* If you have 9 blue bricks, and your stacking pattern is red, blue, yellow, blue, blue, do you have enough blues to keep up that pattern for 15 bricks? *Bonus:* If we round off and say 1,000 Legos stack 30 feet tall, and the Empire State Building stands about 1,500 feet tall, how many bricks do we need to stack — and will our guess be over or under the real number?

Answers:

*Wee ones:* 5 colors.

*Little kids:* 2 more bricks. *Bonus:* 100, 200, 300, 400, 500, 600, 700, 800, 900.

*Big kids:* Yes! You need 3 sets of that 5-brick pattern, each of which has 3 blues, and 3 x 3 = 9. *Bonus:* 50,000 Legos, since you’ll need 50 sets of 30 feet, and there are 1,000 Legos per set. But 1,000 Legos stand taller than that, so you’d need fewer sets — plus the building is shorter than 1,500. So our guess is over the real number, 46,165 bricks (rounding up from 46,164 1/2).

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]]>The post A Surprise Top Dog appeared first on Bedtime Math.

]]>People who love to run love to see who can run fastest. So we have races as short as a 50-yard dash to as long as a 26-mile marathon. It takes hard work to get ready to run even a half-marathon, but a dog in Alabama ran one by *accident*. A bloodhound named Ludivine had stepped outside of her house, somehow found the trail for the half-marathon race that was happening, and ran the whole thing along with 165 human runners. She came in 7th place, and was the fastest “girl” runner. Ludivine did the whole race in just an hour and a half, even though she stopped to pee, sniff animals in the forest, and drink from puddles. Most of the humans couldn’t beat her even without doing those things!

*Wee ones:* If Ludivine finished 7th, how many runners finished before her? See if you can count them up!

*Little kids:* If you went running with Ludivine, how many more legs than noses would you have all together? *Bonus: *If she had started the race at 2:00 and ran for exactly 1 1/2 hours, when would she have finished?

*Big kids:* If Ludivine finished 7th out of 166 total runners, how many people finished after her? *Bonus:* If a marathon is 26 and 2/10ths miles long, how long is a half-marathon?

*The sky’s the limit:* If a bunch of humans, dogs, and squirrels all ran a race together, and there are 23 dogs and squirrels put together, 101 squirrels and people put together, and 120 people and dogs together, how many of each ran the race?

Answers:

*Wee ones:* 6 runners (1, 2, 3, 4, 5, 6).

*Little kids:* 4 more, since you’d have 6 legs but just 2 noses. *Bonus:* At 3:30.

*Big kids:* 159 runners. *Bonus:* 13 and 1/10th miles.

*The sky’s the limit:* 2 squirrels, 21 dogs, and 99 people.

– If there are 23 dogs and squirrels, but 101 people and squirrels, then swapping in people for dogs raised the total by 78. There are 78 more people than dogs.

– But those two together add up to 120. That means if there were only as many people as dogs, and you didn’t add those extra 78, you’d have 42 people and dogs in equal numbers. That gives you 21 dogs.

– From there, if dogs and squirrels make 23, we have 2 squirrels. And if there are 78 more people than dogs, there are 99 people.

(Of course, you can say all of this faster with algebra:

s + d = 23, so s = 23 – d

s + p = 101

d + p = 120

Substituting for s in the second one, we get

(23 – d) + p = 101, so 23 + p = 101 + d, so p = 78 + d (take away 23 from both sides)

d + p = 120, but that p = 78 + d, so…

d + 78 + d = 120

2d + 78 = 120 (to simplify it)

2d = 42

d = 21, so there are 23 – 21 = 2 squirrels, and 21 + 78 = 99 people.)

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]]>The post Who Has How Many Humps? appeared first on Bedtime Math.

]]>Camels are known for a couple of weird things. For one, they have that strange hump on their backs — or is it two humps? It turns out there are 2 living “species” or types of camel: the dromedary, which has 1 hump, and the bactrian camel, which has 2 humps. Their four camel-like cousins have the same long neck and legs, but aren’t quite as lumpy: the alpaca, llama, guanaco, and vicuña (that last one lives in South America). Also, camels can go for days without drinking water, even in the hot dry desert. But they don’t keep extra water in their hump, like people used to think. The hump is just a big lump of fat: it stays up there because it if were spread as a layer all around their bodies, they’d be too hot in the desert. Camels aren’t super friendly — they’re known to spit at you if they get annoyed — but if you can climb up on one, you can enjoy a nice bumpy ride.

*Wee ones:* Who has more humps, a dromedary or a bactrian camel?

*Little kids:* A grown-up camel stands 6 feet tall at the shoulder, but its hump is 1 foot higher up than that. How high is the top of its hump? *Bonus:* If 2 dromedaries and 2 bactrian camels go for a walk, how many humps do they have?

*Big kids:* Camels can live for 50 years. How many years from now will you match that? *Bonus:* If you have 20 humps in the room, and there are twice as many bactrian camels (2-humped) as dromedaries, how many of each animal do you have?

Answers:

*Wee ones:* The bactrian camel, since it has 2 instead of 1.

*Little kids:* 7 feet. *Bonus:* 6 humps.

*Big kids:* Different for everyone…subtract your age in years from 50, or maybe you’ve already passed it! *Bonus:* 4 dromedaries and 8 bactrian camels. Each “set” of a dromedary plus 2 bactrian camels has 5 humps, and there are 4 sets of 5 humps in 20.

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]]>The post Don’t Blink, or You’ll Miss the Movie appeared first on Bedtime Math.

]]>You might not even notice it, but every minute you’re awake, you have to blink your eyelids. Your body does this without you even trying, and for a few reasons. Blinking keeps our eyes wet, pushes dust out of the way, and gives our brains quick, restful breaks from looking at stuff. So our friend Alexis V. asked, how many times do we blink while watching a movie? (And happy birthday Alexis!) To figure that out, we need to know how many times we blink in 1 minute, and that depends on what we’re doing. We normally blink 15-20 times per minute, which means our eyes are closed about 1/10th of our whole time awake. BUT scientists have found that we blink less often when we’re watching something interesting — like a movie. That said, even if we drop to 10 blinks a minute, over a 2-hour movie our minds will still get lots of breaks, as we’ll find out when we do the math.

*Wee ones:* If you blink 8 times, what numbers do you say to count those blinks?

*Little kids:* Kids blink less often than grownups — you blink faster and faster until you’re 14! How many years from now is that for you, or how long ago was it? *Bonus:* Babies blink only 2 times a minute. How many minutes does it take for them to blink 6 times?

*Big kids:* If a movie lasts 2 hours, how many minutes of blinking is that? *Bonus:* If you then blink 10 times every minute, how many times do you miss out on little bits of the movie?

*The sky’s the limit:* If a kid blinks only 2/3 as often as a grown-up, and blinks 20 times less during a Youtube video, how many times does each person blink?

Answers:

*Wee ones:* 1, 2, 3, 4, 5, 6, 7, 8.

*Little kids:* Different for everyone…count up to find the years until you’re 14, or count down from your age to 14. *Bonus:* 3 minutes.

*Big kids:* 120 minutes. *Bonus:* 1,200 times.

*The sky’s the limit:* 60 times and 40 times. If the kid blinks only 2/3 as much, then the difference in their blink counts will be 1/3 of the grownup’s total. We know that difference is 20, so the grownup must blink 60 times, and from there the kid will blink 40 times.

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]]>The post Backpack-Busting Books appeared first on Bedtime Math.

]]>Books are very heavy for their size. After all, they’re basically chunks of wood, just pressed into thin sheets of paper. So our friend Genevieve B. asked, how big is the world’s *biggest *book? Turns out there’s more than one answer, because it depends what you mean by “book.” If we mean a bunch of paper pages stuck together, the Guinness World Record goes to “This the Prophet Muhammed,” a 16-foot tall, 13-foot wide giant with 429 pages. That’s a huge book! Also, the book that explains Brazil’s rules for paying taxes (money to help run the country) is ridiculous: it’s 6 feet 10 inches tall, and has more than 41,000 pages that size. But if the book can be made of something other than paper, the heavyweight winner might be “The Pali Canon” (Buddhist scripture), whose 1,460 pages are actually 5-foot stone tablets. Let’s hope you never need to carry *those* in your backpack.

*Wee ones:* Which is taller, the 5-foot stone “book” or the 6-foot paper book?

*Little kids:* If you can reach 6 feet high off the ground, how many feet taller is the 16-foot tall book? *Bonus:* If Richard Scarry’s “Biggest Word Book Ever” is 2 feet tall, how many would you have to stack end to end to match the 16-foot book?

*Big kids:* When you open that 13-footwide book, it becomes twice as wide! How far across the “table” would it stretch? *Bonus:* Brazil’s tax code weighs “several tons.” If it weighs 4 tons and you can carry 10 pounds on your back, how many kids like you would it take to carry the Brazil book? (Reminder if needed: A ton equals 2,000 pounds.)

Answers:

*Wee ones:* The 6-foot book.

*Little kids:* 10 feet taller. *Bonus:* 8 of them.

*Big kids:* 26 feet — as wide as a small house. *Bonus:* 800 kids, since the book weighs 8,000 pounds!

And thank you Genevieve for a real page-turner of a math problem!

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]]>The post “Answer Your Cat’s Questions” Day appeared first on Bedtime Math.

]]>As we know, they’ve come up with a day for everything, so it’s no surprise someone came up with “Answer Your Cat’s Questions” Day. After all, don’t we wonder what the heck cats are thinking? Of all animals kept as pets, cats are most likely to think they’re the boss of the house, even though we actually feed them and take care of them. In fact, they seem to think we should feel lucky to do all that work. But even so, these beautiful furry friends of ours might need our help explaining some things. They’re not super-smart: their brains are less than 1/100th of their whole body weight, while for us humans it’s more than double that fraction. So if cats could talk, they might have lots of things to ask. So today’s our big chance to give them some answers.

*Wee ones:* “Hey, you! Where’s my dinner?” If you’ve taken 6 minutes to set up the cat’s food and you need 1 more minute to finish, how many minutes total does the cat wait?

*Little kids:* “I’ve caught 9 mice for you this week — whaddaya have for me? How about a treat for every other mouse?” If you agree to this deal and start with mouse #1, how many treats does your cat get? *Bonus:* If your cat talks you into 9 treats instead, how many more treats is that?

*Big kids:* “Hey look, I unraveled 52 feet of yarn! How much is left?” If you started with an 80-foot ball of yarn, how much is left? *Bonus:* “When are you going to get the dog out of here?” If it’s 2:43 pm and your dog goes out for a walk at 6:15 every night, how long does the cat have to wait?

Answers:

*Wee ones:* 7 minutes.

*Little kids:* 5 treats: for mouse # 1, 3, 5, 7, and 9. *Bonus:* 4 more treats.

*Big kids:* 28 feet. *Bonus:* 3 hours and 32 minutes.

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]]>The post How to Lose Weight – in Your Sleep! appeared first on Bedtime Math.

]]>Did you know that you lose weight overnight? Sure, when you run or jump around or do other exercise, you lose weight because you burn off fat. But what’s going on in your sleep? You lose weight because you lose water. Every time you breathe out, you lose water vapor, as lots of teeny tiny droplets. You also sweat out some water through your skin. Water is heavy: a cup of water weighs 1/2 pound. If you weigh yourself right before bed (after peeing) and again when you wake up (before peeing in the morning), you’ll see that you lost weight! Grown-ups can lose more than a pound just lying there. Try weighing yourself before and after sleeping, and see what you find out!

*Wee ones:* Put a small amount of water in a cup, and drink it as you count your gulps. Now try putting about twice as much water, and count again taking the same size gulps. Did you take more gulps?

*Little kids:* If 2 cups of water weigh 1 pound, how much do 4 cups of water weigh? *Bonus:* How much do you weigh in pounds? If you then drink 1 pound of water, how much do you weigh on the scale afterwards?

*Big kids:* If you let out a breath every 5 seconds while sleeping, how many times do you breathe out in 1 minute? Count up by 5s if it helps! (*Reminder:* A minute has 60 seconds.) *Bonus: *Then how many times do you breathe out in 1 hour? (An hour has 60 minutes…and multiplying by 60 is like multiplying by 2 x 3 x 10.)

*The sky’s the limit:* And now…if you sleep 8 hours, how many times do you breathe out water overnight? (*A trick if needed:* 8 is 2 x 2 x 2, so to multiply a number by 8 you can double the number, then double it again, then double it again.)

Answers:

*Wee ones:* See how many gulps you get each time!

*Little kids: *2 pounds. *Bonus: *Different for everyone…find your weight in pounds, then add 1.

*Big kids:* 12 times. *Bonus:* 720 times.

*The sky’s the limit:* 5,760 times!

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]]>The post Look Out for Penguins appeared first on Bedtime Math.

]]>You probably know today is Martin Luther King Jr. Day, but we bet you didn’t know it’s also Penguin Awareness Day. After all, you probably don’t think about penguins very often, because how many penguins do you have wandering around in your life? Almost all of the 17 types live only on the southern half of our planet, in and near Antarctica. And did you ever wonder why they all look like they’re wearing cute black and white suits? It’s “camouflage,” or coloring that helps them hide by looking like their surroundings. When they swim, their black backs match the dark ocean to animals looking down from the sky; for animals looking up at them, the penguins’ white bellies blend with the sunshine coming down through the water. But because their attackers usually come from the water, penguins aren’t afraid of land animals like people, and will walk right up to you — if you’re okay with visiting that Antarctic weather.

*Wee ones:* The tallest penguins, emperor penguins, stand 4 feet tall. Is that taller or shorter than you?

*Little kids:* Penguins can’t fly, but like all birds they each have 2 wings. How many wings do 3 penguins have? *Bonus:* How many more penguins do you need to have 8 wings in total?

*Big kids:* If penguins are taking a nap, and most lie with their white bellies up but every 3rd penguin starting with the 3rd has its black back facing up, what number penguin is the 11th one with its belly up? *Bonus:* On top of Penguin Awareness Day, we’re also going to have World Penguin Day on April 25. If you’re reading this on January 20, how many days will we wait for World Penguin Day? (Waiting until tomorrow would count as 1 day.)

Answers:

*Wee ones:* Different for everyone…find out your height in feet!

*Little kids:* 6 wings. *Bonus:* 1 more penguin, to make 4 birds in total.

*Big kids:* The 16th. The first 10 belly-up penguins are from the first 5 sets of 3, or the first 15. *Bonus:* 96 days. We wait 5 days until January 25, then 31 until February 25, 29 more until March 25 (leap year!), and then 31 more to April 25.

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]]>The post The Greatness of Guinea Pigs appeared first on Bedtime Math.

]]>Guinea pigs are among the furriest, funniest pets you can have. So our friend Katherine T. asked, how many guinea pigs are there in the world? (and sent a guineapigalicious drawing!) It’s tricky even to count up the world’s dogs, much less guinea pigs. But we found some numbers. There were 1,362,000 pet guinea pigs in America in 2007 (that’s more than a million), and another 1 million in England in 2012. There were also 30 million “small mammal pets” in all of Europe in 2010, but that could include mice, hamsters, and gerbils. If 1/10 of those were guinea pigs, that would give us another 3 million. It’s safe to guess there are at least 5 million guinea pigs. They often live in pairs, though…so how many houses have one?

*Wee ones:* If you just got your 3rd pet guinea pig, how many did you have before that?

*Little kids:* If 3 houses on your street have 2 guinea pigs each, how many guinea pigs live on your street? *Bonus:* How many more guinea pigs would you all need to have 10 in total?

*Big kids:* How many furry feet do 5,000,000 guinea pigs have? *Bonus:* Guinea pigs love carrots. If starting on a Sunday you give your guinea pigs carrots every 3rd day, how many times have you given them carrots when they first eat them on a Tuesday?

*The sky’s the limit:* If 5,000,000 pet guinea pigs live in pairs, how many households have guinea pigs?

Answers:

*Wee ones:* 2 guinea pigs.

*Little kids:* 6 guinea pigs. *Bonus:* 4 more guinea pigs.

*Big kids:* 20,000,000 feet. *Bonus:* On the 4th time (Sun, Weds, Sat, Tues).

*The sky’s the limit:* 2,500,000 (2 million, 500 thousand).

And thank you again Katherine for the question and the guineapigalicious artwork!

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