The post Don’t Hold Your Breath appeared first on Bedtime Math.

]]>If you’ve ever tried to hold your breath, you know how it gets harder and harder as time ticks by. Even after 10 seconds it’s tough, right? Your body needs air, so it will try to “inhale” (pull air in) no matter how hard you try not to. But sea creatures that need air can hold their breath a REALLY long time. Whales and dolphins are mammals, not fish, so they need air. So do seals, turtles, and penguins. And think about sea-diving birds: it’s hard to dive into water to grab fish for dinner if you have to keep coming up for air! Many of these birds can hold their breath for a whole 10 minutes, and the emperor penguin can hold it for 20. That’s about the same as a dolphin. But the whale is the winner: sperm whales can swim without breathing for almost 2 hours!

*Wee ones: *Try holding your breath and counting to 5 in your head! What numbers do you think?

*Little kids:* If you hold your breath for 10 seconds and count down from 10, what numbers do you say now? *Bonus:* If a seagull can hold its breath for 10 minutes but an emperor penguin can hold for 20, how many minutes longer can the penguin last?

*Big kids:* If a dolphin needs to store up air for 4 minutes before going under for 27 minutes, how long does that all take? *Bonus:* A sperm whale can hold its breath for 2 hours if resting, but 20 minutes less than that if it’s swimming hard. How long can it hold while swimming?

*The sky’s the limit:* If you could hold your breath for 20 minutes, and you can turn an underwater somersault every 15 seconds, how many somersaults can you do without taking a breath? (A minute has 60 seconds, and a hint if needed: first figure out how many somersaults you can do in 1 minute.)

Answers:

*Wee ones:* 1, 2, 3, 4, 5.

*Little kids:* 10, 9, 8, 7, 6, 5, 4, 3, 2, 1. *Bonus:* 10 more minutes.

*Big kids:* 31 minutes. *Bonus:* 100 minutes, since 2 hours is 120 minutes.

*The sky’s the limit:* 80 underwater somersaults, since you can do 4 per minute for 20 minutes.

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]]>The post Flash Those Feathers appeared first on Bedtime Math.

]]>Peacocks don’t do much all day, but whatever they do, they look great while doing it. This fancy bird is best known for its beautiful, super-colorful tail feathers. The feathers even have funny little dots on them that look like eyes. Sadly, only the boy peacocks have these splashy feathers, so they can show off for the lady peacocks, or “peahens.” Peahens are stuck with boring gray-brown feathers, but this helps them “camouflage,” or blend in with the colors around them as they sit on their eggs. At least no one’s chasing the peahens to pluck their feathers to make dressy hats! Peacocks have about 150 feathers…each year they shed their feathers and grow back even more new ones, so the older the peacock, the more he can show off.

*Wee ones:* If a peacock’s tail has blue, green, orange, black and white, how many colors is that?

*Little kids:* If a peacock takes 7 seconds to fan out his feathers, then shows them off for 2 seconds, how long does that all take? *Bonus:* If you have 10 pea-birds in total and there are 2 more peacocks than peahens, how many of each do you have?

*Big kids:* If a peacock has 150 feathers and 1 falls out, how many are left? *Bonus:* If every 3rd feather that’s left has an eye on it, how many eyes can there be at most?

Answers:

*Wee ones:* 5 colors.

*Little kids:* 9 seconds. *Bonus:* 6 peacocks and 4 peahens.

*Big kids:* 149 feathers. *Bonus:* 50 eyes, since you can start counting on the 1st or 2nd feather instead of the 3rd. Put another way, he could have had 50 eyes at most on the 150 feathers, but could have lost one of the feathers with no eyes.

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]]>The post Swimming in Hot Cocoa appeared first on Bedtime Math.

]]>As winter weather sets in, it’s a great time to warm up a cup of hot chocolate. Or hot cocoa – because those are two very yummy but very different drinks. Hot cocoa uses cocoa powder and sugar, like in the packets from the store. For hot chocolate, though, you melt down pieces of chocolate bar; the rich cocoa butter in them makes a thicker, richer drink. This enormous “cup” of hot cocoa mixed 87 pounds of powdered milk,1,108 pounds of cocoa, and a whopping 880 gallons of water! It took 3 hours and 16 minutes just to heat up the cocoa to 104 degrees F. As you see, they had to serve it in a swimming pool, which of course they shaped like a mug. So if you’re feeling chilly, you can drink some hot cocoa, or just jump right in and swim.

*Wee ones:* If you toss 7 mini marshmallows into your hot cocoa, what numbers do you say to count them?

*Little kids:* If you toss 5 mini-marshmallows into your cocoa and then eat 4 more on the side, how many do you get to enjoy? *Bonus:* If you make hot cocoa on Sunday and then every 3rd day after that, what number is the first cup you drink on a Tuesday?

*Big kids:* If the chefs started heating the cocoa at 2:39 pm and took 3 hours 16 minutes, did they finish in time for dinner at 6? *Bonus:* If you serve hot cocoa to 3 friends and you have 6 marshmallows, how many ways can you divide the marshmallows among them so each friend gets at least 1? (Don’t worry about the order of people, just the ways to split up the marshmallows.)

*The sky’s the limit:* How many people could have sipped hot cocoa from that 880-gallon pool, if each person got 1 cup? (Reminder: There are 16 cups in a gallon…and as a hint, multiplying by 16 is the same as 2 x 2 x 2 x 2, or doubling a number 4 times in a row.)

Answers:

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

*Little kids:* 9 marshmallows. *Bonus:* The 4th cup, since you’ll drink on Sunday, Wednesday, Saturday, and then keep going to Sunday-Monday-Tuesday.

*Big kids:* Yes! They will finish at 5:55 pm. *Bonus:* There are just 3 ways: 1-1-4, 1-2-3, and 2-2-2. that’s because once you give 1 marshmallow to each, the 3 remaining ones can be split up only 3 ways (0-0-3, 0-1-2, and 1-1-1).

*The sky’s the limit:* 14,080 people!

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]]>The post Polka Dot Dog appeared first on Bedtime Math.

]]>Dogs come in all kinds of patterns: solid color, multi-colored splotches, or a splash of white on the ears. But one of the cutest patterns might be spots, like on our friend the Dalmatian. These white dogs with black spots make people think of firefighters, but why? Is it because they look cute wearing a red firefighter’s hat? The real reason is that hundreds of years ago firefighters used horse-drawn carriages to pull the equipment to fight fires. They also needed dogs to help guide and calm down the horses. Dalmatians aren’t just for firefighters, though: lots of people have them as pets, thanks to the *101 Dalmatians* movies and books. If you’d like a friendly, high-energy dog, a Dalmatian might really light your fire.

*Wee ones:* Who has more spots, a Dalmatian puppy with 8 spots, or a puppy with 6 spots?

*Little kids:* If you see 3 Dalmatians, how many more ears than tails does the whole crowd have? *Bonus:* Dalmatians aren’t born with spots! The spots start showing up around 3 weeks after birth. If your pup is 10 days old, is it getting spots yet?

*Big kids:* In the movie *101 Dalmatians*, there’s a mom Dalmatian, a dad Dalmatian, and the rest are puppies. How many puppies are there? *Bonus:* If more than half of the pups are girls, what’s the fewest number of girl puppies they could have?

Answers:

*Wee ones:* The puppy with 8 spots.

*Little kids:* 3 more ears than tails. *Bonus:* No, because that’s just a little more than 1 week.

*Big kids:* 99 puppies. *Bonus:* 50 pups. Half of 98 is exactly 49, so if you add 1 more to the total, that pup has to be a girl too so they still outnumber the boys.

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]]>The post The Weight of Snow, in Chocolate appeared first on Bedtime Math.

]]>If snow is starting to fall where you live, you may be out there building a snowman or chucking snowballs at your friends — and you may notice how the really wet, sticky snow you can pack into shapes is also really heavy. How can those teeny specks falling from the sky weigh so much? Sue Heavenrich at Archimedes Notebook wondered about this, too. She figured out that a snowflake can weigh as much as 1/50th of a gram, and that 235 flakes weigh the same as a Hershey’s chocolate kiss. If you imagine 95 Hershey’s kisses, which weigh about 1 pound, they weigh the same as more than 22,000 snowflakes. Other people have weighed snow by the inch: if you shovel 10-inch-deep snow off a 50-foot stretch of sidewalk, you’re moving about 1,300 pounds of snow! Hopefully you can build a snowman with less than that.

*Wee ones:* Which weighs more, a snowflake or 1 Hershey’s kiss?

*Little kids:* If you love to eat snow, and you take a bite of snowball, then eat a Hershey’s kiss, then a bite of snow, then a kiss…what do you eat on your 8th bite? *Bonus:* If you count out 95 Hershey’s kisses, what number do you say before 95?

*Big kids:* A 5×5-foot square of sidewalk with 1 inch of snow weighs about 25 pounds. How many sidewalk squares would you have to shovel to match your weight in snow? *Bonus:* If you eat 2 Hershey’s kisses, how many snowflakes would you have to eat to match that weight?

Answers:

*Wee ones:* A Hershey’s kiss.

*Little kids:* A Hershey’s kiss, as on all even-numbered bites. *Bonus:* 94.

*Big kids:* Different for everyone…see how many 25s add up to your weight in pounds (or more). *Bonus:* 470 snowflakes.

And thank you Delilah B. for sharing this topic and post with us!

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]]>The post A Bed for Rover, Fluffy, and You appeared first on Bedtime Math.

]]>When you’re really tired, it’s so nice to flop down on your comfy bed. Well, dogs and cats like our beds, too. Some people don’t want to share their bed with scratchy paws and wet noses, but some pet lovers are just fine with it. One couple with 5 cats and 2 dogs finally built a new bed to hold them all! The megabed stretches almost 11 feet across, and fills up half the bedroom. They made it by shoving together a king-size bed and a full bed, then filling in the gap between them. We’re just amazed all those cats and dogs get along so well.

*Wee ones:* If you count up the 5 cats, what numbers do you say?

*Little kids:* If the 2 humans, 5 cats and 2 dogs all sleep in the bed, how many animals is that? (We humans are animals, too!) *Bonus:* If the humans wash the sheets every 4 days and the last time was Tuesday, on what day do they wash them next?

*Big kids:* When the 2 humans, 5 cats and 2 dogs are all in the bed, how many legs are kicking around? *Bonus:* If the bed has just 2 pillows and 2 animals get to use them that night, how many pairs of people vs. dogs vs. cats could there be? (You don’t need to worry about the order, nor which person, cat or dog you’re talking about — just the type).

*The sky’s the limit:* What if you have 3 pillows? What are all the possible triplets of animal types who could use them? (Again, no need to worry about the order or the names — just the types (species).)

Answers:

*Wee ones:* 1, 2, 3, 4, 5.

*Little kids:* 9 animals. *Bonus:* On Saturday.

*Big kids:* 32 legs: 28 pet legs and 4 people legs. *Bonus:* 6 possible pairs. There are at least 2 of each type of animal, so there are 3 pairs where both are the same (2 people, 2 cats, 2 dogs). Then you can pick one of each, giving you 2 pairs that include a person (P-C, P-D), plus C-D.

*The sky’s the limit:* There are 8 possible sets of pillow users:

– There’s only 1 case where all 3 users are the same: 3 cats (since there are only 2 people and 2 dogs).

– There are 6 cases where 2 animals are the same and 1 is different: 2 people with a cat, 2 people with a dog, 2 cats with a person, 2 cats with a dog, 2 dogs with a person, 2 dogs with a cat.

– Then you have just 1 case where there’s 1 of each type of animal: person, cat, dog.

The post A Bed for Rover, Fluffy, and You appeared first on Bedtime Math.

]]>The post A Surprise Inside a Surprise Inside a… appeared first on Bedtime Math.

]]>Have you ever seen those little wooden dolls that split open to show another little doll inside, then another inside that one? Ever wonder what they’re called? They’re matryoshka dolls, which were first made in Russia starting in 1890. Matryoshka means “little mom,” and the outside doll is always a woman, but the inside ones can be boys or girls. The big one is usually painted with colorful loopy designs, and if you twist the top half off the bottom, inside is another version of herself, except smaller. Inside that one there’s a third even smaller one, then another inside that one, and so on till you get down to the last teeny doll, which usually doesn’t open at all. Sometimes even the baby has the pattern, because she likes to look good whenever she actually gets out.

*Wee ones:* If your matryoshka doll has 4 more dolls inside it, how many dolls are in the set all together?

*Little kids:* If you’re counting your 7 matryoshka dolls and you’ve counted 2 so far, what numbers do you say to count the rest? *Bonus:* If every other doll in a set of 9 is a girl, how many boys are there? (Remember: the biggest matryoshka is always a girl!)

*Big kids:* If you have 6 dolls and the biggest doll is 6 inches tall, and each doll is 1/2 inch shorter than the next, how tall is the baby? *Bonus:* How many ways could 3 doll sets give you 10 dolls, if every set has at least 2? (Don’t worry about the order, just the combinations of sizes.)

*The sky’s the limit:* If you have a 10-doll set, then get a 9-doll set, an 8-doll set, and so on down to a single wooden baby, how many separate dolls do you have in total? Can you come up with a shortcut to figure it out?

Answers:

*Wee ones:* 5 dolls in total.

*Little kids:* 3, 4, 5, 6, 7. *Bonus:* 4 boys.

*Big kids:* 3 1/2 inches tall. You go down 5 steps to get to the baby, or 2 1/2 inches. *Bonus:* Just 4 ways: 2-2-6, 2-3-5, 2-4-4, and finally 3-3-4. All other combinations are just those in a different order.

*The sky’s the limit:* 55 dolls. This is a “triangle number,” meaning you’re adding a string of numbers that could stack on each other like a pyramid: 1 on top, then 2 under it, then 3 under those. Notice that when you add 1+2+…+9+10, the 10 and the 1 make 11, and so do the 2 and 9, and the 3 and 8…you end up adding 5 11’s, giving you 55.

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]]>The post Throw Those Snowflakes! appeared first on Bedtime Math.

]]>With December finally here, you might get a snowfall very soon. Snow means snowball fights, so our fan Lucas W. asked, how many snowflakes are in a snowball? We love this kind of question, because it’s way easier to use math than to count the flakes! For starters, Sue at this web page tells us that 50 snowflakes weigh 1 gram, the weight of a paper clip. There are about 28 grams in an ounce (about half a candy bar) and 16 ounces in a pound, so 1 pound of snow has 50 x 28 x 16 flakes, or 22,400 snowflakes. That’s a pretty heavy snowball, but as Lucas pointed out the world’s largest snowball was more than 10 feet across. Better get out of the way from that one!

*Wee ones:* Snow (if it’s clean) is white. Find 5 white things in your room.

*Little kids:* If a snowflake has 6 sides, how many more sides does it have than a square? *Bonus:* If snowflakes fly by and you catch the 3rd one on your tongue, then the 6th, then the 9th…which one do you think you catch next?

*Big kids:* If you catch 300 snowflakes (the weight of 6 paper clips), what numbers would you say to count up by 50s? *Bonus:* If your 1st snowball has 19,000 snowflakes, your 2nd has 37,000 snowflakes, and your 3rd’s number of snowflakes is halfway between, how many flakes does your 3rd snowball have? (Hint: You can ignore the thousands and work with the smaller numbers first, then multiply your answer by 1,000).

Answers:

*Wee ones:* Items might include paper, bed sheets, pillows, socks, or tissues.

*Little kids:* 2 more sides. *Bonus:* The 12th snowflake, since it’s every 3rd flake.

*Big kids:* 50, 100, 150, 200, 250, 300. *Bonus:* 28,000 flakes.

The post Throw Those Snowflakes! appeared first on Bedtime Math.

]]>The post Gold on Fire appeared first on Bedtime Math.

]]>The shiniest spot on the Statue of Liberty is the flame on her torch. It’s made of copper inside, but coated in a thin layer of gold, like a lot of our jewelry. So Bedtime Math fan Emerson S. asked, how *much* gold is on that flame? The torch stands more than 300 feet off the ground, so it’s bigger than it looks. It’s about the same height as the Statue’s pointy finger, which is 8 feet tall. But gold can be pounded really, really thin: 1 ounce of gold, which is 1/2 the weight of a candy bar but only the size of a quarter, can spread to cover 100 square feet — about the size of your bedroom floor! Thankfully, jeweler Kristen Reyes found the actual answer: the torch is covered in 5,000 little 3-inch squares that weigh less than 6 ounces total. We think the Statue likes that more than a pair of earrings.

*Wee ones:* Who’s taller, you or that 8-foot-tall flame? Find out your height in feet!

*Little kids:* If you can make 2 gold earrings from each ounce of gold, how many earrings can you make from 2 ounces? *Bonus:* If half of the 6 ounces of gold on the torch peeled off, how much would be left on there?

*Big kids:* The “surface area” around a ball is always 4 times pi (3.14) times the radius times the radius again, where the radius is 1/2 the distance across. What’s the surface area of the Statue’s 8-foot flame? (You can round pi to 3.) *Bonus:* If you peeled off one of those 5,000 sheets of gold for yourself, how many would be left?

Answers:

*Wee ones:* The flame is taller…almost no people are 8 feet tall!

*Little kids:* 4 earrings. *Bonus:* 3 ounces.

*Big kids:* About 192 square feet, without the fingers of flames. *Bonus:* 4,999 sheets.

The post Gold on Fire appeared first on Bedtime Math.

]]>The post Last Chance for Pumpkins appeared first on Bedtime Math.

]]>November is coming to an end and fall is about to turn into winter, at least for people living on the north half of our planet. So what do you do with all those leftover pumpkins? You can make breads, pies, and soup with the fleshy part, but you’re still left with those giant gobs of goopy seeds inside. The good news is, you can turn that goop into a tasty, crunchy snack: roasted pumpkin seeds. How? Rinse them under running water to rub off all the stringy fibers. Once the seeds are dry, have a grown-up heat the oven to 400 degrees, and spread the seeds on a lightly greased baking sheet. Bake them for 15 minutes, then sprinkle them with whatever seasonings you like: salt, sugar, cinnamon, chili powder, a squirt of lime. Then you just have to decide what to do with the rest of that 80-pound pumpkin.

*Wee ones:* If you sprinkle a pumpkin seed with salt, then the next with sugar, then the 3rd with cinnamon, then start over with salt, then sugar, then cinnamon, then salt…what’s next?

*Little kids:* If you scoop out 8 slippery pumpkin seeds but 3 of them squirt onto the floor, how many are left in your hand? *Bonus:* If you have 3 big pumpkins and each one has 200 seeds inside, how many seeds do you have for roasting?

*Big kids:* If you start roasting your seeds at 3:20 for 15 minutes, at what time do they finish? *Bonus:* If you want to roast 300 seeds and every pumpkin has 80 seeds, at least how many pumpkins will you need to scoop enough seeds?

Answers:

*Wee ones:* Sugar.

*Little kids:* 5 seeds. *Bonus:* 600 seeds.

*Big kids:* At 3:35. *Bonus:* 4 pumpkins, since the first 3 will give you only 240 seeds.

The post Last Chance for Pumpkins appeared first on Bedtime Math.

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