The post The Bird That Really Turns Heads appeared first on Bedtime Math.

]]>When you look around the room or read a book, your eyes roll from side to side in their sockets, so you can see without turning your head. If you were an owl, though, you’d be stuck. Owl’s eyes can’t move in their sockets. So every time an owl wants to look at something, he has to turn his whole feathery head in that direction. Luckily, owls can turn their heads all the way past their own shoulders, in either direction! A full turn of a circle is 360 “degrees,” and an owl can turn 135 degrees to the left and 135 to the right, letting him see a whopping 270 degrees total around them. Add their amazing sense of hearing and their silent wings, and you’ve got one fierce hunter — although he’ll still have trouble reading a book.

*Wee ones:* If an owl looks left, then right, then straight ahead, then left again, right, ahead, then left again…what comes next?

*Little kids:* If an owl catches a mouse, how many legs do they have together? *Bonus:* Many owls are “nocturnal:” they stay awake at night. If an owl goes to bed at 5 in the morning and wakes up at 7 at night, how long does he sleep? (Hint if needed: How many hours from 5 in the morning to 5 in the afternoon?)

*Big kids:* The world’s smallest owl, the Elf Owl, is only 5 inches tall. How many Elfs would have to stack on top of a 33-inch-tall Great Grey owl to match a 53-inch-tall kid? *Bonus:* Owls need to see well because they hunt up so much food: A family of 5 can eat 3,000 mice a year! How many mice does each owl get?

Answers:

*Wee ones:* To the right.

*Little kids:* 6 legs. *Bonus:* 14 hours.

*Big kids:* 4 Elfs, since they need to add 20 inches. *Bonus:* 600 mice.

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]]>The post A Clean Kind of Dirty Money appeared first on Bedtime Math.

]]>It would be great if we could print fake money when we needed it, but it’s a crime — you’ll go to jail if you get caught. That’s because “counterfeit” money messes up the total amount of money relative to the amount of stuff out there to buy. Plus it just isn’t fair. Somehow, that doesn’t stop people from trying to make fake money. In the craziest story we’ve heard yet, a guy tried to use paper napkins as fake money. Cass Alder bought cute party napkins with $100 Canadian bills printed on them. He cut out each money shape, glued them onto pieces of paper, and even baked them. But when he tried to shop with them, the store clerk could tell the bills were fake. Alder was caught and spent 60 days in jail. It might have been the worst arts and crafts project ever!

*Wee ones:* What shape is that $100 bill?

*Little kids:* If you have a real $100 bill and a fake $100 bill, how much money do you look like you have? *Bonus:* How many more bills do you need to total $400 of real money?

*Big kids:* If Alder had glued a fake $100, then a fake $50, then a $100, then a $50…what total value would he have after the 7th bill? *Bonus:* If that pack has 18 napkins and each has $100 printed on it, how much money do they look like altogether?

*The sky’s the limit:* If Alder printed $100s and $50s, how many ways could he combine those 2 kinds of bills to add up to $750? (Don’t worry about the order, just the number of each kind of bill.)

Answers:

*Wee ones:* A rectangle.

*Little kids:* $200. *Bonus:* 3 more, since you start with just 1 real one.

*Big kids:* $550, since he’d had $400 in hundreds, plus $150 in fifties. *Bonus:* $1,800.

*The sky’s the limit:* There would be 8 ways. He could have 7 $100s and 1 $50, or swap in a couple of $50s for one of the $100s to have just 6 $100s and 3 $50s…by swapping another 2 $50s, he’d have 5 and 5…then 4 and 7, then 3 and 9, then 2 and 11, then 1 and 13, and then finally no $100s and 15 $50s. In short, he can have 7, 6, 5, 4, 3, 2, 1, or 0 $100 bills.

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]]>The post When Numbers Are Cute As a Button appeared first on Bedtime Math.

]]>Have you ever used a calculator? It’s an almost magical toy: you press buttons that have numbers on them, and the calculator adds them for you, or multiplies them, or whatever else you want to do, then shows the answer. So Bedtime Math fan Abby W. asked, how many buttons do *100* calculators have on them? (She also sent this fun drawing!) Well, that depends on the number of buttons. The simplest calculator has 10 buttons for the “digits” — 0, 1, 2, 3 all the way up to 9 — and the buttons to add, subtract, multiply, divide, an equal sign, and a “clear” button to start over. That’s at least 16 buttons. But there are LOTS of other cool math buttons on grown-up calculators: buttons that do the math on angles or money, or that tell you how many times to multiply a number by itself. Even with a simple calculator, though, you can make the numbers grow fast.

*Wee ones:* If you’ve pressed buttons 1, 2, and 3, what button should you press next to stay in order?

*Little kids:* If you press 1, then 2, then 1 again, then 3, then 1, then 4…what’s the next button you press? *Bonus:* If you type 707 (which spells “LOL” upside-down), then add 1, what number do you have now?

*Big kids:* If 2 to the 3rd power means 2 x 2 x 2, what does 3 to the 3rd power equal? *Bonus:* If Abby had 100 of those 16-button calculators, how many buttons would they have all together?

Answers:

*Wee ones:* The 4.

*Little kids:* The 1. *Bonus:* 708.

*Big kids:* It equals 3 x 3 x 3, or 27. *Bonus:* 1,600 buttons.

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]]>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. The biggest ever “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 record breakers 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 record-breaking 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 eaten 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 Another Angle on Numbers appeared first on Bedtime Math.

]]>Have you ever seen an old-fashioned clock with letters on it instead of numbers? Those Vs and Xs are Roman numerals from long ago. Romans used the letter I for the number 1; V for 5, because it was shaped like your hand making a V (5 fingers); and X for 10, made by crossing 2 hands (10 fingers total). For numbers 1 less than a major number, they put the I before that letter. So IV = 4, and IX = 9. This became messy as numbers got bigger. Well, in a link shared by our friend Talie B., the Human Calculator tells us how Arabic numerals won everyone over. Each number was drawn to have its own number of angles, to make them easy to remember. As we see here, a 1 had 1 angle, a 2 had 2 angles, and the crazy 9 had 9 angles! It all worked, and now Roman numerals show up only to count hours and Super Bowls.

*Wee ones:* Which number from 1 to 9 is your favorite — and is it more than, less than, or the same as your age?

*Little kids:* In the number 4162, which digit is biggest? *Bonus:* How many angles do they have all together? Try adding them up!

*Big kids:* If you drew a crazy new number with 17 angles, what pairs of numbers could you add to it to get 23? (Don’t worry about the order — just which go with which.) *Bonus:* Try to guess the mystery number…If you double it, add 5, and double it again, you get 42. What is the number?

*The sky’s the limit:* If you’re choosing 2 numbers from 1 to 9, how many ways can you pick 2 odd numbers? (Again, don’t worry about the order — but you can’t pick the same digit twice.)

Answers:

*Wee ones:* Different for everyone…pick your favorite number, and see if you have to go up or down from your age to get there.

*Little kids:* The 6. *Bonus:* 13, since they add up to 13.

*Big kids:* 3 choices. The pairs just need to add to 6, so they can be 1 and 5, 2 and 4, or 3 and 3. *Bonus:* 8. You had 21 before doubling, you had 16 before adding 5…so you had 8 before doubling that first time.

*The sky’s the limit:* There are just 5 odd digits – 1, 3, 5, 7 and 9 – and as you pair each one with other numbers, you cut down the number of pairs left to do with those. So you have 1-3, 1-5, 1-7 and 1-9 (4 choices), then 3-5, 3-7 and 3-9 (just those 3 choices, because you already did 3-1). That leaves 5-7, 5-9 (2 more), and finally 7-9, giving us 4+3+2+1=10.

Thank you again, Talie — and those of you who want to add and multiply really, really fast to wow your friends, watch the video to see how Scott Flansburg the Human Calculator does it!

The post Another Angle on Numbers 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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