The post Enough People for a Party appeared first on Bedtime Math.

]]>What’s the biggest number of people you’ve seen at once? Where were you? Did you see a whole river of people on a city sidewalk, or an even bigger crowd in a stadium? It may have looked like a lot, but it was only a tiny part of all the people in the world. Our fan Maya C. just asked, how many people are there in the world? There are about 8 billion of us, or 8,000,000,000. But we aren’t spread out evenly around Earth. Almost 1 billion 400 million (1,400,000,000) live in China, and more than 1 billion 200 million in India. 1 billion people live in Africa, while Antarctica has more penguins than people. In any case, you don’t have time to count all those people one by one…a billion seconds is almost 32 years, and it would take even longer to say all the numbers!

*Wee ones:* How many people live in your home? Count them up if you can!

*Little kids:* If there are about 4 billion people in Asia and about 1 billion people in Africa, roughly how many billions of people live on those 2 continents together? *Bonus:* If Earth has 8 billion people, how many ears do they all have?

*Big kids:* A billion is a thousand millions. The U.S. has about 300 million people. How many more does the U.S. need to reach 1 billion? *Bonus:* If the U.S. has about 300 million and India has about 1 billion 200 million, how many times as populous is India? (*Hint if needed:* 1 billion 200 million is the same as twelve hundred million, or 1,200 million.)

Answers:

*Wee ones:* Different for everyone…try counting the people in your family, including yourself!

*Little kids:* 5 billion people. *Bonus:* 16 billion ears.

*Big kids:* 700 million more. *Bonus:* 4 times as many people.

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]]>The post The First Fast Driver appeared first on Bedtime Math.

]]>When you drive a car, you can’t just drive as fast as you want. Every road has a “speed limit,” which tells you how many miles an hour you can drive at most. Not everyone follows the rules, though, so police give out speeding tickets: you have to pay money as your punishment. So who got the first speeding ticket ever? That guy was Walter Arnold, back in 1896. He was driving only 8 miles per hour, but in 1896 cars were very new and no one really knew how to drive. So people drove really badly and kept crashing. That’s why the speed limit was only 2 mph – to keep everyone safe. Grown-ups even *walk* faster than 2 mph, but that was the rule. 3 years later, a taxi driver in New York City was arrested for speeding at 12 mph. Thankfully we’re allowed to drive much faster today, but somehow we still get speeding tickets.

*Wee ones:* If the speed limit is 8 miles an hour and you’re driving 7 miles an hour, are you driving too fast?

*Little kids:* If Walter Arnold was going 8 mph in a 2-mph zone, how many miles per hour was he over the speed limit? *Bonus:* If your street has a limit of 20 miles per hour, and the nearest busy street is 10 more than that, what is busy street limit?

*Big kids:* If you drive 20 miles an hour, how far can you drive in 4 hours? *Bonus:* If your family is driving to the beach 180 miles away, and the speed limit is 65 miles per hour, can you get there in 3 hours without breaking the limit? (*Hint if needed:* How fast would you have to drive to get there in time?

*The sky’s the limit:* If a firetruck is zooming at 70 miles an hour, while some slow person is driving only 26 miles an hour, and your speed is halfway between, how fast are you driving?

Answers:

*Wee ones:* No, you’re good! 7 is less than 8.

*Little kids:* 6 miles per hour. *Bonus:* 30 mph.

*Big kids:* 80 miles. *Bonus:* Yes! You can get there by driving 60 miles per hour.

*The sky’s the limit:* At 48 miles an hour. 26 and 70 are 44 mph apart, so the halfway point is 22 from either of them.

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]]>The post Billions of Boxes of Air appeared first on Bedtime Math.

]]>We can’t see it, but all around us is air. But air isn’t *everywhere* — in outer space there’s nothing at all, which is a “vacuum” (if you went in outer space without an astronaut suit, your whole body would explode!). Earth has air for only a few miles above ground, called our “atmosphere.” So our fan Rylan N. asked, how much air does Earth have? Well, about 3/4 of our air by weight is stuffed into the first 6 miles above ground. So we can take Earth with that blanket of 6 miles of air, making a ball 12 miles wider, find its volume, and then subtract the volume taken up by Earth itself. Earth is about 7,926 miles wide, so the 7,938-mile wide ball (12 miles wider) minus the 7,926-mile wide ball gives us more than 1 billion cubic miles of air! Imagine a box 1 mile wide in every direction, filled with air…we have 1 billion of them. That air weighs about 11 quintillion pounds, which is an 11 followed by 18 zeros. Plenty for all 8 billion of us humans, as long as we keep it clean!

*Wee ones:* If you breathe in, then out, then in, then out…what comes next?

*Little kids:* A 6-year-old’s lungs can hold about 1/2 gallon of air, and a 14-year-old’s hold about 1 gallon. How many years does the 6-year-old have to wait to hold a full gallon? *Bonus:* If the 6 year-old takes in 5 full breaths and the 14-year-old takes in 5, who breathed in more air?

*Big kids:* If you fly in a plane 30,000 feet up, are you above or below the 6-mile mark for the thick part of our atmosphere? (Reminder if needed: A mile has 5,280 feet). *Bonus:* Can you “spell” 1 billion as a number?

Answers:

*Wee ones:* You breathe in.

*Little kids:* 8 more years. *Bonus:* The 14-year-old, since it’s the same number of breaths but bigger.

*Big kids:* Below 6 miles…a mile would have to have just 5,000 feet for it to match. *Bonus: *1,000,000,000.

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]]>The post Walking with 4 Left Feet appeared first on Bedtime Math.

]]>You probably don’t remember the day you learned to walk. But you can bet it was exciting to put one foot in front of the other and cross the room. Luckily, we have only 2 feet to move. What’s it like to have 4 legs like a horse, or 6 like an insect, or 8 like a crab? If we people number our feet 1 and 2, walking is just 1, 2, 1, 2. For a horse it’s trickier: with front left/right feet 1 and 2 and back left/right feet 3 and 4, a horse’s steps are 3, 1, 4, 2, then 3 again. An insect walk cycle mixes it up: the very back left and very front left step at the same time as the middle *right* leg. Then on the next step, the back right, front right, and middle left all step together. In what order does a crab or spider move its legs? Let’s find out how our leggy friends keep from tripping over themselves.

*Wee ones:* Who has more legs, a horse with 4 or a ladybug with 6?

*Little kids:* If a horse’s steps are 3, 1, 4, 2, then 3 again to repeat, which foot takes the next step after that? See if you remember the pattern! *Bonus:* Which foot takes the 11th step?

*Big kids:* If a crab steps with all 8 legs before repeating the pattern, how many total steps has it taken when every leg has stepped twice? *Bonus:* In a video of a walking crab, the legs on the left side step in the order 1, 3, 2, 4. If the 4 right legs are numbered 5, 6, 7, 8 and follow the same order at the same time, which 2 legs together take the 30th step?

*The sky’s the limit:* If leg number 6 on the crab takes the 6th step, then the 14th step, then the 22nd, and so on, when will that 6th leg take a step again that ends in a 6? Which step will be the next one after that to end in a 6?

Answers:

*Wee ones:* The ladybug with 6 legs has more.

*Little kids:* Foot #1. *Bonus:* Foot #4.

*Big kids:* 16 steps. *Bonus:* Legs 3 and 7.

*The sky’s the limit:* The 46th step, then the 86th step. After the 6th step, we need to add a multiple of 8 that is also a multiple of 10, to keep a 6 in the final digit. 5 x 8 is the smallest multiple that works, adding 40 each time.

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]]>The post Try Not to Lose Your Marbles appeared first on Bedtime Math.

]]>Marbles are those pretty little glass balls that always roll under the couch, never to be seen again. But at the National Marbles Tournament in Wildwood, NJ this week, marbles play the starring role in an exciting game. It all started in 1588, when two men who both loved the same woman played a marbles match to see who would get to marry her. Today marbles are played many ways. In the world championship, the ref drops marbles for lots of teams inside a circle, then each team tries to shoot its own marbles into a hole. In this week’s U.S. contest, 2 players go head to head. Each one has 13 marbles plus 1 “shooter” marble, which they use to knock the other 13 out of the 10-foot circle. Let’s just hope someone’s catching them before they roll under the couch.

*Wee ones:* If you’ve knocked 4 of your marbles out of the circle, what numbers are the next 3 marbles?

*Little kids:* If you have 13 target marbles plus your shooter marble, how many do you have in total? *Bonus:* If the red team sinks a marble, then the blue team sinks 2, then the green team sinks 1, then the red team sinks 1 to repeat, what color should the 7th marble be to keep the pattern?

*Big kids:* The 13 marbles start lined up in an X, with the shooter in the middle. How many marbles are lined up counting along 1 long stick of the X? *Bonus:* Each player’s marbles are a certain color. If out of 21 marbles left there are twice as many blue as red, how many marbles of each color are left?

Answers:

*Wee ones:* 5, 6, 7.

*Little kids:* 14 marbles. *Bonus:* Blue, since it’s the 2nd blue in that set of 4.

*Big kids:* 7 marbles: 3 in each “arm” of the X, plus the center marble. *Bonus:* 14 blue and 7 red.

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]]>The post The Dog That Chases More Than Its Tail appeared first on Bedtime Math.

]]>That cute face looks sweet and calm. But this border collie works long, hard hours every day, with lots of running and loud barking. Border collies help farmers herd sheep, goats, llamas and other herd animals. The dogs love to chase anything that moves, and by running around the sheep, they steer the sheep to stay in a group, so the farmer can find them all easily. Border collies are super smart, so they learn quickly…that’s why farmers have to train the young dogs early, so the dogs learn to do good things instead of bad. They’re called border collies because they first came from the border between Scotland and England. And all border collies are the great-great-great…grandkid of just one long-ago dog from 1893! If you do the math, you’ll see that the puppies have added up since then. And if you want one as a pet, be ready to do a lot of running, because these furry friends want lots of exercise.

*Wee ones:* Who has more legs, you or that dog?

*Little kids:* If you take your border collie for a walk, how many legs do you have together? *Bonus:*If your border collie is herding 10 sheep and 1 of those sheep gets away, how many are left?

*Big kids:* One super-smart border collie, Striker, rolled down a car window in 11 seconds! At that rate, could he roll down 4 car windows in 40 seconds? *Bonus:* The “smartest dog ever,” a border collie named Chaser, knows the names of 1,000 of her toys! If she fetches 1 for you, how many more does she need to fetch?

*The sky’s the limit:* If a border collie had 4 puppies in 2000, and 4 years later each of them had 4 puppies, and 4 years later each of those had 4 puppies…how many puppies would be born in 2016?

Answers:

*Wee ones:* The dog has more legs.

*Little kids:* 6 legs (4 + 2). *Bonus:* 9 sheep.

*Big kids:* Not quite…he would need 44 seconds (plus time to jump from seat to seat). *Bonus:* 999 toys.

*The sky’s the limit:* 1,024 puppies. 2000 was 16 years ago, which is 4 sets of 4 years. But you also have to count the first set of 4 puppies in 2000, so it’s 5 sets of 4 years. Each new set of puppies is 4 times as big as the last, so in the 5^{th} generation there would be 4 x 4 x 4 x 4 x 4, or 1,024 puppies. Of course, dogs have puppies more often than that, so since 1893 there have been tens of thousands of them!

And thank you William O. for telling us about this great dog!

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]]>The post An Apple a Day Fills the Plane appeared first on Bedtime Math.

]]>Have you ever taken a plane ride? It’s usually at least an hour trip, so the airplanes give us little snacks – but it’s never enough. Maybe that’s why our fan Tristam J. asked, how many apples could you fit inside an airplane? Well, you have to find the space, or “volume”, that 1 apple fills, then find the volume of the plane. If the apples were perfect balls, or “spheres”, and you packed them as tightly as you could, they’d have gaps between them…the balls would take up about 3/4 of the total air space. Now, an apple that’s 2 inches from the peel to the middle takes up 4/3 times pi (3.14) times 2 times 2 times 2 again. That’s 33 cubic inches, or little cubes that are 1 inch wide in every direction. But that’s only ¾ of the air the apple fills if stacked…it actually takes up 44 cubic inches. Thankfully, someone already figured out that a 747 jet has about 1,000 cubic meters of space for both passengers and suitcases, or about 35,000 cubic feet…or about 61,000,000 cubic inches. Dividing by 44 cubic inches per apple, you can fit about 1,386,000 (1 million 386 thousand) apples in there. You could eat all of them, or you could carve one into an airplane, like Tristam did!

*Wee ones:* Do you see any balls in the room around you? Are they bigger or smaller than an apple?

*Little kids:* If you put an apple on the table with 6 apples around it, how many do you have in total? *Bonus:* When you pack another layer on top and below, the apple gets another 3 above and 3 below. Now how many does the center apple touch? (Remember not to add in that center apple itself!)

*Big kids:* If the plane can hold 1,386,000 apples, how many people could you feed apples if each one wants 1,000 of them? *Bonus:* What if each person just wants 100 — now how many people can you feed?

Answers:

*Wee ones:* Different for everyone…see how many you find, and how big they are!

*Little kids:* 7 in total. *Bonus:* 12 apples, because it touches the first 6 plus 3 plus 3.

*Big kids:* 1,386 people. *Bonus:* 13,860 people.

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]]>The post Cross-Country Choo-Choo appeared first on Bedtime Math.

]]>Back in the 1800s, the fastest way to travel was by train. But trains could take you only where the tracks went between cities. There wasn’t one long track across the U.S., because for some stretches of mountain and desert, only a horse-drawn wagon could get through. Some people sailed all the way around South America instead! That trip took weeks and cost a ton of money ($1,000, which was a lot back then). So imagine the excitement when two railroads connected their tracks to make one train track from coast to coast. The Central Pacific company built eastward from California, while the Union Pacific built westward from the Missouri River. They met in Utah in May 1869, and inJune 1876 a train drove all the way across the country for the first time. It choo-chooed from New York to San Francisco in just under 84 hours. Now we can fly it by plane in 6 hours, but compared to horse-drawn buggies, that train flew like lightning.

*Wee ones:* If a locomotive has 6 wheels and the caboose has 4 wheels, which one has fewer wheels?

*Little kids:* If you left New York in March, sailed around South America, and reached California the next month, what month would it be? *Bonus:* If the train trip took 84 hours, how many more hours did it take than our 6-hour flight today?

*Big kids:* If the trip had taken exactly 3 days, would that be faster or slower than 84 hours? *Bonus:* If a plane can fly across the US in 6 hours, how many times can the plane fly across and back in 84 hours?

Answers:

*Wee ones:* The caboose has fewer wheels.

*Little kids:* April. *Bonus:* 78 hours.

*Big kids:* Faster, since that would be 72 hours. *Bonus:* 7 times, since each trip would take 12 hours in total.

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]]>The post Finding Dory – and Drawing Her appeared first on Bedtime Math.

]]>Tomorrow the movie *Finding Dory* comes out, as the follow-up to *Finding Nemo*. Once again we get to watch funny fish search the big ocean for family. These movies don’t show real fish, though. They’re “animated,” meaning the movie shows lots and lots of drawings, called frames. Each frame is just a little different from the one before: maybe the fish moves over a tiny bit, or a turtle lifts his head. When you flick through 24 or 30 drawings every second, the characters look like they’re moving! So our friend Callie S. asked, how many people does it take to make a movie like that? Turns out *Toy Story* needed 27 animators to make the 77-minute film, and 800,000 hours of computer time. Movies since then have used even more — after all, Sulley from *Monsters, Inc.* has 2,320,413 hairs. But don’t worry, animators use math to make all those hairs move! If you work hard at math, maybe you can grow up to do this super-cool job, too.

*Wee ones:* If it takes 5 pictures to show Nemo flicking his fin, what numbers do you say to count them?

*Little kids:* The octopus in *Monsters, Inc.* has only 6 legs, as a joke. How many more legs should it have? *Bonus:* If you got to help those 27 animators draw *Toy Story*, now how many animators would there be?

*Big kids:* If 20 animators each drew 3 minutes of film, would that be enough for 77 minutes? *Bonus:* If you need 30 frames (pictures) each second, how many do you make for 1 minute of movie? (*Hint if needed:* What would 3 frames per second for 6 seconds be? Then, 30 frames for 6 seconds…then how about 30 frames for 60 seconds?)

*The sky’s the limit:* If 50 computers run all week except for an 8-hour break, how many weeks would it take for them to run a whole 800,000 hours of work in total?

Answers:

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

*Little kids:* 2 more legs. *Bonus:* 28 animators.

*Big kids:* Not quite! They’d make 60 minutes. *Bonus:* 1,800 frames just for 1 minute.

*The sky’s the limit:* 100 weeks. First, a week has 24 x 7 or 168 hours. If the computers take off 8 hours, that’s 160 hours for each. So 50 computers together can do 8,000 hours of work. It would take them 100 weeks, or almost 2 years (if the article’s right that it really took 800,000 hours)!

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]]>The post Tricky Trip to Mars appeared first on Bedtime Math.

]]>People have always dreamed about going to the red planet Mars. It won’t be easy to live there, though. Mars doesn’t have safe air to breathe, or water to drink, or nice Earthy temperatures. And it’s at least 60 million miles away from us. As our fan Hailey S. asked, how long does it take to fly to Mars? Even burning fuel as fast as you can. it takes at least 6 months.

Then, once you get to Mars, how do you live? Another fan, Mary Claire A., just shared that one company has a whole new idea for this. Instead of landing right on Mars dirt, Lockheed Martin wants to make a space station that will fly around Mars. It will work a lot like the International Space Station that orbits Earth — it has probably flown right over your head a few times. The astronauts have everything they need to live on the ISS, so let’s just do the same thing around Mars!

*Wee ones:* What shape is Mars?

*Little kids:* If you left for Mars today and flew for 6 months, how old would you be when you landed? *Bonus:* If you had left 6 months ago to land on Mars today, in what month would you have left? (It’s June right now.)

*Big kids:* The Mars space station will be ready for visiting astronauts by the year 2028. How old will you be then? *Bonus:* If you took 1 year to fly that 60 million miles, how many miles would you fly each month? (Hint if needed: What if you took just 6 months, or 1/2 year?)

Answers:

*Wee ones:* A circle, or in 3D, a “sphere” (ball).

*Little kids:* Different for everyone…if you’re having a birthday between now and December 2016, you’ll be 1 year older than now, otherwise you’ll be the same number age. *Bonus:* December 2015.

*Big kids:* Different for everyone…2028 is 12 years from now, so add 12 to your current age. *Bonus:* 5 million miles each month. A 6-month trip would be 10 million miles a month.

The post Tricky Trip to Mars appeared first on Bedtime Math.

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