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 A Fight between Fruits and Veggies appeared first on Bedtime Math.

]]>What’s the difference between a fruit and a vegetable? A fruit comes out of the flower on a plant and holds seeds. Apples and oranges, peaches and apricots, and all kinds of berries do this. Veggies come from other parts of the plant, like lettuce and spinach (which are leaves) or carrots and onions (which are roots). But then the watermelon walks in: which one is it? Some say it’s a fruit because it comes from a flower and it has seeds — between 200 and 800 of them. But other say it’s a cousin of the cucumber! Watermelon is 9/10 water by weight, hence its name. It turns out you can eat any part of it, even the rind — they say it tastes good if you pickle it. Now that summer’s here, it’s your big chance to try it!

*Wee ones:* Watermelons are green on the outside. Try to find 4 green things in your room.

*Little kids:* If you’ve spat out 2 seeds from a watermelon, what numbers are the next 3 seeds? *Bonus:* We can’t tell you how many seeds are in your watermelon slice, but if you double that number and add 1, you get 9. How many seeds does it have?

*Big kids:* If you slice a watermelon into 7 circle slabs, then cut each circle into 4 slices, do you have enough slices for 2 dozen people? *Bonus:* If there are between 200 and 800 seeds in that watermelon, how many numbers of seeds are there that would give each of those 28 slices a multiple of 10 seeds?

Answers:

*Wee ones:* Possible items include shirts, socks, live plants, and building toys like Legos.

*Little kids:* 3, 4, 5. *Bonus:* 4 seeds. If you added 1 at the end to get 9, you had 8 before that, and if you doubled to get 8, you must have started with half of that, which is 4.

*Big kids:* Yes! You’ll have 28 slices for 24 people. *Bonus:* There are just 2 ways: 280 seeds, and 560 seeds. You need multiples of 28 that are also multiples of 10.

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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 they 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 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 barking. Border collies help farmers herd sheep, goats, llamas and other herd animals. The dogs love to chase any moving thing, and by running around the sheep, they steer the sheep into a group, so the farmer can find them easily. Border collies are super smart, so they learn fast…farmers have to train the young dogs quickly, 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 pups have added up since then.

*Wee ones:* Border collies are black and white. Find 2 black things and 4 white things in your room. Of which color do you have more things?

*Little kids:* If you take your border collie for a walk, how many legs do you have altogether? *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 toys 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 have been born in 2016?

Answers:

*Wee ones:* You’ll have more white things (4) than black (2).

*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 earlier, 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 puppies. 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 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 star 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. So how do you play? In one kind of game, each player (or team) gets a marble color, and shoots its own marbles into each other to try to knock them into a hole. In this week’s U.S. contest, 2 players go head to head, each with his/her own 13 marbles plus 1 “shooter” marble, which they use to knock their own 13 marbles out of the 10-foot circle. Let’s just hope someone’s catching them before they roll under the couch.

*Wee ones:* How many marbles can you count in the picture?

*Little kids: *If you’ve knocked your first 4 of your marbles out of the circle, what numbers are the next 3 marbles? *Bonus:* If you have 13 “target” marbles plus your shooter marble, how many do you have in total?

*Big kids:* The 13 marbles start lined up in an X. How many marbles are lined up along 1 long stick of the X? *Bonus:* If the red team sinks 1 marble, then the blue team sinks 2 marbles, then the green team sinks 1, then red sinks 1 to repeat, blue sinks 2…what color should the 19th marble be to keep the pattern?

Answers:

*Wee ones:* 5 marbles.

*Little kids:* 5, 6, 7. *Bonus:* 14 marbles.

*Big kids:* 7 marbles: 3 in each “arm” of the X, plus the center marble. *Bonus:* Blue, since it’s the 3rd marble in that set of 4 starting on 17.

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]]>The post The Cuddliest Octopus appeared first on Bedtime Math.

]]>Usually when we talk about octopuses, “cute” isn’t what we think first. But this eight-legged critter here really *is* cute. Until now, this type of octopus has been called the flapjack octopus, since it looks like a pancake: it has webbing between its legs, like a duck’s feet. It lives as far as 2,000 feet deep in the ocean, where the water is very cold. So the Monterey Bay Aquarium keeps their new flappy friend in a tank of super-cold water. They’ve been waiting more than a year for the octopus to lay eggs, and might have to wait 2-3 more years…cold-water sea creatures don’t lay eggs very often. When they do, you can bet their octopus babies are cute!

*Wee ones:* Who has more legs, you or an octopus? (All octopuses have 8 legs.)

*Little kids:* How many legs do you and an octopus have together? *Bonus:* If it’s June right now and the octopus finally lays eggs 4 months from now, in what month will they show up?

*Big kids:* If you can scuba dive a whole mile deep (5,280 feet), and the cute octopus makes it only to 1,000 feet, how much deeper did you swim? *Bonus:* Which would stretch farther on your kitchen counter, a row of 6 8-inch flapjacks, or 7 of these 7-inch flapjack octopuses?

Answers:

*Wee ones:* The octopus.

*Little kids:* 10 legs. *Bonus:* In October.

*Big kids:* 4,280 feet. *Bonus:* The 7 octopuses, since they’d reach 49 inches, while the pancakes would span only 48 inches.

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

]]>We humans have come a long way since cavemen chucked rocks at each other. Back then the only way to get anywhere was to walk, at 2-4 miles an hour. To cross the U.S., which is more than 2,000 miles, would take a long time. Around 5,000 years ago we invented the wheel, and built carts and wagons for horses to pull. By the 1800s, we had steam trains, which were way faster! But trains could take you only where the tracks went. There wasn’t one long track across the U.S. So the Central Pacific company built tracks eastward from California, while the Union Pacific built westward from the Missouri River. They met in Utah in May 1869. Finally in June 1876 a train drove all the way across the country for the first time, in just under 84 hours. Now we can fly it by plane in 6 hours!

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

*Little kids: *If your car has 4 wheels, how many more wheels does it need to match a 6-wheel train car? Count up if it helps! *Bonus:* If you leave New York in June and ride to California by bike in 1 month, what month do you get there?

*Big kids:* If the train trip across America took 84 hours, how many more hours did it take than our 6-hour flight today? *Bonus:* If you could ride your bike across like a superhero in exactly 3 days nonstop, would you get there before the 84-hour train?

*The sky’s the limit:* If it takes 60 hours to cross the U.S. by high-speed train and 90 hours by car, but you do the trip partly by car and partly by train to take 80 hours, what fraction of the distance did you drive by car?

Answers:

*Wee ones:* The car has fewer wheels.

*Little kids:* 2 more wheels. *Bonus: *July.

*Big kids:* 78 hours. *Bonus:* Yes, you will beat the train! You will take only 72 hours.

*The sky’s the limit: *You did 2/3 of the distance by car, 1/3 by train. 80 hours is twice as close to 90 (just 10 miles an hour off) as it is to 60 (20 miles an hour off), so it means you drove twice as much of the distance by car as by train. And it works: 2/3 of 90 hours is 60, plus 1/3 of 60 hours is 20, and 60 + 20 = 80. If you’d rather practice algebra than use mental math, and you drive fraction c out of 100 by car,

90 x c + 60 x (1 – c) = 80

Multiplying to simplify, you get

90c + 60 – 60c = 80

30c = 20

c = 20/30 = 2/3

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

]]>In the movies *Finding Nemo* and *Finding Dory*, we watch lots of funny fish search the big ocean for family. These movies don’t show real fish, though. They’re “animated,” meaning the movie is made of 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. Some movies used even more — after all, Sulley from *Monsters, Inc.* had 2,320,413 hairs. But don’t worry, animators don’t draw those hairs one by one: they use math to make them move!

*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. If you gave him 2 more legs, would he have a full 8? *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: *Yes! 6 + 2 is 8. *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 Getting Your Kicks from the World Cup appeared first on Bedtime Math.

]]>Yesterday kicked off the World Cup, the big contest where countries send their best soccer players (or football, as most countries call it) to try to win the top prize. That trophy is a ball, not a cup, but they still want to win it! The countries are clumped into groups of 4, and each team plays the other 3. The 2 winningest teams from each group go on to the round of 16. At that point, teams have to win each game to move on to the next. So the 16 teams chop down to 8, then down to 4, then to the 2 best teams left for the final game. It’s very, very hard to kick the ball into the goal, since the field is so huge. When someone does score, it’s a big deal!

*Wee ones:* Soccer is played with a ball. Try to find 3 ball shapes in your room.

*Little kids: *If Iceland becomes 1 of the 16 top teams, how many other teams are still in it with them? *Bonus:* If the top 9 teams lined up, which number team would be exactly in the middle?

*Big kids:* There are 8 groups with 4 teams in each, but only 1 will be the final winner. How many of those teams *won’t* win the World Cup? *Bonus: *In the group games, a country gets 3 points for a win, 1 point for a tie, and 0 points for a loss. In those 3 games, what’s the 1 total score between 0 and 9 that a country *cannot* get?

Answers:

*Wee ones:* Ball shapes can include sports balls like tennis or baseball, toys like bouncy balls, or lightbulbs or world globes.

*Little kids:* 15 other teams. *Bonus:* Team #5.

*Big kids:* 31 teams. *Bonus: *A total score of 8. They can score any other total, e.g. 3=3+0+0 or =1+1+1, then 4=3+1+0…and so on. Try to work out all the rest!

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]]>The post Flip-Flopping Flag appeared first on Bedtime Math.

]]>It’s Flag Day here in America, so it’s a great time to talk about all the crazy math our nation’s flag has done. Each time our country added a new state, we added a star to that blue box. We also tried adding a *stripe* for each new state. But after adding Vermont and Kentucky (#14 and #15), we realized the flag would turn into a pink blur of teeny stripes! So we went back to 13 stripes and used stars for states after that. Sometimes a bunch of states joined at once, sothe number of stars made some big jumps, like from 38 to 43 when we added the Dakotas, Idaho, Montana, and Washington. Thankfully, today’s 50-star flag has lasted the longest, so we can remember what it looks like!

*Wee ones:* If the flag has 7 red stripes and 6 white stripes, which color has more stripes?

*Little kids:* Since the stripes on our flag are red, then white, then red, then white…what color is the 8th stripe? (Don’t peek!) *Bonus:* When the flag jumped from 48 stars to 50, how many states had we added?

*Big kids:* One flag in 1818 had the stars laid out in a star shape: 1 star in the middle, 10 more around it to make a pentagon, and then 3 in each of the 5 points. How many states did we have at that time? *Bonus:* How many more states would we need today to double that number of stars?

*The sky’s the limit:* After we had our first 13 stars, for what number of states could we have had by now where the stars could make a perfect square (same number of rows across and down), and where the digits add up to 9?

Answers:

*Wee ones:* More red stripes.

*Little kids:* White. *Bonus:* 2 more states – Alaska and Hawaii, in 1959.

*Big kids:* 26 states, since it’s 1+10+15 stars. *Bonus:* Double would be 52, so we’d need 2 more states.

*The sky’s the limit:* 36. The only perfect square numbers between 13 and 50 are 16, 25, 36, and 49. 36 is the only one where the digits add to 9 — because it’s the only one divisible by 9!

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