The post Time to Line Up… appeared first on Bedtime Math.

]]>When you look at a digital clock, do you get excited when a cool number show ups? Like a time when all the digits are the same, or when the first two add up to the third? Only a few times each day does the clock do fun tricks like that. On a long car trip, Bedtime Math fans Miriam, Silas, and Titus R. decided to count up how many cool times clocks can show us. They figured out how many times the clock shows all one digit, like 1:11, 2:22…and remembered that those times all show up in the morning, then again in the afternoon. Can you figure out how many times have all the same digit? Let’s find out how many other cool times are worth waiting for — and how often to check the clock to catch them.

*Wee ones:* A clock shows the numbers 1 to 12 on it. Can you name all the numbers between 1 and 12?

*Little kids:* If the time is 5:55, what was the last time before that when all the digits were the same? *Bonus:* Times like 2:35 are cool too, because the numbers can be an equation: here it’s 2+3=5. What equation is happening in the times 7:34 and 2:48?

*Big kids:* How many different times in one day does the clock show all the same digit, like 3:33? *Bonus:* What’s the longest you have to wait between two of those times?

*The sky’s the limit:* What’s the longest you have to wait between times where the first two digits add up to the third — and there’s no 4th digit?

Answers:

*Wee ones:* 2, 3, 4, 5, 6, 7, 8 ,9 ,10, 11.

*Little kids:* 4:44. *Bonus:* We’re subtracting in the first: 7 – 3 = 4. And we’re multiplying in the second: 2 x 4 = 8.

*Big kids:* There are 12 times in one day: 1:11, 2:22, 3:33, 4:44, 5:55, 11:11 in the morning, and then those 6 times repeat in the afternoon. *Bonus:* The gap from 5:55 to 11:11, which is 5 hours 16 minutes (5 hours to get to 10:55, then another 5 minutes to get to 11:00, then another 11 minutes).

*The sky’s the limit:* 3 hours 52 minutes. The earliest time in the day that does this, using the smallest numbers, is 1:01. The latest time is 9:09 since you can’t do 9:90 (only 60 minutes in an hour). Many times work during each of the hours in between, so our biggest wait will be the multi-hour jump from 10:00 through 12:59. So we’re going from 9:09 am to 1:01 pm. That’s 8 minutes less than 4 hours, or 3 hours 52 minutes.

And thank you Miriam, Silas and Titus for sharing this great waiting game!

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]]>The post Monster on Wheels appeared first on Bedtime Math.

]]>Monster trucks don’t look like monsters. They don’t have fur or claws or big drippy tongues. They’re just really huge. How huge? Their tires have to be at least 66 inches tall, which might be taller than you are! Then our fan Mero H. asked, how fast can a monster truck go? It turns out they do drive more slowly than the long skinny trucks on the highway. Back in 2014 Mark Hall broke the world speed record for a monster truck, at 99 miles an hour. Even at that pokey speed, these trucks can do tricks: the year before that, a 10,000-pound monster truck drove off a ramp and jumped 237 feet! Good thing it had big poofy tires for the landing.

*Wee ones:* What shape is a truck tire? What food has the same kind of shape?

*Little kids:* If a monster truck turns left, then right, then right, then left again to repeat the pattern, then right…which way should it turn next? *Bonus:* Which weighs more, two 4,000-pound cars together, or a 10,000-pound truck?

*Big kids:* How many feet and inches tall is a 66-inch monster tire? *Bonus:* Who’s taller, you or that 66-inch monster tire — and by how many inches?

*The sky’s the limit:* If you jump a truck 237 feet, then on your 2^{nd} try you jump just 189 feet, then on your 3^{rd} try you land between those 2 spots but twice as far from your 2^{nd} jump as your 1^{st}…how long is your 3^{rd} jump?

Answers:

*Wee ones:* A circle, or in 3-D a “torus” — which is the shape of a donut!

*Little kids:* Right. *Bonus:* The 10,000-pound truck, because it weighs more than 8,000 pounds.

*Big kids:* 5 feet 6 inches. *Bonus:* Different for everyone…find your height in inches, and subtract from 66 or subtract 66 from your height. Imagine a truck tire that tall standing next to you!

*The sky’s the limit:* 221 feet. The 2 jumps are 48 feet apart, and if the gap from one is double the gap from the other, that bigger gap is like 2 of the smaller gaps. So that 48 feet is the same as 3 of the smaller gaps. 1/3 of 48 is 16, so you land 16 feet short of the 1^{st} jump, putting you at 221 feet (which is 32 feet more than 189, like we hoped!).

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]]>The post A Lot of Rings to Count appeared first on Bedtime Math.

]]>It’s fun to celebrate birthdays with friends, balloons, presents, and cake. And we think it’s about time the Methuselah Tree gets to enjoy a party, too: at about 4,850 years old, this Great Basin bristlecone pine tree is one of the oldest individual living things in the world. If you got invited to its birthday party, you might have a hard time finding it, though. The tree is located somewhere in a grove of trees in the White Mountains of California. But the U.S. Forest Service keeps its exact location secret to keep people from hurting it. So if you want to celebrate with the Methuselah Tree, be prepared to sing “Happy Birthday” to all the trees in the grove.

*Wee ones:* If you photograph 9 pine trees on one slope of the grove, and one of them is secretly the Methuselah Tree, how many pine trees are not it?

*Little kids:* Dendrochronology is the science of figuring out a tree’s age by counting its rings: if you cut across a tree trunk or pull out a piece, the number of rings you see tells you how many years old the tree is. If this year you count 9 rings in a tree, how many will there be next year? *Bonus:* How much older is a tree with 16 rings than the one with 9 rings?

*Big kids:* If a tree were just half as old as the Methuselah Tree, how old would it be? *Bonus: *There’s another bristlecone pine that’s about 4,600 years old. How many years younger than the Methuselah Tree is it?

Answers:

*Wee ones:* 8 pine trees.

*Little kids:* 10 rings. *Bonus:* 7 years older.

*Big kids:* 2,425 years old. *Bonus:* 250 years.

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]]>The post Fat Dog appeared first on Bedtime Math.

]]>Just a couple years ago, Dennis the dachshund weighed 56 pounds, about 4-5 times what a dog like him should weigh. He had been eating fast food hamburgers and pizza — really unhealthy human food that made him blow up like a blimp. Think how sad that must have been: no running, no jumping up on the couch, no chasing cats and squirrels. The good news is, his owner’s relative was so worried about him that she adopted him as her own pet. She put him on a “diet,” meaning she changed the foods Dennis ate. Thanks to eating right, Dennis lost 3/4 of his weight! Now his body is so much smaller, but he’s kept his nice long ears — and he can finally chase cats again.

*Wee ones:* If Dennis eats pizza, then a burger, then a bowl of ice cream, which food did he eat 2nd?

*Little kids:* If Dennis ate burgers 3 days a week and pizza the other days, how many days did he eat pizza? *Bonus:* If he ate twice a day every day, how many junk-food meals did he eat in a week?

*Big kids:* Before his new diet, what did Dennis (56 pounds) weigh compared to *you*? *Bonus:* If at 56 pounds Dennis weighed 4 times as much as he should have, what does he weigh now? (*Hint:* To divide a number by 4, you can just cut it in half, then cut it in half again.)

Answers:

*Wee ones:* The burger.

*Little kids:* 4 days. *Bonus:* 14 fatty meals.

*Big kids:* Different for everyone…subtract 56 from your weight in pounds, or even more scary, subtract your weight from Dennis’ 56! *Bonus:* 14 pounds.

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]]>The post Running Around the Whole World appeared first on Bedtime Math.

]]>Our fan Valeria M. in Spain asked us, how long would it take to run all the way around the world? Believe it or not, a few runners have already done it. Kevin Carr of England ran around Earth in…can you guess how long it took him? Weeks? Months? Years? He did it in an amazing 621 days! (One year has 365 days.) That’s a distance of about 25,000 miles if you ran the biggest possible circle. The question is, what would be the absolute fastest time if a person could run without stopping? Remember, Kevin had to sleep, eat, and rest his feet. As we’ll find out below, running without stopping would be way faster.

*Wee ones:* If you run 4 miles and your dog runs 1 mile farther, how far does your dog run?

*Little kids:* If you run 2 miles from home to the park, then 3 miles more to the ice cream shop, and finally 4 more miles home, how many miles do you run? *Bonus:* If you wanted 11 miles total of running, which part of that trip should you run again?

*Big kids:* If you could run 10 miles an hour for a whole 24-hour day, how many miles would you cover? *Bonus:* Then about how many days would it take to run the 25,000 miles around our planet?

*The sky’s the limit:* If Kevin finished this 621-day run in April 2015, in about what month and year did he start, and how old were you back then? (You can assume 30 days per month, and count from end of April so the 21 days beyond 600 don’t carry you over another month).

Answers:

*Wee ones:* 5 miles.

*Little kids:* 9 miles. *Bonus:* From home to the park, since you need 2 more miles.

*Big kids:* 240 miles. *Bonus:* About 100 days.

*The sky’s the limit:* In August 2013. He took about 20 months from the beginning of April. 12 months takes us to the previous early April, in 2014, and 8 months before that brings us to the previous August. As for your age, that’s different for everyone: August 2013 was 4 years 3 months ago, so subtract 4 years from your age, or 5 years if your birthday is between early August and mid-November!

And thanks again Valeria for keeping us on our toes with the math!

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]]>The post Dog on Wheels appeared first on Bedtime Math.

]]>The skateboard is such a cool, simple toy: a board with wheels under it. You just stand on it while pushing against the ground with one foot, and you can roll really fast. People do all kinds of tricks on skateboards, including flipping the board, riding down handrails, and other stunts. But it’s even more exciting when it’s a dog doing the tricks. A bulldog in Lima, Peru named Otto set the world record for the longest ride on a skateboard through a human tunnel. 30 people stood in a line with their legs spread apart, and Otto rolled through all those Vs. It all started with an accident, when Otto was riding on his skateboard at full speed towards his owner. She jumped up and let him zoom between her legs. A tunnel of 30 people is much trickier, but Otto may want to break his own record, so watch out!

*Wee ones:* If a skateboard has 2 little wheels in the front and 2 in the back, how many wheels does it have?

*Little kids:* If you counted off those 30 tunnel people in sets of 10, what numbers would you say? *Bonus:* In 2015 when he set the world record, Otto was 3 years old. In what year was he born?

*Big kids:* If you’re one of the 30 people helping Otto, how many people are making the tunnel with you? *Bonus:* How many legs do Otto and those 30 people have all together?

*The sky’s the limit:* If every 3rd person starting with the 3rd patted Otto’s head and every 4th person starting with the 4th slipped him a doggie treat, how many of the 30 people patted him but didn’t give him a treat?

Answers:

*Wee ones:* 4 wheels.

*Little kids:* 10, 20, 30. *Bonus:* In 2012.

*Big kids:* 29 people. *Bonus:* 64 legs, since the people have 60 and Otto has 4.

*The sky’s the limit:* 8 people. 10 people patted him, but 2 of those people also fed him (the 12th and 24th).

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]]>The post Crayons by the Billions appeared first on Bedtime Math.

]]>When you draw with a crayon, did you ever wonder how it was made? If you’re ever in Philadelphia, Minneapolis, or Orlando, you can head to the local Crayola Factory and watch crayon-making in action. The machine in this photo pours sloshy melted red wax into hundreds of skinny round tubes. When the wax cools, it pops out as smooth red sticks. Then the blue wheel rolls glue and paper onto them. The wrapped crayons tumble out the bottom to be shoved into boxes. In the old days people could glue about 10-15 crayons per minute; this machine wraps 200 a minute! That means more coloring fun for all of us.

*Wee ones:* If today the factory is making lime green, macaroni-n-cheese, wild strawberry, and atomic tangerine crayons, how many colors is it making?

*Little kids:* If you hope to glue 7 crayons in a minute and you do 1 better than that, how many did you glue? *Bonus:* How many more do you need to glue to fill a box of 24 crayons?

*Big kids:* If the machine makes blue-violet crayons the 1st day, lime green the next day, mac ‘n cheese the next, and then blue-violet again to repeat the pattern, what color does it make on the 20th day? *Bonus:* When does it make the 7th batch of blue-violet?

*The sky’s the limit:* The last time we visited the Easton, PA factory, the counter sign said the factory had made (PARENTS: show or read this aloud as just digits) 146,037,500,000 crayons! Can you say that number in words?

Answers:

*Wee ones:* 4 colors.

*Little kids:* 8 crayons. *Bonus:* 16 more.

*Big kids:* Lime green, since it’s the 2nd crayon in the new set of 3 starting on 19. *Bonus:* On the 19th day, since it will have just finished 6 full batches of the 3 colors.

*The sky’s the limit:* One hundred forty-six billion, thirty-seven million, five hundred thousand crayons!

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]]>The post Just for Kicks appeared first on Bedtime Math.

]]>Have you ever kicked a ball as hard as you could? How far did it go? Can you imagine it flying over a couple of houses? That’s what happens every year in American football. The game uses a funny-looking, pointy brown ball, which players have to bring to the other end of the field by throwing it or running with it. If they make it to the end zone, they score a “touchdown,” for 6 points. But if the team with the ball thinks they can’t make it, they can try to kick the ball between 2 yellow bars and over the bar holding them up. The other team tries to block the kick, but if the kicker can get the ball over their arms and through that U shape, his team scores 3 points for a “field goal. So from how far away can the kicker kick the ball through those bars? That’s where the math comes in!

*Wee ones:* If the kicker kicks the ball through, then misses on the 2nd try, then makes the 3rd try, then misses the 4th…what do you guess happens on the 5th try?

*Little kids:* If a team scores all its points from 3-point field goals, could they have a total score of 10? *Bonus:* The longest high-school football kick was 68 yards — longer than 2-3 houses in a row! But the longest college kick ever was 1 yard longer. How long was that kick?

*Big kids:* If you kick the ball right over your 30-foot house, how many *yards* long is that? (Reminder: A yard equals 3 feet.) *Bonus:* If you have a big foot and can kick the ball 70 yards, how many feet would that be?

*The sky’s the limit:* If the best 10-year-old can kick the ball 36 yards and the best college player kicked that 68-yard kick, how far can you kick it if your distance is halfway between those?

Answers:

*Wee ones:* The kick makes it.

*Little kids:* No, because 3s can’t stack up to add to 10 — you will get 9 or 12. *Bonus:* 69 yards.

*Big kids:* 10 yards. *Bonus:* 210 feet.

*The sky’s the limit:* 52 yards. 36 and 68 are 32 yards apart, so your kick will be half of that more than the 36, or 16 yards farther.

The post Just for Kicks appeared first on Bedtime Math.

]]>The post Getting Carried Away – by Ants appeared first on Bedtime Math.

]]>And yet another wild fan question: Sophia Y. asked, how many ants could pick you up and carry you? Ants are famous for being strong: a leafcutter ant can carry 50 times its own weight! Of course, an ant weighs only 1/200th of a gram at most. So that big ant can carry only about 1/4 gram. A gram is only 1/28th of an ounce, and an ounce is 1/16th of a pound…so it would take several hundred ants to pick up each pound of the person. Luckily, there are lots of ants to help out: scientists think there are about 1 million trillion ants on Earth, or one *quintillion* — and that together they weigh the same as all of us humans! So let’s not get carried away here.

*Wee ones:* Who has more legs, you or one of those 6-legged ants?

*Little kids:* If 4 ants can pick up a 1-gram paper clip, how many ants does it take to pick up 2? *Bonus:* Which needs more ants to pick it up, a 16-oz bag of chips or a 24-ounce bag of cookies?

*Big kids:* If you carried a truck that weighed 50 times your weight, how heavy would that be? (You can round off your weight to the nearest multiple of 10 if you like.) *Bonus:* If we round off that it takes 500 ants to carry 1 pound, how many ants does it take to carry *you*?

Answers:

*Wee ones:* The ant has more legs.

*Little kids:* 8 ants. *Bonus:* The bag of cookies.

*Big kids:* Different for everyone…multiply your weight in pounds by 50. *Bonus:* Again, different for everyone…multiply your weight by 500, which is the same as your previous answer here times 10. Now try imagining that many ants!

And thank you again Sophia for some very antsy math! If any of you out there has a question you’d like us to solve, just send it in to feedback@bedtimemath.org and we’ll give it a try!

The post Getting Carried Away – by Ants appeared first on Bedtime Math.

]]>The post Sheep Parade appeared first on Bedtime Math.

]]>If you’re reading this at bedtime, what better way to fall asleep than to count sheep — and better yet, a whole parade of them? Ever since the year 1273, Spanish shepherds have “migrated” (moved) their sheep from northern Spain to the warmer, sunnier southern parts for winter. For centuries the farmers have used the exact same 78,000 miles of paths, which run right through the giant city of Madrid. In early November nearly 1 million sheep walk past cafes, clothing stores and other places sheep don’t normally go. The shepherds pay a small coin to City Hall to parade through, and the sheep get to see all the great wool sweaters they’ve helped make.

*Wee ones:* If a sheep has 4 legs and you have 2, who has more?

*Little kids:* If the shepherds herded 600,000 sheep and 100,000 cows, how many animals was that in total? *Bonus: *If the sheep marched through on November 2, how many days ago was that? (Today is Nov. 13.)

*Big kids:* If the sheep walked 12 miles of Madrid streets and saw 10 shops per mile, how many shops did the sheep see? *Bonus:* Spain is about 700 miles tall from north to south. If a sheep has to walk just half that distance, how far does it walk?

Answers:

*Wee ones:* The sheep.

*Little kids:* 700,000 animals. *Bonus:* 11 days ago.

*Big kids:* 120 shops. *Bonus:* 350 miles.

The post Sheep Parade appeared first on Bedtime Math.

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