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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]]>Whipping air bubbles into cream makes it take up a lot more “volume,” or space. In the Bedtime Math test kitchen, 1 cup of heavy cream generated 3 cups of whipped cream. With something as important as dessert, that’s a key fact.

The post Whipped into Shape appeared first on Bedtime Math.

]]>Whipped cream is such a tasty treat. In the summer take a bowl of fresh berries, toss some whipped cream on it — mmm. So when was this stuff invented? About 500 years ago, by a bunch of guys with long Italian and French names that are hard to say. But what made them think to whip up cream in the first place? Did they know what would happen? By the way, there was no electricity back then — they had to whip it by hand. Luckily, it was worth the work. Whipping air bubbles into cream makes it take up a lot more “volume,” or space. In the Bedtime Math test kitchen, 1 cup of heavy cream turned into 3 cups of whipped cream. For something as important as dessert, that’s a key math fact!

*Wee ones: *Whipped cream is white. Try to spot 4 white things in your room.

*Little kids:* If you can whip 2 cups of heavy cream into 6 cups of whipped cream, how many cups of air did you whip into it? *Bonus:* If you’re making whipped cream for a party, and 1 cup of heavy cream makes 3 cups of whipped cream, how much whipped cream does 3 cups make?

*Big kids:* If a can of whipped cream holds 6 cups, and when you open it it explodes and squirts 1 1/2 cups on you, how much whipped cream is left in the can? (Hint if needed: What if only 1 cup came out, and how is this different?) *Bonus:* If you then try to squirt half of what’s left into your mouth, how much is left after that? (*Hint:* To cut 4 1/2 in half, you can cut the 4 in half, then cut the 1/2 in half, then add the 2 parts back together.)

Answers:

*Wee ones: *Possible items include socks, underwear, bedsheets, toy balls, and (in the bathroom) towels and bar soap.

*Little kids:* 4 cups of air. *Bonus:* 9 cups of whipped cream (by the way, at 800 calories per cup of cream, that’s 2400 calories – about as much food as a grown-up eats in a day. Don’t try eating that all at once!).

*Big kids:* 4 1/2 cups. *Bonus:* 2 1/4 cups left.

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]]>The post Perfect Paper Pets appeared first on Bedtime Math.

]]>This feathery white baboon almost looks real. You’ll never believe what he’s really made of: paper! Canadian sculptor Calvin Nicholls shapes animals out of thousands of tiny pieces of paper. So we asked him how he does it. All that fuzzy fur is made out of rectangles of paper ½-inch wide. He cuts 50 little slits in each piece of paper to make all the little hairs. Then he glues down those pieces of paper, with just the fuzzy part sticking out. He squeezes about 25 of them in each tiny 1-inch-by-1-inch area, to make lots of fuzziness. It takes him about 10 hours to study the animal and sketch drawings of it, then about 8 hours to cut and glue all that paper to match it. At least when he’s done, he has a new pet that doesn’t need to be fed!

*Wee ones:* If Calvin glues the next 5 pieces of paper onto that baboon, what numbers would he say to count them?

*Little kids:* If he makes 3 claws on the bear’s left paw and 3 on the right paw, how many claws does he make? *Bonus:* If each claw nail uses 10 little rolled-up pieces of paper, what numbers do you say to count up the pieces in 10s?

*Big kids:* If Calvin starts gluing the fur at 9:00 in the morning, and spends 8 hours working and takes a 1-hour lunch break, when does he finish? *Bonus:* If he can cut and glue 1 piece of paper per minute, how many pieces can he power through in that time?

*The sky’s the limit:* If the baboon’s fur covers an area 8 inches tall and 10 inches wide, how many tiny fuzzy pieces of paper does it use if there are 25 pieces per square inch? (Hint if needed: How many pieces of paper are there in 4 square inches?)

Answers:

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

*Little kids:* 6 claws. *Bonus:* 10, 20, 30, 40, 50, 60.

*Big kids:* At 6:00 in the evening (9 hours later). *Bonus:* 480 pieces, since he worked for 8 hours x 60 minutes each hour.

*The sky’s the limit:* 2,000 pieces of paper!

And thank you Calvin for sharing the numbers behind your amazing work! You can all check out more photos here.

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]]>The post What Do Marshmallows, Batteries, and Glue Have in Common? appeared first on Bedtime Math.

]]>Today is Corn on the Cob Day, a great time to celebrate a very math-y food. For starters, what are all those bumpy kernels for? Unlike fruits that come from a fluffy flower, for corn the ear IS the flower, and the kernels are the seeds. It turns out that every ear of corn has to grow an even number of rows. Most ears have 16 rows, which hold 800 kernels in total. Those kernels add up fast: A “bushel” is an 8-gallon barrel, and a bushel of corn will have about 72,000 kernels and weigh 56 pounds! We use corn to make more than 3,500 things, including foods like cereal, peanut butter and marshmallows. The starch is also used to make stuff like fireworks, glue, and batteries. Very cool, but the foods sound yummier!

*Wee ones:* Corn can grow in many colors: purple, green, blackish, bluish, red, white, and of course yellow. How many colors is that?

*Little kids:* A number is even if it can be cut into 2 equal parts. What numbers from 1 to 10 are even? *Bonus:* All even numbers end in the same digits as those 5 numbers. If an ear of corn has to have an even number of rows, can it have 15 rows?

*Big kids:* If you eat every 3rd row of corn as you go 1 full time around a cob with 16 rows, at most how many rows can you eat without passing where you started? *Bonus:* A bushel (8-gallon barrel) of corn holds enough sugar to sweeten 400 cans of soda. If you drink 1 of those cans, how many cans are left?

Answers:

*Wee ones:* 7 colors.

*Little kids:* 2, 4, 6, 8 and 10. *Bonus:* No, because 5 isn’t even, either.

*Big kids:* 6 rows at most: rows 1, 4, 7, 10, 13, and 16. *Bonus:* 399 cans.

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]]>The post Clock-a-Doodle-Doo appeared first on Bedtime Math.

]]>Most of us don’t live on farms, but we all know a rooster’s crow means it’s time to wake up. Roosters like their role as alarm clock — and they work like clocks more than we realized. Scientists figured out that even when roosters stay in a dim room all day and all night, the birds crowed at the right time anyway! It’s as if they have a clock inside them.

Even wackier is that roosters crow in order based on who’s boss. Many animals have a “pecking order,” meaning they all know which bird, bear or gorilla is the biggest and scariest. Roosters all let the big “alpha” rooster crow first, then the others crow in order by less and less bossiness. Even if you sleep through your clock alarm, these guys will wake you up!

*Wee ones:* If 8 roosters have crowed, what number rooster crows next?

*Little kids:* Roosters actually crow about 2 hours before sunrise. If the sun rises in your town at 7:00 am, at what time would roosters crow there? *Bonus:* Once the sun rises, how many hours pass until the rooster crows again the next morning? (Reminder: There are 24 hours in a day.)

*Big kids: *If 4 roosters — Redford, Rickles, Rupert and Ray — all agree to shuffle their order of crowing every day, from how many line-ups can they choose? *Bonus:* If instead they assign numbers for pecking order 1 through 4, and Redford’s, Rupert’s and Ray’s numbers add up to the same as Ray’s number times itself (“squared”), what number did Ray have to get?

Answers:

*Wee ones:* Number 9.

*Little kids:* At 5:00 am. *Bonus:* 22 hours.

*Big kids: *It will be 4 x 3 x 2 x 1, or 24 line-ups. Once you choose 1 of the 4 for the 1st slot, you have 3 choices for the 2nd, giving you 4 x 3 pairs. Then each of those pairs has 2 choices for the 3rd slot (now we have 4 x 3 x 2), and then each of those triplets just gets the leftover in the last slot. *Bonus: *Ray has to be #3. The only set of 3 numbers that can add up to a perfect square (a number times itself) is 2 + 3+ 4. That adds up to 9, which is 3 x 3.

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