The post Double-Trouble Dominoes appeared first on Bedtime Math.

]]>Dominoes are little toy rectangle tiles with dots on them. People like to stand them up on end in a long row, so when the first domino falls over, it knocks over the next domino, which knocks over the next…pretty soon you have a rippling wave of falling dominoes. In this simple but amazing video, Stephen Morris shows that a little domino can knock over another one that’s 1 1/2 times as big in each direction. Then that one can tip over one that ‘s 1 1/2 times as big again. In this domino chain, the first one is only 1/4 inch tall, but the 13th domino weighs more than 100 pounds! If he kept going, the 29th domino would be as tall as the Empire State Building (1,454 feet). We’d all better get out of the way!

*Wee ones:* The chain uses 13 dominoes. How many of them can you count starting from 1? Count as high as you can!

*Little kids:* If there are 13 dominoes and only the 1st has fallen, how many are left standing? *Bonus:* If the dominoes start falling, but you stop the wave by pulling out the 5th domino, how many dominoes are left standing?

*Big kids:* If each domino could tip over a domino twice as tall…how many times as tall as the 1st domino would the 5th one be? *Bonus:* If the first domino is 1 inch tall and they keep doubling, which domino would be the first one that’s taller than you are?

Answers:

*Wee ones:* 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.

*Little kids:* 12 dominoes still standing. *Bonus:* 8 dominoes still standing.

*Big kids:* 16 times as tall, since the 2nd is twice as tall, the 3rd is 4 times as tall, and the 4th is 8 times as tall. *Bonus:* Different for everyone…compare your height to the few that are human-sized: if the 5th domino is 16 inches tall, the 6th is 32 inches (2 feet 8 inches), and the 7th is 64 inches (5 feet 4 inches). The 8th is 128 inches, more than 10 feet tall!

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]]>The post The Best Cupcake Combo appeared first on Bedtime Math.

]]>Do you know what a number cake is? Guess what — you’ve probably eaten one! That’s what cupcakes were called when they were first made in the 1800s. The first recipes called for 1 cup of butter, 2 cups of sugar, 3 cups of flour, 4 eggs…okay, and 1 cup of milk and 1 spoonful of baking soda. We now mix in other flavors and smear frosting on top. We love this set of cupcakes here because it puts each type of frosting (chocolate, coffee, and vanilla) on top of each cake flavor (chocolate and yellow). Of course, people like some frosting flavors more than others…so you have to do the math to see if you’ll get your favorite.

*Wee ones:* How many cupcakes can you count in each row going across?

*Little kids:* How many cupcakes can you count in the whole box? *Bonus:* If 4 of them have coffee frosting, how many don’t?

*Big kids:* If you instead had 3 kinds of cupcake cake — chocolate, yellow, and red velvet — with 5 kinds of frosting — chocolate, vanilla, coffee, cream cheese, and pink — how many combinations of 1 cake flavor and 1 frosting flavor could you come up with?* Bonus:* If you have 5 cake flavors and you want to make at least 32 different cake/icing pairs, how many icing flavors do you need to make?

*The sky’s the limit:* If the number of cake flavors and icing flavors add up to 10, and together they can make 24 cake/icing pairs, how many cake and icing flavors could there be?

Answers:

*Wee ones:* 4 cupcakes.

*Little kids:* 12 cupcakes. Bonus: 8 cupcakes.

*Big kids:* 15 combinations: 5 icings for each cake flavor. *Bonus:* You’ll need 7 flavors, since 6 flavors would give you only 30 pairs.

*The sky’s the limit:* There are either 4 cake flavors topped with 6 types of icing, or 6 cake flavors and 4 types of icing. If there are 24 pairs possible, you need 2 numbers that multiply to 24 that also add up to 10. The factor pairs that multiply to 24 are 1 and 24, 2 and 12, 3 and 8, and 4 and 6. 4 and 6 is the only one that adds up to 10, so they are the number of cake and icing flavors, or the other way around.

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]]>The post Monkey Bars in the Sky appeared first on Bedtime Math.

]]>Hey, are those people flying through the sky? Not quite: they’re climbing through it! What you see is a set of ropes crisscrossing the inside of a big poofy blow-up dome. On monkey bars, you can swing only forwards or backwards (1 dimension). And on a rock wall, you can climb only up and down, or side to side (2 dimensions). Here you can go up and down, front to back, AND side to side. Best of all, you can let the air out of this giant jungle gym, roll it up, and carry it somewhere else. Maybe they’ll make a smaller size that can fit in a kid’s bedroom…

*Wee ones:* What shapes can you see the ropes make in the top picture?

*Little kids:* If you climb up 2 ropes, then up 3 more ropes, then up 2 more ropes, how many ropes have you climbed? *Bonus:* If the ropes are all spaced 2 feet apart, how far do you climb if you reach the 5th rope? Count up by 2s!

*Big kids:* If one wall has 12 rows of ropes with 10 ropes in each, how many ropes are coming out of that side? *Bonus:* If there are the same number of ropes running up/down and back to front as there are side to side, how many different ropes are there in total?

Answers:

*Wee ones:* Triangles, then all kinds of 4-sided shapes like rectangles, squares and trapezoids; you might even find a pentagon (5 sides)!

*Little kids:* 7 ropes. *Bonus:* 10 feet.

*Big kids:* 120 ropes. *Bonus*: 360 ropes.

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]]>The post Bouncing off the Walls appeared first on Bedtime Math.

]]>Tractors, steam rollers and other trucks may seem like all work and no play. But when a couple of guys stuck a basketball hoop on a spinning forklift, that changed everything. A forklift is a small truck with two poles that stick out to lift heavy objects. In this video, two friends strap a basketball hoop onto the sticks, which the forklift jacks up a good 20 feet into the air. Then one guy does a whole set of amazing shots. He bounces the ball onto the floor and it shoots all the way up to fall into the basket; then he chucks the ball at the forklift while it’s moving, or at a wall so it can bounce into the hoop. We don’t know the numbers behind these amazing shots, but we can use math to guess!

*Wee ones:* What shape is a basketball, or any ball you like to play with?

*Little kids:* If the ball bounces 23 feet high above the ground, does it go as high as the 20-foot basketball hoop? *Bonus:* If you’re 4 feet tall and bounce a ball twice as high, how high does the ball bounce?

*Big kids:* If the basketball guy hurls the ball 25 feet at the wall and it bounces off to fly 11 feet to reach the hoop, how many feet does it travel in total? *Bonus:* If the guy tries 26 crazy shots like this and 1/2 of them go in, how many does he make?

*The sky’s the limit:* If the guy throws the ball at the forklift at 10 feet per second, and at the same time the forklift drives straight at him at 20 feet per second, how many feet from the guy will the ball and the forklift meet if they start 90 feet apart?

Answers:

*Wee ones:* A circle — or in 3 dimensions, a “sphere.”

*Little kids:* Yes. In fact, it bounces 3 feet higher than the hoop. *Bonus:* 8 feet.

*Big kids:* 36 feet. *Bonus:* 13 shots.

*The sky’s the limit:* 30 feet. For every chunk of distance the ball travels, the forklift travels twice as much. So the ball will go 1/3 of the total distance and the forklift will travel 2/3 of it.1/3 of 90 feet is 30 feet.

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]]>The post A Surprise Prickly Pet appeared first on Bedtime Math.

]]>Animals don’t want other animals to eat them. So they find clever ways to hide. Some bugs and birds are the same color as the leaves or dirt around them, meaning they’re “camouflaged” and are hard to see. Chameleons can turn the same color as the colors around them in just minutes. But the mutable rainfrog from Ecuador might be the winner: it can change the shape of its skin, turning from smooth to spiky in just 3 minutes. This helps it blend in with tree bark and other scratchy stuff. Scientists studying it were at first really confused: they had scooped up the spiky frog in a cup, then an hour later it looked totally different! They wondered if the frog had swapped places with a friend. But no, he had just changed his skin — and had become a nicer, less prickly pet.

*Wee ones:* If the frog is spiky, then smooth, then spiky, then smooth…what shape does it take next?

*Little kids:* If you have 6 of these funny frogs in spiky mode and 1 more who’s smooth, how many rainfrogs do you have? *Bonus:* If the frog can switch from spiky to smooth in 3 minutes, then changes right back in the next 3 minutes, how many minutes did it spend changing its shape?

*Big kids:* If you make your hair go from flat to spiky, and it takes 7 times as long as the 3-minute rainfrog, how long does your hair change take? *Bonus:* If you start spiking your hair at 3:50 pm, when is it finally fully spiky?

Answers:

*Wee ones:* Spiky.

*Little kids:* 7 frogs. *Bonus:* 6 minutes.

*Big kids:* 21 minutes. *Bonus:* At 4:11 pm.

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]]>The post Real-Life Treasure Hunt appeared first on Bedtime Math.

]]>You never know what’s buried in your backyard. Well, one California couple found real treasure in theirs! When they saw a can sticking out of the ground, they dug and dug, and found eight cans filled with 1,427 gold coins! The mix of $5 coins, $10 coins and $20 coins was minted (made) between 1847 and 1894, back when Americans used coins for those amounts. If you add up all those $10s and $20s, the coins have a total face value of almost $28,000. But they’re worth far more than that, because the older a coin, the fewer of that coin we still have, and so the more people will pay to own that coin. One of the coins is worth over $1 million all by itself, and all together the collection could sell for about $10 million!

*Wee ones:* Which has a bigger number on it, a $5 coin or a $10 coin?

*Little kids:* If you found two $5 coins, how much money would you have? *Bonus:* If the coins are worth $10 million total and just 1 of them is worth $1 million, how much are the others worth all together?

*Big kids:* If you pulled out a $5 coin, then a $10, then a $20, then a $5 again to repeat the pattern…how much would the first 6 coins be worth together? *Bonus:* If the couple buried the 1,427 coins again in bags, with at most 100 coins in each, at least how many bags would they need?

*The sky’s the limit:* If there were equal numbers of $20s, $10s and $5s, how many of each would you need for the face value to add exactly to $28,000?

Answers:

*Wee ones:* The $10 coin.

*Little kids:* $10. *Bonus:* $9 million.

*Big kids:* $70. *Bonus:* At least 15 bags, since 14 bags would hold only 1,400 coins.

*The sky’s the limit:* One trio of a $20 coin, a $10 and a $5 adds up to $35, so you just need to find out how many sets of $35 go into $28,000 — and you can guess it will go evenly, since both are divisible by 7! 8 sets of $35 are worth $280, and you need 100 times as much as that, so you need 800 of each coin.

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]]>The post When Garbage Goes Flying appeared first on Bedtime Math.

]]>Do you recycle? Recycling means you take used plastic, paper and metal, and turn it into clean new plastic, paper and metal. A lot of towns let us mix all our recycling in one bag. How do they unmix it all? This wild video shows how Philadelphia does it. Once the workers pull out big plastic toys and other non-recyclable junk, everything else flips and bounces over big turning gears. Paper floats up and away over the top, while heavier pieces fall down through the cracks. A huge vacuum sucks up all the plastic bags. Then a giant magnet pulls out all the metal cans. Every pound of that recycled paper or plastic saves enough energy to light a few light bulbs. So keep recycling!

*Wee ones:* If you recycle paper, plastic, glass and metal, how many materials are you recycling?

*Little kids:* If you throw a plastic bottle into the recycling bin, then a glass one, then a plastic and so on, what kind of bottle will the 8th one be? *Bonus:* If the tractor claw grabs 100 pounds at a time from the garbage truck, how many times does it need to grab to get 400 pounds?

*Big kids:* If they can pull out glass, metal, plastic, and paper in any order EXCEPT paper gets pulled first, in how many different orders can they pull stuff? *Bonus:* Every bottle you recycle saves enough energy to run a computer for 25 minutes! How much computer time do you get from saving 5 bottles?

Answers:

*Wee ones:* 4 materials.

*Little kids:* A glass bottle. *Bonus:* 4 times.

*Big kids:* The other 3 materials can fall in 6 orders: GMP, GPM, MGP, MPG, PGM, PMG. *Bonus:* 125 minutes.

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]]>The post Bus-ting Out appeared first on Bedtime Math.

]]>Whoa — is that bus really running on 2 giant toy batteries? Nope — that’s a trick of the eye. Those batteries are painted on. It’s amazing what you can do with paint if your artwork looks real. On the bus below it, someone painted around the wheels to make them look like eyes. And in the third, the stretchy part of the bus looks like the bendy part of a toothbrush. Buses are a good 40-50 feet long, so these eyes, batteries and brushes are way, way bigger than real ones. How much bigger are they?

*Wee ones:* How many batteries do you see on the first bus?

*Little Kids:* If the bus tire is 3 feet wide and the eye painted around it is 5 feet wider, how wide is that eye? *Bonus:* If your whole body is 4 feet tall, how much longer is that eye than you if you lie down next to it?

*Big kids:* If the bus toothbrush is 10 feet long and your own toothbrush is just 8 inches, how many inches longer is the bus toothbrush? (Reminder: 1 foot has 12 inches.) *Bonus:* If the 2 eyes together stretch across 20 feet of the bus, and your own eyes span just 6 inches of your face, how many times as wide is the bus’s “face”?

Answers:

*Wee ones:* 2 batteries.

*Little kids:* 8 feet wide. *Bonus:* 4 feet longer.

*Big kids:* 112 inches longer, since the big toothbrush is 120 inches long. *Bonus:* 40 times as wide!

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]]>The post The Cat in Charge appeared first on Bedtime Math.

]]>Cats love to chase mice, and love to catch them. That usually doesn’t turn out well for the mouse. But if you don’t want live mice running around your house, then a cat can help you a lot. At 10 Downing Street, where the United Kingdom’s Prime Minister lives, there’s an official job for a cat called Chief Mouser. It’s all pretty simple: the cat lives in the house, and knows what to do without being told. They’ve had an official mouse-catching cat since the year 1515, as house mice were a problem back then too. The cat who was Chief Mouser the longest was Wilberforce, who served for 18 years under 4 Prime Ministers in a row. It must be nice to have a job where all you have to do is eat!

*Wee ones:* Wilberforce was Chief Mouser for 4 PMs, ending with Margaret Thatcher. How many Prime Ministers did Wilberforce serve before her?

*Little kids:* If Chief Mouser catches a mouse, how many feet do they have together? *Bonus:* If Wilberforce served for 18 years. how much longer than your whole life is that?

*Big kids:* If the Chief Mouser is fed 2 meals a day and also catches 1 mouse every day, how many times does the cat eat in 1 week? *Bonus:* If the Chief Mouser catches 3 new mice every day, how many mice does the Chief Mouser catch this month? (Reminder: March has 31 days).

*The sky’s the limit:* We can’t tell you how many mice the Chief Mouser likes to eat each day, but if you multiply that number by itself and add 6, you get 42. How many mystery mice does the Chief Mouser eat?

Answers:

*Wee ones:* 3 more Prime Ministers.

*Little kids:* 8 feet. *Bonus:* Different for everyone…subtract your age in years from 18. If you’re 18 or older, you can find out how much longer you’ve lived!

*Big kids:* 21 meals per week. *Bonus:* 93 mice.

*The sky’s the limit:* 6 mice. If we added 6 to the number as the last step, we had 42 – 6 = 36 before that. The number that we multiply by itself (or “square”) to get 36 is 6, meaning that 6 is the “square root.”

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]]>We all like different music from each other. You and your friend might like some of the same songs, but not every song, and your parents *definitely* don't like all the same songs as you. So what about cows: do cows all like the same music? And is there one kind they like best? Scientists studied this a few years ago by playing different songs for cows to see if the cows made more milk during certain songs. They found that when listening to songs with fewer than 100 beats a minute - maybe about 1 beat per second - the cows gave 3% more milk: in the time the farmers normally got 100 cups from them, they now got an extra 3 cups. Even though people have been studying this since the 1930's, no one's sure whether music really makes cows make more milk - or more importantly, whether the milk tastes better.

The post Good Moo-sic appeared first on Bedtime Math.

]]>We all like different music from each other. You and your friend might like some of the same songs, but not every song, and your parents definitely don’t like all the same songs as you. So what about cows? Do cows all like the same music? And is there one song they like best? Scientists studied this a few years ago by playing music for cows, to see if the cows made more milk during certain songs. They found that when listening to songs with fewer than 100 beats a minute, the cows gave 3% more milk. That means that in the time the farmers normally got 100 cups from them, they now got an extra 3 cups. Even after discovering this, we still don’t know why this happens — or more importantly, whether the milk and butter taste any better.

*Wee ones:* If this picture shows 6 cows and 9 women playing music for them, were there more people or cows in the barn?

*Little kids:* There were 6 songs the cows liked best, all by different singers. If one was by Aretha Franklin, how many other singers made the list with her? *Bonus:* If your list of favorite songs has 10 more songs than that, how many favorite songs do you have?

*Big kids:* If 60 cows listened to the music and 1/2 of them made more milk, for how many cows did the test work? *Bonus:* If you normally jump 2 feet off the ground, but can jump 17 inches higher than that when you hear your favorite song, how high can you jump now? (Reminder: A foot has 12 inches.)

Answers:

*Wee ones:* More women than cows.

*Little kids:* 5 other cow singers. Bonus: 16 songs.

*Big kids:* 30 cows. Bonus: 41 inches, since you normally jump 24 inches.

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