Howling at the Moon

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There’s a full moon tonight, and a full moon makes many of us think of wolves howling at the moon. But the truth is, that isn’t what wolves are howling at. Wolves use howls to locate other wolves in their pack. They also howl to keep away other packs of wolves. So why did we ever think it had to do with the moon? One theory is that wolves howl more when the moon is full because they can see each other better. Also, for the thousands of years we didn’t yet have electricity and lamps, we humans tended to be out and about more on nights when the moon was full because we could see better ourselves, so we were more likely to see and hear the howling those nights. Either way, those wolves always seem to make a racket right when we’re trying to sleep.

Wee ones: If you hear 2 wolves howling and then 3 other wolves join in, how many wolves are howling now?

Little kids: Wolves can hold their howl for a good half minute, to give other wolves in the pack enough time to find them. If you can howl for 21 seconds but a wolf can last for 29 seconds, for how much longer than you can the wolf howl?  Bonus: If a wolf can howl only 20 seconds and a fellow wolf needs him to howl 3 times to find him, for how many seconds in total does the wolf need to howl?

Big kids: Wolves can cover great distances, up to 9 miles in a single day. If a wolf keeps up that pace for a whole week, how many miles does he travel?  Bonus: If a wolf travels 8 miles a day for a week, then cuts his pace in half for a second week, how many miles does he travel in total?

The sky’s the limit: Sound travels 1 mile every 5 seconds. If a wolf’s howl echoes off a cliff towards you, and at that moment you’re 4 miles from the cliff and driving toward it at 90 miles an hour, what fraction of a mile have you traveled by the time you hear the echo?

 

 

 

Answers:
Wee ones: 5 wolves.

Little kids: 8 seconds longer.  Bonus: 60 seconds (1 minute).

Big kids: 63 miles.  Bonus: 84 miles: 56 the first week, 28 the second.

The sky’s the limit: 4/9 of a mile. Sound travels 1 mile every 5 seconds, whereas you’re traveling 1 ½ miles every 60 seconds; 1/12 of that comes to 1/8 of a mile in 5 seconds. So the sound is traveling 8 times as fast as you, and when you meet it will have covered 8/9 of the distance and you will have covered 1/9. So you will travel 4/9 of a mile.
To show this with algebra: if d is the distance you travel, d+8d=4 miles, so 9d=4 and d=4/9.

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Next Floor: Space!

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Elevator rides are fun to begin with, especially when you jump right when it’s slowing down and you fly up higher than usual. But how would you like to take an elevator into space? Scientists think it may be possible. Basically it would use a very long rope attached to the ground here on Earth, with a “counterweight” of over 100,000 pounds at the other end way up in space. That weight would keep the rope tight because as Earth spins, it would sling the weight around, just like when you twirl a yo-yo around your head and the string stays tight. The counterweight would circle Earth in “geostationary orbit,” meaning it would stay above the same spot on Earth so you don’t have a crazy elevator ride on an angle. It all depends on finding a strong enough material for that cable – but as soon as we do, we’re pressing Up for the next ride.

Wee ones: If someday we build 4 space elevators, then 1 goes out of service for repairs, how many elevators are left running?

Little kids: The super-strong cable for the space elevator would be about 24,000 miles long. To compare, Earth is about 25,000 miles around. How many miles longer would the cable have to be to wrap all the way around Earth? (Hint: just think in chunks of a thousand.)  Bonus: How much cable would you need to build 2 elevators?

Big kids: 100,000 pounds is a lot of weight. If a big car weighs about 4,000 pounds, how many cars would you have to strap together in space as the counterweight?  Bonus: If the space elevator travels 240 miles an hour, how long would it take you to ride the 24,000 miles from the ground up to the top in space?

 

 

 

Answers:
Wee ones: 3 elevators left.

Little kids: 1,000 miles longer (1 thousand).  Bonus: 48,000 miles (48 thousand).

Big kids: 25 cars.  Bonus: 100 hours.

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How to Look Like a Math Whiz

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Numbers are very regular and make beautiful patterns, and if you know those patterns, you can do some pretty cool tricks. Some tricks let you add and multiply big numbers in your head. It’s easy to multiply a big number by 11, and to square numbers ending in 5 (to square a number means to multiply it by itself). As this video on vedic math shows, you can even multiply big numbers by other big numbers in your head. Today we’ll show you some of the coolest number tricks out there, so you can wow your family and friends!

Wee ones: A fun trick is to figure out whether you can cut a number into 3 equal pieces (called dividing). If its digits add up to something divisible by 3, then the original number is divisible, too! Is 141 divisible by 3?

Little kids: To multiply a 2-digit number by 11, you just add its two digits and stick the answer in between the 2 digits. So for example, 32 times 11 is 352 (because 3+2=5). Quick, can you multiply 43 x 11?  Bonus: To multiply a big number by 5, you cut it in half and tack on a zero. Quick, what’s 24 x 5?

Big kids: That works in the opposite direction, too: to divide by 5, you chop a zero off and then double what’s left. Quick, what’s 620 divided by 5?  Bonus: To get the square of any 2-digit number that ends in 5, you take the first digit, multiply it by the next digit up, and then tack on 25 to the end. So for example, 35×35 is 1225, because 3×4=12, and then you tack on 25. Quick, what’s 55×55?

 

 

 

Answers:
Wee ones: Yes, because 1+4+1=6, and if you hold up 6 fingers, you see that you can group them into sets of 3.

Little kids: 473.  Bonus: 120, because half of 24 is 12.

Big kids: 124, since that’s 62 x 2. A great way to figure out the tip at restaurants.  Bonus: 3025, since 5 x 6 is 30, then tack on a 25.

And a big thank-you to Talie B. for sharing that video!

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Flipping Coins with Mickey

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You probably think toys today are really cool compared to the bummer ones your parents must have had. Well, even though your parents lived in caves and ate dirt for dinner, we all had some cool toys ourselves – like the Mickey Mouse coin sorter, shown here. This toy hails from decades ago, or at least that’s when I got mine (let’s not focus on which decade…), and is both piggy bank and marvel of machinery. When you stick a coin into the slot at the top right, if it’s a quarter it’s heavy enough to tip the first red seesaw and fall into Mickey’s right arm. If it’s a nickel, it shoots straight through to his left arm. Pennies and dimes are narrower so they fall through a hole in that seesaw, then either tip or shoot through the bottom seesaw into the correct leg. So smart and simple, all without batteries, lasers or digital screens. Even without electricity or blinking lights, the money still adds up.

Wee ones: If you stick 2 quarters, 3 dimes, 2 nickels and a penny into Mickey, how many coins did you sort?

Little kids: If Mickey has 4 coins in each arm and 4 coins in each leg – 4 quarters, 4 dimes, 4 nickels, 4 pennies – how many coins is he holding?  Bonus: How many seesaw tips did those coins make happen? (Again, quarters and pennies each tip one seesaw; dimes and nickels shoot through.)

Big kids: If you put 5 of each type of coin into Mickey, how much money is that, in cents?  Bonus: If you swap out all the pennies and replace them with 5 extra quarters, now how much money do you have?

The sky’s the limit: If you put in 82 cents and exactly 4 seesaw tips happened, how many combination of coins could you have put in?

 

 

 

Answers:
Wee ones: 8 coins.

Little kids: 16 coins.  Bonus: 8 tips.

Big kids: 205 cents or $2.05, since it’s 5 times 41 cents.  Bonus: $3.25.

The sky’s the limit: 4 possibilities. You had to have put in 2 quarters (one tip each) plus 2 pennies for 2 more tips, so nickels or dimes make up the remaining 30 cents. Possible combinations are 3 dimes 0 nickels, 2 dimes 2 nickels, 1 dime 4 nickels, and 0 dimes 6 nickels, always with 2 quarters and 2 pennies.

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On the Block

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We aren’t talking about building blocks here, or street blocks: we’re talking about the auction block.  Sometimes when lots of grown-ups (or kids) want to buy the same item, the seller can put it up for “auction.”  All the interested buyers decide what they’re willing to pay – they “bid” – and the highest bidder wins the item and has to pay that amount. In a live auction, bidders call out higher and higher numbers and the last one standing wins it…so sometimes people get competitive and get stuck paying a lot more than they planned. In a “sealed auction,” you just put your bid in an envelope and all envelopes are opened at once; the high bid wins and that’s it, no second chances. As we’ll see here, there are other ways to run auctions – and maybe to score an awesome deal.

Wee ones: If someone bids $3 for a 1960′s Raggedy Ann doll, and you bid $3 more than that, how much will you have to pay?

Little kids: Live bidding goes up in “increments,” or jumps of a certain size. If an old-fashioned Mickey Mouse coin sorter has a current bid of $25 with increments of $5, how much will the next bid be?  Bonus: If the increments after that become $10, what will be the next bid after that?

Big kids: If there’s a sealed auction for the first American Girl doll ever, and the 3 bids are $54, $12 more than that, and then $25 more than the middle bid, what’s the winning bid?  Bonus: In a “Dutch auction,” the auctioneer calls out prices that get lower until the first person who’s willing to pay calls out. If bidding starts at $90 with $2 increments for each drop in price, and you have $75 on you, how many prices do you have to skip before you can bid?

 

 

 

Answers:
Wee ones: $6.

Little kids: $30.  Bonus: $40.

Big kids: $91, since the middle bid is $66.  Bonus: 8 prices to skip. The price has to drop to $74, which is $16 lower, requiring 7 drops in prices that you skip along with the original $90 bid.

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