Bedtime Math

How to Look Like a Math Whiz

laura — Wed, 22 May 2013 20:00:35 +0000

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!

Flipping Coins with Mickey

laura — Tue, 21 May 2013 20:00:05 +0000

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.

On the Block

laura — Mon, 20 May 2013 20:00:52 +0000

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.

Behind Bars

laura — Sun, 19 May 2013 20:00:41 +0000

Have you ever looked at a toy, book, or box of cereal and noticed a little rectangle of black stripes, with little numbers under it? That’s called a bar code, and that symbol tells the scanner at the store which thing you’re buying, so the store can charge you. Every item has to have its own number so prices don’t get mixed up. And each digit has its own combo of 2 or 3 thin and thick bars, which the scanner can see and count up. Now there are QR codes which show a square full of teenier squares, and smartphones can snap a photo of them. But stripey ones really set the bar.

Wee ones: If a bar code has 5 numbers in the first half and 5 in the second half, how many numbers does it have in total?

Little kids: If the digit 8 is shown using 2 fat bars and a 3 uses 1 fat bar and 1 thin, how many bars does the code 33333 88888 have? Bonus: If a 4 needs 3 bars, how many bars for the code 43434 34343?

Big kids: If an 8 uses 2 fat bars and a 9 uses 1 fat and 2 thin, how many 8s are there in a code with 12 thin bars and 14 fat ones, if the code contains only 8s and 9s? Bonus: What if the same bar code has 4 0s in the mix, where each 0 uses 2 thin bars – now how many 8s?

The sky’s the limit: If 10-digit codes can run from 00000 00000 to 99999 99999, how many codes have only odd digits for the first 5 digits?

Answers:
Wee ones: 10 digits total.

Little kids: 20 stripes, since it uses 10 digits each using 2 stripes. Bonus: Now you have 25 stripes.

Big kids: There are enough thin bars for 6 9s, which use up 6 fat bars. That leaves only 8 fat bars for 4 8s. Bonus: The 0s use up 8 thin bars, leaving only 4 unclaimed thin ones, so now there are only 2 9s. That now leaves 12 fat bars for 6 8s.

The sky’s the limit: An odd first digit knocks out half the codes, and the next knocks out half of the remaining codes, and so on. So only 1/32 of the 10,000,000,000 codes are possible. That cuts you to 5 billion, then 2.5 billion, then 1.25 billion, then 625 million, then 312.5 million, or 312,500,000. The other approach is that the first odd digit enables 5 families of codes, times 5 for each digit that follows…giving you 5x5x5x5x5x10x10x10x10x10.

Triple Crowns

laura — Sat, 18 May 2013 20:00:58 +0000

Three really is a magic number, and we love it when things happen in threes. It’s very exciting in sports, like when a hockey player scores three goals in one game, which is called a hat trick. An even more exciting threesome is the triplet of major US horse races: the Kentucky Derby, the Preakness Stakes, which happens tonight, and the Belmont Stakes. When the same horse wins all three of those races in the same year, it’s called a Triple Crown. This almost never happens: only 11 horses have ever managed to do it, and the most recent did so in 1978! But every year since Sir Barton won all three in 1919, we wait with bated breath to see if the Derby winner can at least win the Preakness and set the stage for a triple crown…and tonight it’s Orb’s big chance.

Wee ones: If a horse wins the first 2 of the 3 major races, how many races does the horse have left to win to score a Triple Crown?

Little kids: Starting in 2002, 5 horses have won the first 2 races but not the third, including I’ll Have Another last year. How many years from 2002 through 2012 have we not had a double winner? Bonus: From 2002 to 2012, how many major races were run in total?

Big kids: The last horse to get a Triple Crown was Affirmed in 1978. How many years ago was that? Bonus: If 20 horses ran in each race, and each time they all had the same chance of winning, what are the chances of the Derby winner winning the Triple Crown?

Answers:
Wee ones: 1 more race.

Little kids: That span includes 11 seasons, not 10 (this is the “fencepost problem” where you have to count both ends), so there have been 6 years with no double winner. Bonus: 33 races in those 11 years.

Big kids: 35 years. Bonus: 1 in 400. The winner of the first has a 1/20th chance the second time, and then faces those chances again. (Just to clarify, the chances of a specific horse winning all three are 1 in 8000, whereas the chances of any horse winning all three are 1 in 400.)