Give Me a Sign

Billboards are those big rectangular signs along the side of the highway, usually trying to talk you into buying something.  Since they’re a good 50 feet above you, these signs are even bigger than they look – they’re 20, 30, or even over 40 feet wide. The size depends on the speed of the traffic: the faster you’re driving, the easier it has to be for people to read it, so the bigger the letters and pictures need to be. The signs along slower streets in town, called “posters,” are 22 feet wide, but the big “bulletins” along the highway are up to 48 feet wide. Now we have digital billboards that light up like a computer screen and change the picture every few seconds, showing drivers even more things they should buy. Either one works, as long as we read it quickly: the more important thing as a driver is to keep your eyes on the road.

Wee ones: Which one is wider, a 20-foot-wide poster or a 40-foot-wide billboard?

Little kids: If a billboard is 10 feet tall and the bottom is 50 feet off the ground, how many more of those same signs could you stack edge to edge below it?  Bonus: If you want to climb up to that 50-foot sign but all you have is an 8-foot ladder, how many more feet does your ladder have to reach?

Big kids: If an adult’s face is 9 inches tall, and all objects on a billboard are 12 times life size, how tall is a face shown on a billboard?  Bonus: These giant highway signs are about as big as a house. If the front of a house has a 15-foot-wide kitchen, a 6-foot-wide hallway, and an 18-foot-wide living room, which one is wider, the house or a 48-foot-wide highway billboard?

The sky’s the limit: Suppose as a prank you decide to climb up a billboard at night and wrap a string of lights around the edge. If you need exactly 82 feet of strung lights to cover all four sides, and the area of the billboard (length times width) is 400, what are the width and height of the billboard?

 

 

 

Answers:
Wee ones: The billboard is the bigger number.

Little kids: 5 more of those signs.  Bonus: 42 more feet.

Big kids: 108 inches, or 9 feet!  Bonus: The billboard would be wider if leaned up against the house – 48 feet vs. 39.

The sky’s the limit: It’s 25 by 16 feet. We know that the width and height have to add to 41, since those two sides will use up half the lights. Those same two numbers also multiply out to 400. You can use trial and error to test the factors of 400 numbers: 40 by 10 doesn’t work, nor does 20 by 20, but 16 by 25 does. Expressing this using algebra:
w + h = 41, so h=41-w
w x h = 400. Replacing h, you get
w x (41-w)=400
41w – w^2=400, or w^2-41w+400=0
…and then you still need trial and error to break it down into
(w-25) x (w-16)=0.  So w=16 or 25.

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Jailbreak

Groundhogs usually don’t do anything exciting. They’re the round, brown, kind of boring animals waddling alongside highways and across our backyards. So you can imagine everyone’s surprise last week when a groundhog came barreling into a kids’ baseball practice in New Jersey and started chasing after the kids, even though he himself was only the size of a soccer ball. When the coach ran over to fend him off, the groundhog started chasing the coach, who dove into his car for safety. To make sure the animal didn’t bite anyone, the police captured the groundhog with a loop, but he broke the rope. Then after being caught again and caged in an animal shelter, he broke out of there. That’s one groundhog who doesn’t want to be in captivity – or who just really wants to play baseball.

Wee ones: If there are 9 kids practicing baseball and the groundhog joins in the game, now how many players are there including him?

Little kids: If you have 9 kids and a groundhog running around the field, how many little feet are on the move?  Bonus: If you can sprint (run your fastest) 100 feet but the groundhog can make it only 70 feet, by how far can you outrun the groundhog?

Big kids: The coach estimated that the terrifying groundhog weighed 20 pounds. How much more do you weigh?  Bonus: If you have 9 kids averaging 50 pounds each, how much more does the baseball team weigh than the feisty groundhog?

 

 

 

Answers:
Wee ones: 10 “players” total.

Little kids: 22 feet: 18 people feet and 4 groundhog feet.  Bonus: 30 feet farther.

Big kids: Different for everyone…subtract 20 from your weight in pounds.  Bonus: 430 pounds more (450 minus the 20).

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Sticky Fingers

If you’ve ever looked closely at your own fingertips, you’ve probably noticed that the skin is grooved with very, very thin lines in a spirally pattern.  That’s your fingerprint, and it is your very own: every single person has his or her own special pattern. There are six basic styles of fingerprints, though: loop from right, loop from left, arch, whorl, double loop, and “eclectic,” which basically covers all the weird remaining ones that don’t have a name. These grooves in our fingers help us grip objects — but as a special bonus, fingerprints also leave tracks showing exactly whose fingers they are. You can use your fingerprints on scanners to get permission to open doors, but your fingerprints can also show that you were the thief who opened the cookie jar.  Just one more good reason to wash your hands.

Wee ones: There are 6 types of fingerprints, but half of those involve “loops.” How many loopy fingerprint types are there?

Little kids: If you have messy chocolate all over one hand, and you fully touch the table with that hand 3 times, how many total fingerprint marks do you leave on the table?  Bonus: If 2 friends each have both hands covered with chocolate and they each rest all 10 fingers on the table, now how many total fingerprints are there?

Big kids: One way to see your fingerprint is to press your finger on an ink pad, then on a fresh empty balloon, and then blow up the balloon to watch the design stretch out. If your fingerprint covers a space that gets 5 times as tall and 5 times as wide when you inflate the balloon, how many of your original fingerprint could fit in that new space?  Bonus: If that area now doubles in each direction, now how many times as big is it relative to your original fingerprint?

The sky’s the limit: Suppose your class at school has 12 boys and 12 girls, all with loop, arch or whorl fingerprints.  If half the boys and 2/3 of the girls have loopy fingerprints, and half the remaining kids have arch fingerprints but that includes 3 more boys than girls, how many girls have whorls?

 

 

 

Answers:
Wee ones: 3 loopy types.

Little kids: 15 fingerprints.  Bonus: 35 fingerprints, since the friends added 20.

Big kids: 25 fingerprints.  Bonus: 100 times as big.

The sky’s the limit: 6 boys and 8 girls have loops, leaving 6 boys and 4 girls with other types.  Half, or 5 in total, have arches, but if that includes 3 more boys than girls, then only 1 girl has arches (along with 4 boys). That leaves 3 girls with whorls.

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Water Shooter

It’s pretty exciting when a volcano explodes and shoots red-hot lava, which is melted rock. Well, nature does this with water, too. A geyser is a rare underground spring that sometimes bursts up through the ground.  One of the most famous geysers is Old Faithful in Yellowstone National Park.  It gets its name because it is very predictable: it erupts every 91 minutes, shooting hot water and steam up to 185 feet in the air for as long as 5 minutes at a time. In the old days, people tried to use Old Faithful to wash their clothes, but found that it was too powerful and the blasting water tore everything to shreds.  Because of changes in the earth, the length of each eruption and the amount of water that comes out have both changed, too. But Old Faithful still deserves its name, as it still shoots boiling water high into the air about every hour and a half – whether you’re waiting to do laundry or not.

Wee ones: If you can spray water out of your mouth for a whole minute straight, but Old Faithful can blast water for 5 minutes straight, how much longer than you can Old Faithful spray?

Little kids:  Is 185 feet about as tall as a person, a building, or a mountain?  Bonus: If the last eruption ended at 3:10 pm, at what time will you see the next one if it’s 91 minutes later? (Reminder: there are 60 minutes in an hour.)

Big kids: For a sense of how tall 185 feet is, you can compare it to other tall things, like a house. If each story adds 10 feet of height and so does the roof, about how many houses with 2 stories and a roof do you have to stack to match Old Faithful?  Bonus: You can also compare to an American football field, which is 120 yards long. About what fraction of a football field standing on end would the highest eruption match? (Reminder: a yard equals 3 feet.)

 

 

 

Answers:
Wee ones: 4 minutes longer.

Little kids: About as tall as a building with 18 floors.  Bonus: 4:41 pm.

Big kids: Each house is 30 feet tall, so you’d need about 6 houses, which stack to 180 feet.  Bonus: A football field is 360 feet high, so 185 feet is about half a football field.

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Cicadian Rhythms

Okay, let’s get this straight once and for all. We’ve heard that cicadas, those fat grasshoppers that make that loud, high-pitched chirping noise, come around every 17 years. We’ve also heard there’s another type that shows up every 13 years. And the fact is, we feel like we see or hear a couple of them every year. It turns out the 17-year cicada lives in the Northeast U.S. and the 13-year is its Southern cousin.  This year is apparently the big year for the 17-year cicada crowd to come out from underground, lay eggs, and then disappear. If you live in the Northeast and listen carefully while outdoors, you’ll hear the loud, whirring sound they make. Apparently their 90-decibel shriek is as loud as a subway — of course, as one person pointed out, if you’d been stuck underground for 17 years, you’d be screaming, too.

Wee ones: A cicada is an insect and therefore has 6 legs. How many more legs does it have than a person?

Little kids: Were you around when the cicadas last showed up 17 years ago?  Bonus: How old will you be when the 17-year cicadas come again?

Big kids: In what calendar year will the 17-year cicadas return again?  Bonus: Cicadas come out when the weather reaches 64 degrees. If it’s 49 degrees out where you are, how much warmer would it have to be?

The sky’s the limit: If the 17-year cicada shows up, and then 3 years later the 13-year cicada shows up, how many years after that will they both show up the same year?

 

 

 

Answers:
Wee ones: 4 more legs.

Little kids: Different for everyone…see if your age is less than 17!  Bonus: Add 17 to your age today.

Big kids: In 2030.  Bonus: 15 degrees warmer.

The sky’s the limit: Every cycle of the 13-year cicada leaves the 17-year cicada behind by another 4 years. So to start, the 17-year has 14 years to wait. The next time the 13-year shows up, the 17-year is just 1 year behind. Counting from there, it will then be 5 years behind, then 9, 13, and finally 17 years behind, which means they both show up that year. That makes 5 cycles of the 13-year cicada, or 65 years.

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