The post Your Fruit’s Favorite Number appeared first on Bedtime Math.

]]>Have you ever looked at an apple or banana from the store and noticed a sticker with a 4-digit number? Maybe a 4138 on a Granny Smith, or a 4432 on a pineapple? That number is a code telling stores all around the world exactly what kind of fruit or vegetable it is. They’re called Price Look-up Codes (PLUs), and they range from 3000 for Alkmene Apples to 4961 for Yellow Mangos (though they don’t run alphabetically — the list starts over at A more than once). Sure, a banana may look like a banana, but there’s more than one kind of banana, and stores sell different kinds to us for different prices. So they need to know which is which at the checkout counter. Next time you shop, take a look at the carrots or peppers you buy, and find out the codes for your favorite foods!

*Wee ones:* If you buy an apple, a banana, a pineapple, a pear, a kiwi, and a tangerine, how many fruits do you buy?

*Little kids:* If you buy 2 fruits, how many digits do their 4-digit codes have together? *Bonus:* If both codes have a 9 and a 7 in them, how many total different digits do they have?

*Big kids:* If your favorite kind of apple has code 4129 (a Fuji), and your next favorite has a code 10 more than that, what’s the other apple’s code? *Bonus:* There’s a type of apricot whose code has the same digits as your favorite apple in a different order. If that code is not quite 100 more, what does it have to be?

*The sky’s the limit:* If a code has a 1, 2, 3, and 4 in it, how many working codes can you make from those, given that all codes are between 3000 and 4961?

Answers:

*Wee ones:* 6 fruits.

*Little kids:* 8 digits. *Bonus:* Just 6 digits.

*Big kids:* 4139. *Bonus:* 4219, since 4291 would be too much.

*The sky’s the limit:* 12 possible codes, starting with 3124. The codes can start with either a 3 or a 4, and for each set the remaining digits have 6 possible orders (ABC, ACB, BAC, BCA, CAB, CBA). If you’d like to see them: 3124, 3142, 3214, 3241, 3412, 3421, then in the 4000’s we have 4123, 4132, 4213, 4231, 4312, and 4321.

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]]>The post A Fun Swim with Killer Whales appeared first on Bedtime Math.

]]>Imagine floating on the ocean and having a giant whale swim right under you! That’s what happened to Rich German in California, when he was paddling around and five orcas suddenly swam up to him. A paddleboard is just a small board that you float on – it doesn’t have sides like a boat. So there was nothing between him and them. Orcas are the huge, beautiful black-and-white cousins of the dolphin: males can be up to 30 feet long and weigh up to 6 tons. That fin on top can be 6 feet tall! Even though they’re nicknamed “killer whales,” luckily Rich knew that they’re gentle animals, so he wasn’t scared. To see what he saw, check out this video (the orcas show up about 2 minutes in).

*Wee ones:* 5 orcas swam up to Rich. What numbers would he say to count them up?

*Little kids:* If you’re 4 feet tall and the orca’s fin is 6 feet tall, how many feet above you does it reach? *Bonus:* If your bedroom is about 10 feet wide, how many rooms like that would you have to line up to match a 30-foot orca?

*Big kids:* An orca weighs about the same as a school bus. If your bus weighs 10,000 pounds and the orca weighs 1/5 more than that, how heavy is the orca? *Bonus:* If you and your friends each weigh 50 pounds, and an orca can carry 200 pounds, how many of you can ride that orca at once?

Answers:

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

*Little kids:* 2 feet more. *Bonus:* 3 rooms – that’s how huge they are!

*Big kids:* 12,000 pounds, since it weighs 2,000 pounds more. *Bonus:* 4 of you.

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]]>The post The People Flying over Your Head appeared first on Bedtime Math.

]]>Have you ever watched an airplane in the sky and wondered how many people are in there, and where they’re going? Now multiply that by all the planes in the air at any time. This webpage made a 2-minute video showing all the planes that flew over the Atlantic Ocean on a single day. There were over 2,500 flights in just 24 hours! Air traffic controllers have to tell the pilots where to fly so they don’t run into each other. So the ocean is divided into 6 areas that airports watch. As we see in the video, they divide the sky into “tracks” for planes to follow – almost like lanes on a highway – and make sure every plane is at least 10 minutes behind the next. With about 100 people or more on many planes, that’s a lot of people airborne at once.

*Wee ones:* If you’re the 9th person to get on the plane, what number passenger boards after you?

*Little kids:* If plane #1 lands and they’re all spaced to land every 10 minutes, how long until the 3rd plane lands? *Bonus:* If 400 flights fly during each busy hour in the morning, how many planes fly in a 2-hour stretch?

*Big kids:* If 7,000 people fly in the morning and twice as many fly during the afternoon, how many fly that stretch in total? *Bonus:* If there were exactly 2,500 flights and they each filled up with 100 passengers, how many people flew over the ocean that whole day?

Answers:

*Wee ones:* The 10th passenger.

*Little kids:* 20 minutes, since the 2nd plane will come in 10 minutes. *Bonus:* 800 flights.

*Big kids:* 21,000 people. *Bonus:* 250,000 people – a quarter of a million!

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]]>The post Your Own Crazy Tie-Dyed Crayons appeared first on Bedtime Math.

]]>We all know some crayon colors are more popular than others. The blue and red get used over and over until they become short little stubs, while the green-yellow might not have much work to do. But what can you do with all the leftover pieces that are too short to hold? You can melt them down and make *new *crayons. As this page on instructables.com shows, crayons melt at just 275 degrees. So if you toss the stubs in the cups of a mini-muffin tin and bake them, when they cool down you’ll have swirly, tie-dyed crayons shaped like mini-muffins. You can mix colors in each muffin cup, or make solid colors if you have, say, zillions of orange pieces. The edges will be sharp enough to draw thin lines, and if you want to switch to a different color, just flip the muffin over in your hand!

*Wee ones:* If you have to unwrap the crayons, put the pieces in tins, bake them, cool them, and then pop them out, how many steps does the project take?

*Little kids:* If you mix the white, blue and black pieces in a “cool” swirl, and the orange, yellow and green in a “warm” swirl, how many colors do you use in total? *Bonus:* If you always mix 3 new colors, how many colors will 5 muffin crayons have?

*Big kids:* The crayon muffins take up to 13 minutes to bake. If you start at 3:45 pm and bake them for 13 minutes, when do they finish? *Bonus:* If you need 8-10 pieces in each muffin cup, what’s the greatest number of muffins you can make with 50 pieces?

*The sky’s the limit:* If you have blue, red, and purple crayon pieces, and in your 24-muffin tin you put blue in 1/2 of the cups, red in 1/3 of them, and the purple in 1/4 of them, what’s the smallest number of crayon muffins that have to hold at least 2 different colors?

Answers:

*Wee ones:* 5 steps.

*Little kids:* 6 colors. *Bonus:* 15 colors.

*Big kids:* At 3:58 pm. *Bonus:* 6 muffins: you’ll make the most with 8 pieces in each, which uses 48, and the 2 leftover pieces can’t start a new muffin.

*The sky’s the limit:* 2 crayon muffins. The blue will go into 12 of the cups, and red can go into 8 of the other 12 cups. That leaves just 4 empty cups, but purple has to fill 6 cups, so there will be 2 that have to pair purple with either red or blue.

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]]>The post So You Wanna Be A…Food Stylist appeared first on Bedtime Math.

]]>The messiest foods often taste the best, but a Sloppy Joe spilling over with cheese might not look so tasty on a magazine cover or a T.V. screen. That’s why some people, like John Carofoli, actually sculpt, polish, and primp food so that it looks yummy to people, even when they can’t smell it. John sat down with us to talk about the math behind being a food stylist!

*BTM: So how did you get into food styling? Was it something you’ve always wanted to do? *

John: I can’t say that I always had this specific career in mind, but I think most people grow up with a love for good food, and I’m no exception. I was writing at the Boston Globe, and found a photographer to provide pictures for my articles. Then I actually ended up working with that photographer as a food stylist. I worked for Dunkin Donuts for 18 years, and I also wrote a book on food styling, called Food Photography and Styling.

*BTM: How do you use math to make a good-looking meal to photograph?*

John: Well, there’s lots of math in planning the entire photo shoot. Once we decide on a menu of food to photograph, we have to buy the right amount of every ingredient for each recipe. So we can save a lot of time and bother by adding up the common ingredients of all the recipes and making one shopping trip. For example, if we have 3 recipes and 2 of them call for 1/4-cup of butter and the other one calls for 1/2-cup, then we know we need to buy 1 cup of butter (2 sticks). We always have extra ingredients too, because cooking doesn’t always go as planned – if we’re doing a Thanksgiving photo shoot, we’ll usually have 20 turkeys to be sure we can make 1 look perfect!

*BTM: And what’s the best way to make that Thanksgiving bird look tasty on camera?*

John: It depends on how we’re photographing it. Here’s a secret: if a picture shows a whole turkey, it’s probably not cooked inside, because it doesn’t need to be cooked to look appetizing! We can make the bird look crispy and brown in about fifteen minutes by using a thin layer of browning agent on the turkey’s skin and putting it in an oven four or five times, spraying a new layer of browning agent each time we take it out of the oven.

*BTM: So preparing the food has all the math that you need in any kitchen, with some extra tricks. What about styling and photographing the food?*

John: Food styling is a lot like painting. Just like a painter, I work with colors, patterns, and the positive and negative shapes they create. I use those geometric ideas to create a beautiful-looking plate. But before I even style the food, we have to arrange and photograph its background: all the plates, utensils and other props. Every detail matters, right down to the angle of the fork and knife. Then we look at the photos of the background and adjust the setting so that everything will fit perfectly into the space where the photo will be published, whether that’s in print or online. Finally, after that’s all set, we can bring the food in and get our photos.

*BTM: You probably have to do that quickly, too?*

John: Oh, certainly. We fit a lot of work into a very short time. You can make food look fantastic, but all your work can be undone pretty quickly by time or gravity or other facts of life.

*BTM: So if a kid wants to grow up to be a food stylist, what math skills will they need?*

John: I think timing is everything. Well, not everything, but being able to make and stick to a schedule is definitely important. Measurements, ratios, the math used in chemistry – these skills are important for cooking in general, as well as styling food. Lastly, playing around with geometry is important to develop an artistic eye, so that you can always find a new way to present an old recipe!

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]]>The post When a Pillow Fight Isn’t Enough appeared first on Bedtime Math.

]]>How would you feel if you went to bed at night ready to conk out, and found someone — or something — already sleeping in your spot? You’d be pretty ticked off, right? Well, that’s what happens to a small dog in this video, when the cat of the house decides to take over the doggie bed. The dog, a French bulldog, is not happy at all, and as we can see, he gets to work trying to get the cat to scram – while the cat just sits there and doesn’t seem to care. Cats weigh around 8 to 12 pounds, while French bulldogs don’t weigh that much more, about 20-28 pounds for a boy dog. Sure, ants can move objects that are 50 times their own body weight, but most animals can’t do that. So this tug of war is hard work for the pup.

*Wee ones:* If the pup drags the doggie bed (and cat) 6 feet down the room, takes a breath, and then drags it 1 foot more, how many feet did he drag it?

*Little kids:* If the cat weighs 14 pounds and the dog weighs double that minus 4, how much does the dog weigh? *Bonus:* If the dog is 5 years old and moved there when he was 2, and the cat is 9 years old and moved there when he was 4, how long have they lived there together?

*Big kids:* If the cat pulls this stunt every 3rd day starting on a Sunday, how many times does he do it till it’s on a Sunday again? *Bonus:* If the dog weighs 20 pounds and could move 50 times its own weight, how heavy a cat could he shove?

Answers:

*Wee ones:* 7 feet.

*Little kids:* 24 pounds. *Bonus:* For 3 years, once the dog got there.

*Big kids:* 7 more times: since the week isn’t divisible by 3, he has to cycle through 21 days. *Bonus:* 1,000 pounds!

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]]>The post The Coldest Town on Earth appeared first on Bedtime Math.

]]>Imagine a place that is always colder than your freezer, or than the coldest day you’ve probably ever felt yourself. For whatever reason, some people like to live in places like this. The coldest town on Earth is Oymyakon, Russia, home to 500 people. The temperature is around negative 24 F in the “warmer” months — and averages negative 58 in the winter, when it’s dark for 21 hours of the day. The winter weather is so bad that planes can’t fly there, so visitors have to drive from the nearest city, which is 576 miles away. The one store in town burns all its paper trash at night to warm things up, and people have to leave their cars running all the time, 24 hours a day, so they won’t freeze up. Photographer Amos Chapple traveled 10,000 miles from New Zealand to see this crazy place himself, and found it really hard to take pictures because his camera kept freezing!

*Wee ones:* If it’s dark for 21 hours a day in Oymyakon and 20 hours in the nearest city, Yakutsk, which town has a longer nighttime?

*Little kids:* If it’s dark for 21 hours of the day, for how many hours do they have some sunlight? (Reminder if needed: A day has 24 hours.) *Bonus:* If the photographer traveled 10,000 miles to get there and another 10,000 to get back home, how long was his trip in total?

*Big kids:* Which is warmer, -30 degrees F or -55? *Bonus:* The record in Oymyakon is -90 degrees! How much colder than the usual -58 is that?

*The sky’s the limit:* If on a “warm” summer day the temperature (in degrees F) is 1/3 of the number of hours of sun, and is 8 less than that number, what’s the temperature and how long does the sun shine?

Answers:

*Wee ones:* Oymyakon.

*Little kids:* 3 hours. *Bonus:* 20,000 miles.

*Big kids:* -30 degrees. *Bonus:* 32 degrees colder.

*The sky’s the limit:* If the temperature is 1/3 of the number of hours, then the difference between them is 2/3 of the hours. That difference is 8, so 8 is 2/3 of the number of hours, giving us 12 hours of sun, and then 12-8 or 4 degrees. If you want to solve this with algebra, we know that:

t = 1/3 h , so h = 3t

and

h – 8 = t

Substituting, we get

3t – 8 = t

2t – 8 = 0

2t = 8, so t = 4 and then h = 12.

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]]>The post Digging to the Center of the Earth appeared first on Bedtime Math.

]]>Has anyone actually *tried* to dig to China? We know our planet Earth is a ball, so if you’re on one side and just dig straight through, you’d end up on the other side, right? Well, the deepest anyone has ever dug is 7 1/2 miles down: in 1970 a drill in Kola, Russia started drilling straight down into the ground. It drilled with stops and starts until 1992, when the rock became too hot for the drill bit. 7 1/2 miles sounds pretty deep – it’s a third of the Earth’s outer crust – but not when you remember that Earth is about 8,000 miles across in total! Since that time, a couple of companies have drilled longer holes from other spots, but the Kola hole still runs farther below the surface than any other hole. They’ve closed off the top so no one will fall in, but if you could drop a coin down that tunnel, it would take a long, long time to hear it hit the bottom.

*Wee ones:* If you slide down the tunnel 5 miles, then went 1 more mile, how deep have you slid?

*Little kids:* If you drilled the 7 1/2 miles and then drilled another 1/2 mile, now how deep is that hole? *Bonus:* If Earth is 8,000 miles across and you traveled “just” to the center of the Earth, how many miles deep would you be?

*Big kids:* The drillers found the rock was 363 degrees F, hot enough to bake a cake! If your cake needs to bake at 375 degrees, how much hotter would the hole need to be? *Bonus:* If Earth is 8,000 miles “deep” to the opposite side and you slid down the 7 1/2-mile tunnel, how many more miles do you have to go?

Answers:

*Wee ones:* 6 miles.

*Little kids:* 8 miles. *Bonus:* 4,000 miles.

*Big kids:* 12 degrees hotter. *Bonus:* 7992 1/2 miles.

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

]]>Lots of dogs get to hang out as people’s pets (and wear costumes, as we saw on Wednesday). But some dogs actually work real jobs, such as police dogs. They’re called the K9 unit, since “canine” means “dog-related,” and they’ve been helping cops and detectives for hundreds of years. K9 unit dogs, who are usually German shepherds like these, help chase down bad guys, sniff for drugs and other materials that break the law, and also work as rescue dogs to find missing people. The dogs can’t talk, so they have to show what they think by doing the right action: barking, or sitting very still next to what they’ve found, and behave at all times. Here in this photo the dogs are working on their self-control by watching a cat without chasing it. K9 dogs train for a few hours every week, and can work for about 6-9 years. Then they get to rest and relax like millions of other pet dogs.

*Wee ones:* How many dogs can you count in the photo? Count as high as you can!

*Little kids:* If a dog trains until age 3 and then works for 7 years, how old is the dog when he stops working? *Bonus:* If an 11-year old dog has worked for 9 years, how old was she when she started?

*Big kids:* If a dog starts training at 9:30 each day and goes 8 hours straight, at what time does training end? *Bonus:* If 1/5 of those 15 dogs just can’t take it any more and start chasing the cat, how many dogs sit still like they should?

*The sky’s the limit:* If in self-control training there are 10 times as many dogs as cats, and there are 72 more dog paws than cat paws, how many of each animal do we have?

Answers:

*Wee ones:* We can count about 15 in total, but see what you find!

*Little kids:* 10 years old. *Bonus:* At 2 years old.

*Big kids:* At 5:30 pm. *Bonus:* 12 dogs, since 3 dogs pounce.

*The sky’s the limit:* 2 cats (which have 8 paws) and 20 dogs (which have 80 paws). Doing mental math, for every cat there’s a dog plus an extra 9 dogs, which have 36 paws. So we have 2 such sets of cats and dogs here. To solve with algebra, for c cats and d dogs we have:

4d = 4c + 72

and

d =10c

Substituting for d in the first equation, we get

40c = 4c + 72

36c = 72

c = 2 So there are 2 cats, giving us 20 dogs.

And thank you Emily B. for sharing this great photo!

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]]>The post Underwater Jungle Gym appeared first on Bedtime Math.

]]>Next time you walk through a park, imagine that it’s actually covered with water and you’re swimming over it. That’s what happens every year at a lake called Grüner See in Austria. During the winter the lake is very small and only a couple of feet deep, surrounded by green grass and park benches. But when spring comes and brings heavy rain, the water rises, and by June the whole park is under 40 feet of water! Grüner See means “green lake,” a perfect name since the grass gives the lake a beautiful emerald color. People put on scuba diving suits, which let them breathe underwater, and swim around to look at the trees, park benches and other park-y things. Can you imagine swimming around your favorite swingset or sandbox, or having your slide turn into a real waterslide? By July the water level starts dropping and by fall the grass is showing, so you can go for a normal walk again.

*Wee ones:* Which is deeper, a 20-foot deep lake or a 10-foot deep lake?

*Little kids:* If the lake fills up starting mid-May for 2 full months, in what month does it reach its deepest? *Bonus:* If it then takes just as long to drain, for how many months each year is the lake just normal? (Hint if needed: There are 12 months in a year.)

*Big kids:* If the swings at your park hang 3 feet above the ground, and the park becomes 42 feet deep with water, how far up from the swing would you have to swim to reach the top? *Bonus:* If the tallest jungle gym is 1/3 as tall as that water, how deep *down* would you have to swim to reach it?

Answers:

*Wee ones:* The 20-foot lake.

*Little kids:* In July. *Bonus:* For 8 months, since it spends 4 months rising and falling.

*Big kids:* 39 feet. *Bonus:* 28 feet.

And thank you Emily B. for telling us about this amazing place!

The post Underwater Jungle Gym appeared first on Bedtime Math.

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