The post When Your Fridge Spits Candy appeared first on Bedtime Math.

]]>If you live in America, you may come home today from trick-or-treating with a huge pile of candy, or have leftovers from the candy you give kids who visit you. Where are you going to put it all? One candy-loving guy has the answer. Have you ever used a fridge where there’s an ice dispenser on the outside, where you push your glass against a lever and ice cubes shoot out? Well, a guy known as dericpeace emptied the ice out of his freezer machine and filled it with candy pieces instead. Now when he pushes a glass against the door, his cup fills up with frozen Reese’s Pieces! as you can see in this video. Frozen candy has a crunchy yumminess all its own, and now he can fill up by the cup. Given that Americans buy 600 million pounds of candy every Halloween, our freezers’ ice machines might be working hard for a while.

*Wee ones:* If Deric’s freezer lets out orange, yellow and brown Reese’s Pieces, how many colors is that?

*Little kids:* If instead Deric filled the machine with M&Ms and they have twice as many colors as the 3 Reese’s colors, how many colors of frozen M&Ms do you get to eat? *Bonus:* If you eat 2 of each color, how many M&Ms do your teeth get to crunch?

*Big kids:* Of the 600 million pounds of candy bought every Halloween, 1/3 of that is candy corn (which might work well in the ice dispenser, too). How many pounds of candy corn does the country buy? *Bonus:* If each of America’s 320 million people puts 1/2 pound of candy corn in the freezer, how many pounds of candy corn are still sitting around at room temperature?

Answers:

*Wee ones:* 3 colors.

*Little kids:* 6 colors. *Bonus:* 12 rock-hard M&Ms.

*Big kids:* 200 million pounds. *Bonus:* 40 million pounds, since the 320 million people will freeze 160 million pounds.

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]]>The post So You Wanna Be A…Balloon Sculptor! appeared first on Bedtime Math.

]]>You’ve probably seen balloon sculptures consisting of 1 or 2 balloons twisted into the shape of a dog or a hat. But have you ever seen a balloon gorilla that’s as big as the real thing? Ryan Freeman makes incredible balloon sculptures of that scale – and larger! He was nice enough to talk with us about the math behind inflatable art.

I’ve been making sculptures since I was about 10 years old. My mother is a clown, which I know sounds like a joke, but she really is, and she gave me my first balloons. I studied 3-D animation in college, and a professor challenged us to make 3-D art without using any software. So I made a giant Road Runner character from Loony Tunes, and I realized I could keep making these giant creations.

That would be the Santa’s Village we made in a mall for the holidays. It had over 18,000 balloons and took 40 hours for my team of 14 people to make. That sculpture was also unusual because the balloons needed to last from Thanksgiving until the end of December, which meant we had to add a special chemical to the inside of the balloons.

You’re certainly right about that. Normally planning a sculpture takes longer than actually building it. To use the Santa’s Village example, we had to experiment to find out how many milligrams of the chemical were needed to make each size of balloon hold their air for 6 to 8 weeks. There are many different sizes of balloons – they vary by length, diameter, and the maximum volume – and we had to calculate the correct amount of chemical for each size. Then we had to multiply that amount of milligrams by the number of each size of balloon to make sure we ordered the correct amount of the preserving chemical. We had to do similar math to order the right volume of air tanks to fill those 18,000 balloons.

We actually use nitrogen more often than helium, but both come in different sizes of tanks. The extra-large is what we typically use, and it holds 291 cubic feet, which would make a cube of balloons about 6.5 feet in each dimension. We used 22 of those tanks for Santa’s Village.

Oh, yeah! We normally get a bunch of volunteers, hand out forks, and have a popping party. It can get pretty loud, but it’s a lot of fun.

I’d say the other two big pieces are being comfortable with measurements and being creative with geometry. For example, we’re building a giant spider for Halloween with heart-shaped foil balloons. So there’s a great optimal packing problem in measuring those heart-shaped balloons and then figuring out how to make a round spider belly using thousands of balloons. Anyone can dream up a crazy sculpture, but you need math skills to actually build it!

*If all this talk of balloons and clowns has put you in the mood for a circus, be sure to check out our latest printable activity guide, Ringmaster-ed Math Games! *

*Image courtesy of Ryan Freeman*

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]]>The post Cloudtrackers appeared first on Bedtime Math.

]]>When you look up at the sky, for a moment a big fluffy cloud might block the sun, and then you’re in the shade. You’re standing in the cloud’s shadow, and on a windy day when the clouds move fast, you can see the edge of the shadow come towards you on the ground as you enter the sunshine again. The cool thing is that the cloud shadow on the ground is about the same shape and size as the cloud itself (if the sun’s close to overhead). When your hand makes a bunny-rabbit shadow on the wall, that shadow becomes bigger if the lamp is close by, smaller as the lamp moves away. Same thing with our Sun. Sure, clouds are high over our heads: rainclouds start around 6,000 feet, wispy cirrus clouds at 19,000 feet and up, and giant storm clouds called cumulonimbus can reach 60,000 feet high. But the Sun is 93 *million miles* away, so the clouds are obviously a lot closer to us. Next time you chase the edge of a cloud shadow, see if you can do the math to find its size!

*Wee ones:* If your hand is 4 inches tall and you make a bunny-rabbit shadow that’s 1 inch taller, how tall is the bunny shadow?

*Little kids:* Which is higher in the sky, a horse-tail cirrus cloud at 21,000 feet or a raincloud at 12,000 feet? *Bonus:* If that chunk of raincloud is half as wide as it is high in the air, how wide is it (and its shadow)?

*Big kids:* If your street block has 15 houses on each side of the street and the bottom 1/3 of the block is in shadow, how many houses are still in the sun? *Bonus:* If it takes 10 minutes for a cloud to pass across the Sun and that cloud is blowing across at 12 miles an hour, how wide is that cloud? (Hint if needed: An hour has 60 minutes…so what fraction of an hour is 10 minutes?)

*The sky’s the limit:* If you’re riding a bike down a long, straight road, and the edge of the cloud shadow is 100 feet up ahead and moving 20 feet per second and you’re riding at 40 feet per second, how soon will you reach the edge and ride into the sunshine?

Answers:

*Wee ones:* 5 inches tall.

*Little kids:* The cirrus at 21,000 feet. *Bonus:* 6,000 feet wide (a bit more than a mile).

*Big kids:* 20 houses are in the sun, because 10 are in shadow (5 on each side). *Bonus:* 2 miles wide.

*The sky’s the limit:* Just 5 seconds. You’re moving 20 more feet each second than the cloud, so it will take only 5 seconds to do 5 of those 20-foot chunks and catch up over the 100 feet.

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]]>The post Trick Ice Cream appeared first on Bedtime Math.

]]>Ice cream is already a pretty exciting treat: cold, yummy sweetness that melts on your tongue, sometimes with crunch or caramel mixed in. But ice cream that changes color when you lick it might be even better. Manuel Linares, a Spanish physicist, has invented ice cream that turns from light purple to pink as soon as your tongue touches it. The chemical he mixed in changes not only because of the change in temperature (since your tongue is warm), but also because of the acids in your mouth. He’s keeping his tricks a secret until he gets a “patent,” which names him the official inventor so no one else can steal the idea and make money from it. But you can taste the ice cream yourself at Manuel’s shop in Blanes, Spain. He’s named the flavor “Xamaleon” after the chameleon, the lizard whose skin can change color. If he can make ice cream change to other colors, you could scoop yourself one crazy ice cream cone.

*Wee ones:* If the ice cream could turn pink after the 1st lick, then blue, then back to purple, then pink, then blue…what are the next 2 colors?

*Little kids:* If you scoop 4 scoops of Xamaleon and 1/2 of them turn from purple to pink, how many of each color do you have now? *Bonus:* If you scoop a super-tall 13-scoop cone, and lick every 3rd scoop to make it pink starting with the 1st, what color will the 10th scoop be?

*Big kids:* If Manuel charges just $2 for a regular cone but $5 for a Xamaleon cone, how much more money in total does he get for 10 Xamaleon cones? *Bonus:* If you can get 78 scoops out of a big tub of Xamaleon, how many 2-scoop cones can that tub give you?

Answers:

*Wee ones:* Purple, then pink!

*Little kids:* 2 scoops of each color. *Bonus:* Pink, along with the 4th and 7th scoops.

*Big kids:* $30, since he fetches $3 more for each. *Bonus:* 39 cones.

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]]>The post Royal Measuring Wand appeared first on Bedtime Math.

]]>Long ago, a foot was not 12 inches, but rather the actual length of the king’s foot. Of course, that meant when there was a new king, there would be a new definition of the length of a foot. Over time people realized it made sense to standardize measurements, but wouldn’t it be neat for your child to have a personal measuring system? Make a *royal measuring wand* for that very purpose.

No need to stick to just measuring feet. In fact, if you measure a bunch of parts, you’ll learn some interesting things about your body:

- Which is longer – your palm or your face from your hairline to your chin?
- Which is thicker – your knee or your neck?
- Is your waist measurement longer than the distance from your neck to your waist line?

Supplies:

- A variety of colorful ribbons
- Measuring tape
- A stick or dowel rod about one foot long
- White glue or glue dots

You can start by answering the questions above. Discuss the start and end point for each measurement and measure this body part with a ribbon. Cut a ribbon of one color for one body part and a ribbon of another color for the second body part. Lay them against each other and measure which one is longer.

Hold the ribbons next to the measuring tape and note the conventional length of each.

Attach the ribbons near the tip of the dowel rod with glue or glue dots for a whimsical royal measuring wand.

Invent silly comparison questions of your own or let children of different ages compare different body parts against each other trying to find body parts of the same size. For example, *my palm is as long as your foot!*

You may notice certain patterns based on ratios found in the human body. For example, a person’s height is typically 3 times the circumference of her head.

Now get really silly. Roam your royal kingdom (your house or backyard) and measure things like:

How many legs long is your bed?

How many heads high is your table?

How many royal feet long is your kitchen?

If your little king or queen is ready for a big challenge, do the math to translate those measurements into feet or meters.

Measuring has never been so personal and yet so fun!

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]]>The post Scooter Dog appeared first on Bedtime Math.

]]>We’ve seen dogs ride skateboards and surfboards, which takes great balance. But for a dog to ride a *scooter* is a different story. That means the dog has to stand on just 2 legs, hold the handlebars, and then use one furry back paw to push. Well, a French sheepdog named Norman became really good at doing this, and set the doggie scooter-riding world record. He zipped across a gym floor for 30 meters (about 98 feet) in just 20 seconds, without falling over or having to stop to pee. Norman’s human friends had to train him to understand certain words: “up” to get on the scooter, “scoot” to push with his feet, and “coast” to relax and enjoy the ride when he’s picked up some speed. But judging from the photo, Norman is happy to do this sport without being told.

*Wee ones:* If Norman understands the words “up,” “scoot” and “coast,” how many words has he learned?

*Little kids:* If Norman had to train for exactly 3 months and set this record in July 2013, when did he start training? *Bonus:* Norman scootered 98 feet. How many more feet would he have to scoot to reach 100 total?

*Big kids:* If Norman had scootered a full 100 feet in 20 seconds, about how long would it take him to go 1000 feet? *Bonus:* If on his 98-foot ride Norman had stopped every 20 feet to sniff the bystanders for 3 seconds, how much longer would his ride have taken?

*The sky’s the limit:* 22 feet per second is the same as 15 miles per hour. If Norman scootered 100 feet in 20 seconds, about how many miles per hour was he going?

Answers:

*Wee ones:* 3 words.

*Little kids:* In April of that year. *Bonus:* 2 more feet.

*Big kids:* 200 seconds, which is 3 minutes 20 seconds. *Bonus:* 12 seconds longer, since he would have stopped 4 times (at 20 feet, then 40, 60, and 80).

*The sky’s the limit:* 100 feet in 20 seconds equals 5 feet per second. So his speed is 5/22nds of 15. That comes to 75/22, which is just shy of 3 1/2 miles per hour.

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]]>The post Glow-in-the-Dark Trees appeared first on Bedtime Math.

]]>We all love stuff that glows in the dark: T-shirts, bracelets, blinking shoelaces. But what if *trees* could glow in the dark? A Danish designer and an American scientist have figured out how to take DNA (chemicals that tell your body how to grow) from tiny “bioluminescent” sea creatures and splice them into the DNA of baby plants; the plants then grow up to glow. “Bioluminescent” means that a living thing’s own body glows naturally, the way fireflies and some jellyfish do. So far the team hopes to grow whole trees that glow so brightly that they can light our roads at night instead of street lights. When you think of all the street lights using up electricity — at least 15 million lamps in the US alone — letting glow-in-the-dark trees do the job is definitely a bright idea.

*Wee ones:* If at night you go outside and spot 6 fireflies, what numbers do you say to count them?

*Little kids:* If it’s 6:00 pm and the sun will set 2 hours from now, when will you start to see these trees glow? *Bonus:* If you have 7 hours of dark each night in the summer and 11 hours in the winter, how much longer do you get to see the trees glow on a winter night?

*Big kids:* If your street block has 15 street lights, and 2 trees can light up the street as much as 1 light, how many glowing trees would your street need? *Bonus:* One man figured out that it costs him about 25 cents total to light 16 street lamps each night. If there are now 16 million street lights in America (16,000,000), how much money could glowing trees save us every night?

Answers:

*Wee ones:* 1, 2, 3, 4, 5, 6.

*Little kids:* 8:00 pm. *Bonus:* 4 more hours.

*Big kids:* 30 trees. *Bonus:* $250,000, or a quarter million (since it costs a quarter of a dollar for just 16).

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]]>The post Folded Paper Banners for Dia de los Muertos appeared first on Bedtime Math.

]]>How many times can you fold a sheet of paper? Popular myth has it that you cannot fold a sheet of paper in half more than seven times. Strictly speaking, that isn’t true: the current record for paper folding, held by Britney Gallivan, is actually 12 folds. To accomplish this, Britney had to use a special, extra-thin roll of toilet paper, 1.2 km in length!

World records aside, most people probably won’t get past seven folds, especially when using regular paper. The difficulty lies in exponential growth: each time you fold a piece of paper in half, its thickness doubles and its area halves. So after 2 folds, the paper is 4 times as thick and a 1/4 of its original size. After 6 folds, it’s 64 times as thick and 1/64th of its original size!

This is a fun challenge that any child will love: take a sheet of tissue paper, 8×12 inches, and fold it in half. Keep folding the paper in half and see how many folds you can reach until it becomes too difficult to continue.

Now that you have all this tissue paper, don’t let it go to waste: use it to make a *papel picado* banner to decorate your home to celebrate *Dia de los Muertos*, or Day of the Dead. On the eve of November 1, Mexican families create *papel picado* (pierced paper) banners to adorn altars honoring deceased family and loved ones. More intricate designs such as birds and skeletons require punches and chisels, but you can create a simple, symmetrical version using nothing but your tissue paper and scissors.

You’ll need:

- Multicolored tissue paper sheets, 8×12 (purple, pink, and orange are traditional Day of the Dead colors)
- Scissors
- Glue stick
- String

1) Take a sheet of tissue paper, fold it in half, then fold in half again. The more times you fold the paper, the more times your pattern will be repeated and the more intricate your *papel picado* will be. Fold your paper a minimum of 3 times; 4 or 5 folds are sure to produce a nice overall design. Don’t be tempted to fold it seven times, or it will be too thick to cut out any designs!

2) Cut out shapes along the edge of the folds. Be sure to leave some space between your cut-outs to prevent an entire section of your tissue paper square from falling off. Because the paper is folded over and cuts are made along the folds, the shape will be mirrored along the axis of the fold — this is known as reflective symmetry. This means that a semicircle cut will produce a circle, a triangle cut will produce a diamond, a diagonal parallelogram will produce a V. Ask your child to predict what shapes he or she will see, once the paper is unfolded.

3) Unfold the paper and examine your patterns. Ask your child to count how many times the pattern was repeated. How many times was the paper folded? Is there a relation between the number of patterns on the paper and the number of times it was folded?

4) Fold the top 1/4 inch of the paper over a long piece of string and glue in place. Cut multiple pieces of paper in different colors and arrange them on the string in the colorful pattern of your choice.

This delicate design will no doubt be a conversation piece wherever you hang it.

*Images courtesy of Ana Picazo*

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]]>The post Will the Real Tallest Mountain Please Rise… appeared first on Bedtime Math.

]]>Mount Everest is the tallest mountain on Earth, right? Well, not quite. At 29,035 feet, Mount Everest is the highest peak above sea level (the surface of the ocean), but it isn’t the tallest mountain from top to bottom — if you count what’s underwater. Mauna Kea on Hawaii already stands a dizzying 13,796 feet above sea level. But if you measure all the way down its slope to the ocean floor, Mauna Kea runs more than 19,000 feet deep, making it over 32,000 feet tall in total! Meanwhile, because the Earth isn’t a perfect ball — it’s more of a squashed egg shape — there’s another mountain whose peak is the farthest from Earth’s *center*. That’s Mount Chimborazo in Ecuador, in South America. Ecuador is the Spanish word for “equator,” the imaginary line around the middle of Earth, where Earth is widest. Chimborazo is right on the equator, so even at only 20,703 feet it “sticks out farther” than any other mountain. Wonder how Everest feels about that…

*Wee ones:* Which is higher, 13,000 feet or 10,000 feet?

*Little kids:* Mauna Kea is 13,796 feet tall. Can you remember that number and say it back? *Bonus:*If Everest is about 29,000 feet tall and Mauna Kea is actually 32,000 feet tall top to bottom, by how many feet does Mauna Kea beat Everest in height?

*Big kids:* Nothing can live on top of Mount Everest, with air so thin and cold. But the bar-headed goose can fly 21,000 feet high. How much higher is Mount Everest at 29,035 feet? *Bonus:* If your airplane can fly twice as high as that goose, how high can you fly?

*The sky’s the limit:* Mauna Kea stands about 14,000 feet above the ocean and another 20,000 deep underwater. If it were a perfect symmetrical triangle when looking at it from the side, and it were 21,000 feet wide at the water’s surface, how wide is the mountain at the bottom?

Answers:

*Wee ones:* 13,000 feet.

*Little kids:* Try to say thirteen thousand seven hundred ninety-six, and see how long you can remember it! *Bonus:* By 3,000 feet.

*Big kids:* 8,035 feet. *Bonus:* To 42,000 feet.

*The sky’s the limit:* For any right triangle like this one, the ratio between its height and width is the same at any height, meaning if you divide the distance down from the top by its width, you’ll always get the same number. So if it’s 21,000 feet wide when you’re 14,000 feet down from the top, that means its width is always 1 1/2 of that distance. Another 20,000 feet deeper, you’re 34,000 feet from the top, so it would be 1 1/2 of that or 51,000 feet wide – almost 10 miles!

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]]>The post Recycling for Fido and Fluffy appeared first on Bedtime Math.

]]>Whenever you “recycle” a plastic water bottle instead of throwing it out, you’re helping our planet by letting that plastic be re-used, so we don’t have to make it from scratch again. But it gets even better than that in Istanbul, Turkey: when you recycle you’re also helping to feed stray cats and dogs. Turkish company Pugedon built machines that collect the empty bottles, and when you stick a bottle in there the machine spits out a scoopful of dry food for animals to eat. People can also pour any leftover water into the machine for the animals to drink – after all, cats and dogs get thirsty, too. Stray cats and dogs are a huge problem in Istanbul, with 150,000 of them in a city of about 14 million people, meaning they’re more than 1% of the whole population. The Pugedon machines get people to recycle more and help our fuzzy friends at the same time.

*Wee ones:* If you get a snack for a cat, a dog, and yourself, how many of you are snacking?

*Little kids:* If every bottle you recycle makes 2 scoops of food come out, how much food do you give the animals if you toss in 3 bottles? *Bonus:* If 3 dogs come up to eat, then a cat, then 3 dogs, then a cat again and so on, what’s the 13th animal to come up?

*Big kids:* If twice as many dogs as cats use the machine, and today 18 animals ate from it, how many cats and dogs was that? *Bonus:* If there were exactly 14,000,000 people in Istanbul and exactly 1 stray animal for every 100 people, how many stray animals would there be?

Answers:

*Wee ones:* 3 “animals.”

*Little kids:* 6 scoops. *Bonus:* A dog.

*Big kids:* 12 dogs and 6 cats. *Bonus:* 140,000 stray animals.

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