The post Ketchup-Squirting Robots appeared first on Bedtime Math.

]]>Do you like ketchup on your burger, fries, or hot dog? We’re loving this video of a robot that squirts the ketchup for you. Sure, we can squirt it ourselves, but why not have a robot help out? Of course, it helps only if the ketchup actually *lands* on the food — and as this video shows, that doesn’t always work out. If you’re wondering how it works, the robot has sensors that “see” when the robot is near the burger or hot dog, and tell it to turn towards it; then the computer knows to squeeze the two “hands” holding the ketchup bottle. The computer should also tell the hands to stop squeezing after 1-2 seconds…but it’s clear that someone isn’t doing the math right.

*Wee ones:* If the hot dog is 6 inches away but the ketchup squirts 1 inch farther than that, how far does it squirt?

*Little kids:* The robot tries to squirt ketchup on 1 plate of fries, 1 burger, and 4 hot dogs. How many items does it try to squirt? *Bonus:* What if it then tacks on a serving of fries for every burger and hot dog? Now how many items get squirted?

*Big kids:* If the ketchup was supposed to drip on the hot dogs for 5 seconds but squirts for 4 times as long, how many *extra* seconds does the ketchup drip out? *Bonus:* The robot squirts lots of hot dogs by driving along a line of them. If it can pass and squirt 2 hot dogs every second, can it squirt 28 of them in 15 seconds?

Answers:

*Wee ones:* 7 inches.

*Little kids:* 6 items. *Bonus:* 11 items since it has added 5 new ones.

*Big kids:* 15 extra seconds, since it drips for 20. *Bonus:* Yes, because it can squirt 30 — even if not very well.

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]]>The post Llamas on the Loose appeared first on Bedtime Math.

]]>Llamas are tall, woolly, four-legged animals that live high in the South American mountains. They usually aren’t found running down a city street. But that’s what happened this week in Sun City, Arizona, when two llamas broke loose from an open trailer and went on a tear through the town. Police cars chased them through the streets, but could barely keep up with the zigzagging escape artists. Then cops chased their fluffy new friends on foot, and couldn’t keep up any better. Finally, regular people watching the scene lassoed the black llama, then the white one. Llamas grow to 6 feet tall and weigh about 450 pounds, so walking one of those down the street on a rope isn’t easy — as you can see in the videos here.

*Wee ones:* The 2 llamas left 1 friend behind in the trailer. How many llamas were there in total?

*Little kids:* If the llamas ran 2 blocks north, turned left and ran 4 blocks west, then turned left again and ran 2 blocks south, how many blocks did they run? *Bonus:* Did they wind up back where they started?

*Big kids:* If the cops could drive 35 miles per hour and the llamas could run 17 miles per hour, how much faster were the cop cars? *Bonus:* If a neighbor on a motorcycle drove the speed halfway between the llamas and the cops, how fast did that guy drive?

Answers:

*Wee ones:* 3 llamas.

*Little kids:* 8 blocks in total. *Bonus:* No – they are 4 blocks away (to the west) of the starting point.

*Big kids:* 18 miles per hour. *Bonus:* 26 miles per hour. The gap is 18 miles, so the midpoint will be 9 miles per hour more than 17 and 9 less than 35.

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]]>The post Getting Snow in the Mail appeared first on Bedtime Math.

]]>People who’ve gotten tons of snow this winter might be sick and tired of it. Meanwhile, the people who hoped to get snow but got none are totally bummed out, because snow is actually a lot of fun to play with. So a very smart guy in Boston has started selling snow by shipping it to people. (Maybe he got the idea from the guy who drove a truck of snow to his 4-year-old granddaughter.) Kyle Waring, whose backyard has several feet of snow, began by packing about 1 pound of snow into bottles, which he sold for $19.99. But that small amount melted by the time it reached people. So he went bigger, and now ships a box of 6 pounds of snow for $89. Even with some of that snow melting along the way, there’s enough left that people can make 10-15 snowballs and have a good snowball fight. As we do the math, we’ll see he can make a lot of money before spring comes and melts his backyard stash.

*Wee ones:* Which weighs more, you or a 6-pound box of snow? (You can weigh yourself, or ask a grown-up for a guess at your weight.)

*Little kids:* Kyle now sells 10-pound boxes for people who really, really want more snowballs. How much more does that weigh than the 6-pound box? *Bonus:* If you bought 1 box of each size, how much snow would you get?

*Big kids:* If the 6-pound box makes 12 snowballs, how many snowballs can people probably make from the 10-pound box? *Bonus:* If Kyle has sold 600 pounds of snow already in 6-pound boxes for $89 each, how much money has he made?

*The sky’s the limit:* If Kyle has 60 pounds of snow left in his yard, which way will he make more money, selling it in 10-pound boxes for $119 each, or 6-pound boxes for $89 each? (Don’t worry about extra packaging or shipping costs.)

Answers:

*Wee ones:* You do, unless you were just born yesterday!

*Little kids:* 4 pounds more. *Bonus:* 16 pounds.

*Big kids:* 20 snowballs, since it makes twice as many snowballs as pounds. *Bonus:* $8,900, for 100 boxes.

*The sky’s the limit:* He makes more by selling 6-pound boxes. If he sells the snow in 6-pound chunks, he’ll sell 10 boxes, which at $89 each will earn him $890. If he sells it in 10-pound chunks, that comes to 6 boxes; at $119 each they will total $714. Smaller amounts bring in more money for the same amount of stuff, which you’ll find true for lots of items at the grocery store and elsewhere.

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]]>The post That’s One Weird-Looking Animal appeared first on Bedtime Math.

]]>The poor platypus must feel so confused. It has a duck’s bill, a beaver’s flat tail, and an otter’s feet. It also has no teeth. To top it off, it’s a mammal but it lays eggs the way a duck would. What the heck? (And that’s not as bad as its cousin, the short-beaked echidna, who has the same weird body plus sharp spines like a porcupine, and a long sticky tongue like an anteater.) The platypus is so weird-looking that when English scientists first found it in Australia, they had to bring a few back to England because no one believed any animal could look like that! The platypus is a great swimmer thanks to its otter and beaver body parts, but once it finds food underwater, it stuffs it all in its mouth and swims up to the surface, where it grinds its meal between its gums. And as we’ll see from the math, the platypus eats a lot.

*Wee ones:* A platypus has 4 otter-like feet. What numbers would you say to count them?

*Little kids:* A platypus eats 1/2 its own weight every night! If it weighs 4 pounds, how much does it eat? *Bonus:* If you had a pet platypus and a pet otter, how many feet would you all have together? (Hint if needed: They each have 4 feet.)

*Big kids:* If it eats 1/2 its weight every night, how much does a 4-pound platypus eat in April? *Bonus:* If *you* ate 1/2 your weight every night, how much would you eat in 1 week?

Answers:

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

*Little kids:* 2 pounds. *Bonus:* 10 feet – don’t forget yourself.

*Big kids:* 60 pounds, since April has 30 days. *Bonus:* Different for everyone: take your weight in pounds, cut in half, and then multiply by 7. As an example, a 50-pound kid would eat 175 pounds of food a week!

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]]>The post The Most Exciting One-Block Train Ride appeared first on Bedtime Math.

]]>Imagine the moment when caveman invented the wheel, and suddenly people could roll their junk from one place to another instead of carrying it. Then people hooked horses to their carts to pull them, and then in the 1800’s, they strung together cars with an engine to make a train. Now imagine running that train through an underground tunnel! That’s what happened on this day in 1870, when a guy named Alfred Beach opened the first subway ever in New York City. It ran for just 1 block underneath Broadway, the major road through town: yes, it just ran to one end of the block, stopped, and drove back. But this was still super exciting, and Beach sold rides to 11,000 people in just 2 weeks. In that first year he sold 400,000 rides! Today we can ride for miles on subways in New York and other cities, but Alfred got the idea rolling.

*Wee ones:* New York’s subways are named after letters and numbers. There’s the 1 line, and the 2 line…and what number comes next?

*Little kids:* The new subway was just 312 feet long. If a city block is normally about 250 feet long, was this subway longer or shorter than that? *Bonus:* If you wanted the subway’s length to end in a nice neat 5, how many feet longer would you make it?

*Big kids:* If the red lines in New York run for 8 miles and the blue lines together run for twice as far, how many miles do all those lines run together? *Bonus:* If you could ride all those lines exactly once and each ride took 10 minutes, how long would your tour of the city take?

*The sky’s the limit:* If Alfred sold 400,000 rides in one year, about how many was that per day – just a rough estimate? And was that more or less than the average daily rides the first couple of weeks?

Answers:

*Wee ones:* The 3 line.

*Little kids:* Longer. *Bonus:* If you wanted 315 feet, you’d add just 3 feet…or you could add 13, or 23, or bigger numbers ending in 3!

*Big kids:* 24 miles – that’s 8 for the reds, 16 for the blues. *Bonus:* 240 minutes, which is 4 hours.

*The sky’s the limit:* A little over 1000 rides a day. The 11,000 in the first 14 days comes to less than 1,000 per day, so it looks like more people got brave enough to try it over time.

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]]>The post Lighting up Your Garbage appeared first on Bedtime Math.

]]>We love it when people invent cool projects, like this wacky multi-shape lamp we just found. The creator chopped off the corners of plastic juice and milk cartons, glued them together to make 4-sided pyramids, or “tetrahedrons,” and stuck them all onto a string of lights. Better yet, there’s a small magnet glued inside each pyramid. So as you push and prod the lamp, the shapes move around and stick together in new ways. You can sculpt this lamp into any shape on your desk, or even wear it on your head (then you really *will* have a light bulb over you when you have a bright idea). A tetrahedron has a triangle on the bottom with 3 triangles coming up from the sides to meet at the top, and every side is the same….as we’ll see here, that leads to some very cool math.

*Wee ones:* How many sides does a triangle have?

*Little kids:* If the artist cut 12 tetrahedrons but used only 10 in the lamp, how many are still waiting for a light bulb? *Bonus:* If each tetrahedron uses 2 carton corners, how many carton corners do those 10 tetrahedrons use?

*Big kids:* Each tetrahedron has 4 faces. If the magnets make a tetrahedron stick to each face, how many outer faces do all *those* tetrahedrons have? *Bonus:* If a tetrahedron has 4 triangular faces, which share edges where they meet, how many edges does the whole tetrahedron have? (Hint if needed: How many edges would the triangles have if they weren’t touching?

Answers:

*Wee ones:* 3 sides.

*Little kids:* 2 tetrahedrons. *Bonus:* 20 corners.

*Big kids:* 12 faces, since there are 3 showing on each of the 4 new tetrahedrons. *Bonus:* 6 edges. If they weren’t touching the triangles would have 12 edges; we then divide by 2 because every edge is used by 2 triangles, not 1.

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]]>The post What You’re Really Wearing appeared first on Bedtime Math.

]]>When you put on a shirt or pants, you can see the colors and patterns: that it’s bright green, or blue and white striped, or some other combo. But have you ever looked closely at how your clothes are made? If you look at them through a magnifying glass to see what the threads are actually doing, you might be amazed. The left photo here shows blue jeans, which are woven: some threads run up and down while others run side to side through them. And the right one shows a turquoise T-shirt that’s knit, where the threads link together in a chain. Humans have been weaving for at least 9,000 years, but over time machines have helped us twist cotton and wool into skinnier threads and weave them into softer cloth. If you can find a magnifying glass, look at your clothes in a whole new light and find out what you’re really wearing.

*Wee ones:* If your jeans weave together white, blue and black threads, how many colors is that?

*Little kids:* If your shirt crosses 2 up and down stripes with 2 stripes across, how many places do they cross? *Bonus:* What if you cross 3 stripes with 3?

*Big kids:* If the leg of your jeans is 100 threads wide and every other thread is blue, how many blue threads are there? *Bonus:* If there are actually 3 colors in a repeating order – blue, white and purple – what’s the greatest number of purple threads there could be?

*The sky’s the limit:* If there are 77 threads across, which one is exactly in the middle?

Answers:

*Wee ones:* 3 colors.

*Little kids:* 4 overlaps. *Bonus:* 9 overlaps.

*Big kids:* 50 blue threads. *Bonus:* 34 threads, if the very first is purple, because then after 33 sets (bringing us to 99) the 100th will be purple also.

*The sky’s the limit:* The 39th thread. If you had just 76 threads, the 38th would be the end of the first half and the 39th would start the second half – they would share the center. Once you bump up to 77 threads, the 39th becomes the middle one, with 38 threads before it and 38 after it.

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]]>The post When Toilets Fly appeared first on Bedtime Math.

]]>What do you picture when you think of a rocket? Probably a tall, thin, round pointed shape with fiery engines at the bottom to shoot it through the air. But we’ve just learned that almost anything can be a rocket – including a toilet. This winter the Michiana Rocketry Club in Michigan decided to launch a portapotty into the air. A portapotty is a box-shaped closet with a potty inside that you can park anywhere, and usually they stay on the ground. But the Michiana folks strapped it to an engine, nailed on four metal fins to help it fly straight, and shot the 450-pound result up into the air. The toilet flew for 38 seconds, eventually landing about 2,000 feet away — and using $2,600 of fuel on the trip. Thankfully, there are cheaper, quieter ways to use the potty down here on Earth.

*Wee ones:* The guy who ran the project said “anyone” can strap together a nosecone, a round frame, and 4 fins to make a rocket. How many parts is that?

*Little kids:* If this flying toilet cost $1,800 in parts, which cost more, the parts or the $2,600 in fuel? *Bonus:* If you launched a flying vacuum cleaner using only $2,000 in fuel, how much less did you spend on fuel than the potty crowd?

*Big kids:* If the toilet reached its highest point halfway through its 38-second flight, how long into the flight did it peak? *Bonus:* If someone had ridden this toilet rocket, and peeked out for the middle 10 seconds of the flight, how long after takeoff would they have started?

Answers:

*Wee ones:* 6 parts.

*Little kids:* The fuel. *Bonus:* $600 less.

*Big kids:* 19 seconds. *Bonus:* At 14 seconds (5 seconds before 19, until 5 seconds after 19).

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]]>The post Going Nuts in the Jungle appeared first on Bedtime Math.

]]>Hawai’i may have steaming volcanoes, as we saw last night. But it’s also home to some tasty tropical treats, including macadamia nuts. The macadamia is one of the butteriest, yummiest nuts you can eat — *if* you can crack it open. The macadamia has the toughest shell of any nut; even a hammer can’t smash it open. You need to squash the nut with 300 pounds per square inch to crack it! In the old days Hawaiians would put the nuts on the road under wooden boards and drive a truck over them to crush them. Today machines at the Mauna Loa factory do all the work, and the island still grows almost all the world’s macadamias. The nuts are sold straight roasted, garlic-flavored, coated with dark chocolate, milk chocolate, even cookies and cream — and you’ll be happy to hear that “truck tire” isn’t one of the flavors.

*Wee ones:* If you first eat a dark chocolate-coated macadamia, then a milk chocolate-coated, and keep switching from dark to milk, what flavor is the 6th nut?

*Little kids:* If you eat a dark chocolate macadamia, then a milk chocolate one, then a roasted one, then repeat over and over since they’re so yummy, what flavor is the 9th nut you eat? *Bonus:* What flavor is the 19th nut?

*Big kids:* If you and 4 friends each drive a car over a batch of macadamias, how many nut-crushing tires do you have altogether? *Bonus:* If you and your friends each weigh 50 pounds, how many of you need to pile onto a 1-inch-square nut to weigh 300 pounds to crack it?

*The sky’s the limit:* A macadamia’s shell is closer to a 1/2-inch by 1/2-inch square. How many pounds of weight do you have to put on *that* area to crack it?

Answers:

*Wee ones:* Milk chocolate.

*Little kids:* Roasted, like all the multiples of 3. *Bonus:* Dark chocolate – it’s 1 more than a multiple of 3, so it follows roasted.

*Big kids:* 20 tires, since you have 5 cars. *Bonus:* 6 of you.

*The sky’s the limit:* 75 pounds, since now you’re crushing just ¼ of a square inch of shell.

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]]>The post A Live Volcano – Right in Someone’s Backyard appeared first on Bedtime Math.

]]>Hawai’i, the U.S.’s 50th state, is a string of hundreds of beautiful islands in the Pacific Ocean. But of the 8 main islands, the biggest one is home to 5 volcanoes! 4 of them aren’t doing much right now, but Kilauea has been erupting continuously since 1983. That means at times, hot, melted rock called lava oozes out of it. Flowing lava, which is at least 1,300 degrees F, gushes down towards the ocean, where it splashes into the cool water and hardens immediately into rock. So the island is actually growing on that side. This past October a 2,000-degree river of lava slid towards the town of Pahoa, where this photo shows how it oozed around a fence as it cooled. Most of it cooled in time, but jets of steam still rise from cracks in the ground – reminding us that we are in fact hanging out next to a live volcano.

*Wee ones:* The Big Island is just 1 of the 8 main islands of Hawai’i. How many other main islands are there?

*Little kids:* If you explore the Big Island’s 5 volcanoes for 2 days each, how long will that take you? *Bonus: *1,000 degree lava is dull red in color, and at double that temperature it becomes bright yellow. How hot is it then?

*Big kids:* The hot lava oozed at about 20 feet per hour. If you sleep 9 hours one night, how far does it travel by the time you wake up? *Bonus:* The Pahoa lava cooled down about 20 degrees per day. How many days would it take to cool from a 1600-degree orange to a 1300-degree bright red?

Answers:

*Wee ones:* 7 other islands.

*Little kids:* 10 days. *Bonus:* At 2,000 degrees F.

*Big kids:* 180 feet. *Bonus:* 15 days, since it’s a 300-degree drop.

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