The post A Quick Drink for a Big Dog appeared first on Bedtime Math.

]]>It’s much easier to be a person than a dog. When you’re thirsty, you can fill a glass with water from the faucet. But a dog has to wait for someone to fill his bowl. Well, this Great Dane doesn’t want to wait. He figured out how to step on the water fountain pedal to make water come out. So now he just drinks from there! Great Danes are one of the biggest dog breeds. They can stand almost 3 feet tall at the shoulder, and can weigh up to 200 pounds. These huge dogs look a little scary, but Great Danes are very sweet and gentle with kids. And this one is polite: as we see in the video, he’s nice enough not to lick the faucet while drinking!

*Wee ones:* If the Great Dane slurps up 7 sips of water, what numbers do you say to count them?

*Little kids: *If the dog starts the water fountain with his left paw, then his right, then his right again, then starts over with his left paw, then his right…which paw does he use next? *Bonus:* If that Great Dane weighs 200 pounds and his puppy friend already weighs 100 pounds, how much do they weigh together?

*Big kids:* If a Great Dane is 34 inches tall at the shoulder and the top of his head is 10 inches above that, who’s taller, you or the dog? *Bonus:* Every 2 cups of water weighs 1 pound (16 ounces). If the Great Dane weighs 180 pounds, then slurps up 8 cups of water, how much does he weigh on the scale now if he doesn’t pee first?

Answers:

*Wee ones:* 1, 2, 3, 4, 5, 6, 7.

*Little kids:* The right paw. *Bonus:* 300 pounds.

*Big kids:* Different for everyone…see if you’re taller or shorter than 44 inches! *Bonus:* 184 pounds, since the 8 cups of water weigh 4 pounds.

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]]>The post The Bounciest Mile appeared first on Bedtime Math.

]]>It’s easier to do one thing at a time than two things. Sometimes grown-ups get carried away doing lots of things at once. It’s called multitasking, and it usually ends with them dropping their phone into a pot of tomato sauce (don’t ask). Well, fortunately some grown-ups CAN do two things at once – and do it quickly, too! This guy named Dylan Sorensen just set the world record for fastest running while dribbling a basketball. He ran 1 mile in just 4 minutes and 37 seconds while bouncing the ball to beat the old record. This is the 3rd time a new record has been set in the past year…do you think you could bounce around the track faster?

*Wee ones: *What shape is a basketball?

*Little kids: *If Dylan dribbled the basketball switching between his hands in this pattern: right, right, right, left, then right again to start again… which hand did he use for the 6th dribble? *Bonus: *What hand did he use for the 16th dribble? Can you figure it out without counting out?

*Big kids: *The world record for running 1 mile without a basketball is 3 minutes 43 seconds. How much less time is that than this record of 4 minutes 37 seconds? *Bonus: *If Dylan ran all 4 laps in the exact same amount of time, how long did each lap take? (Round to the nearest whole second.)

Answers:

*Wee ones: *A circle, or in 3D, a “sphere”.

*Little kids: *His right hand, because the pattern restarts with the 5th dribble. *Bonus:* Left, because every 4th dribble – which means every multiple of 4 – is left.

*Big kids: *54 seconds less. You can subtract 37 seconds to reach 4 minutes, then another 17 to reach 3 minutes 43 seconds – or you can “count up” from 3 minutes 43 seconds.* Bonus: *1 minute 9 seconds. 4 minutes divides neatly by 4, leaving 37 seconds. 4 goes into 37 9 times, with a remainder of 1.

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]]>The post A Million-Dollar Speedbump appeared first on Bedtime Math.

]]>You never want to bump into something with your car – that’s called an accident. But sometimes an accident can turn out for the best. The Moser family was driving when their car ran over some lumpy bags left on the road. It turns out those bags were full of money! The family did the right thing and brought the mystery money to the police, who figured out it was supposed to go to a bank. And whoever lost those moneybags had a million and one reasons to be thankful.

*Wee ones: *Which is more: 1 dollar, or 2 dollars?

*Little kids: *If you find a lost hat on Monday and then find the hat’s owner 2 days later, does the owner get their hat back before the weekend?* Bonus: *If you split up 10 dollars evenly between your 2 pockets, but 1 pocket has a hole and you lose the money, how many dollars are left in the other pocket?

*Big kids: *Can you “spell” 1 million out in numbers? *Bonus: *Sometimes there’s a reward for returning lost items. If there was a 10% reward on $200 lost dollars, how many dollars would that reward be?

Answers:

*Wee ones: *2 dollars is more, because 2 is more than 1.

*Little kids: *Yes, the owner gets the hat back on Wednesday. *Bonus: *5 dollars.

*Big kids: *1,000,000. *Bonus: *20 dollars, because 10% is 10 parts out of every 100, or 1/10, and 1/10 of 200 is 20.

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]]>The post Don’t Set the Food on Fire appeared first on Bedtime Math.

]]>Today America celebrates Memorial Day, the day we honor all the soldiers who protect our country. As we do for many celebrations, we spend the day eating. Memorial Day kicks off barbecuing season. It’s the dads’ big chance to prove they can cook something, and to pretend they set the food on fire on purpose. But running the grill is a lot of pressure. Not all foods cook for the same amount of time, nor do they take up the same amount of space on the rack. Plus some people want their burger “rare” (lightly cooked) or really “well done” (cooked to a crisp). It’s a giant, flame-throwing juggling act, so the chef had better know how to count.

*Wee ones:* If you’re grilling burgers, hot dogs, fish, and corn on the cob, how many kinds of food are you cooking?

*Little kids:* If the griller needs to cook 3 hot dogs, 1 steak and 5 ears of corn, how many items need to fit on the grill? *Bonus:* If the grill can hold 12 hot dogs, but 3 of them fall through the rack and 1 rolls off onto the ground, how many hot dogs are left?

*Big kids:* If the griller cooks 2 burgers the 1st round, then 3 hot dogs the 2nd round, then 2 burgers to repeat, then 3 hot dogs…how many items have been cooked by the end of the 6th round? *Bonus:* Which will take longer to cook, 4 rounds of burgers that take 7 minutes each, or 9 rounds of hot dogs that take just 3 minutes each?

*The sky’s the limit:* If the grill can hold 10 hot dogs or 5 burgers, and hot dogs take 5 minutes and burgers take 8 minutes…what’s the fastest you can cook 12 hot dogs and 6 burgers? (Assume any chunk of space can hold either 2 dogs or 1 burger…and you’ll probably want pencil and paper for this one!)

Answers:

*Wee ones:* 4 foods.

*Little kids:* 9 items. *Bonus:* 8 hot dogs.

*Big kids:* 15 items, since each pair of burger and hot dog rounds covers 5 items. *Bonus:* The burgers take just a little longer: 28 minutes compared to 27 minutes.

*The sky’s the limit:* The fastest we could get is 16 minutes, by cooking 4 hot dogs (2 burger spaces) at the same time as 3 burgers (3 burger spaces). The 12 hot dogs cook in 3 rounds, taking 15 minutes; at the same time, the 6 burgers cook in 2 rounds, which take 16 minutes; then everything is done. Note that cooking all the hot dogs before all the burgers takes longer. You cook the first 10 dogs, then 2 final dogs with the first 4 burgers…but when those last 2 dogs finish, you can replace them with only 1 more burger. The 6th burger has to wait until the first 4 burgers finish. That means a 3rd round of burger-cooking, making 5 minutes plus 2 sets of 8 minutes. If you find an even faster time, let us know!

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]]>The post Watch Out for Space Junk appeared first on Bedtime Math.

]]>Our friend Chloe H. asked us, how many times could you fly around the world in a spaceship in one day? It turns out it’s a lot. Satellites, the floating pieces of metal that send phone calls and videos to us, fly at 17,000 miles an hour. So they fly around Earth in just an hour and a half! But at these speeds, we have a new problem: space junk. Some of those satellites don’t work anymore, but there’s no way to bring them back down. There are also floating leftover pieces from rocket boosters, tools dropped during astronaut walks, and so on. Now these things are starting to crash into each other. If you’re up there doing a space walk, grab some garbage to help us clean up!

*Wee ones:* If you have 4 pieces of space junk, and 1 of them breaks in half, how many pieces do you have now?

*Little kids:* If you’ve made 9 trips around Earth so far today, what number is your next trip? *Bonus:* How many more trips after that can you make today if you can make 16 trips in total?

*Big kids:* If you start your orbit at 3:30 pm and the trip takes 1 1/2 hours, at what time will you finish? *Bonus:* If there are 40 pieces of space junk in your path, and on each of your 16 trips today you scoop up 3 pieces, can you catch them all?

*The sky’s the limit:* If you start orbiting Earth today (May 24) and make 16 junk-collecting trips each day, on what date will you make your 100^{th} orbit?

Answers:

*Wee ones:* 5 pieces.

*Little kids:* The 10th. *Bonus:* 6 more trips.

*Big kids:* At 5:00 pm. *Bonus:* Yes! You’ll be able to catch 48 pieces.

*The sky’s the limit:* On May 30. You finish 16 trips today, and another 80 trips 5 days after today, which is May 29. That brings you to 96 trips, so the 100th trip happens on May 30.

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]]>The post A Day for Lucky Pennies appeared first on Bedtime Math.

]]>“See a penny, pick it up, and all day you’ll have good luck!” Today in America we celebrate National Lucky Penny Day: even though 1 penny by itself can’t buy much. Back in the 1800s, though, it used to be worth a lot: a penny could buy a candy bar, sheets of paper, and pieces of cloth to make clothes. Thanks to “inflation” (money becoming weaker over time), a penny isn’t worth very much today. Now you might need 50, 70, or even 100 pennies to buy a candy bar. That’s why people happily put them in penny-crushing machines to stamp pictures on them, like the one shown here — and they pay an extra 25 cents along with it to run the machine! The question is, will that penny still bring you good luck?

*Wee ones:* What shape is a real, unsquashed penny?

*Little kids:* If you find a penny each day — Sunday, Monday, and so on — how many do you find in 1 week? *Bonus:* If you put in the penny plus 25 cents to make a stamped penny, how much money do you spend in total?

*Big kids:* If you’ve been collecting lucky pennies, and just 1 more will bring you to 1 dollar (100 pennies), how many do you have? *Bonus:* If you have 85 cents, how many funny squashed pennies can you make if it costs the extra 25 cents to stamp one, and how much money will you have left over?

Answers:

*Wee ones:* A circle – and in 3D, it’s actually a very short, squat cylinder.

*Little kids:* 7 pennies. *Bonus:* 26 cents.

*Big kids:* 99 pennies. *Bonus:* 3 squashed pennies, which will cost 78 cents (25+25+25+1+1+1). You’ll have 7 cents left over.

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]]>The post Lego by the House-ful appeared first on Bedtime Math.

]]>Lego is one of those toys that every kid has heard of, and that almost every kid has played with. Ever since it was invented in 1958, Lego pieces have had the exact same thickness of brick, and the same size studs (the little bumps on top). They’ve made 4* billion *minifigures since then, which equals half the world’s population! Now they design 130 new sets each year, like the Star Wars sets, plus they keeping selling the longtime sets. So our longtime fan Benjamin H. asked, how many Lego pieces are made every day? In one year, Lego makes around 36 billion pieces! If we divide by 365, that comes to 125 million pieces a day, and a bout 5 million every hour. Given that a 1-foot cube can hold only about 400 pieces, you can imagine how many houses you can fill every day with Lego!

*Wee ones:* If you snap together a red Lego brick, a blue brick, a green, a yellow, a white and a black, how many bricks have you snapped together?

*Little kids:* If a Lego brick has 2 rows with 4 knobs (bumps) each, how many knobs does it have? *Bonus:* If you snap a 2-knob piece on top, how many knobs from the bottom piece are still showing?

*Big kids:* To find how many 1-foot cubes a room can hold, you just multiply the length times the width times the height to the ceiling. If your bedroom is 10 feet by 10 feet with an 8-foot ceiling, how many cubic feet of Lego can you fill it with? *Bonus: *If each cubic foot can hold 400 pieces, can the room hold 1 million Legos? Can it hold the amount made in about an hour? (*Hint if needed:* What if each cubic foot held only 4 pieces…then try 40 pieces…)

*The sky’s the limit:* How many different rectangle shapes (number of knobs across and front to back) can a piece with 36 knobs on top have? (Assume that you have at least 2 knobs in either direction, but you don’t have to worry about which way each combo is facing.)

Answers:

*Wee ones:* 6 bricks.

*Little kids:* 8 knobs. *Bonus:* 6 knobs — or 7 if the 2-knob piece is hanging off the edge.

*Big kids:* 800 cubic feet. *Bonus:* That room holds 320,000 pieces…so no, it doesn’t hold 1 million…and you’d need more than 15 bedrooms to hold the more than 5 million Legos made in 1 hour!

*The sky’s the limit:* There are 4 ways: 2 knobs x 18 knobs, 3 x 12, 4 x 9, and 6 x 6.

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]]>The post Tricky Triangles appeared first on Bedtime Math.

]]>The word “puzzle” can mean a lot of things: peg puzzles, number games, and jigsaws with squiggly pieces. But our favorite at Bedtime Math is the “tangram.” This ancient Chinese puzzle uses 7 shapes that you move around to match a picture. The picture gives no clues about where the shapes go — you have to figure that out! Here we’ve made this turtle by lining up the shapes as shown. The 7 shapes fit with each other in a special way: the medium triangle is the same size as 2 tiny triangles put together, and a big triangle is the same as 2 medium ones. The square and parallelogram also each equal 2 tiny triangles. Check out this page to print and cut out your own tangrams, and to match some puzzles yourself!

*Wee ones:* Point to all the triangles in the picture. What colors are they?

*Little kids:* If 2 tiny triangles make a medium triangle, and 2 medium triangles make a big triangle, how many tiny triangles do you need to make a big triangle? *Bonus:* The 2 tiny triangles against the green square make a shape called a “trapezoid.” Imagine that shape is all one color. How many sides does it have?

*Big kids:* How many tiny triangles can you fit in the whole big square that holds all the shapes? (*Hint: *the whole big square can fit 4 big triangles.) *Bonus:* If a giant tangram square covers 128 square inches, how much area does each tiny triangle cover? Can you figure out a handy way to divide by that number?

Answers:

*Wee ones:* Red, purple, pink, blue, and orange.

*Little kids:* 4 tiny triangles, since it takes 2 pairs. *Bonus:* 4 sides. It’s a “quadrilateral” just like squares and rectangles!

*Big kids:* 16 tiny triangles. *Bonus:* 8 square inches. To divide by 16, you’re just cutting in half 4 times in a row, since 16 is 2 x 2 x 2 x 2.

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]]>The post A One-Squiggle Cat appeared first on Bedtime Math.

]]>Cats are cute, but what’s weird about this drawing of a cat? If you look really, really closely, you’ll see that the whole thing is 1 single line! The line keeps bending in on itself to fill the paper. In places where the line pieces come close to each other, the picture becomes darker. Those different shades of color make it look like a picture of a real thing. This kind of line is called a Hilbert curve. As we see in this video, the artist actually programmed a printer to draw those squiggles. Cats may have 9 lives, but we don’t have enough lives to draw that whole long line ourselves!

*Wee ones:* Try drawing as straight a line on paper as you can. If you’re able, try to draw 2 straight lines close together without them touching!

*Little kids:* If you draw a line to make a shape with 5 sides, what do you call that shape? *Bonus:*If you draw 9 straight, non-crossing lines all in the same direction, how many spaces do they make between them?

*Big kids:* If a picture is 2 feet across and each squiggle is 1 inch wide, how many squiggles fit across the page? (*Hint if needed:* A foot has 12 inches.) *Bonus: *A 4-inch-wide square would hold 4 1-inch squiggles across and 4 squiggles up and down, giving us 16 squiggles. How many squiggles would fit in that square if the squiggles were just 1/2 inch tall and 1/2 inch wide?

Answers:

*Wee ones:* Try drawing a straight line, or two!

*Little kids:* A pentagon. *Bonus:* 8 spaces.

*Big kids:* 24 squiggles, since 2 feet = 24 inches. *Bonus: *64 squiggles, since you can now fit 4 of them (not 2!) in each square inch. Another way to think of it: you can now fit 8 squiggles across and 8 down.

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]]>The post There Goats the Neighborhood appeared first on Bedtime Math.

]]>Have you ever met a goat? These cute animals can chew through just about anything, which makes them perfect lawn mowers. A herd of 200 goats was doing just that, eating all the grass on a big hill behind a neighborhood. But they got bored and started looking for something else to eat, like people’s flowers and gardens. The goats ignored the people who tried to shoo them away – after all, there were 200 of them, and just a few people. But luckily they listened to one dog, who herded them all back to the hill. That’s one pup who knows how to get your goat!

*Wee ones: *Look at the picture. Are there more goats in that picture than there are people in your house?

*Little kids: *If you and the dog are chasing the last goat, how many legs do the three of you have together? *Bonus: *If 7 goats start munching cardboard, but 1 of those goats doesn’t have horns and the others do, how many horns do they have?

*Big kids: *If there were 200 goats in this herd, and 1 out of every 10 went to the grocery store instead of storming this neighborhood, how many went to the grocery store? *Bonus: *Some goats climb trees! If there were 6 trees with 7 goats in each tree, how many of the 200 goats stayed on the ground?

*The sky’s the limit: *if the herd of goats digs through the neighborhood garbage and eats twice as many apple cores as watermelon rinds and twice as many banana peels as apple cores, and they eat 140 things in total, how many of each thing do they eat?

Answers:

*Wee ones: *Different for everyone, but unless you have a really really really big family, we bet there are more goats!

*Little kids: *10 legs. *Bonus: *12 horns, since 6 goats have them.

*Big kids: *20 goats. There are 20 sets of 10 in 200, so 1 goat in each of those sets of 10 makes 20 goats getting groceries. *Bonus: *158 goats on the ground. 6 x 7 = 42, and 200 – 42 = 158.

*The sky’s the limit:* 20 watermelon rinds, 40 apple cores and 80 banana peels. If there are twice as many cores as rinds, then each rind has 2 apple core “friends,” and if there are twice as many banana peels as apple cores, then that rind and those cores also have 4 peel “friends.” That makes 7 things in each set of friends. 140 things in total fits 20 of those sets. So there are 20 rinds, and then you multiply out the rest.

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