The post The Trees You Eat for Breakfast appeared first on Bedtime Math.

]]>When you drizzle real maple syrup onto your pancakes, you probably use just a few tablespoons. What’s amazing is that bottle of syrup came from gallons of maple tree sap! This month the maple tree farms collect maple sap from their trees. They drill holes in the bark and stick a “tap,” or tube, into the tree. As the sap runs up the inside of the tree trunk, some of it drips out through the taps into buckets. Then the farm folks cook the sap until almost all the water boils away, leaving behind thick, yummy syrup. The thing is, they have to boil down 30 to 50 gallons of sap to make just 1 gallon of syrup! To get that sap, the farm has to tap a huge area of trees. One farm we talked to makes 600 gallons of syrup a year from its 20 acres of forest, which have thousands of trees. It’s much easier for us to fit a bottle of syrup in the fridge!

*Wee ones:* If you eat 4 waffles and 3 pancakes, of which food did you eat more?

*Little kids:* If you drizzle syrup into the 1st square hole in your waffle, then the 3rd, then the 5th, then the 7th…what number hole gets syrup next? *Bonus:* What number is the 10th hole that gets syrup?

*Big kids:* If you use 3 tablespoons of syrup on your pancakes, and it took 40 times as much sap to make that, how many tablespoons of sap made your breakfast syrup? *Bonus:* To imagine what that would look like, about how many cups is that? (A cup has 16 tablespoons.)

Answers:

*Wee ones:* More waffles.

*Little kids:* The 9th hole. *Bonus:* The 19th hole.

*Big kids:* 120 tablespoons of sap. *Bonus:* More than 7 cups! It’s 7 1/2 to be exact.

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]]>The post From Bug Soup to Butterfly appeared first on Bedtime Math.

]]>The start of spring is all about baby animals. So our fan Audrey C. asked, how does a caterpillar turn into a butterfly? (with a beautiful drawing for us!) Well, the change from caterpillar to butterfly is kind of gross, but also really amazing. First, the caterpillar eats nonstop, and grows really fast for about 2 weeks. The bug ends up weighing 200 times as much by the end of it! Then it attaches itself to a tree branch and sheds its skin, under which there’s a hard skin called a “chrysalis.” Over 2 more weeks, most of the caterpillar’s body turns into goop, and re-forms itself into a butterfly. Finally the butterfly crawls out and pops open its wings. After 4 weeks of sitting with nothing to do, that butterfly must be excited to fly.

*Wee ones:* Like all insects, a butterfly has 6 legs. Is that more or fewer legs than you have?

*Little kids:* If the caterpillar eats for 2 weeks, how many days is that? *Bonus:* If that all starts on a Monday, what’s the 5th day the caterpillar pigs out?

*Big kids:* If *you* started eating nonstop today (March 20), what’s the date of your 14th day of eating? (*Reminder if needed:* March has 31 days.) *Bonus:* What if you weighed 200 times as much after that as you do now? What would you weigh? (*Hint if needed:* Multiplying by 200 is the same as multiplying by 2, then by 100.)

*The sky’s the limit:* If the whole caterpillar “metamorphosis” (growth and chrysalis) takes exactly 4 weeks, and a caterpillar partway through that has 6 times as much time left as it’s already done, how many days of metamorphosis has the little guy done?

Answers:

*Wee ones:* The butterfly has more legs!

*Little kids:* 14 days. *Bonus:* That Friday.

*Big kids:* April 2. March 21 is the 2nd day, so March 31 is the 12th day, then we count forward 2 more. *Bonus:* Different for everyone…multiply your weight in pounds by 200.

*The sky’s the limit:* 4 days down, 24 days to go. Whatever part the caterpillar has lived already, it has 6 parts left of the same size, so there are 7 of those parts total…and 1/7 of 28 is 4 days.

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]]>The post The Best Way to Serve 20 Pies appeared first on Bedtime Math.

]]>When we picture a pie, we almost always think of a circle. But these fine folks figured out how to bake a “pie-cosahedron” — that is, an icosahedron, or 20-sided shape, made of pie! They cut and bent their own triangle-shaped pie tins out of metal. Then they made pecan pie, changing the recipe to be less drippy and gooey so the upside-down pies on the bottom wouldn’t fall apart. They then baked the 20 triangle pies, and used magnets to hold all the tins together in this shape, with the pies still inside. The question is, how many people does this geo-dessert feed?

*Wee ones:* If your pecan pie recipe uses flour, sugar, butter, pecans and a pinch of salt, how many ingredients does it use?

*Little kids:* How many triangles come together at each vertex (corner) of the icosahedron? *Bonus: *If you eat 1 pie from this 20-sided shape all by yourself, how many are left?

*Big kids:* Which will serve more people, 9 of those pies cut into 5 slices each, or 8 of those pies cut into 6 slices each? *Bonus:* If every pie has 3 sides, but every edge of the icosahedron (line between triangles) is shared by 2 pies…how many edges does the shape have?

Answers:

*Wee ones:* 5 ingredients.

*Little kids:* 5 triangles. *Bonus:* 19 pies left.

*Big kids:* The 8 pies cut into 6 apiece. That gives you 48 slices, while the 9 pies give you just 45. *Bonus:* 30 edges. The 20 faces have 60 sides all together when they’re laid flat and not touching…then when brought together, every pair of sides makes just 1 edge in the final dessert.

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]]>The post A Better Friend Than a Porcupine appeared first on Bedtime Math.

]]>Fun furry animals like mice, rats, squirrels, beavers, and porcupines are all part of one big family. They’re “rodents,” meaning their front teeth grow all the time, and their chewing wears them down. But who’s the biggest rodent of all? The capybara. It almost looks like a small bear or a very big-nosed dog, and it’s happy to hang out with other creatures. At an animal shelter in Arkansas, a group of puppies met a rescued capybara named Cheesecake, and right away decided she should be their new mom. They snuggle up to her, climb on her, and splash in the kiddie pool with her. Cheesecake also happily shares watermelon with a baby deer and a turtle. They’re probably all glad she isn’t a porcupine!

*Wee ones:* If there are 9 puppies plus the capybara, how many furry animals are in this “family”?

*Little kids:* If you took Cheesecake for a walk, how many legs would the two of you have together? *Bonus:* How many legs do the capybara, deer and turtle have all together?

*Big kids:* Porcupines weigh about 35 pounds, but capybaras weigh around 100 pounds more than that! About how much does a capybara weigh? *Bonus:* If Cheesecake is exactly 4 feet long, is she longer or shorter than you – and by how many inches?

*The sky’s the limit:* If the shelter has twice as many turtles as capybaras and 10 times as many puppies as turtles, and there are 69 animals in total, how many animals of each type do they have?

Answers:

*Wee ones:* 10 animals.

*Little kids:* 6 legs. *Bonus:* 12 legs.

*Big kids:* 135 pounds. *Bonus:* Different for everyone…subtract 48 inches from your height, or subtract your height from 48 inches.

*The sky’s the limit:* 3 capybaras, 6 turtles and 60 puppies. Each capybara is part of a “set” of 23 animals: 1 capybara, 2 turtles, and 20 puppies – and 69 is 3 x 23. So there are 3 sets in total.

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]]>The post How to Make a River Green appeared first on Bedtime Math.

]]>It’s St. Patrick’s Day, the feast when we dye our least favorite foods green to see if they’ll taste better that way. Today people will dye just about anything green, including their hair, their pets…and in Chicago, the river running through town. So how do they do that? Amazingly, the dye is an *orange* powder — it turns green only when it hits the water! At 9:15 in the morning of the parade, 2 boats go out into the water: a bigger boat holding 4 plumbers, and a smaller boat with just 2 plumbers. The guys on the big boat sprinkle the orange powder over the water using flour sifters. Then the smaller boat follows to make waves and spread the color. The 25 pounds of dye keep the river green for about 5 hours — plenty of time to show off your green hair.

*Wee ones:* If the big boat has 4 people on it and the little boat has 2 people, what numbers would you say to count all those people?

*Little kids:* Back when Chicago used 100 pounds of dye, the river stayed green for 5 days! If March 17 was the 1st day, what date was the 5th day? *Bonus:* If that first day was a Tuesday, what was the 4th day of green river?

*Big kids:* If the dye goes in at 9:15 in the morning and lasts 5 hours, until what time will the river stay green? *Bonus:* About 400,000 people go to the Chicago parade. How many more would need to show up to make it a million?

*The sky’s the limit:* One favorite green object for St. Patty’s is the very rare 4-leaf clover: if you pick 10,000 clovers, you’ll find only 1 that has 4 leaves. If all the rest have 3 leaves, how many 3-leafers will you have?

Answers:

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

*Little kids:* March 21st. *Bonus:* Friday.

*Big kids:* 2:15 in the afternoon. *Bonus:* 600,000 more people.

*The sky’s the limit:* 9,999 clovers.

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]]>The post Bugs on Stilts appeared first on Bedtime Math.

]]>Do you know what stilts are? They’re sticks you strap to your legs to make you taller. Well, scientists decided to strap very tiny stilts on ants to see how far they’d walk. Why? Ants in the desert always find their way home, even though all the sand looks the same. The ants use the sun to find the right direction, but how do they know how far they walk? It turns out they use math: they count their steps. Scientists made tiny stilts out of pig hair and strapped them onto the ants’ legs. When the ants tried to walk home, the stilts made their steps bigger. They didn’t fix it by taking fewer steps — they walked way past their anthill!

*Wee ones: *How many steps do you take to get from your kitchen to your room? Try counting them up!

*Little kids:* How many more legs does an ant have than you? (*Hint if needed:* All insects have 6 legs.) *Bonus:* If you have a pair of ants and you put a tiny stilt on every leg, how many stilts do you need to make?

*Big kids:* If you can trim 6,000 hairs off 1 pig, for how many ants can you make stilts for all their legs? *Bonus:* If an ant thinks it’s walking 52 miles to get home, but the stilts make it walk twice that distance, by how many miles does the ant overshoot its home?

Answers:

*Wee ones:* Different for everyone, but starting with 1, 2, 3, 4…

*Little kids:* 4 legs more…that’s 6 for the ant vs. 2 for you. *Bonus:* 12 stilts.

*Big kids:* 1,000 ants. *Bonus:* By 52 miles! It walks 104 instead of 52.

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]]>The post Two Peas a Day Keeps the Dentist Away appeared first on Bedtime Math.

]]>How many tooth brushings should you get out of a tube of toothpaste? And if you’re getting more than that, are you using too little toothpaste? What *is* the right amount of toothpaste, anyway? These questions came up when our fan Maggie H. asked, how many squeezes can you get from one tube? We can figure it out easily using math. Dentists say you should use a blob the size of a pea. Peas are about 8 millimeters wide, which if you do some grown up math (half the width times itself times itself, times 4/3 of pi), that comes to about 0.01 fluid ounces. That gives us about 100 squeezes per ounce. Then it depends on the size of the tube. Now let’s see how that shakes out with your toothbrushing routine!

*Wee ones:* A pea can fit on the tip of your finger. Find 3 things in your room that can fit on your fingertip.

*Little kids: *Give your tube of toothpaste 1 big squirt onto a clean counter (so you can still use it!). How many peas of toothpaste do you think you see? *Bonus:* If you brush twice on Sunday, once on Monday, twice on Tuesday, once on Wednesday…how many times will you brush Friday to keep the pattern?

*Big kids: *If you get 300 squirts from one tube, 400 from another, and the 3^{rd} tube’s number is halfway between, how many squeezes did you get in TOTAL from the 3 tubes? *Bonus:* If you can get 400 tooth brushings out of your tube starting January 1, and you brush only once a day, what date will be your last day on that tube? (Assume no leap years.)

Answers:

*Wee ones:* Items might include a teeny Lego piece, a fluff of lint, or a crumb.

*Little kids:* Different guesses for everyone…if you have peas handy, line them up to check your answer! *Bonus: *You will brush once.

*Big kids:* 1,050 squirts, since you get 350 from the 3rd tube. *Bonus:* On February 4 the following year. You use 365 the first year, leaving you 35 brushings for the next year. You use 31 of those in January, leaving 4 for February.

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]]>The post A Secret about Citrus Circles appeared first on Bedtime Math.

]]>It’s Pi Day, 3/14, the day we celebrate a very special number. When you multiply the width of a circle by “pi” (3.14159265…), you get the distance around its edge! So today we can also celebrate our favorite circle-shaped foods, like the glowing oranges, lemons and limes in this photo. If you slice across any citrus fruit, you’ll see a circle divided into sections called “liths.” How many liths does an orange or lemon have? Turns out there’s no exact number. Most lemons have 8 or 9 segments; oranges and limes can have up to 12; and grapefruit can have 14 or even more. And you can figure out the number before cutting the fruit — read on to learn the trick!

*Wee ones:* How many full orange circles can you see in the picture? Count as many as you can!

*Little kids:* Which has more sections, a 10-lith lime or an 8-lith lemon? *Bonus: *If your orange has 12 cute little sections, and 4 of them have seeds you have to spit out, how many don’t?

*Big kids:* SECRET: If you pull that bellybutton thing off a citrus fruit and count the little white dots under it, it tells how many sections the fruit has! If each of your 2 grapefruits have 14 dots, how many liths do they have together? *Bonus:* If your pile of 9-segment lemons and 14-segment grapefruit has 51 sections in total, how many of each fruit must you have?

Answers:

*Wee ones:* We count 3 big orange circles.

*Little kids:* The lime. *Bonus:* 8 seed-free sections.

*Big kids:* 28 liths. *Bonus:* 3 grapefruit and 1 lemon. If you keep subtracting 9 from 51, the only result that is divisible by 14 is 42 (51 minus 9).

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]]>The post A Fluffy Friend for Life appeared first on Bedtime Math.

]]>When someone does you a big favor — a really big one, like saving your life — you remember it forever. It turns out penguins feel thankful like that, too. In a story sent by our fan David S., back in 2011 a man in Rio de Janeiro, Brazil found a penguin lying on the rocks, covered with oil. The poor bird couldn’t swim to find food. So the man, Joao Pereira de Souza, cleaned up the penguin, fed him and took care of him, naming his new buddy Dindim. Once Dindim was strong and healthy again, he swam off into the ocean — but he comes back to Rio every year to visit Joao! Most penguins live in or near Antarctica, far from warm, sunny Rio. So Dindim swims 5,000 miles every year to visit Joao, just to say think-you.

*Wee ones:* Joao used to work as a fisherman. If he catches 3 fish and Dindim catches 1, how many fish do they catch together?

*Little kids:* If Joao catches 3 fish and Dindim catches 1 *more* than that, now how many fish do they catch? *Bonus:* If Dindim made his 1st visit in 2012, in what year did he make his 5th visit?

*Big kids:* Penguins are super-fluffy, with up to 100 feathers in just a square inch of skin! If you count 200 feathers counting by 10s, what are the last 3 numbers you say? *Bonus:* Joao was 67 years old in 2012. If in 2009 he was 8 times as old as Dindim was at the time, how much older than Dindim is Joao? (Hint if needed: 8 is 2 x 2 x 2, so to divide by 8, you just cut the number in half, then halve it again, then halve a third time.)

*The sky’s the limit:* Maybe Joao should swim partway to meet Dindim in the ocean. If Dindim swims to him from 2,500 miles away, and Dindim swims 4 times as fast as Joao, how far from Rio do they meet if they start at the same time?

Answers:

*Wee ones:* 4 fish.

*Little kids:* 7 fish, since they catch 3 and 4. *Bonus: *In 2016. If 2012 was the 1st, then the 5th visit is just 4 years later, not 5. Having to count an endpoint like that is called the “fencepost problem.”

*Big kids:* 180, 190, 200. *Bonus: *56 years older. In 2009 Joao was 64, making Dindim 8 years old at the time, and 64 – 8 = 56.

*The sky’s the limit:* 500 miles. If Joao swims 1 “part” and Dindim swims 4 parts, there are 5 parts in total, so each part is 500 miles.

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]]>The post Chargogga-what? appeared first on Bedtime Math.

]]>If you’ve wondered what place in America has the longest name, there’s a clear winner. Chargoggagoggmanchauggagoggchaubunagungamogg is the real name of a lake in Massachusetts. It has 44 letters in it including 15 g’s! Named by the Nipmuck Indians, it means something like “You fish on your side, I’ll fish on my side, and no one fishes in the middle.” Most people agree that that’s what it means, but no one can agree on how to spell it. The spelling on the town’s website doesn’t match the lake’s road sign pictured on that same page, and some folks say both spellings wrong. Maybe that’s why people just call it Lake Webster. The funny thing is, it’s the longest lake name in the world — but not the longest name of* any* place, as we’ll see here!

*Wee ones:* Which has more letters, your first name or your last name? Are they the same?

*Little kids:* How many letters does the name of your town have? *Bonus: *Chargoggagoggmanchauggagoggchaubunagungamogg has 14 “syllables” (the number of times your mouth opens). How many more syllables does it have than your first name?

*Big kids:* A town in North Wales called Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch probably has the longest place name in the world, with 58 letters (it means “St. Mary’s Church in the hollow of the white hazel near the rapid whirlpool of Llantysilio of the red cave”). How many more letters does it have than the 44-letter lake? *Bonus:* That town name has 11 Ls. If you swap the town’s 11 Ls with the lake’s 15 Gs, how much longer is the new town name than the lake name?

*The sky’s the limit:* If a crazy town name has a vowel every 4th letter, and a letter in the 2nd half of the alphabet only every 6th letter, what’s the 2nd letter that could be an O?

Answers:

*Wee ones:* Different for everyone…count up your first and last name letters, and compare!

*Little kids:* Again, different for everyone…count ’em up! *Bonus:* Find the syllables in your first name by counting how many times your jaw drops, then subtract from 14.

*Big kids:* 14 more letters. *Bonus:* 22 letters. The town will go up from 58 to 62, and the lake will drop from 44 to 40.

*The sky’s the limit:* The 24th letter, because the first that could be an O is the 12th.

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