The post Spotted on Halloween appeared first on Bedtime Math.

]]>With Halloween just a week away, lots of us have decorated our homes for the big day. And if you’re a little creeped out by all those giant spiders and webs on people’s bushes — even though you know 3-foot-wide spiders probably aren’t real — you can try something a little less yucky and a little more colorful. We’re loving this idea from the Momma Owl’s Lab blog: Take a paper towel tube, punch little holes in it with a holepuncher, then stick a handful of glowsticks inside — those glowsticks you normally connect end to end to make a glowing bracelet or headband for yourself. Then take your polka-dotted decorations outside and put them on top of your bushes. Of course, that doesn’t stop you from putting out big spiders and webs with them, but if you’d rather not freak yourself out while decorating, the glowsticks might be the ticket. Just remember, glowsticks last only a few hours once you snap them, so you’ll have to wait till Halloween itself!

*Wee ones:* How many glowsticks outside the tube can you see in the picture?

*Little kids:* If you grab 5 orange glowsticks and 4 yellow ones, how many do you have? *Bonus:* If you took those glowsticks from a pack of 50, how many are left in there to make glow-in-the-dark bracelets?

*Big kids:* If you punch 7 holes in each paper tube (all on one side so you can see them all), how many glowing spots can you get by filling 8 tubes with glowsticks? (Hint if needed: Multiplying by 8 is like doubling a number 3 times in a row.) *Bonus:* If a real spider is normally just 1/2 inch wide and the big decoration ones are 26 times as wide, how wide is the fake spider?

Answers:

*Wee ones:* 4 glowsticks.

*Little kids:* 9 glowsticks. *Bonus:* 41 glowsticks.

*Big kids:* 56 spots. *Bonus:* 13 inches.

And thank you to blogger Rachel Ford for this great idea!

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]]>The post Dangling Doughnuts appeared first on Bedtime Math.

]]>We like to get into the swing of fall by enjoying some of our favorite flavors of doughnuts, apple cider and pumpkin spice, with a unique math twist! As much as we love eating those doughnuts as they are, we like to play a fun game with them that gets everyone in a silly mood: the dangling doughnut game!

This is a fun challenge because once it’s bumped, the dangling doughnut starts swinging and it’s hard to get it to stop. The swaying doughnut becomes a pendulum. A pendulum is any object hung from a fixed point so that it swings freely back and forth under the action of gravity. It’s hard to eat a moving target!

Before you get to eating, take a few minutes to observe your doughnuts in motion. Once your doughnut pendulum gets swaying, it will move in a regular pattern. See for yourself! Get out a timer or stopwatch and measure how long it takes to complete a period, that is, the amount of time it takes the doughnut to return to its original position. Did that take more or less time that you predicted?

- One doughnut or more per player (fun fall flavors optional)
- Flat ribbon (string or thread will cut through the doughnut)

Hang the doughnuts from something taller than the participants. Use a tree branch, a clothesline, or something similar to hang the doughnuts. If you don’t mind a few crumbs on your floor, use a door frame. In a pinch, you could hang them from a long rod and have an adult hold it above everyone’s head.

Each doughnut’s ribbon needs to be customized for the player’s height. To do this, tie the ribbon around the doughnut. Then measure out the length of ribbon you’ll need to hang the doughnut so that the player can reach the doughnut with his or her mouth.

Measure the player’s height standing flat-footed, and then have them stand on their tip-toes and measure them again. Determine the difference between the two heights and subtract the difference from the length of your ribbon. You could also try measuring players in squatting position for another challenge. Make them work for that doughnut!

Once you have all the doughnuts tied, have the players line up in front of their doughnut. As soon as everybody is lined up, yell “Go!” No cheating, now – you can only use your mouth! Hands must be kept clasped behind backs. The first person to eat the whole doughnut wins. Really, everyone who plays wins, too, because … doughnuts, of course!

While the group is digesting, try to think of other examples of pendulums. How about the swings on the playground, the pirate boat rides at amusement parks, a yo-yo, or a grandfather clock?

Galileo spent quite a bit of time studying pendulums, and was able to express the motion of a pendulum in a mathematical equation. It turns out that the only thing that affects the period of a pendulum (the time it takes for one pendulum to swing) is the length of the string. Try it with your doughnut and different lengths of ribbon. Which doughnut swings faster – one on a long string or one on a short string? In the name of mathematical experimentation, you might as well grab another dozen doughnuts and eat your way to the correct answer!

You might think the weight of the object would affect the period of pendulum. Shouldn’t heavier objects move slower than lighter objects? Test it out. Have the kids find something heavier than the doughnut as well as something lighter than the doughnut. They can estimate which objects are heavier or lighter just by feel of the hand. If you have a kitchen scale, weigh the objects as well and compare how their estimates hold up to real numbers.

You know who else depends on the math of pendulums? Trapeze artists! After you read about how they use math skills to fly, check out our latest, circus-themed free printable activity guide, Ringmaster-ed Math.

*Image courtesy of Angie Six*

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]]>The post When Zoo Animals Jump appeared first on Bedtime Math.

]]>Running a zoo is a lot of work: feeding all the animals, scooping their poop, and keeping critters from chasing (and eating) each other. For that last one, building the zoo is an even bigger project. The designers who plan it have to understand how every animal in the zoo lives and moves around. They have to know how much space each animal needs to feel comfortable. They need to know how high animals can jump so the fences are tall enough. A jaguar can leap 10 feet high off the ground, and some kangaroos can rocket 20 feet into the air, while an anteater isn’t quite so brave (or strong) and probably needs just a 3-foot of fence. And while some animals jump, others might try to climb instead, so their walls better not have holes for their claws. Thankfully, the giraffes can reach 20 feet tall but don’t jump or climb at all, or we’d need some pretty tall walls.

*Wee ones:* Even big antelope can jump 8 feet high. If the fence is 7 feet high, can the antelope jump over it?

*Little kids:* If a 6-foot anteater that tries really, really hard can jump 1/3 its length, how far does it jump? *Bonus:* A red kangaroo can jump 25 feet. If the stream around his pen is just 2 feet wider than that, how wide is the stream?

*Big kids:* If a red kangaroo makes 3 25-foot leaps in a row, how many feet does it travel? *Bonus:* If the zoo divides a 50-foot-wide square into 4 equal pens, with a fence all around, a fence running through the middle back to front, and another left to right, how much fence does the zoo need?

*The sky’s the limit:* If the anteaters live in a pen that’s totally inside the jumpy antelope pen, and the jumpy antelope pen is totally inside the jumpy kangaroo pen, and there are 22 animals that begin with “a”, 38 jumpy animals, and 24 more kangaroos than antelope, how many are there of each?

Answers:

*Wee ones:* Yes! Because 8 is more than 7.

*Little kids:* 2 feet. *Bonus:* 27 feet.

*Big kids:* 75 feet. *Bonus:* 300 feet total: 200 around the edge, then a 50-foot piece across and another 50-foot piece back to front.

*The sky’s the limit:* 15 anteaters, 7 antelope and 31 kangaroos. If we have a anteaters, p antelopes, and k kangaroos,

a + p = 22

p + k = 38

k – 24 = p

Substituting the 3rd equation into the 2nd,

k – 24 + k = 38

2k = 62

k = 31

So there are 31 kangaroos. That gives us 24 fewer antelope, or 7 antelope, which then gives us 22-7 anteaters, or 15 anteaters.

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]]>The post 100-Year-Old Math Teacher appeared first on Bedtime Math.

]]>100 is a great number, and it’s even better if it’s your age — and you’re a math teacher. Madeline Scotto just turned 100 years old last week, and is still working 3 days a week as a math-team coach. For years she’s taught and coached at St. Ephrem’s Elementary School in Brooklyn, New York, the same school she went to herself as part of its very first graduating class. She started teaching there when she was 40, and we’re sure she learned her math well as a kid: she grew up back when we didn’t yet have calculators or computers to help us along. While most people “retire” at age 65 (stop working and live on their savings), Madeline is still playing with numbers with her students, some of whom are the children of students she had long ago. At age 100 she has a full life, as she has 5 children, 9 grandchildren and 16 great-grandchildren. She won’t use a cane or join a senior citizens club because awesomely, she just doesn’t think of herself as old — no matter what the numbers say.

*Wee ones:* If Madeline has 5 children and 9 grandchildren, does she have more children or grandchildren?

*Little kids:* How old will Madeline be a year from now? *Bonus:* If Madeline started teaching at age 40 and is now 100, how many decades has she been teaching? (Hint if needed: A decade is 10 years.)

*Big kids:* If Madeline has 5 children, 9 grandchildren and 16 great-grandchildren, how many descendants does she have in total? *Bonus:* If she’s taught since she was 40 and has had 20 students every year, how many students has this amazing lady taught?

Answers:

*Wee ones:* More grandchildren.

*Little kids:* 101 years old. *Bonus:* 6 decades, since she’s been teaching for 60 years.

*Big kids:* 30 descendants. *Bonus:* 1,200 students over 60 years!

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]]>The post Best of Bedtime Math: Let’s Go LEGO appeared first on Bedtime Math.

]]>It can be hard to commit to doing something every day, even if that thing is as fun and special as Bedtime Math. We understand that sometimes life gets in the way. That doesn’t mean you should miss out on our favorite Bedtime Math problems! We’re pleased to bring you another monthly round-up, and this time it’s all about one of the world’s favorite toys.

LEGO and math fun fit together like LEGO pieces and…other LEGO pieces. So it’s not surprising that we’ve found tons (literally, tons) of brilliant LEGO creations worth writing home about.

Here are 6 of the best tricks that use bricks:

- You might not see a point to this creation at first, but we bet you’ll come around, and round, and round…
- We just hope no one is sneaking bricks off of these plastic people, because they’re already in a great shape.
- If you don’t have time to visit all 50 states, there are 50,000 words worth of pixilated pictures to show you what you’re missing.
- Lego creations don’t just look good, they can help
*you*look good! - Finally, food follows function, and sometimes that function is play. There hasn’t (yet) been a LEGO carved out of
*Manchego*, but we’ve seen chocolate bricks and a sturdy stack-able cake!

And just a reminder – you can find a brand-new Bedtime Math problem on our homepage every day at 4 PM EST. If you prefer, you can have it delivered to your inbox, or download our free iPhone/iPad or Android app. We make it easy to add Bedtime Math to your daily routine!

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]]>The post Eye-Popping Puzzling Paper-Play appeared first on Bedtime Math.

]]>We’re loving the site Papermatrix, where super-talented people show us how to weave strips of colored paper into wild-patterned boxes, balls, and other shapes. And these cool crafts have a ton of math in them. The tube-shaped box shown here repeats 3 regular diamond shapes lined up to look like cubes. It’s made by weaving red upward to the right, blue upward to the left, and yellow down between them. Because of the angles, it becomes an optical illusion: the blue diamonds look like the tops of cute little cubes with red and yellow sides slanted at you, even though they’re close to flat. Another project on the site – which they say is easy to make but takes lots of time – is a “triacontahedron,” meaning a 30-sided shape where each diamond-shaped side is made of 4 smaller diamonds. It weaves 6 colors such that the 30 sides mix every possible pair of colors. If you have enough hands and eyes to track all those parts, give it a try!

*Wee ones:* How many colors can you count on this cube-patterned box?

*Little kids:* How many rows of “cubes” can you count from top to bottom on the box? *Bonus:* If you count 1 cube in each row and each one’s made of 3 diamond shapes, how many diamonds do they have in total?

*Big kids:* Each blue strip (paired with each red and yellow strip) makes 5 cubes on its way from bottom to top. If the box weaves 14 strips of each color, how many cubes do they make together? *Bonus:* For the triacontahedron, how many different pairs of colors can you choose from 6 colors, ignoring the order?

*The sky’s the limit:* Suppose you’re weaving 1 red strip sideways over 20 blue strips. If you start by making every 2nd diamond (multiple of 2) show blue, then you go back to the start and flip-flop the color on all diamonds that are multiples of 3, then start again and flip-flop the color on every multiple of 4, then every multiple of 5, for all multiples up to 20…which squares from 1 to 20 will end up red?

Answers:

*Wee ones:* 3 colors: yellow, red and blue.

*Little kids:* 5 rows. *Bonus:* 15 diamonds.

*Big kids:* 70 cubes. *Bonus:* 15 pairs. The 1st color has 5 to pair with; the 2nd has 4 new colors to pair with since it already paired with the first…you get 5+4+3+2+1=15. (The box then makes 2 different sides for each of those, with each color in the pointy corners vs. the wide ones.)

*The sky’s the limit: *1, 4, 9, and 16 — and what do you notice about those? They’re all perfect squares! The reason is factors. If all diamonds start off red, any prime number will get switched once to blue — when we do multiples of that number — and never change again. And any composite number (any number that has factors other than itself or 1) also has an odd number of factors other than 1, so for example, 6 will flip-flop to blue for multiples of 2, red for multiples of 3, then back to blue for multiples of 6, and then it’s done. HOWEVER, perfect squares have an*even* number of factors other than 1, because the square root pairs with itself. So for example, 9 changes to blue on 3s, then back to red on 9s. 16 changes to blue on the 2s, to red on the 4s, back to blue on the 8s and to red on the 16s, then it’s done!

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]]>The post Licking Your Own Eyeball appeared first on Bedtime Math.

]]>Of all the animals who blend into what’s around them using shape and color, the leaf-tailed gecko might be one of the coolest. It lives on Madagascar, an island off the coast of Africa, where all kinds of strange animals live, because they’ve been trapped there for thousands of year without mixing with other animals. The leaf-tailed gecko looks the way it sounds like it should: its tail looks like a leaf, and its whole brown-colored body matches the sticks, dirt and tree trunks around it to “camouflage” it, so bigger animals don’t see it and eat it. Even so, the gecko comes out only at night to eat insects with its long, sticky tongue, which it also uses to wipe its eyeballs clean since it has no eyelids. Leaf-tailed geckos grow to be only 6 inches at most, making them the smallest of all geckos and also a popular pet. Hopefully they lick only their own eyeballs and not their owners’.

*Wee ones:* If a gecko has 4 sticky, tree-climbing feet and you have 2 not-so sticky feet, who has more feet?

*Little kids:* If you think you see 15 leaves on the ground, but all but 1 are gecko tails, how many geckos do you see? *Bonus:* The gecko has 5 cute, chubby toes on each foot. How many toes does it have in total?

*Big kids:* If you’re counting leaves on the Madagascar forest floor, and every 3rd leaf is a gecko tail starting with the very 1st, does the 29th leaf belong to a gecko? *Bonus:* If every 9th leaf starting with the 9th is a gecko tail, is the 198th leaf a gecko tail? (Hint if needed: Multiples of 9 have digits that add up to a multiple of 9 themselves…so you can test their total the same way!)

Answers:

*Wee ones:* The gecko has more feet.

*Little kids:* 14 geckos. *Bonus:* 20 toes.

*Big kids:* No, because the 28th does (1 more than a multiple of 3). *Bonus:* Yes, because 1+9+8=18, and that’s a multiple of 9 itself (1+8=9).

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]]>The post Boo to You! appeared first on Bedtime Math.

]]>With the advent of GPS and maps on our phones, our paper maps are gathering dust in the attic. Our kids are so used to an electronic voice telling us when to turn, they might never get the chance to unfold a map or flip the pages of a road atlas. That’s a shame, because old-fashioned map reading teaches many more skills than just finding their way around. This Halloween season, ditch the GPS and give your kids the chance to learn about distance, measurement, estimation and other math skills by developing a *Boo Your Neighbors *attack plan!

Boo’ing neighbors and friends is one of my family’s favorite Halloween traditions. We fill up little bags with candy and treats, attach a *You’ve Been Boo’ed* note (see above), and, without being spotted, leave the Boo Bags on the porches of our neighbors and friends. Each recipient is supposed to “pay it forward” and Boo another neighbor or friend, so that the mystery, excitement, and math skills can spread all over the neighborhood.

Boo Bag delivery requires strategy. You definitely want to leave your friends guessing which friendly ghost stopped by with treats. It can be a challenge to drop the Boo Bags off without being seen. My kids plan this activity with all the intensity of a military operation! It certainly goes a long way towards developing their mapping, measuring, estimating, and timing skills.

1) Print out or draw a map of your neighborhood and locate the houses you plan to Boo.

2) Have your child figure out the best order in which to Boo his friends. Which houses are nearest to yours? What is the shortest route that will take you past all their houses? How many steps or miles will you walk or drive on Boo Night? Make an estimate and use a pedometer or old- fashioned map skills to determine the actual distance.

3) If you’re fast on your feet, ring the doorbell and then rush to the nearest hiding spot (behind a bush or a fence, etc.). How much time does your child think he’ll have to ding-dong ditch? If you’re not in it for the adventure, simply leave the Boo Bag in a spot where it’s likely to be noticed and head off to the next house.

4) Discuss what time would be best to begin the drop-offs; you want it to be fairly dark, but not so dark that your child risks tripping over unseen objects. Go back to your map and ask your child to estimate how long the whole Boo operation will take. Don’t stay out too late; you want to be alert enough for the evening’s Bedtime Math problem!

With all that preparation, Boo Night itself promises all the thrills of a spy mission. You can add to the excitement by bringing a stopwatch and timing your child as he makes each Boo Bag drop-off. The next day, as he listens to his friends wonder who left that bag of treats, your child can silently congratulate himself on a Mission Accomplished and a job well done.

*Images courtesy of Ana Picazo*

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]]>The post Facing the Soccer Ball appeared first on Bedtime Math.

]]>Have you ever wondered how many shapes a soccer ball has on it? It has 12 pentagons and 20 hexagons, and no pentagons touch each other: each one, usually black, has 5 white hexagons around it. It turns out there are only 5 ways to fit together lots of identical shapes with all equal sides – like a cube, which has 6 perfect squares as its faces (it’s also called a “hexahedron” for that reason). And can you picture a pyramid with triangle sides and a triangle bottom? That’s called a tetrahedron since it has 4 faces. You can also make an octahedron out of 8 triangles, a dodecahedron out of 12 pentagons, and an icosahedron out of 20 triangles! These are called platonic solids. Soccer balls “cheat” a bit, since they mix hexagons with the pentagons. Oddly, a soccer ball has 15 lines of symmetry, meaning the ways you can cut it into 2 mirror-image halves. Next time you spin one around, see if you can figure out why!

*Wee ones:* How many sides does a pentagon have? (the black shapes on the ball shown here)

*Little kids:* If you kick the ball and your foot touches a pentagon and all 5 hexagons touching it, how many “faces” or shapes did your foot touch? *Bonus:* How many of the 12 pentagons did you not touch?

*Big kids:* Since the ball has 20 hexagons and 12 pentagons, how many faces does it have in total? *Bonus:* If you can keep the ball in the air by bouncing it 13 times on your knee and then twice as many times off your foot, how many times in a row can you hit the ball to keep it in the air?

*The sky’s the limit:* When someone makes a soccer ball, each shape edge is sewn together with another shape’s edge. How many of those lines does the maker sew in total? (Hint if needed: Every shape edge is shared with 1 other shape…)

Answers:

*Wee ones:* 5 sides.

*Little kids:* 6 shapes. *Bonus:* 11 pentagons.

*Big kids:* 32 faces. *Bonus:* 39 times.

*The sky’s the limit:* 90 lines. The 20 hexagons have 6 edges apiece, giving us 120 edges in total, while the 12 pentagons have 5 edges each, or 60 in total. That gives us 180 edges that need to meet up with each other. Each one takes another one away from the pile, so there are 90 pairs.

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]]>The post Top Pick appeared first on Bedtime Math.

]]>If you’ve ever played with a calculator, you might have seen that some screens make the numbers using all straight lines, and those numbers look like letters when turned upside down: for example 7738 becomes “BELL” when flipped over. But even when they stay right side up, numbers made of sticks give you all kinds of games to play. Here in this picture we see 9 numbers, laid out 3 across and 3 up and down — and if you move just 1 toothpick from one number to another number to change both, you can make every up-and-down set add up to the same number, and every row running across add up to that same number, too. Can you spot it and solve the puzzle? Read on to do more math tricks with picks!

*Wee ones:* What’s the biggest number you see on the board?

*Little kids:* What do the 3 numbers in the top row add up to? *Bonus:* If you could change any number in that row to a 9, what’s the biggest total you’d get, and which one would you have to change? (By the way that isn’t the mystery toothpick.)

*Big kids:* Do you see any other rows or columns that add up to the same as the top row? *Bonus:*And now for our challenge…can you figure out which toothpick you can move to change 2 numbers and make all totals across and down add to the same number?

Answers:

*Wee ones:* 8.

*Little kids:* 10. *Bonus:* If you change the 1 to a 9 you get your biggest jump, to 18.

*Big kids:* Yes: the bottom row, and the rightmost column. *Bonus:* If you take away the toothpick in the middle of the 8 (in the center box) and use it to make the 6 just to its left into an 8, now that row has 8+0+2 = 10, the left column now has 1+8+1=10, and the center column now has 4+0+6=10.

The post Top Pick appeared first on Bedtime Math.

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