The post Prairie Dog Party appeared first on Bedtime Math.

]]>These animals munching on carrots look like they’d make cute pets. They’re prairie dogs, who live down in holes in the…you guessed it, the prairie. They dig “burrows,” or tunnels, in the flat grassy fields. These tunnels keep the prairie dogs cool during the hot summer, and comfy through the cold winter. Our furry friends also hide there from animals who might eat them. The tunnels can be more than 30 feet long, and connect to make whole underground “towns.” The biggest known town stretched for 25,000 square miles in Texas, and was home to about 400 million prairie dogs — more than the number of people in the U.S.!

*Wee ones:* How many prairie dogs can you count in the picture?

*Little kids:* If you’re the 6th prairie dog to show up for snacks, how many showed up before you? *Bonus:* If there are just 13 carrot pieces and each of the 6 prairie dogs gets 1, how many more dogs can get a snack after that?

*Big kids:* If a prairie dog town has 42 dogs the first day, 53 the next day, and 64 the day after that, what number do you guess comes next? *Bonus:* How many more prairie dogs were in that 400-million-dog town than the 320 million people in America?

Answers:

*Wee ones:* 6 prairie dogs.

*Little kids:* 5 prairie dogs. *Bonus:* 7 more prairie dogs.

*Big kids:* 75 dogs, since we add 11 each time. *Bonus:* 80 million more prairie dogs than people!

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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 paper strips into amazing boxes, balls, and other shapes. And these cool crafts have a ton of math in them. The tube-shaped box shown here repeats 3 diamond shapes, so they almost look like cubes in an optical illusion. It’s made by weaving red upward to the right, blue upward to the left, and yellow down between them. Because of the angles, the blue diamonds look like the tops of cute little cubes, with red and yellow sides. Another project — which they say is easy but takes a bit of time — is a “triacontahedron,” meaning a 30-sided shape! 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 different colors can you choose from 6 colors, ignoring the order?

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.)

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]]>The post Play That Carrot! appeared first on Bedtime Math.

]]>If you don’t love every vegetable out there, this guy might change your mind. Junji Koyama has figured out how to take a carrot, a potato, or a head of broccoli, and turn it into a musical instrument. In this video he takes a drill, like you’d use on wood, and drills right into a carrot to make a tube. Then he cuts a notch for the air to come through, and drills tiny holes to play notes. When he blows into it, wow, it’s a carrot flute! Junji also did this with other veggies, played Happy Birthday on each of them, and then ran the videos all at the same time; it sounds pretty amazing — and shows that we SHOULD play with our food.

*Wee ones: *In “Happy Birthday” Junji plays a carrot, broccoli, potato, and Japanese radish. How many veggies does he play?

*Little kids:* If Junji plays on his carrot the notes C, E, G, then back to C to repeat, what’s the 7th note he plays? *Bonus:* What number note is the 3rd G?

*Big kids:* If 6 musicians each want 4 of his musical veggies, how many veggies does he have to carve? *Bonus:* If the musicians eat 1/3 of their veggies before ever playing them, how many veggies are left to play?

*The sky’s the limit:* If Junji buys a total of 48 veggies, and there are 4 more broccoli stems than potatoes and 4 more carrots than broccoli stems, how many of each instrument will he have?

Answers:

*Wee ones:* 4 veggies.

*Little kids:* C. *Bonus:* The 9th, since it’s the end of the 3rd set of 3.

*Big kids:* 24 veggies. *Bonus:* 16 vegetables, since they ate 8.

*The sky’s the limit:* 12 potatoes, 16 broccoli and 20 carrots. The mental-math shortcut is that if there are 4 *fewer* potatoes than broccoli and 4 *more* carrots than broccoli, that’s the same total as equal numbers of all 3 veggies, which would be 16 of each. That gives us 16 broccoli as before. plus 4 fewer potatoes (12 total) and 4 more carrots (20 total).

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]]>The post Tic-Tac-Toe with a Twist appeared first on Bedtime Math.

]]>In tic-tac-toe, 2 players take turns writing Xs and Os on a grid, each hoping to line up 3 in a row. Well, try tic-tac-toe times 10: You make a giant tic-tac-toe board like this, where EACH square is its own little tic-tac-toe board! Each time a player wins a board, that whole square now counts as that player’s shape (X or O), and whoever gets 3 giant squares in a row wins. How do you play? When a player fills in any little square, the next player has to go to the mini-board in the matching part of the giant board. So if someone fills in the top left square of any board, the other player must go now to the top left board. As the boards fill up, you have to avoid sending the other player to a board where he or she could win. Then you could make a board with 9 of these boards on it…and play even longer!

*Wee ones:* How many spaces does a regular tic-tac-toe board have? See if you can count them all!

*Little kids:* If 5 squares are filled in with Xs on a regular tic-tac-toe board and the rest are filled with Os, how many Os are there? *Bonus:* If you fill in the top left corner of the board, in how many directions could you win 3 in a row?

*Big kids:* In this giant board with a mini tic-tac-toe board in each square, how many tiny squares are on the whole page? *Bonus:* If you can fill in any square on the center board, and then that player can fill in any square on the next board, how many possible pairs of first 2 moves can the game have?

Answers:

*Wee ones:* 9 spaces.

*Little kids:* 4 Os. *Bonus:* In 3 directions: across, down, or on the diagonal to the bottom right.

*Big kids:* 81, since it’s 9 x 9. *Bonus:* 80 pairs. Each of the 9 squares leads to 9 possible choices on the next board which would be 9 x 9 = 81…but if you fill the center square on that center board, now there are only 8 squares open on that board, not 9.

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]]>The post Crazy Circle appeared first on Bedtime Math.

]]>An optical illusion is a picture that looks different from what is really happening. Like straight lines that look bent, or still shapes that look like they’re moving. One of our favorites is this video, where a ring of little white balls rolls around the inside of a bigger circle that’s twice as wide. It turns out that each ball moves back and forth on a totally straight line! If you don’t believe it, watch closely to see. Think about it: if you had a teeny ring of balls, each one would make little loop-de-loops around the edge. Meanwhile, balls in a big ring would never make it to the middle. The half-wide ring works perfectly. Now see if you can look at this drawing and imagine the balls tracing straight lines…it might still be hard!

*Wee ones:* How many little white balls can you count?

*Little kids:* If you take away 1 of the 8 white balls, how many white balls are left? *Bonus:* If instead you took the 8 balls and shoved another 5 in there to make more lines, how many do you have now?

*Big kids:* Each line cuts across the big circle through the middle, like slicing a pizza. How many pizza pieces should 8 lines eventually make? *Bonus:* If it takes 5 seconds for the balls to travel around the circle and you have to watch it 13 times to believe it, how long do you watch?

*The sky’s the limit:* If there were 2 rings of balls rolling around starting at the top at the same time, and one takes 6 seconds to go around and one takes 15 seconds, how many times has the fast one passed the slow one just after 1 minute?

Answers:

*Wee ones:* 8 balls.

*Little kids:* 7 balls. *Bonus:* 13 balls.

*Big kids:* 16 pieces. *Bonus:* 65 seconds.

*The sky’s the limit:* 6 times. In 30 seconds, they are both at the top again and the faster ring has made 5 rotations while the slower one has made only 2; the faster one passes on its own 2nd lap (after rolling through the bottom), then its 4th (before reaching the bottom), and then finishing its 5th (at the top). From that point they repeat this whole pattern: as the faster one finishes its 10th lap, the slower ring is finishing its 4th lap. So at 1 minute, the faster ring is passing the slower one for the 6th time.

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]]>The post How to Jump out of the Zoo appeared first on Bedtime Math.

]]>Running a zoo is a lot of work: feeding all the animals, scooping their poop, and keeping animals from chasing (and eating) each other. For that last one, people who build the zoo walls really need to know how high animals can jump. A jaguar can leap 10 feet high off the ground, and some kangaroos can rocket 20 feet through the air. An anteater, though, isn’t quite as bouncy…he probably needs just a 3-foot fence. Other animals might climb instead, so their walls had better be slippery. Good thing the giraffes can’t jump!

*Wee ones:* Which is higher, the antelope’s 8-foot fence or the anteater’s 3-foot fence?

*Little kids:* If a 6-foot anteater that tries REALLY hard can jump 3 feet, and you can jump 1 foot farther, how far can you 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 square pens, with a fence all around, a fence running through the middle back to front, and another through the middle left to right, how much fence does the zoo need?

Answers:

*Wee ones:* The antelope’s 8-foot fence.

*Little kids:* 4 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.

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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 (5-sided shapes) and 20 hexagons (6-sided shapes). Each pentagon, 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. That’s why soccer balls need to “cheat” a bit by mixing hexagons with pentagons…but they’re much easier to kick across the field!

*Wee ones:* See if you can count how many sides a pentagon has (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 shapes did your foot touch? *Bonus:* If you touched just that 1 pentagon, 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 bounce the ball 13 times on your knee and then twice as many times off your foot, how many times in a row can you bounce the ball 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 (13 + 26).

*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 Crayon Parade appeared first on Bedtime Math.

]]>We just love this map of Crayola crayon colors. It shows how Crayola has added more and more shades over the years. Back when the company started in 1903, there were just 8 crayon colors: red, orange, yellow, green, blue, purple, brown and black. By 1935 there were 16 colors. The chart creator, Stephen von Worley, chose years with an exact multiple of the original 8 colors, so the stripes line up nicely. For instance, by 1949 there were 48 colors, 6 times as many 8. 2010 shows about 15 stripes per chunk, giving us 120 colors. It all helps us draw much better pictures today!

*Wee ones:* The “primary colors,” which we mix to make all other colors, are red, yellow and blue. How many colors is that?

*Little kids:* If your crayon box has 3 crayons in the front row and 1 more than that in the second row, how many crayons do you have? *Bonus:* If you mix any 2 primary colors in equal amounts, you get a secondary color. Since there are 3 primary colors, how many ways can you mix 2 of them?

*Big kids:* By 1972 there were 9 times as many shades as the first 8. How many colors were there that year? *Bonus:* If the vat of wax for red-orange uses twice as much red wax as yellow, and it uses 36 cups in total, how many cups of each color are in there?

Answers:

*Wee ones:* 3 colors.

*Little kids:* 7 crayons, since it’s 3+4. *Bonus:* 3 ways: blue + yellow (to make green), red + yellow (to make orange), and blue + red (to make purple).

*Big kids:* 72 colors. *Bonus:* 24 cups red and 12 cups yellow. There are 2 parts red and 1 part yellow, making red 2 parts out of 3, and 1/3 of 36 is 12.

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

]]>Dogs love to ride in the car with their head sticking out the window. Looks like they love riding trains, too. Eugene Bostick, an 82-year-old man in Texas, built a dog train that he pulls with his tractor. He takes care of dogs he finds who don’t have a home. When he had just a couple, they’d ride in the tractor with him. But now there are too many dogs to fit in his lap. So he connected a bunch of blue carts, and ta-da, we have a dog train!

*Wee ones:* What shape are the tractor wheels?

*Little kids:* If there’s 1 dog in each cart, how many dogs are in front of the 7th dog? *Bonus:* If there are 8 carts and you ride in the 5th one, how many dogs are behind you?

*Big kids:* If the dogs ride every 4th day starting on Sunday of the 1st week, in what week do they get to ride on a Tuesday? *Bonus:* If the dogs ride twice a week, how many rides do they get in a 52-week year?

Answers:

*Wee ones:* Circles.

*Little kids:* 6 dogs. *Bonus:* 3 dogs are behind you.

*Big kids:* In the 3rd week (Sunday/Thursday, then Monday/Friday, then Tuesday/Saturday). *Bonus:* 104 rides.

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]]>The post Alligators, Windmills, and One Small Ball appeared first on Bedtime Math.

]]>Golf is the grown-up sport where you use a skinny iron stick, or “club,” to hit a very small ball over and over until it goes into a very small hole. The 18 holes are spread out across giant fields of grass, so it takes hours to finish a game. Thankfully, someone invented “miniature golf,” where the holes are much closer to each other — and the ball rolls through fun buildings and toys. Mini golf players have to “putt,” or hit, the little ball through waterwheels, windmills, and fake animals with their jaws wide open. Today is Miniature Golf Day, so let’s celebrate — and let’s hope no real gators show up.

*Wee ones:* If you putt the ball through the alligator’s mouth, then around the castle, then over the bridge, then through the windmill, how many obstacles have you passed?

*Little kids:* If the spinning windmill blocks every 4th player’s ball starting with the 4th, who’s the next player to get blocked? *Bonus:* If you’ve played all 18 holes except the alligator at the end, how many holes have you played?

*Big kids: *If you get through the windmill on just 2 strokes, but then take 4 putts for the alligator and for each of the next 4 animals, how many strokes is that so far? *Bonus:* If you have a final score of 72 after 18 holes, how many strokes did you take per hole (on average)?

*The sky’s the limit:* If you score a “hole in one” (get the ball into the hole on 1 putt) on every 3rd hole starting with the 3rd, and your friend gets a hole in one on every 5th hole starting with the 5th, on how many of the 18 holes does nobody get a hole in one?

Answers:

*Wee ones:* 4 obstacles.

*Little kids:* The 8th player. *Bonus:* 17 holes.

*Big kids: *22 strokes. *Bonus:* 4 strokes per hole.

*The sky’s the limit:* 10 holes. You will score on 6 holes: 3, 6, 9, 12, 15 and 18. Your friend will score on 3 holes: 5, 10 and 15. But you already counted hole #15 in your set. So that makes just 8 holes total, leaving 10 holes with no hole in one.

The post Alligators, Windmills, and One Small Ball appeared first on Bedtime Math.

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