The post Circular Logic appeared first on Bedtime Math.

]]>Quick, which orange circle is bigger? Believe it or not, both orange circles are the same size! The blue circles are playing a trick, or optical illusion, on you. An optical illusion is a picture that looks different from what is really happening. The different sizes of the blue circles surrounding the orange circles make this trick work. Try covering up some of the blue circles with your fingers or a piece of paper to see the truth!

*Wee ones: *Point to one of the bigger blue circles, then count up all of them! How many bigger blue circles are there?

*Little kids: *If there are 8 small blue circles and 6 big blue circles, how many more big blue circles are there? *Bonus: *How many blue circles does that make all together?

*Big kids: *How many circles would you have to add to the picture to have 20 total circles? *Bonus: *If you show this illusion to 24 people and 1/3 of them figure out the truth, how many people get fooled by it?

Answers:

*Wee ones: *There are 6 bigger blue circles on the left side of the picture.

*Little kids: *2 more blue circles. *Bonus: *14 blue circles.

*Big kids: *4 more circles, because there are 16 circles already in the picture. *Bonus: *16 people get fooled. 1/3 of 24 makes 8 people that don’t get fooled, and 24 – 8 = 16.

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]]>The post Snacktime for Sharks appeared first on Bedtime Math.

]]>One of the trickiest jobs at a zoo is feeding the sharks. Ripley Aquarium in Toronto, Canada gives a great behind-the-scenes peek here at mealtime in their “Dangerous Lagoon.” First the zoo workers, or “aquarists,” have to scoot the sea turtles out of the tank. Each turtle has been trained to see and swim towards its own colored stick (who knew turtles were that smart?). Then the fish who like to eat at the top of the water are fed; the workers drop the food into the corners of the tank, so the hungry fish swim there. For fish who eat along the bottom, their food is shot down there through tubes. Finally, with everyone else out of the way, the aquarists stick fish on a long pole and hold it out over each shark’s special spot in the water. The sharks eat just 3 times a week, but together they chow down 1,000 pounds of fish in that time!

*Wee ones:* If the sharks eat 3 times in a week and have eaten twice already, how many more meals do they have left?

*Little kids:* If the sharks eat every other day starting on Monday (meaning they eat, then skip a day, then eat…), on what days do they eat their other 2 meals? *Bonus:* If the sharks eat 3 times in a week, how many days do they *not* eat?

*Big kids:* If the sharks are fed 300 pounds on each of their days, do they get their full 1,000 pounds of fish? *Bonus:* If there are 5 sharks in the tank and they all eat the same amount, how much food is each one eating in a week?

Answers:

*Wee ones:* 1 more time.

*Little kids:* Wednesday and Friday. *Bonus:* 4 days.

*Big kids:* No, since that will add up to “only” 900 pounds. *Bonus:* 200 pounds per shark.

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]]>The post Lego Set-ting the Bar appeared first on Bedtime Math.

]]>If you love Lego, you’ve probably built some of their sets by following their instructions. Maybe you’ve also used the pieces to invent your own crazy cars, castles, and animals. Someone else might want to build your idea, too! So Lego has a webpage where anyone like you can share what new sets they think Lego should sell. You build a new cool invention, take a picture, write down what pieces you needed, and then send it to them. Then you try to get people to vote for your idea. If you get 10,000 votes or more, the Lego folks will look at your idea and might choose it as a new Lego set! Send in your pink and silver spaceship, checkerboard ice fort, or 2-foot-tall giraffe, and maybe other kids will love it, too.

*Wee ones:* If you’ve thought up a new spaceship, ice fort, stripey giraffe and robotic bird, how many new Lego set ideas do you have?

*Little kids:* If your crazy new Lego giraffe uses 6 colors, but Lego thinks it needs some orange and blue, how many colors does it use now, if orange and blue weren’t already in? *Bonus:* If the giraffe’s neck uses 2 blocks of each color, how many blocks does it use?

*Big kids:* If your new ice fort is a checkerboard of 60 white blocks and the same number of blue blocks, how many blocks does it use? *Bonus:* If Lego wants the set to have exactly 180 blocks, and you make all those new blocks white, how many times as much white as blue does it have now?

*The sky’s the limit:* If your spaceship needs wing pieces, twice as many engine pieces as wing pieces, and 52 regular blocks, and they want the whole set to have 76 pieces, how many wings and engines will it have?

Answers:

*Wee ones:* 4 ideas for sets.

*Little kids:* 8 colors. *Bonus:* 16 blocks.

*Big kids:* 120 blocks. *Bonus:* Twice as much white as blue, since it now has 120 whites and 60 blues.

*The sky’s the limit: *The wings and engines will together have 24 pieces, since it’s 76-52=24. Each wing has 2 engine pieces to itself, so they come in sets of 3. 24 pieces will have 8 sets like that. So there will be 8 wing pieces and 16 engine pieces.

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]]>The post Cabin Fever Math Videos! appeared first on Bedtime Math.

]]>Check out these videos for a deeper dive on some of our favorite Cabin Fever Math activities!

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]]>The post A Record-Breaking Beagle appeared first on Bedtime Math.

]]>It’s always exciting when someone breaks a world record, doing something bigger or faster than anyone. But it’s even more fun when a pet does it. This cute dog holds the world record for running a ball the longest distance. Purin, a 9-year-old beagle, ran while standing on top of a big yellow ball, and her quick little paws rolled it 33 feet (10 meters). She did this in less than 12 seconds, making her the fastest dog to run a ball 10 meters. This is her 2nd world record, as she has also caught more balls with her paws in 1 minute (14 total) than any other dog. What will Purin try next? Baseball? Volleyball? Whatever it is, we hope she’s on our team.

*Wee ones:* Purin is 9 years old. Is she older or younger than you are, or the same?

*Little kids:* If you and Purin race, how many legs do you have all together? *Bonus:* How many puppies would have to join in for there to be 14 legs all together?

*Big kids: *If Purin barks when she catches the 3rd ball thrown to her, then the 7th ball, then the 12th… on what ball should she bark again to keep up the pattern? *Bonus: *If Purin rolled her ball 33 feet in 12 seconds, how long would she take to roll the ball 66 feet at the same speed?

*The sky’s the limit: *If Purin runs her ball at you at 3 feet per second, and you’re running yours twice as fast toward her from 30 feet away, where will the two of you meet if you started at the same time? (*Hint if needed:* It doesn’t matter how many feet per second either of you can run…all that matters is that you’re twice as fast!)

Answers:

*Wee ones:* Different for everyone…see if your age in years is more than 9 or less than 9, or maybe it’s actually 9!

*Little kids:* 6 legs. *Bonus:* 2 more, to add 8 legs.

*Big kids:* The 18th ball. She started on 3, then added 4, then 5, so she then adds 6. *Bonus:* 24 seconds, since it’s twice as far.

*The sky’s the limit:* 10 feet from Purin’s starting point. If you run twice as fast, for each part she runs you’ll run 2 parts, making 3 parts total. So she will run 1 of those 3 parts, or 1/3 of 30 feet.

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]]>The post Hand It Over! appeared first on Bedtime Math.

]]>When you do one simple thing, like flicking a light switch, your body is actually doing tonsof things. Your eyes and brain have to work together to send your hand to the right spot. And your hand isn’t one thing, but a crazy connection of muscles, bones, and tendons. Our friend Maggie K. wanted to know: just how many muscles are in my hand? Well, there are 17 muscles in the palm of your hand, but that’s not enough – there are also 18 muscles in your forearm that help move your fingers! Sounds like we all have some serious muscle.

*Wee ones: *Can you find 3 things smaller than your hand?

*Little kids: *There are 18 muscles in your forearm and 17 in your hand. How many more muscles are in your forearm? *Bonus: *How many more muscles are in both your forearms than in 1 of your hands?

*Big kids: *If you add up the muscles in both hands and both forearms, how many muscles is that? *Bonus: *Not everyone agrees on what counts as a muscle: some people say there are 650 muscles, while others say it’s 840. What’s the difference between those two numbers?

Answers:

*Wee ones: *We bet you can! Items could include small toys, berries or other foods, paperclips, seashells or leaves of a houseplant…

*Little kids: *1 more muscle in your forearm. *Bonus: *19 more muscles.

*Big kids: *70 muscles, because there are 17 + 18 = 35 muscles on each side, and 35 + 35 = 70. *Bonus: *190 muscles. You can either subtract by regrouping (840 – 650 = 700 – 600 + 140 – 50 = 100 + 90 = 190) or you can add up from 650 (50 brings you to 700, 100 brings you to 800, 40 brings you to 840; 50 + 100 + 40 = 190).<

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]]>The post Explosion of Diamonds appeared first on Bedtime Math.

]]>When a volcano blows up, it gushes with glowing red-hot melted rock called lava. It’s hotter than 1300 degrees F, so it can melt just about anything in its way. But one thing it can’t melt is diamond. So some cooled lava rocks have diamonds inside them! Now, there aren’t a lot of diamonds mixed in, so you’d have to sort through about 250 full dump trucks of lava to find 1 carat of diamonds (less than 1/100th of an ounce). But there are specks of other materials inside lava, too. If you ever buy lava rocks for a grill, put a rock in a sock and hit it with a hammer to split it open (with a grown-up’s help). Here at Bedtime Math we smashed 6 lava rocks, and found a chip of white quartz in 3 of them. See if you find anything in yours!

*Wee ones: *Lava rocks for the grill are about the size of your fist. Find 3 objects in your room about that size.

*Little kids: *If you smash 6 rocks and 1 has a diamond in it, how many don’t? *Bonus:* If you buy a bag of 10 lava rocks and count them as you crack them open, what’s the second to last number you say?

*Big kids:* If you’re cracking open 40 lava rocks, of which 22 have a diamond and 27 have gold inside them, what’s the smallest possible number of rocks that have both? *Bonus:* If you can find one diamond in every 250 dump trucks of lava, how many should you find in 1,000 trucks?

Answers:

*Wee ones:* Items might include small stuffed animals, toy balls, or regular rocks from outside!

*Little kids:* 5 rocks. *Bonus: *9.

*Big kids:* 9 rocks, since only 18 of the 27 gold ones can have no diamond. *Bonus:* 4 diamonds, since you have 4 sets of 250 trucks.

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]]>The post Buried Treasure in Oobleck appeared first on Bedtime Math.

]]>Oobleck is a mixture of cornstarch and water mixed in a ratio of 2:1. Plan on at least ½ cup of cornstarch per child. So for one child mix ½ cup of cornstarch with approximately ¼ cup of water in a small bowl. It looks like a simple recipe, but oobleck is anything but simple- it’s a non-Newtonian fluid. That means it has properties of both solids and liquids. It’s crazy fun and a sensory delight!

How can you tell if you have the right mix? The contents of your bowl should react like a solid in response to pressure. Tap the surface hard and fast. Does it feel solid? If not, add a bit more cornstarch a sprinkle at a time and mix it up. Next, gently rest a finger on the surface of the oobleck. Does it sink down?

Oobleck is fascinating. Scoop up a handful and press it tightly in your fist to make a ball. After you’ve got a nice compact ball, relax and open your hand. Watch the ball melt away, dribbling through your fingers.

Toss a coin into the oobleck with some force and observe how it is slowly absorbed into the mixture. Now gently place the coin down and see what happens? What other factors affect interaction of the oobleck and the coins? Do you think each coin’s mass affects it journey down through the oobleck?

According to the US Mint, here’s the mass of common coins:

- Penny 2.5 grams (g)
- Nickel 5.0 g
- Dime 2.3 g
- Quarter 5.7 g

Maybe coin density plays a role?

Now that your coins are good and buried, give each little pirate a chance to fish out a coin one at a time until the all coins are gone. If you used different denominations, add up the coins to see who has the highest total. If you used one type of coin, a winner can be determined based on the year the coin was minted. Who has the oldest? The newest? Whose coin was pressed closest to their year of birth? There are many options for bringing numbers into the conversation

You can use small beads, buttons or coins as hidden treasure, too. These options open up a whole world of math as you ask the kids to assign values to the different sizes or shapes. Who wouldn’t value a shiny, plastic gem at $1,000,000?

Properly covered, the oobleck will stay fresh for a few days. Be sure to dispose of it in the trash, oobleck is bad for your plumbing, so don’t send it down the drain!

*Photos courtesy of Kim Moldofsky*

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]]>The post A Pretty Muddy Pig appeared first on Bedtime Math.

]]>This fellow doesn’t look so excited about standing in the mud, does he? Truth is, he probably loves it. He’s a wild boar, a cousin of our mud-loving farm friend, the pig. Wild boars are a lot less friendly, though. The boy boars have sharp 2-inch long tusks, and if they chase you they’ll poke those tusks right into you! Like their pig cousins, boars eat just about anything, and use their long snouts (noses) to dig up roots and tubers out of that mud. They can’t see very well, but they have a great sense of smell to make up for it. Boars do get dangerous if they think you’re attacking them, so you don’t want to hang out with these guys — even if you like hanging out in the mud.

*Wee ones:* We like to think of pigs as pink, but boars can be black, brown, red, or grey. How many colors can board be?

*Little kids:* Baby boars are called piglets. If you have 2 mama sows and twice as many piglets, how many boars of all ages do you have? *Bonus:* If a boar can smell you from up to 40 feet away and you’re only 30 feet away, what’s the shortest distance you need to run to be safe?

*Big kids:* Let’s say a “sounder” (group of boars) has some number of boars, and if you take that number, double it and add 5, you get 23. How many boars are in the sounder? *Bonus:* Only male boars have those tusks. If you have 24 boars chasing you but only 1/4 of them are male, how many tusks do they have all together?

*The sky’s the limit:* If you’re being chased by 16 boars, and together they have 4 times as many feet as tusks, how many of the boars must be males with tusks?

Answers:

*Wee ones:* 4 colors.

*Little kids:* 6 boars, since you have 4 piglets. *Bonus:* Anything more than 10 feet.

*Big kids:* 9 boars. If you added 5 to get 23, you had 18 before that, and you doubled to get 18. *Bonus:* 12 tusks, since you’re chased by 6 boars.

*The sky’s the limit:* 8 males. If they have 4 times as many feet as tusks, there must be 8 feet for every pair of tusks…which means for every 2 boars (8 feet), there’s just 1 pair of tusks. So 1/2 of the boars are male. Another way to solve it: 16 boars have 64 feet, which means they have 16 tusks, or 8 pairs.

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]]>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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