The post Why Corn Is Cool appeared first on Bedtime Math.

]]>*Wee ones:* If there are 7 continents (big chunks of land on Earth) and corn grows on all but 1 of them, how many continents grow corn?

*Little kids:* Can an ear of corn have 7 rows? *Bonus:* How about 26 rows?

*Big kids:* If you buy 91 ears of corn and save 20 ears to make popcorn, how many ears do you have left to eat off the cob? *Bonus:* If there are 800 kernels in 16 equal rows on an ear of corn, how many kernels are there in each row?

*The sky’s the limit:* If an ear of corn has 800 kernels divided evenly among at least 10 rows but no more than 100, how many ways can the kernels be lined up?

Answers:

*Wee ones:* 6 continents.

*Little kids:* No, because 7 is odd. *Bonus:* Yes, because 26 is even, just like the number 6.

*Big kids:* 71 ears. *Bonus:* 50 kernels.

*The sky’s the limit:* In theory there are 9 ways to line up the kernels. To solve this, you need to find all the numbers from 10 to 100 that are “factors” of 800, meaning they can be divided evenly into it. 800 is 2*2*2*2*2*5*5, so only numbers that are products of some set of those can work (e.g. multiples of 3 like 12 or 24 won’t work). The winning combinations are:

- 10 rows of 80 kernels each

- 16 rows of 50 kernels each

- 20 rows of 40 kernels each

- 25 rows of 32 kernels each

- 32 rows of 25 kernels each (here we pass the halfway mark of the pairs of factors)

- 40 rows of 20 kernels each

- 50 rows of 16 kernels each

- 80 rows of 10 kernels each

But as you see, one of these has an odd number of rows, 25, which corn can’t have. It also can’t really fit 80 or even 50 or 40 rows. But in a perfect world, these would be the arrangements.

- 100 rows of 8 kernels each

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]]>The post A Worm in Every Meal appeared first on Bedtime Math.

]]>*Wee ones:* If 3 birds go hunting for worms, how many stomping feet do they have?

*Little kids:* In this video, the very hungry bird catches a worm only some of the times that it pecks the ground. If the bird pecks 10 times but grabs a worm 3 times, how many pecks were misses? *Bonus:* If the bird is hungry enough for 8 worms, how many more worms does he need to find?

*Big kids:* If a robin can find 6 worms every 10 minutes, how many can he find in an hour? *Bonus:* If it eats just 1/4 of those worms and gives the rest to the mommy robin, how many yummy worms does she get?

Answers:

*Wee ones:* 6 feet.

*Little kids:* 7 pecks. *Bonus:* 5 more worms.

*Big kids:* 36 worms, since there are 6 sets of 10 minutes. *Bonus:* 27 worms, since he keeps just 9.

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]]>The post Ship Shape Math Fun appeared first on Bedtime Math.

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When you drop a penny into a cup of water it sinks. So how does a boat made from copper-coated zinc not sink? The tendency of an object to float in water is called buoyancy. Buoyancy is also defined as the power of a fluid (we usually think of water) to exert an upward force on something that is placed in that fluid. Shape is an important factor that affects buoyancy. Density, an object’s mass in relation to its volume, is also significant. You can read more about this at Science Buddies.

Little pirates don’t need a shipyard to learn more about buoyancy; they can experiment right in the bathtub. Or in the backyard. But we don’t recommend trying this in a bathtub in your backyard!

Building your own pirate ships and testing them will require the following items:

- aluminum foil
- scissors
- ruler
- container with water (kiddie pool, sink, or bathtub)
- pennies, marbles, or other items for cargo
- paper towels

Give each of your buccaneers their own 12-inch square of aluminum foil. Design a boat with a large surface area and sides that will allow you to add as much cargo as possible. Set the ships into water and make sure they float and there are no leaks. Now load your cargo onto the boat, slowly and carefully, one item at a time.

Can your crew predict how many items the will be able to hold before it sink?

Add more weight to the ship until it’s time to send an SOS distress signal because the vessel is sinking or leaking. Count up the items and keep track. If you want to be more accurate, dry them off and weigh them. After all, pirates do like to keep track of their prized possessions.

Keep trying different shapes and sizes of the foil. We made square, rectangular, triangular, and circular ships. Older kids will notice how the surface area of the boat makes a difference in the ability to haul more weight.

If your family of pirates wants to continue to test ships, try making ships that are the same shape, but made of different materials like duct tape. Pirates also set sail in salty seas. Add salt to your water and note how that affects your ship’s capabilities.

*Argh, we just found a bit of buried treasure! Set sail for math success with this archived Bedtime Math problem.*

*Photo courtesy of Beth Levine*

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]]>*Wee ones:* Which is longer, a 4-foot board or a 6-foot board?

*Little kids:* If you grab 2 5-foot boards to put a roof on your treehouse, how many board feet is that? (Assume they’re 1 foot wide and 1 inch thick for true “board feet.”) *Bonus:* What if you decide you need 3 times as much to keep the rain out – now how many board feet do you need for your roof?

*Big kids:* If a tree has a 50-foot trunk, how many full 6-foot-long boards can you cut from a 1-foot-wide,1-inch-thck slice that’s the full length? *Bonus:* If you’re building a wall that’s 12 feet wide and 8 feet tall, will 100 board feet of wood be enough for the project?

*The sky’s the limit:* Let’s say all your lumber is in 6-foot or 8-foot pieces (both are 1 foot wide). What’s the least amount of wood you need to cut the necessary pieces to fill a 13-foot-long by 9-foot-tall wall? You can run the boards either side to side, up and down, or a mix of both.

Answers:

*Wee ones:* The 6-foot board.

*Little kids:* 10 board feet. *Bonus:* 30 board feet.

*Big kids:* 8 boards, and you’ll have 2 board feet left over. *Bonus:* Yes, since you need just 96 board feet.

*The sky’s the limit:* For the first wall, you can place 13 8-foot pieces vertically, then run a 6-footer and an 8-footer across the top end to end. You’ll need to cut just 1 board foot off the end of the last piece as waste. Alternatively, you could run 9 boards of each length horizontally end to end with each other, but that’s 14 feet of width, so you have to cut 1 foot off each of the 9-foot rows and you waste a lot of wood. The first option is better, using 112 board feet of 8-footers and 6 feet from the 6-footer for a total of 118 board feet. The other option uses up 126 feet.

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]]>*Wee ones:* If Kacy had to climb ladders, slide up poles, run across a tilting mat, swing onto a net, and hang from hoops, how many types of tricks is that?

*Little kids:* Kacy had to hang from the 2 red hoops and “walk” across 3 beams by hooking the hoops onto the remaining pegs. If the first beam had 6 pegs and the next had 5, how many pegs is that? *Bonus:* There were 15 pegs in total. How many pegs were on the 3rd beam?

*Big kids:* If you try out for American Ninja Warrior, and you start the final “spider climb” at 8 minutes 13 seconds and take 14 seconds to do it, what’s your time at the end of that? *Bonus:* If it then takes you 3 seconds more to hit the buzzer for your final time, by how much do you beat Kacy’s final time of 8 minutes 59 seconds?

Answers:

*Wee ones:* 5 types of tricks.

*Little kids:* 11 pegs. *Bonus:* 4 pegs.

*Big kids:* 8 minutes 27 seconds. *Bonus:* 29 seconds.

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