The post Symmetry Drawing appeared first on Bedtime Math.

]]>I love to draw, and it seems my children have inherited that love. All three of them can spend hours doodling and recreating whatever fantasy worlds they’ve spun in their imaginations. They also love to copy their favorite characters and objects, but often end up frustrated because their drawing looks nothing like the original. I tell them every artist has his or her own style, but there’s always room for improvement. The key is lots of practice, and a knowledge of concepts such as perspective, light, proportion, and *symmetry*.

Terms like shading, vanishing points, and horizon lines may be too complex for beginning artists, but even young children can understand basic symmetry. An object displays the simplest type of symmetry — *reflection symmetry* — when one half of the object is the mirror image of the other half. The line that separates the two halves is called the *line of symmetry*.

Here are 3 fun fall drawing ideas for kids that help explore the concept of symmetry while building their drawing skills. Start with the easiest one, then move on to more challenging projects!

Spiders are great examples of symmetry; there are four legs on each half of a spider’s body! Get started on your Halloween home decor with this spooky spider collage:

- Find a small or medium-sized plastic spider. Halloween decorations are already appearing in stores, so you’ll find plenty of plastic spiders and spider rings in the dollar aisle!
- Cut the spider in half.
- Glue the right half of the spider on a piece of paper.
- Draw in the left half of the spider. If you have a preschooler, ask them to predict how many legs they need to draw!

Most leaves are naturally symmetrical; when a leaf is split down its stem, the right and left halves of the leaf are mirror images of each other. The next time you go for a walk with your child, gather a few leaves and try to identify which leaves are most symmetrical. Then pick a favorite leaf or two for this fall leaf collage:

- Collect several different types of leaves.
- Carefully cut each leaf in half, lengthwise. Save the other half for later.
- Glue one half of your leaf on a piece of paper.
- Using a pencil, draw in the other half of the leaf, using the half glued to the paper as your guide. Trace over your pencil marks and fill in your leaf with a marker or crayons.
- Take the other half of the leaf and compare it with what you’ve drawn. How identical are they?

School portraits are part of our annual fall rituals. Why not combine a new school photo with a symmetry drawing challenge to capture both how your child looks and how well he draws?

- Take a close-up photo of your child, looking straight into the camera.
- Print the photo, then cut it in half, lengthwise, right through the middle of the face.
- Glue one half of the photo on a piece of paper.
- Using a pencil, draw in the other half of the face. If your child is having difficulty, draw light pencil lines across from the top of the head, hairline, eyebrows, top of the eyes, bottom of the eyes, nostrils, lips, and chin. This will help keep all the facial features at the correct level.

*Add more symmetry to your day with this Bedtime Math problem.*

*Images courtesy of Ana Picazo*

The post Symmetry Drawing appeared first on Bedtime Math.

]]>The post Fruit Fight appeared first on Bedtime Math.

]]>*Wee ones:* If the crazy 40-fruit tree can grow peaches, almonds, plums, cherries, nectarines, and apricots, how many types of stone fruit is that (yes, almonds are a stone fruit)?

*Little kids:* If you try your favorite 10 types of fruit today and 7 more types tomorrow, how many types have you tried? *Bonus:* If the 40-fruit tree has 10 kinds of peaches, how may other kinds of fruits does it have?

*Big kids:* If the tree grows 40 kinds of fruits and right now there are 5 of each ripe and ready to pick, how many pieces of fruit can you pick? *Bonus:* If you pick a new fruit type each day, then after finishing the 40 you start over in the same order, how many *full* times will you cycle through all fruit types in 1 year? (Reminder: A year has 365 days, a leap year has 366.)

*The sky’s the limit:* If the tree has exactly 40 pieces of fruit, and there are equal numbers of peaches and cherries, equal numbers of almonds and plums, twice as many nectarines as almonds, and 2 more cherries than plums, how many of each fruit are there?

Answers:

*Wee ones:* 6 types of fruit.

*Little kids:* 17 types. *Bonus:* 30 more.

*Big kids:* 200 pieces of fruit. *Bonus:* 9 full cycles, since that brings you to 360 and you can’t then fit another cycle.

*The sky’s the limit:* 8 peaches, 8 cherries, 6 plums, 6 almonds and 12 nectarines. We know that (using m for plum)

p = c and a = m

n = 2a, which also = 2m

c = m + 2

And it all adds up to 40: p + c + a + m + n = 40

Substituting, we get

2c + 2m + n = 40

2(m + 2) + 2m + 2m = 40

6m + 4 = 40

6m = 36

m = 6

So that means 6 plums, as well as 6 almonds. There are 2 more cherries than that (8) which is also the number of peaches. And there are twice as many nectarines as almonds, which gives us 12. Adding that up, 6 + 6 + 8 + 8 + 12 does equal 40.

The post Fruit Fight appeared first on Bedtime Math.

]]>The post Holy Cannoli! appeared first on Bedtime Math.

]]>*Wee ones:* Which is longer, a 2-inch cannolo or a 2-foot cannolo? Can you show with your hands how long an inch is vs. a foot?

*Little kids:* How much longer than you would a 12-foot cannolo be? (You can round your height to the closest number of whole feet.) *Bonus:* The world’s largest cannolo was made in 2010. We’re in 2014 right now. How long has the record stood?

*Big kids:* The world’s largest cannolo weighed 123 pounds. If this one weighs 200 pounds more, how much will it weigh? *Bonus:* If the round chocolate chips on a 2-inch cannolo are 1/20th as wide as the cannolo is long, how big should the chocolate chunks be on a 10-foot cannolo so they look the right size?

Answers:

*Wee ones:* A 2-foot cannolo.

*Little kids:* Different for everyone…subtract your height (in feet) from 12. *Bonus:* For 4 years.

*Big kids:* 323 pounds. *Bonus:* 6 inches, about the size of a softball, since they’ll need to be 1/20th of 120 inches. Alternatively that’s 1/2 foot, since they’ll be 1/20th of 10 feet.

The post Holy Cannoli! appeared first on Bedtime Math.

]]>The post Avast, Ye Landlubbers! appeared first on Bedtime Math.

]]>So, ye landlubbers be ready to talk like a pirate? Did ye get yer parrot to stand on yer shoulder and say “Arrrrr!”? Avast, there be lots of math in them peg legs and hook hands. If ye have keen eyes for the numbers, time to drink some grog and set sail on ye Wee Ones. Arrrrrgh!

*Wee ones:* If 6 pirates on yer ship yell “Ahoy!” and 1 more pirate yells “Shiver me timbers!”, how many pirates are yelling?

*Little kids:* If there be 8 pirates on yer ship, and each one wears an eyepatch over 1 eye, how many eyes can ye still see? *Bonus:* If just 5 of the 8 pirates have an eyepatch and 5 of the pirates like to say “Arrrr!”, what’s the fewest number of pirates who must have an eyepatch and also say “Arrrr!”?

*Big kids:* If there be 36 pirates and 1/2 have a peg leg, how many real legs did them thar pirates still have fer walkin’? *Bonus:* If 1/3 of all the pirates also have a hook for a hand, and 5 of those also have a peg leg, how many pirates still have both hands and both legs?

Answers:

*Wee ones:* 7 yelling pirates.

*Little kids:* 8 eyes (1 on each pirate). *Bonus:* 2 pirates, since there are only 3 non-patch pirates who could be saying “Arrrr!”

*Big kids:* 54 legs: 36 on the pirates with no peg, 18 on the pirates with a peg. *Bonus:* 11 pirates. There are 18 who have a peg leg and 12 who have a hook, but those groups overlap by 5 pirates, so there are only 7 additional pirates with a hook to add to the peg leg. That gives us 25 pirates missing at least 1 body part. So of the 36 pirates, that leaves us 11 who have both hands and both legs.

The post Avast, Ye Landlubbers! appeared first on Bedtime Math.

]]>The post So You Wanna Be A…Buccaneer appeared first on Bedtime Math.

]]>Anne Bonny was an unlikely pirate. First of all, there weren’t many female pirates in her day, and most wore disguises to look like men. But not Anne. Second, she came all the way from Ireland to the Caribbean to commandeer her ships. And most impressive of all, she did all this sailing as a red-haired and freckly person in an age before sunscreen existed! We caught up with Anne on board her sloop while it was anchored in a secret cove, and she shared some numeric tricks of the trade with us!

Here be the tale, landlubber: I happened across two swashbucklers possessin’ great courage, Mary Read and John Rackham. Such a fine time we had together, we took our adventures to the high seas. We cobbled together a hearty crew of seadogs and have been sailin’ on this sloop ever since!

Why *wouldn’t* a pirate need to be cunning with numbers? Ye need knowledge just to *look* like a proper pirate – ye ever try to make an eye-patch or peg leg without a measuring tape?

The clever among us do – ye don’t want to be caught on the high seas with month-old drawers or smelly shirts, so I always bring a chest of cloth and thread and make new clothes as needed. That means consultin’ me calendar and multiplyin’ the cloth needed for one outfit by the number of weeks at sea.

It not be work if ye love it, and I love piratin’ more than anything! But to ye point, preparin’ for plunder is nothing but math – from bringin’ sufficient rations to studyin’ the wind and tide charts and readin’ treasure maps. Then once the anchor’s aweigh, it be crucial to know how speedy our sloop be, and how many knots quicker it needs to be to outpace other cursed vessels. I’ve spied many a young buccaneer befuddled by compass and map – thank Davy Jones I be steerin’, or we’d be sailin’ in circles from dawn to dusk!

Well, I’m co-captain with Mary and John; I just be the best navigator on deck. After every raid, thar be the dividin’ up of our booty, which can be a bit complex dependin’ upon the size of our crew. Whoever planned the mission takes home 1/3 of the treasure – that’s always Mary, John, or me. The two captains who didn’t plan the plunder split another 1/3 of the lot, which leaves 1/3 to be split evenly amongst the regular crew.

Thar be no complaints yet! Ye must understand how much our chests be burstin’ with gold. Our cabin boy makes more than ye average capt’n!

All the skills ye need to read a map and steer a ship – takin’ the correct angles to archipelagos, accountin’ for currents and wind speed, understandin’ speed in knots and knowin’ when ye need to increase ye speed. And I know it be surprisin’, but the best buccaneers be meticulous planners – like most endeavors, piratin’ be a matter of timing and preparation. Lesser pirates think we be lucky, but we just be more clever with the numbers!

* Argh! Practice ye pirate math skills with our Swashbucklin’ Sums printable.*

The post So You Wanna Be A…Buccaneer appeared first on Bedtime Math.

]]>