Author Archives: laura

Whaling Away

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Contrary to what Dad says after you explain how your bike ended up on the roof of the house, he hasn’t really “heard it all.” In fact, no one has heard it all. We people can hear only a certain range of sounds, or frequencies. Some animals, like bats, make sounds that are too high for us to hear, while others such as elephants make sounds too low for our ears to pick up. Meanwhile, whales hear so well that they can sing to each other over hundreds, even thousands of miles of water. Well, okay, they’re not actually singing, but their sounds have rhythm and melody similar to human music. Some people listen to whale songs just because they sound nice. But marine scientists try to eavesdrop on these underwater divas to understand their language. Or maybe they’re just trying to pick up some pointers for singing in the shower.

Wee ones: If a whale is singing a 9-minute song, and he has already sung for 3 minutes, how many more minutes are left in the song?

Little kids: Sound travels about 1 mile in 1 second underwater. About how long will it take a whale song to travel 10 miles?  Bonus: Sound travels much slower through air than through water – only 1 mile every 5 seconds. How far would the song travel on land in the time it would travel 10 miles through water?

Big kids: Whale songs apparently string together repeated “themes,” which are 3 minutes long. If there are 3 themes in a particular whale song, each repeated 3 times, how long is the song?  Bonus: With more ships traveling the oceans, it becomes harder for whales to hear each other. If a whale has to sing a 20-minute song over and over for 6 hours each day, 4 days in a row, how many times does she sing that same song?

 

 

 

Answers:
Wee ones: 6 minutes remain in the song.

Little kids: It will take 10 seconds.  Bonus: 2 miles.

Big kids: 27 minutes, since you have 3 themes x 3 minutes x 3 times around.  Bonus: She sings the song 72 times, since she sings it 3 times per hour.

Eight is Enough

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The countdown is on: only 8 more days till the big Bedtime Math book comes out! And that has us thinking about the number 8 and how special it is. It’s definitely special to all those animals out there who have 8 legs, from spiders and scorpions to lobsters and crabs to octopus and shrimp.

So what’s it like to have 8 legs? How do you walk when you have to keep track of that many feet? For us humans it’s easy to walk: if we number our feet 1 and 2, walking is just 1,2,1,2. For a horse it’s a little trickier: with front feet 1 and 2 and back feet 3 and 4, a horse’s steps are 1,4,2,3, then 1 again. But in what order does a crab or spider use its feet? Let’s find out how all these animals keep from tripping over themselves.

Wee ones: If a horse’s steps are 1, 4, 2, then 3, and so far the horse has stepped 1,4,2,3,1,4, which foot takes the next step?

Little kids: If a crab steps with all 8 legs in a certain order before repeating the pattern, how many total steps has it taken when every leg has stepped twice?  Bonus: If the crab then takes a 3rd step with 6 of its legs, now how many steps has it taken?

Big kids: In this home video of a crab walking sideways, it looks like the feet on one side step in the order 1,3,2,4. If the 4 legs on the other side follow the same order but a split-second later, the pattern is 1,5,3,7,2,6,4,8. Which leg will take the 37th step?  Bonus: Leg number 6 takes the 6th step in this order; then the 14th step, then the 22nd, and so on. After the first round of steps, when will that 6th leg take a step that also ends in a 6?

 

 

 

Answers:
Wee ones: Foot #2 is next in the pattern.

Little kids: 16 steps.  Bonus: 22 steps.

Big kids: Leg #2. 32 is the largest multiple of 8 less than 37, which means 4 full rounds of steps…then the crab takes 5 more steps, and leg #2 is 5th in the pattern.  Bonus: 46 steps. At that point the crab has taken 5 full rounds of steps, bringing it to 40, plus 6 more to get to leg #6.

Dad Tails

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It’s Father’s Day today, a day when we celebrate our dads for all the awesome stuff they do for us. In doing so, we really should remember all dads, including one of the most noble groups of fathers out there: seahorses. Usually it’s the mom who lays the eggs or gives birth to the kittens or pups, and then feeds and cares for them. But seahorse dads get very involved. The mom lays the eggs right into a pouch on the dad’s tummy, and he carries the eggs until they hatch into miniature seahorses. Seahorses are tiny — some grow to be only 0.6 inches tall (just over half an inch), and the largest are only 14 inches. But they’re big eaters: They have no teeth and no stomachs, so the food they eat passes through their stomachs very quickly, and they have to eat almost constantly. And that sounds a lot like a few dads we know.

Wee ones: If 2 daddy seahorses are each carrying 6 eggs, how many are they carrying altogether?

Little kids: Thanks to their curly shape, seahorses are among the slowest swimmers in the ocean, with some managing only 5 miles per hour. If you can swim 15 miles per hour, how many more miles can you swim in an hour?  Bonus: How many more can you swim in 2 hours?

Big kids: If a seahorse eats 3,000 brine shrimp per day, how many shrimp is that per week?  Bonus: That said, a real horse is way bigger than a seahorse (and eats a lot more, too). If seahorses can grow to up to 14 inches long and your regular horse is 7 feet long, how many times as long is the real horse?

The sky’s the limit: If you have a whole bunch of seahorses and real horses as pets, and together they have 24 more horse feet than horse snouts and 2/3 as many horse tails as horsefeet, how many of each kind of pet horse do you have? (Reminder: seahorses have fins, but no legs. But everyone has a tail and snout!).

 

 

 

Answers:
Wee ones: 12 eggs total.

Little kids: 10 miles more.  Bonus: 20 more miles.

Big kids: 21,000 shrimp.  Bonus: 6 times as long, since it’s 84 inches.

The sky’s the limit:  You have 30 seahorses and 18 real horses. The number of snouts equals the number of tails (one per pet), so there are 24 more feet than tails, and that number is also 1 1/2 times the number of tails. In algebra, t + 24 = 3/2 t, so 24 = 1/2 t and hence t=48. Now you see you have 48 tails, which means 48 pets with 48 snouts. There are 24 more feet than snouts, or 72 feet, which means 18 real horses. You have 48 pets in total, so that leaves you with 30 seahorses.

Booking Down the Hall

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Have you ever played dominoes? They’re the little rectangular tiles with two sets of dots, which you match to line up end to end. But you can also stand them on end in a long row so when you knock the first one over, it knocks down the next, then the next, until you get a rippling wave of falling tiles. The thing is, you can create this “domino effect” using bigger items – like books. As you see in this video, the Seattle Public Library set a new world record by lining up 2,131 books around and around the tables, chairs, shelves and fountains. And guess what – you can do this, too! Grab as many books as you can from around the house and stand them on end in a line, close enough so that each one will reach the next one and knock it over. Make wavy lines and spirals, have the line split into 3 or 4, and then give that first one a shove and watch the action!

Wee ones: Only hard books can stand up on end, of course. If you start with 4 board books and 5 hardcover books, how many books do you have for your domino chain?

Little kids: If you line up 10 books each spaced 1 foot from the next, how long is the chain from the 1st standing book to the 10th? (Think carefully…)  Bonus: If that 10th book knocks down 2 different rows that each have 10 books themselves, how many books do you have in your Y-shaped domino chain?

Big kids: If you line up 70 books that then kick off 4 new rows of 70 books – one through the den, one under the kitchen table, and so on – how many books have you used?  Bonus: If the books have to be 8 inches apart, how long is the chain from the 1st book to that 70th book? (Hint: you might want to turn those inches into fractions of a foot.)

 

 

 

Answers:
Wee ones: 9 books.

Little kids: It’s only 9 feet, because 10 books have 9 spaces between them (this is called the “fencepost problem.”)  Bonus: 30 books in total.

Big kids: 350 books.  Bonus: 46 feet. Again, you have only 69 gaps between books, not 70. 8 inches equals 2/3 of a foot, so you have 2/3 of 69 feet, or 46 feet.

And a big thank-you to Laurel P. for sending us this awesome video!

Star (and Stripe) Student

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Have you ever gotten a grade at school that was lower than you thought it should be? Well, a high-school kid named Robert Heft felt that way at one point, but it all worked out in the end: his school project became our 50-star flag! In 1958 the United States had only 48 states, but Alaska and Hawaii were on deck to become the 49th and 50th. Mr. Heft spent a weekend designing a flag with 50 stars for a school assignment, but his teacher told him it wasn’t very exciting – adding that he could earn a higher grade only if he got Congress to accept his version of the flag. So that’s exactly what Mr. Heft did: he sent it to his representative in Congress (part of the U.S. government). The rep got Congress to vote it in, and when Alaska and Hawaii became new states, Heft’s flag was ready for the occasion. Today on Flag Day we’re still flying Mr. Heft’s flag – and we’re still doing school projects, because you never know where they can go.

Wee ones: If you’re adding the bottom row of 6 stars and you’ve already sewn 3 stars on, how many do you need to finish the row?

Little kids: The American flag is almost 2 times as long (fly) as it is wide (hoist). If your flag is 5 feet wide, about how long should it be?  Bonus: Mr. Heft put the stars in 5 rows of 6 stars alternating with 4 rows of 5 stars. How many stars do the 6-star rows have in total?

Big kids: 26 of the 50 United States lie east of the Mississippi River. If you made a flag for only the states west of the Mississippi, how many stars would it have?  Bonus: There are 5 points on each star on the flag. How many star points does it have in total?

 

 

 

Answers:
Wee ones: 3 more stars.

Little kids: 10 feet long.  Bonus: 30 stars.

Big kids: 24 stars.  Bonus: 250 points.