That cute face looks sweet and calm. But this border collie works long, hard hours every day, with lots of running and barking. Border collies help farmers herd sheep, goats, llamas and other herd animals. The dogs love to chase any moving thing, and by running around the sheep, they steer the sheep into a group, so the farmer can find them easily. Border collies are super smart, so they learn fast…farmers have to train the young dogs quickly, so the dogs learn to do good things instead of bad! They’re called border collies because they first came from the border between Scotland and England. And all border collies are the great-great-great…grandkid of just one long-ago dog from 1893! If you do the math, you’ll see that the pups have added up since then.

*Wee ones:* Border collies are black and white. Find 2 black things and 4 white things in your room. Of which color do you have more things?

*Little kids:* If you take your border collie for a walk, how many legs do you have altogether? *Bonus:* If your border collie is herding 10 sheep and 1 of those sheep gets away, how many are left?

*Big kids:* One super-smart border collie, Striker, rolled down a car window in 11 seconds! At that rate, could he roll down 4 car windows in 40 seconds? *Bonus:* The “smartest dog ever,” a border collie named Chaser, knows the names of 1,000 of her toys! If she fetches 1 for you, how many more toys does she need to fetch?

*The sky’s the limit:* If a border collie had 4 puppies in 2000, and 4 years later each of them had 4 puppies, and 4 years later each of those had 4 puppies…how many puppies would have been born in 2016?

Answers:

*Wee ones:* You’ll have more white things (4) than black (2).

*Little kids:* 6 legs (4 + 2). *Bonus:* 9 sheep.

*Big kids:* Not quite…he would need 44 seconds (plus time to jump from seat to seat). *Bonus:* 999 toys.

*The sky’s the limit:* 1,024 puppies. 2000 was 16 years earlier, which is 4 sets of 4 years. But you also have to count the first set of 4 puppies in 2000, so it’s 5 sets of puppies. Each new set of puppies is 4 times as big as the last, so in the 5^{th} generation there would be 4 x 4 x 4 x 4 x 4, or 1,024 puppies. Of course, dogs have puppies more often than that, so since 1893 there have been tens of thousands of them!

Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.