This mama duck and her ducklings look like they should be swimming on a lake. But they’re happy: They’re walking to the pizzeria next door to Bedtime Math. That mama duck has a lot of kids to herd down the sidewalk! Ducks normally lay between 7 to 12 eggs at once, so this is a big family. “Ducks” get their name from the Olde English word for “diver,” because that’s how ducks eat. While swimming, they stick their heads and necks under water to catch fish, plants, worms, and bugs. They have lots of body fat, which keeps them from sinking as they do this. Of course, eating a slice of pizza sounds a lot easier — and yummier.

*Wee ones:* If the mama duck takes 6 ducklings to pizza and the daddy duck takes 5 ducklings out for ice cream, which duck took more ducklings?

*Little kids:* How many ducklings can you count in the picture? How did you go about counting them? *Bonus: *If there were 9 ducks here including the mama, how many ducklings would there be?

*Big kids:* If 100 ducklings walk down the street, and 1 duck goes into the pizzeria, then 4 more, then 9 more…what number comes in next to keep the pattern? *Bonus: *What number comes in after that — and can you tell what is special about these numbers? (*Hint if needed:* What numbers can you multiply together to make each of those numbers?)

*The sky’s the limit:* If some number of ducks goes in for pizza, then double that number walks in the 2nd set, then double *that* number for the 3rd round, and there are now 56 ducks in there, how many ducks walked in in the 1st round?

Answers:

*Wee ones:* The mama duck, with 6.

*Little kids:* We count 13 ducklings…see if you can find them all! *Bonus:* 8 ducklings.

*Big kids:* 16 ducks, since you started with 1, then added 3, then added 5…now you add 7. *Bonus:* 25, and what’s cool is that these are the “perfect squares”: 1 x 1, 2 x 2, 3 x 3, 4 x 4, and 5 x 5. The pattern works forever!

*The sky’s the limit:* 8 ducks. Each duck that walks in is followed by 2 more ducks, then 4 more ducks. So they enter in sets of 7. 7 goes into 56 8 times, so there are 8 sets. We have 8 ducks, then 16, then 32, which all adds up to 56.

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.