If you’ve heard the fairy tale of the princess and the pea, you know it’s about a very picky princess. She can feel a tiny pea under her bed, even though it’s under a stack of 20 mattresses and 20 poofy blankets. That’s how the prince knew she was a real princess. But what Bedtime Math fan Tanisha T. wants to know is, how many peas could we stuff into a whole mattress? We think the peas are used to being squashed, since they grow all jammed together inside a long, skinny green pod. They’re also really good for you: a serving of peas has more vitamin C than 2 apples. None of this sounds like good stuffing for a bed, by the way. But now that we know we can fit 3 peas per inch (see photo), let’s find out how many can fit under that prickly princess.
Wee ones: What shape is a pea?
Little kids: If you can fit 3 peas in a row, and then make 3 rows to fill a square inch, how many peas fit in that square? Bonus: If they came from just 2 pods, and each pod had at least 2 peas, how many ways could they have been split between the pods? (Don’t worry about the order of pods.)
Big kids: A cube that’s 1 inch wide in every direction can fit 3 layers of those 9-pea squares. How many peas fit in a cubic inch? Bonus: They say that British people eat 9,000 peas per year on average. If you ate 20 per day, would you be keeping up? (Hints if needed: A year has 365 days…and multiplying by 20 is like multiplying by 2 and then by 10.)
The sky’s the limit: If there are 3x3x3 peas in a cubic inch, and a mattress is 200 inches long, 50 inches wide, and 10 inches thick, how many peas can we fit after all?
Wee ones: A circle, or in 3 dimensions, a “sphere.”
Little kids: 9 peas. Bonus: 3 ways: 2 and 7, 3 and 6, or 4 and 5.
Big kids: 27 peas. Bonus: Not quite: you would eat only 7,300 per year.
The sky’s the limit: 2,700,000 peas. The mattress has 200x50x10 cubic inches of space in it, or “volume,” which comes to 100,000 cubic inches. It can hold 27 peas in each of those little cubes, bringing us to almost 3 million peas!
And thank you Tanisha for this perfect-for-bedtime math question!
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.