If you’ve ever tried to touch a cactus, you know it wasn’t so easy. Cacti are those strange-shaped plants that are famous for their spiky prickles. The crazy thing is that those prickles are the cactus’ leaves! They do the same thing as leaves on any plant: collect sunlight to make food. But cacti live in very hot places, so they need very skinny leaves that have less area to dry out in the sun. If you can get around those spikes, you can eat some kinds of cactus, like the prickly pear plant shown here. The little flowers along the edges of the “paddles” will turn into fruit, called a prickly pear fig. You can eat that fruit, and you can also eat the paddles, as long as you pluck the prickles off first. Beware when taking a bite out of cactus, or it might take a bite out of you.
Wee ones: If you eat 6 prickly pear paddles, then eat one more, how many have you had?
Little kids: If you pick a 6-pack of prickly pear paddles, and the 2nd and 6th paddles have prickles, which numbered paddles were not prickly? Bonus: If every 4th paddle has prickles, what number is the next prickly paddle?
Big kids: If a branch on that cactus has 6 sets of 5 paddles each, how many paddles are there? Bonus: If you eat every 4th paddle, what’s the greatest number you could eat from that cactus?
The sky’s the limit: If the 3rd paddle you pick is prickly, then the 8th, then the 15th, then the 24th…what numbers are the next 3 prickly paddles, and how would you describe this pattern?
Wee ones: 7 paddles.
Little kids: The 1st, 3rd, 4th and 5th paddles. Bonus: The 10th paddle.
Big kids: 30 paddles. Bonus: 8 paddles. If you start on the 4th paddle, you eat 7 (the last is 28). But if you start on the 1st or 2nd, you can fit one more in, with the 29th or 30th as your last.
The sky’s the limit: The 35th, the 48th, and the 63rd paddles. You’re jumping by odd numbers — you start with 3, then add 5 to get 8, then add 7, then add 9…but what’s really cool is that’s the same spacing for perfect squares (2×2, 3×3 and so on). Every number here is 1 less than a perfect square!
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.