We know that bugs like to eat our people food: just go on a picnic and watch the ants sneak up on you. So our fan Joey K. asked a great question: how fast could a grasshopper eat a cookie? Well, if grasshoppers like cookies as much as ants do, we can figure this out! Scientists aren’t sure how fast a grasshopper eats, but they do know that it can eat 16 times its own weight in 1 day, which is crazy. These bugs each weigh about half a gram, so the grasshopper could eat only 8 grams of cookie…to compare, 2 teaspoons of water weigh about 10 grams. Cookies come in all sizes, but if we go with the average of 16 grams, the bug would take 2 whole days to finish it off. We humans snarf them down a lot faster!
Wee ones: Most cookies are circles. Try to spot 4 circles in your room.
Little kids: If the grasshopper has taken 4 bites of cookie, what numbers are the next 3 bites? Bonus: If the grasshopper counts down the 8 grams of cookie while eating, what numbers does she say starting with 8?
Big kids: If the grasshopper starts eating 4 average cookies on a Monday, what’s the soonest day he can finish eating them? (Reminder: the grasshopper takes 2 days to eat 1 average cookie.) Bonus: If a giant grasshopper can eat 50 grams of cookie in a day, on what number cookie is his last bite? (They’re all 16-gram cookies.)
The sky’s the limit: If a grasshopper eats 1/4 of a cookie, then the next day she eats 1/3 of what’s left, then on the 3rd day she eats 1/2 of what’s still left, what fraction of the total cookie is still there?
Wee ones: Items might include a clock face, a plate, the edge of a cup, a button, or the flat end of a crayon.
Little kids: Bites 5, 6 and 7. Bonus: 8, 7, 6, 5, 4, 3, 2, 1!
Big kids: On the Tuesday a week later, since it takes 8 days. He’ll finish cookies on Weds, Fri and Sun. Bonus: The 4th cookie, since 3 cookies will weigh 3 x 16 = 48 grams.
The sky’s the limit: 1/4 of the starting cookie. When the grasshopper eats 1/4 of the cookie, 3/4 are left. When she eats 1/3 of that, that’s like leaving 2/3 of it behind. And just as you multiply by 2 if you want 2 of them, you multiply by 2/3 if you want just 2/3 of it. So we do 3/4 x 2/3 = 1/2. The last day she eats 1/2 of what’s left, which is like leaving 1/2. So again we multiply: 1/2 x 1/2 = 1/4 left.
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.