100 ants were singing, and marching in a row, "We're going to a picnic, a hey and a hi-dee ho!"
One Hundred Hungry Ants, by Elinor J Pinczes and illustrated by Bonnie MacKain is a sweet story about hungry ants trying to get to a picnic left in the forest so they can pick up "some yummies for our hungry tummies".
As they walk, we see larger animals moving the opposite direction, carrying off bits of the picnic, until the littlest ant cries out "Stop! We're moving way too slow -- some food will be long gone unless we hurry up. So.... with 2 lines of 50 we'd get there soon I know!"
The ants scurry about to reform into two rows, then happily march along, but we see more large animals carrying away more of the picnic, so the littlest ant again tells them to make more rows -- "4 rows of 25!", then "5 rows of 20!", and finally "10 rows of 10!" with the other ants getting more and more discouraged and worried that all the food will be gone when they finally arrive.
Which is exactly what happens, "OH NO!"
And the littlest ant flees the wrath of the others after saying "You took too long with rows!"
I love it. It's got so much going on in a simple story. Just on the surface it has:
- Multiplication and arrays
- Divisibility (why don't they make 3 rows?)
- Does rearranging make the ants go faster?
And there's subtext about
- manager / employee relationships
- youthful exuberance and "book smarts" vs. experience
But then there's also a really interesting question about what efficiency means. The joke that my kids got immediately is that the ants don't move faster when they rearrange into columns, so the littlest ant's attempts to optimize had, at best, no effect, and at worst, cost them all a lot of time because it takes time to organize!
Did the littlest ant think that forming into two rows would get them there in half the time?
Suppose the littlest ant was thinking about how much time it would take the last ant to get to the picnic? That's called worst case analysis and it's an important thing to think about in designing an algorithm. Focusing only on when the front of the line gets to the picnic ignores the fact that the food stuff is big and it's going to take many ants to carry it all away. If they are trying to beat the larger animals to it, they're going need to get all the ants there not just the first one.
How would I explore this story interactively?
- I'm thinking about an array-former to explore what arrangements of rows is possible, as a multiplication / division / factoring visualization
- Visualization of the time it would take to move into different formations, as one cost of different approaches
- Arrival time of first ant (best case), middle ant (average case), and last ant (worst case) for different arrangements, including or ignoring the formation costs
Other questions about this story:
- What kinds of tasks benefit from working in parallel? And which don't?
- Are there issues with taking up more space if they march in rows? (predators)
- How do ants manage to navigate? (usually in one row using scent trails, or in swarms when seeking) Makes me think about search algorithms
One Hundred Ants is a part of a planned series of posts analyzing mathematical, computational, and scientific themes in children's stories as part of possibly writing a book playing some fun games with these stories.