In case you're wondering what kinds of math problems sixth graders in the Minneapolis public schools are working on these days, I recently heard Lydia FaceTiming a friend about what turned out to be:

*A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocked over all the containers of eggs. Though she is unhurt, every egg is broken. So she goes to her insurance agent, who asks her how many eggs she had. She says she doesn't know, but she remembers some things from various ways she tried packing the eggs. *

*When she put the eggs in groups of two, three, four, five, and six there was one egg left over, but when she put them in groups of seven they ended up in complete groups with no eggs left over.*

*How many eggs were in her cart?*

First, let me put my Old Fogeyism on hold and admit I think it's cute when kids use their smart phones to put their heads together about math homework. It's when they spend hours playing Roblox that I get pissed off, except for when it allows me to watch Twins games on tv without interruption. Lydia and her friend didn't have a better idea than to "horse it": that is, work through all the multiples of 7 until they came to one that satisfied all the other described properties. This was proving tedious, and leading to "Eurekas" that were then discovered to be mirages, and ultimately there was frustration and despair. Their worksheet more or less predicted this process, for another instruction stated: "Describe what you did in attempting to solve the problem. . . . Include things that didn't work out or gave you unexpected results."

The "trick" is to use the supplied information to proceed with efficiency, instead of "horsing it" and just hoping you will soon hit on the answer. If there's one egg left when they're placed in groups of five, then the answer must end with 1 or 6 (since multiples of 5 are 5, 10, 15, 20, &c). But it can't end in 6, because when placed in groups of two there is also one left over. So the answer ends with 1 and is divisible by 7. The first possibility is 21, which doesn't work. The next possibility is 21 + x, where x is a multiple of 7 (so that the number is still divisible by 7) *and* a multiple of 10 (so that the number still ends with 1)—in other words, x is 70 and the next possibility is 91, which fails the test since 91/4 yields a remainder of 3. What about 161? No, divide it by 3 and you have 2 left over, not 1. We're still "horsing it," sort of, but considering only one out of every ten multiples of 7 is way more efficient. The next possibility, 231, doesn't work on account of being divisible by 3—no remainder at all. But 301: ding! ding! ding! ding! Sixth grade gonna be fun for dad!

I think Lydia is okay with the help and simultaneously a little exasperated about the old man being such a dweeb. I tried to explain that I come by it honestly. When as a kid I asked her grandpa for math help, he would peruse my book, to get the lay of the land, and then begin grousing about how he had half a mind to call school since it was obvious the author of the textbook "knows nothing of mathematics." Good grief, I just want help with this one problem, don't make it an issue in the next school board election, for God's sake. He would regale my sister and me at supper with math anecdotes, like the one about the child prodigy who, during an elementary school arithmetic lesson, was disrupting the class by tapping his pencil loudly on his desk. The teacher told him to stop several times before finally admonishing him, "I don't want to hear another peep from you until you've summed the first hundred integers." He stared at the teacher defiantly, still tapping his pencil. "I mean it!" the teacher said. "Five thousand fifty!" he said.

And my dad explained that rather than thinking "one plus two is three and three is six and four is ten"—"horsing it," and soon having to sharpen your pencil while risking confusion and error—the "prodigy" thought of it as:

(1+100) + (2+99) + (3+98) + … + (50+51).

That is, 50 paired sums of 101, so that the solution is 50 x 101 = 5050. And my sister and I, forebears of Lydia: "Great, what's for dessert?"

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