Here are a couple to ponder. I've got answers (as well as the inevitable pedagogical discussions) over at You Do the Math.

1. If a perfect square isn't divisible by three, then it's always one more than a multiple off three, never one less. Can you see why?

2. Given the following

A B D _______________________________________________

C E F G

Where does the 'H' go?

Paul Krugman: The Medicare Miracle

3 hours ago

For 2 I didn't think of anything mathematical. My solution was to swap sides if the letter to be placed rhymed with the previous letter and stay the same side otherwise.

ReplyDeleteWhich would diverge from your answer at k.

There are usually multiple patterns that hold early in the sequence. My way of handling that in class would be to say, "that certainly works so far... Let's see what happens when we get more data."

DeleteI might follow that with "Now let's see how the rhyming pattern looks." and have the class call out the answers. The important thing is to leave the kids with the understanding that a problem can have more than one right answer but sometimes we can narrow it down with more information.

Another solution could be that "closed" letters (those with an open space with a line all around, like in D) are on top, while the "open" letters are at the bottom.

ReplyDeleteThat is the pattern -- check out the full explanation at You Do the Math

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