Impossible Flips (Age 6)

The Activities

  1. Topic: Puzzles:  Book: Taro Gomi’s Playful Puzzles for Little Hands.  Still haven’t quite finished, this time it was mostly mazes.
  2. Topics: Number Line, Number Recognition.  We revisited higher/lower number guessing again, mostly from 1-100.  As usual, the theme of the game was a bear who wants to steal our picnic food.  But the bear print-out was missing so kids took turns standing next to the wall and using their finger as the bear.  I did a few numbers, and then each kid took turns thinking of their own number.  At the end, we had a discussion about what makes a good or bad guess, and then I did one from 1-1000.
  3. Topics: Combinatorics, Geometry:  Using wooden pattern blocks, find as many ways as possible to make a 2×2 diamond.patternblockdiamonds
  4.  Topic: Logic:  We did the Seven Flipped activity from youcubed.org.  Starting with 7 shapes face-down (we used Scrabble tiles), you could flip 3 tiles at a time.  The goal is to flip all the tiles face up.  After they solved that, I switched to 7 tiles, flip 4 at a time (which is impossible) and then 5 tiles flip 2 (also impossible), and we discussed why it might be impossible.

How Did It Go?

We had all five kids this week.

Number Guessing

There is a very wide range of abilities in this game.  By the end, three of the kids completely understood how the game worked, and during the discussion two of them worked together to figure out that they should guess half-way in between each time.  One of the other kids usually made proper guesses, but the final kid frequently made guesses outside of the current range (even when they were just reminded of what the current range was).  I also made a couple “illegal” guesses when I was playing, but was called out on it.  1-1000 is still pretty challenging even for the kids that get it.

Diamond Variants

The kids weren’t as in to this activity as I expected.  A couple of them went off task pretty quickly, building whatever they felt like.  One kid tried hard to use the skinny white diamonds, which doesn’t work.  Another kid was trying but kept building diamonds that were 3 units on the side.  One kid tried for a while to use squares, without success, but then eventually figured out a key insight for building different diamonds, which is that you can swap two adjacent triangles for a diamond, or vice-versa.  So that kid generated more than half of the variants we found.

Seven Flipped

The kids each had their own set of tiles.  There was lots of cheating, but it didn’t matter because I would just ask them to show me again.  At first the kids decided it wasn’t possible, but after a few minutes one of the kids figured it out.  Another kid watched them demonstrate, and then the two of them taught the other three.  Then I switched to 7/4.  There were lots and lots of claims of having done it, but it’s impossible :).  After a while, I asked them to try 5/2 instead.  A couple of the kids started to get the idea that it was impossible.  I myself made a bunch of moves on this problem with the kids watching, and we kept track of how many were face up.  With a hint the kids noticed is was only 0, 2, and 4.  I made a set of maybe 11 tiles with 6 flipped up, and then showed them all the possible moves (2 down -> 2 up, 2 up -> 2 down, and 1 up, 1 down -> 1 down, 1 up), and they saw that it could only be +2, -2, or 0.  One or two of the kids might have understood this proof that 5/2 is impossible.

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