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Squares of Differences III: a surprising solution

[See Squares of Differences I and Squares of Differences II, and apologies for the tardiness of the posting] I’ve learned a lot about Squares of Difference in the last months. First, they’re sometimes known as Difference Boxes, or Diffy Boxes, or sometimes Ducci Sequences, or the 4 number game, and references to them are indeed available online. However, my favorite …

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Squares of Differences II: Changing Direction

[Note: this is a continuation to the first Squares of Differences post. Read that before continuing.] A week after introducing her class to squares of differences (seeĀ  for the first post on this lesson), one of Katherine’s students walked in with a list of squares that they claimed would continue for 20 steps before reaching all zeroes. Here’s an example …

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Squares of Differences: subtraction practice toward a greater purpose

Here is a phenomenal lesson, accessible to any child who knows how to subtract, and compelling to everyone, up to and including professional mathematicians. Get a kid engaged in it, and they’ll do hundreds of subtraction problems without complaint, because it’s helping them solve an honest mathematical mystery. I’ve seen this idea discussed in math education circles, but I haven’t …