The Rearrangement Puzzle

On the topic of puzzles, my puzzle in in the NYTimes Numberplay column this week. It’s built to look hard, but come apart easily if you attack it from the right direction. The Rearrangement Puzzle The number 1,525,354,555,657,585,950 is, as it happens, evenly divisible by 99. Fix all the 5s digits where they are in the number, and rearrange the …

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This Week’s NPR Puzzle: Extra Challenge

This week’s Sunday puzzle on NPR is a classic from Sam Loyd. Here’s Will Shortz: This is one of the “lost” puzzles of Sam Loyd, the great American puzzlemaker from the 19th and early 20th centuries. It’s from an old magazine with a Sam Loyd puzzle column. The object is to arrange three 9s to make 20. There is no …

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Goodbye hexagon, hello 6-gon!

A colleague of mine once remarked how strange it is that while the Greeks talked about 6-cornered shapes and 4-sided shapes, we talk about hexagons and quadrilaterals. Why is it, aside from the historical accident that it is, that we persist in making people learn Greek to talk about shapes they see everyday? And quadrilaterals and hexagons are the easy …

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The Four Questions

We’ve argued for a long time that the real experience of mathematics is inextricably tied to play. But if you’re a parent or teacher, you’ve seen kids play in mathematically irrelevant ways. How do we hit that sweet spot of mathematical play? One way is to recognize mathematical questions and ideas when they arise from the play itself. Another is …

The Problem We All Live With

Back in 2006, I had the chance to see Jonathan Kozol when he visited Seattle touring his new book, The Shame of the Nation. The country, he said, had more educational racial segregation in 2006 than it did in 1968, when his first book, Death at an Early Age came out. While the US rejected the doctrine of “separate but …

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5 principles of extraordinary math teaching

We’re just finishing up a massive project of creating a supplementary curriculum for Seattle’s Summer School program. We realized that the spirit of the lessons was even more important than the content. To this end, we designed the activities to encourage students to own their mathematical experiences, to give kids an opportunity—and a reason—to fall in love with math. So …

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Math that makes worlds

From the May 18 New Yorker article World Without End, by Raffi Khatchadourian: The design allows for extraordinary economy in computer processing: the terrain for eighteen quintillion unique planets flows out of only fourteen hundred lines of code. Because all the necessary visual information in the game is described by formulas, nothing needs to be rendered graphically until a player …

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Quick Physical Games for the Math Classroom

We hold these truths to be self-evident, that kids need to move around, and creating opportunities to move during math class can pay off in spades. Therefore, we have a collection of some of our favorite math/movement quick activities to share. These are especially good for K-4, though they’re adaptable to older and younger grades too. They provide a dose …

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Counting Collections and Dots and Boxes, fractional version

I just rewrote our write up of Counting Collections, and reclassified it on our Lessons page as a Foundational Activity. The reclassification was motivated in part by a conversation with a Kindergarten teacher, who mentioned that she had been having the kids in her room count collections every Friday. “I help kids who need it,” she said, “but honestly, they’re …

Cheryl’s Birthday Party, Meta-logic, and the known unknown

I almost missed the Cheryl’s Birthday Party internet phenomenon this week. An awkwardly written logic problem went viral, and the internet was abuzz with attempts to solve it. Check out the NYTimes treatment of the origial pnroblem, and the afterparty. The problem is an example of a metalogic puzzle. Logic puzzles usually consist of organizing what you know and don’t …