Thursday, August 26, 2010

Math Without Words, by James Tanton

Way back in the spring James Tanton kindly sent me seven of his books to review.  Ever since then I've been trying to look them over thoroughly enough to do a good job reviewing them. I think I'd better do the reviews one at a time, or I'll never get to it. The books are so full of goodies it might take me years to feel like I've looked them over properly.

You may have noticed a few interesting sheets of puzzles in the video of my math salon. Here's one:

These came from Math Without Words, a compendium of 75 delightful puzzles. Each puzzle has one or a few sections that are filled in to show show the puzzle works. Then there are more sections ready to be thought about and puzzled over. The puzzles get you thinking mathematically in new ways, and range from easy enough to engage five year olds, to hard enough to stump the grownups.

Folks at the math salon really loved these puzzles, and I think you will too. You can buy a print copy of the book for $27.50 or download an electronic version for $19.50. Both are available at Lulu. I just now bought the electronic version, so I can more easily make copies for the groups I work with.

That first puzzle may look too easy. But for young kids it really is a great puzzle. Here's another puzzle we enjoyed at the math salon:

And I'll leave you with a more challenging puzzle that we haven't tried at the salon yet:

If you'd rather have a dozen of the puzzles in wall calendar form, that's available too. Next up for review is Thinking Mathematics, Volume 1: Arithmetic = Gateway to All.


  1. If you say, "1...2...3...5...8 to me I think Fibonacci...

  2. Ahh, yes. I suppose that means this puzzle isn't particularly challenging. But figuring out why might be harder. And you know how some patterns start out one way, and veer off in another direction...

  3. Thanks for the review! I saw this link on the living math group, and I'm planning to get the download for my math club this fall. With the recent kerfuffle over MathCounts, and with having enjoyed your video so much, I decided to try your "system" of putting stuff out and letting people play --- and as soon as registration opened, my group overflowed onto a waiting list. Should be a fun semester...

  4. Denise, what age range do you have in this 'class'? I'm sure you'll get to do lots more structured activities if you meet weekly with a constant group. What title did you use for your 'class'?

    At the college, our beginning and intermediate algebra classes have an extra 'hour by arrangement'. The students who come to me for that will get the games and puzzles treatment. Today is the first day for that and I'm deciding what to pack.

  5. This looks really cool! I tutor 5th graders after school, and this seems like it would get them thinking. They have all missed out on lots of math basics and are now afraid of/hate "MATH". Now if only I could get my principal to cough up the money...

  6. For 27, that diagram is always part of our solution to "Ghost the Bunny" - the first Fibonacci problem solving we run into.

    The why part is cool. Here's one approach I like:

    Take all the blocks two lines above, and append a long one to the right, and then take all the blocks one line above, and append a short one to the right -- we've got two sets, all are the same length, but none are repeated. And we can't be missing any, unless we were missing some on the previous lines...

    But there's tons more approaches.


  7. Jonathan, that's lovely! Now I'm disappointed in myself, that I didn't play with this more before.

    Will you tell us more about "Ghost the Bunny"?

  8. There is a more or less standard argument (for example, Proofs that Really Count by Benjamin and Quinn.)

    Let F_n be the number of ways to combine 1×1 and 1×2 blocks into an 1×n arrangement.

    Any such arrangement may end with either 1×1 or 1×2 block. There are F_(n-1) of the former kind and F_(n-2) of the latter kind.

  9. Does the book come with solutions - cuz I would love for my kids to play with these - but honestly I don't "get" most of them. I am severely math challenged!!

  10. Sue, Does this book come with answers? Thank you.

  11. I have the pdf version of the book with me on vacation, and it has what James Tanton calls "oh so brief solutions". I'm assuming the paper copy of the book has solutions also, but I can't check until I get home in 2 weeks.

    If anyone is still puzzled after looking at a solution, feel free to ask me or James Tanton himself.

  12. I wonder if the book explains a very mysterious symbol it uses: = . I think If I didn't know what the equals sign means, I would be totally lost from the git-go.

  13. I don't think it does. But those who don't know what = means are usually young enough that they're looking at the book with someone older, who explains simply.


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