Topics: Logic and Proof, Puzzles

Mathematical Domain: Operations & Algebraic Thinking

**KenKen(R) puzzles were not built into Think Math! but are a wonderful material to make regularly available to children.**

These puzzles give excellent arithmetic practice while building essential mathematical skills: logical deduction, looking around for vital information, shifting strategies (sometimes factoring, sometimes using process of elimination, sometimes…), and increasing problem-solving stamina.

Start with the 4×4 puzzles. When students are feeling really successful with these and want a bit more challenge, they can graduate to 5×5 or 6×6 puzzles. Larger puzzles are not just “more work” but require some new strategies and new arithmetic thinking. The Boston Globe and The New York Times and other newspapers now commonly include these puzzles. You can find these puzzles on line. One of the on-line sites allows you to choose the level of difficulty of puzzles.

For detailed suggestions for introducing KenKen(R) puzzles for the first time, see Introducing KenKen puzzles.

Why a “social” approach to puzzles?

Puzzles are often done alone, of course. For classroom use, it is often best to work in pairs. Two people will see different things, and find different things easy. Working with someone else, as long as it feels collaborative and friendly, helps each student see new strategies, and also takes the pressure off. When one person is “stuck,” it helps to see that the other is, too.

Students tend to see mathematics as a collection of rules to follow. Genuine problems — in mathematics and in life outside of school — are not so cut and dried. Tests, like the MCAS, typically give problems that require students to think beyond the rules. Even standard word problems require students to figure out where to start and what to do next, and there is no “formula” for how to do that.

Certain kinds of puzzles place that particular skill front and center. In Sudoku, for example, you have to look around and check several possibilities before you know what you can do. But Sudoku offers no other benefits. In crossword puzzles, too, one might have to try several “across” and “down” clues before finding one that can be filled in with certainty, and that gives one more help for the other clues that were too hard at first.

Puzzles also provide a perfect way to differentiate learning. Once 4×4 KenKen puzzles have lost their challenge, one can try 5×5 or 6×6, each with not just “more work” but requiring some new strategies and more arithmetic thinking.

Why puzzles and playfulness in a mathematics class? See Tracing the Spark of Creative Problem-Solving, Benedict Carey, Dec 6, 2010 NY Times.

KenKen puzzles are particularly good at sharpening several elementary arithmetic skills, and logical skills as well. In a 4×4 puzzle, a clue like

- could be filled with (4,1,4) or (2,4,2). Either way, we know it must contain at least one 4.
- In an 8×8 puzzle, it might be filled in one more way.
- If, in a 4×4 puzzle, the same shape space needed to be filled with a product of 32 rather than 16, there would be only one possible way to fill it.

- KenKen This kind of puzzle can be found under various names. KenKen is a trade name of Nextoy, LLC. The official Nextoy KenKen site offers one new puzzle each day at each size — 4×4 (a few minutes of work) through 9×9 (can require a half hour or more of hard thinking for two people).
- MathDoku This site offers the same kind of puzzle without using the trade name. You can choose from three different sizes — 4×4, 6×6, and 8×8 — and you can also choose the difficulty level at each size (so, easy or hard 4×4, easy or hard 6×6). Easy puzzles, even of 6×6 size, can be very suitable for beginners.

A New Puzzle Challenges Math Skills (New York Times)

How KenKen Puzzles can Help You Learn Math (Education Articles – edarticle.com)