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# Puzzles

Puzzles are not "dessert" for after the "real" work is done. Selected properly and introduced thoughtfully, they can be the real work.

## Why Puzzles?

Students often see mathematics as a collection of rules to know and follow. Genuine problems -- in mathematics and in life outside of school -- are not so cut and dried. State tests 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. There is no "formula" for how to do that and that is one reason why students find it hard.

Puzzles place that particular skill front and center. In KenKen(R) and Sudoku, for example, you have to look around and check several possibilities before you find something that you can do. In crossword puzzles, too, you might have to try several "across" and "down" clues before finding one that you can fill in with confidence, and that helps you with other clues that were too hard at first. Suitably designed puzzles -- like the Mystery Number Puzzles, Who-Am-I, and other puzzles of Think Math! -- offer more mathematical ideas than either Sudoku or crossword puzzles.

## So, why puzzles?

Puzzles give permission not to know the answer or method before starting.

Students build stamina and confidence for problem solving by playing with puzzles.

• They are genuine problems to solve -- true to real life -- not exercises in following a rule or template.
• They allow high cognitive demand with flexible prerequisite math knowledge.
• They give plentiful skill practice while allowing the mind to engage: drill and thrill, not drill and kill.
• They exercise important habits of mind: experimenting, juggling multiple constraints…
• They engage the intellect. They are fun.

Puzzles also provide a perfect way to differentiate learning.

The ability to solve puzzles is also highly valued in the "real world"! Logic puzzles are used as basic exercises not only in mathematics but in law. The Law School Admission Test (LSAT) is full of logical puzzles, and the preparatory materials are called Logic Games. Such puzzles often appear in recreational mathematics websites and magazines and books. Riddles and puzzles are as ancient as literature.

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

## When?

Full lessons on puzzles are not the way to get the benefit of puzzles. Setting a "puzzle day" apart from "serious work" defeats most of the value of puzzles.

• Introducing a new kind of puzzle may require a significant part of a lesson: ten minutes or so for a group (or the whole class) to play through one or two together with you, learning the rules and getting a feel of the strategy, and then some more time to try it themselves, preferably working in pairs. See introducing KenKen puzzles for an example of introducing a puzzle, with particular emphasis on "social solving."
• After children know how the puzzle works, the puzzles are generally best used as periodic infusions in a lesson -- possibly as a day-starter, or warmup to a particular lesson.
• Puzzles are not "dessert" for after the "real" work is done. Selected properly and introduced thoughtfully, they can be the real work that gives the message that your class is about thinking and sticking with a problem until you puzzle it out.
• "One-a-day vitamins": If puzzles are seen as rare, or for special days, they are discounted as play time. A single puzzle on most (but not all!) days, is good. Give it just enough attention to let the class know you consider it an important part of your lessons, and not just filler to give you a break from teaching.

Some types of puzzles