A Puzzling Math Situation

Why is 6 scared of 7? Because 7, 8, 9. A silly little play on numbers I know, but this was the response from my younger daughter when I asked her for some “fun math inspiration” for writing this article.  Surprisingly, I was inspired. I started thinking about number and logic puzzles and asking myself why don’t we spend more time in math doing puzzles and/or number tricks? Puzzles and number tricks can help students develop critical thinking skills, number sense, persevere and engage in arguments and engage in conversations about math and thinking. Students don’t get the chance to experience the pure fun and wonder that numbers and logic entail because we spend so much time drilling and killing them with rote practice in the never-ending standardized test prep. I say let’s bring the fun back! There is of course the real-world application argument. The Common Core Standards of Mathematical Practiceare reemphasizing the need for relevant application of math content. Teachers and textbooks are continually trying to provide real-world applications.  The CC modeling standard says  “mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.” But does it all have to be real-world? I suggest we also provide students with the opportunity to solve puzzles and do number tricks. These are viable ways of helping students develop the reasoning and number sense supported by the following Common Core Standards:

  1. Make sense of problems and persevere in solving them
  2. Reason abstractly and quantitatively
  3. Construct viable arguments and critique the reasoning of others
  4. Look for and make use of structure

Scott Farrand’s Ignite talk at the California Math Conference North sums up this idea of using puzzles to challenge students to think critically in mathematics.

What kind of puzzles and number tricks am I talking about?  There are a plethora of examples out there, so I am just going to list some of my favorites, many of which I used with my middle and high school students and some of which I just discovered. If anyone else has some suggestions for logic and number puzzles, send them our way. Let the fun and games begin!

  1. Algebra Magic Tricks
  2. Soduku
  3. What’s Wrong with This Picture?
  4. The Murderous Maths Books
  5. Rapid Math Tricks
  6. Smart Moves (this is a new one I saw at NCTM)

4 thoughts on “A Puzzling Math Situation”

  1. Thank you Karen for highlighting my first puzzle book Smart Moves. Why did you cross out my other puzzle book What’s Wrong With This Picture? another favorite of many?
    My next puzzle book, Pirate Math, will be out this summer and I will be showcasing it at my talk at the Denver NCTM regional in April.

    1. Hey Michael, great to hear from you. The cross through is because the link was broken, so I fixed it. Not intentional… You were in my list of suggestions!! Exciting to hear about your new puzzle book coming out. Can’t wait.


      1. I too am concerned about what I feel is an over emphasis on all content being a “real-world” application. Here is a favorite quote on the that:

        Good mathematical problems are necessarily artificial. In contrast, “realistic” problems tend to elicit “realistic” responses involving little or no mathematics. In mathematics teaching, what matters is not whether a problem is plausibly real or artificial, but whether it is such that pupils are prepared to enter into the spirit of the mental world it conjures up.
        —A. Gardiner

        All the best,

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