4 Replies Latest reply: Sep 17, 2010 9:42 AM by Illuminations RSS

Great Problems for the Beginning of the School Year

pvennebush New User
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What are your favorite problems to use with students?


At the beginning of the year, I think it's important to foster a culture where solving problems (not just completing exercises) is a critical element. Great problems help to create a culture where kids are allowed to think, struggle, and talk about their mathematical discoveries.


Here is my all-time favorite problem:

Assign each letter a value equal to its position in the alphabet, that is, A = 1, B = 2, C = 3, and so forth. The product value of a word is equal to the product of the value of the letters. For instance, the product value of CAT is 60, because C = 3, A = 1, T = 20, and 3 * 1 * 20 = 60.

  • What is the product value of your name? Now, find a (common) English word that has the same product value as your name.
  • Which U.S. state has a name with a product value of 3,105?
  • (attributed to John Horton Conway) Find an English word whose product value is 3,000,000.


The lessons on the Illuminations website contain a lot of great problems, too. Here are my favorites at three levels…



Create A House Number, http://illuminations.nctm.org/LessonDetail.aspx?id=L225


Middle School:

Paper Pool, http://illuminations.nctm.org/LessonDetail.aspx?id=U165


High School:

This Sweet Problem, http://illuminations.nctm.org/LessonDetail.aspx?id=L766

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