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
Currently Being Moderated

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…

 

Elementary:

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

More Like This

  • Retrieving data ...

Legend

  • Correct Answers - 4 points
  • Helpful Answers - 2 points