Patterns and Algebraic Thinking

The Web offers a host of patterns, geometric puzzles, and algebraic lessons that will hone your students' problem-solving skills and add enjoyment to the process. So, get ready and put on your hiking shoes, er, thinking caps.

Start your Web trek at the fascinating world of Fibonacci Numbers. The well-known pattern 0, 1, 1, 2, 3, . . . where the last two numbers in the series are added together to get the next number — can be found throughout nature. This site offers many other examples from nature, such as seashell spirals, flower petals, and leaf distribution. There are also exploration activities so students can use the number series in many different contexts.

Spark students' creativity at Totally Tessellated, the next stop along the trail. Any repeating pattern of interlocking shapes is a tessellation. The mathematical explanation that underlies tessellation patterns is given here as well as many visual examples, including the familiar designs of M.C. Escher.

Continue your voyage in the world of patterns at Magic Squares, a comprehensive site that offers many examples of these timeless number patterns. In a pure magic square, all rows, columns, and the two main diagonals must add to the same value and the numbers must be consecutive from 1 to n², where n is the number of places in the square. Other magic squares add up to the same value in all rows and columns. Students will enjoy many examples and be challenged to create magic squares of their own.

Fibonacci Numbers and Nature
http://www.mcs.surrey.ac.uk/
Personal/R.Knott/Fibonacci/
fibnat.html

Magic Squares
http://www.geocities.com/
harveyhd/magicsquare.htm