Teachers should help students develop the ability to form generalizations by asking students questions such as “How could you describe this pattern?”, “How can it be repeated or extended?” or “How are these patterns alike?” For example, students should recognize that the color pattern “blue, blue, red, blue, blue, red” is the same in form as “clap, clap, step, clap, clap, step.” This recognition lays the foundation for the idea that two very different situations can have the same mathematical features and are the same in some important ways. Knowing that each pattern could be described as having the form AABAAB is an early introduction to the power of algebra for students.1 Teachers can explore functions with students by pairing counting numbers with a repeating pattern, as in the figure below.

Problem:

Look at the three patterns below and tell how they are alike and different.

1 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics (pp. 91–92). Reston, VA: Author.