Mathematics unfolding: Functions
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Students’ understanding of functional relationships builds on their exploration of patterns in earlier grades. In the animation below, students analyze the pattern as a sequence of alien creatures to predict what subsequent creatures in the sequence will look like.

Students begin by connecting the verbal description of the pattern to the concrete representations of the creatures. The concrete representations are then connected to numerical, algebraic, and graphical representations of the relationship between a creature’s position in the sequence and the total number of body parts the creature has. Connecting five different representations of this relationship gives students a good foundation for a more formal study of functions in subsequent mathematics courses.

Even when students are comfortable using a pattern to predict the "next" value in a sequence, they often struggle when trying to generalize a direct relationship between the value and its position in the sequence. Focusing students on what stays the same and what changes in each new creature is important. Giving students small tiles that they can use to build the creatures can help them make sense of the constant and changing quantities in this situation.