Chapter 17: Powers: Situation 11 From the MACMTL–CPTM Situations Project

During an Algebra 1 lesson on exponents, the teacher asked the students to calculate positive integer powers of 2.A student asked the teacher, “We've found 2² and 2³. What about 2^2.5?”

The Prompt centers on the extension of the domain of the exponent to selected supersets of the integers. The Foci explore the nature of exponents numerically, graphically, and analytically. The table with integral values in Focus 1 suggests a pattern for a curve and an extended domain that is illustrated in the graphical representation in Focus 2. Although Focus 1 and Focus 2 yield an estimate, the analytical treatment in Focus 3 generates an exact value. These Foci illustrate expansion of the concept of exponentiation beyond repeated multiplication to accommodate the use of some noninteger exponents.