National Benchmarks, Project 2061 for Grades 68 The Nature of Mathematics 2a Patterns and Relationships:
The Mathematical World 9a Numbers:
9b Symbolic Relationship:
9c Shapes:
Common Themes 11d Scale:
Habits of Mind 12b Computation and Estimation:
12d Communication Skills:
National Science Education Standards grades 58 A Scientific Inquiry
Scientists are always faced with the manipulation of very large numbers. Whether we talk about stars in the galaxy, cells in our bodies, or atoms in a cell we are dealing with numbers that dwarf those of everyday experience. The mathematical notation we use in describing everyday situations quickly becomes unwieldy when dealing with very large numbers. These labs will help your students to understand the manipulation of scientific notation, and to begin to graph and interpret exponential behavior. This experience will be useful in all further scientific investigations, in other ASPIRE lessons and beyond. Activity 1  Scientific Notation I: The Exponent In the first of two lessons on interpreting and manipulating scientific notation, students are introduced to the concept of the "exponent" or "poweroften" in a number expressed in S.N. Two short JAVA labs show, first by demonstration and then by practice, how the exponent relates to the number of powers of ten and the number of "zeros" of a number expressed in conventional notation. A third lab  a stepthrough tutorial  then illustrates how numbers expressed in exponent form are multiplied and divided. Activity 2  Scientific Notation II: The Mantissa In the second of two lessons on interpreting and manipulating scientific notation, students are introduced to the concept of the "mantissa" of a number expressed in S.N. Two short JAVA labs show, first by demonstration and then by practice, how the mantissa together with the exponent complete the description of a number expressed in scientific notation, and how these can be related to conventional notation. A third lab  a stepthrough tutorial  then illustrates how numbers expressed in mantissa/exponent form are multiplied and divided. Activity 3  Linear Versus Exponential: As an application of the scientific notation skills obtained in Activities 1 and 2, students are introduced to the concept of exponential (as opposed to linear) behavior of a system using the example of bacterial growth on a petri dish. The relevance of this to human population growth is also described. Students first perform an interactive lab in which they "seed" a petri dish with initial populations of bacteria and growth parameters, and record population data as a function of time. After graphing this data  by which the students should appreciate the inadequacy of "linear" graphing techniques to express exponential growth  students are guided through a logpaper graphing exercise. Finally, students plot their bacterial "data" and answer a series of questions on the relationship of the various growth curves.
Technical consultation and assistance is freely available to teachers and schools interested in using the ASPIRE website, online labs, and curriculum materials. In time resources will be made available to assist schools lacking the computer technology required to access the labs. For technical assistance and resource information please contact the following:
Teacher materials and information: Technical support and update registration:
