Key Terms

Algebraic reasoning is the use of generalized variables and formal relationships between them, rather than numbers, as a means of constraining solutions.

Arithmetic according to Wikipedia: a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them – addition, subtraction, multiplication and division.

Instrumental error is fixed by the resolution of the device used to make a measurement, and can usually only be reduced by using a more precise instrument.

In our context, the word isometric means that any change in one spatial dimension of a shape (e.g., length) is matched by a proportional change in all other dimensions.

A model in this context means an approximate mathematical representation of the real system from which predictions about the behavior of the real system may be made and tested.

Modeling in this book refers to the construction of a simplified representation of real or hypothesized systems, often described with one or more equations relating variables to one another and to system properties, and used to explore complex or unobservable phenomena or relationships.

Numerical reasoning, as used in this book, is the manipulation, characterization, comparison, and interpretation of numerical values (such as data) in the service of problem solving.

The order of magnitude of a quantity is essentially the value of the exponent when expressed in scientific notation.

A right triangle is defined as a triangle with one right, or 90° angle.

Spatial reasoning is the use of spatial information or relationships, like lengths, areas, volumes, or directions, in the solution of problems.

Systematic errors result in data that deviate systematically from the true values. These errors may often be more difficult to detect and correct, and data collection efforts should make great pains to eliminate any sources of systematic error.