powered cars, wind-propelled skimmers). The testing involves measuring speed, distance, direction, and duration in conjunction with the systematic manipulation of key variables that affect vehicle performance (e.g., balloon inflation, sail size and shape, gear ratios, wing placement, nose weight). The data are organized into tables or graphs to see if they reveal patterns and relationships among the variables. The conclusions based on the data are then used to inform the design of subsequent vehicles.

Similar instances of gathering and using data for vehicle design were found in the Models and Designs unit in the “Full Option Science System” and the Gateway to Technology unit of “Project Lead the Way.” Other materials engage students in counting and measuring, completing tables, drawing graphs, and making inferences, such as evaluating pump dispensers, conducting surveys, and testing materials.

Engineers often use mathematical equations and formulas to solve for unknowns. Young people can learn about the utility of this application of math in various ways, such as by calculating the amount of current in a circuit based on known values for voltage and resistance or determining the output force of a mechanism based on a given input force and a known gear ratio. Several instances of this kind were found in the “Engineering the Future” curriculum. In one activity, students calculate the weight of a proposed product (an organizer) based on three different materials prior to prototyping. Another requires that students calculate the mechanical advantage of a lever to determine how much force is required to test the strength of concrete.

However, most of the mathematics in the “Engineering the Future” curriculum is used to teach science concepts by illustrating relationships between variables, rather than to assist in solving design problems. For example, simple algebraic equations are used to represent the relationship between the cross-section of a pipe and its resistance to fluid flow, to calculate the output pressure of a hydraulic pump, and to determine the power produced by an electrical circuit. In these cases, mathematics is used to build domain knowledge in much the same way mathematics is used in science classes.

Several projects (e.g., “A World in Motion,” “Building Math,” Gateway to Technology, “Design and Discovery,” “Designing for Tomorrow”) introduce and require the application of basic geometry principles in conjunction with the development of technical drawings. For example, “Engineering the Future” includes lessons dealing with the concepts of scale and X, Y, and Z axes in the context of making orthographic, isometric, oblique, and perspective drawings. Introduction to Engineering Design, a unit in “Project