describing how each variable (nozzle size, balloon inflation, vehicle weight, and friction) affects vehicle performance (speed and distance).

Another example of trade-offs is embedded in the Models and Designs unit in the “Full Option Science System” curriculum. In the course of making and modifying a rubber-band-powered cart, the students are likely to engage in optimization because each challenge inevitably introduces unanticipated cause-and-effect relationships. For example, the size of the wheels affects how far the go-cart travels. If the wheels are bigger, the amount of force required to propel the go-cart may have to be increased. If more tension is applied to the rubber bands to propel the cart a greater distance, traction is likely to become an issue. The increase in tension is also likely to exacerbate the problem of friction. Each of these adjustments introduces the need for trade-offs. However, neither the concept of trade-offs nor the concept of making trade-offs in the interest of optimization is addressed directly in the curricular materials.

The unit on Inquiry: The Ultimate School Bag in the “Invention, Innovation, and Inquiry” curriculum includes the redesign and improvement of a backpack for carrying schoolbooks and personal items. Redesign intrinsically involves optimization, although the concept is not addressed directly here, either.

Some references are made to the concept of trade-offs in the Building Structure with Young Children unit in the “Young Scientist Series.” Teachers are encouraged to prepare and ask questions about the advantages and disadvantages of different design options. For example, in the context of building a model house, teachers are encouraged to entertain ideas such as making the roof out of a lightweight material that requires less support but is not likely to be strong. If children chose to make a strong roof, they might also have to build in more support.

In the Gateway to Technology” curriculum, trade-off is defined as “an exchange of one thing in return for another, especially relinquishment of one benefit or advantage for another regarded as more desirable.” Although several assignments involve identifying the positive and negative impacts of various technologies, students do not directly address the balance between competing factors. For example, from a student’s point of view, the main goal of an activity involving the building a compressed-air dragster is to design the fastest vehicle possible. In this exercise, speed is a function of the vehicle’s mass, assuming that the propulsive force remains constant. Even though mass also affects the stability of the vehicle, the instructional materials do not require that students directly confront the trade-offs between mass, stability, and speed.

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