Visualize Multi-Step Equations: Solving with Seesaws
The seesaw activity set-up.Copyright 2011 Ronald Poveda, Polytechnic Institute of NYU
Students use a simple seesaw to visualize solving a two- or three-step mathematics equation, while solving a basic structural engineering weight balance problem in the process. They solve two-step equations on a worksheet and attempt to solve the challenge of "balancing a beam" through hands-on problems. The use of sensor equipment for correct position monitoring aids students in balancing the structure, as well as balancing the equation as they solve it on paper.
Accurate step-by-step visualization of a design or plan is crucial for all scientists and engineers when conducting scientific inquiries, research experiments, and most of all, design assessment. The fundamentals of building design require a balance of force, or weight, in all parts of the design, much like a seesaw. A typical seesaw is a structure that handles the weight of multiple people, and can be considered still and balanced if equal weight is placed on both ends, and/or if the weight is distributed equitably along the seesaw beam.
In the world of structural engineering, beams inside buildings are assessed in a similar manner. Weight, or forces, acting on beams must balance in order for the beam and the building itself to stay still and rigid. Small-scale structures and systems are used to test calculations before full-sized structures and systems are constructed, particularly when dealing with designs that millions of people depend on for everyday use, such as a bridge, house or skyscraper. In fact, civil engineers sometimes use seesaw-sized models to test models for force balance and structural stability. Active tinkering, especially when operating a structure or a system, allows for a successful engineering design and helps engineers visualize and assess designs during service use.
After this activity, students should be able to:
- Demonstrate how to solve two-step equations.
- Identify terms in the mathematical equation.
- Explain the use of sensors in a system, especially in feedback control.
- Explain the importance of solving equations in basic structural design.