ExploreLearning News

Expert Corner: Equilibria Everywhere

Kurt Rosenkrantz is a science curriculum writer and Gizmo designer for ExploreLearning. Kurt holds a Master of Science in Geology from the University of Cincinnati, and a bachelor's degree in Earth Science from Harvard. He taught high school and middle school science for eight years before joining ExploreLearning in 2005.

In much of life we seek to balance opposing forces: money earned vs. money spent, weight gained vs. weight lost, heat vs. cold. When opposing forces are perfectly balanced, the system is said to be in equilibrium and no overall change is observed. For example, if you spend exactly as much as you earn, your total amount of wealth won't change.

The concept of equilibrium plays a prominent role in every field of science: from the delicate balance of Earth's climate to the forces that keep a satellite in orbit. A simple example of equilibrium occurs when an object is hung from a spring, as shown in the Determining a Spring Constant Gizmo. The force of the spring pulling upward increases as the spring is stretched, while the pull of gravity on the object is constant. Eventually the spring is stretched enough that the spring force is exactly equal to the weight of the object. At this point the spring force and gravitational force are in equilibrium and the object remains in place.

When a system in equilibrium is perturbed, the system will often oscillate, or swing back and forth from one state to another. Oscillations can be seen when you pull down a spring or release a pendulum, as illustrated in the Simple Harmonic Motion Gizmo.

A similar oscillation can occur in the populations of predators and prey in isolated environments, such as the classic case of the wolves and moose of Isle Royale, shown at left. As predator populations rise, prey populations are depleted until the predator population crashes. With fewer predators, prey populations recover and the cycle begins again. These oscillations are illustrated beautifully in the Food Chain Gizmo.

Recently we published two new Gizmos which directly address the topic in the field of chemistry: Equilibrium and Concentration and Equilibrium and Pressure. Both Gizmos explore reversible chemical reactions. In a reversible reaction, the rates of the forward and reverse reactions depend on the concentrations of reactants and products. As the forward reaction proceeds, the concentration of products increases. This causes the rate of the reverse reaction to increase as the forward reaction slows. In the Gizmos, you can measure the rate of each reaction by observing the blue flashes (representing the forward reaction) and red flashes (representing the reverse reaction) over time. As equilibrium is approached, the rates of each reaction become approximately equal.

See how many examples of equilibrium you can find in your class!

Graham Whisen: ExploreLearning Educator of the Month

For the past seven years, Graham Whisen has been teaching at Fletcher's Meadow Secondary School in Ontario. He has taught grades 9 through 12 and specializes in Physics education. Graham is passionate about science, educational technology, and inspiring a love of learning.

That passion is evident in his teaching style. When he introduces a new lesson, sometimes he starts by having his students launch a Gizmo and explore its features. He doesn't provide any structure, instead just allowing them to have fun playing with the Gizmo and seeing what it can do. Then he introduces the lesson, and revisits the Gizmo later when he wants to use it to delve deeper.

As an example of a lesson where Gizmos are particularly helpful, he points to the concept of projectile motion. Students often have trouble grasping the idea that horizontal and vertical motion are independent. But the Golf Range Gizmo clears that up, both because it depicts motion and vectors visually, and because students can manipulate variables and see the results.

Graham presents a series of Gizmo-based challenges to help draw out the main ideas in this lesson. He asks which angles launch the ball highest and farthest, how the initial height affects the range, what the impact of air resistance is, and what golf would be like on the moon. These questions work for students of all ability levels, enabling them to interact with the Gizmo and derive meaning at their own pace. Meanwhile, he can circulate the room and reinforce or extend as appropriate.

"Gizmos are designed for inquiry and this is what makes them so useful. Any one Gizmo can be used to connect to many different concepts, so teachers are able to use them in creative ways. I always love hearing about how other teachers use Gizmos in their classes because the methods are always innovative and expand my own teaching practice."

You can see more of what's on Graham's mind by visiting his blog.

New Math Lesson Materials Published

We've just published 2 new sets of Lesson Materials for two of our most popular math Gizmos!

Polygon Angle Sum - Activity B

Quadratics in Polynomial Form - Activity A

As usual, each set of updated Lesson Materials includes 4 documents (Student Exploration sheet, SE Answer Key, Teacher Guide, and Vocabulary sheet), all of which are available as a .doc or a .pdf.  (Note: You will need to be logged in to see all the documents.)

This brings us to 20 math Gizmos with updated Lesson Materials (well, 60 if you count the more modern "purple ones" that have never had anything but Lesson Materials). We still have a long way to go in this project, but there's plenty of progress happening "behind the scenes."

We hope these new Lesson Materials are a help to you and your students - lots of good explorations and thought-provoking questions here.