Predict the correct amount of roofing material needed to reroof a house while learning about the importance of proper planning. This interactive exercise focuses on measurement, calculating the area of trapezoids, and combining the areas with the roofing information provided to take math out of the classroom and into the real world.
Learn about the math behind predator-prey population cycles in this video from NOVA Digital. In this example, zombie and human populations fluctuate. The zombie population increases as zombies convert humans into zombies. However, without enough humans to eat, zombies die and the population shrinks. The human population increases as humans reproduce but decreases as zombies eat humans. The populations of humans and zombies change through time according to a pair of differential equations. Because human and zombie populations are related, the growth rate of each population depends on the current numbers of both humans and zombies.
Learn about tangent vectors in this video from NOVA Digital. In this hypothetical world, zombies always move straight toward humans. This means that the tangent vector of a zombie's path points at the intended target. However, when the human moves, the zombie's tangent vector points to where the human is at that instant, not to where the human is going. The zombie is not smart enough to move toward where the human will be. Therefore, the zombie takes a longer path, giving the human the chance to get away. If the human moves faster than the zombies in a circular path, multiple zombies will eventually converge on a smaller circular path that follows the human's path.