Ask students to write their answers to this question: “Which do you think is smarter—a robot, or the person who designs robots. Explain your answer.” Accept some answers and tell students that they are going to get a chance to meet both by watching Futures Channel Movie #1005 An Engineer and Her Robot. Ask them, as they watch, to list some of the things that the engineer has to know to do what she does. After the movie, discuss some answers, and then explain that one of the things a robotic engineer has to understand is the way machines work. Then draw the diagram below on the board and explain it.
Tell students that there is a relationship between x, which measures how long the arm is, and W, the amount of weight that can be lifted. Ask them to work in pairs to decide whether, as x increases, the amount of weight that can be lifted would increase or decrease, and why.
Then write this equation:
W = 300/(3 + x)
Explain that this equation shows the exact relationship between W and x, and ask students now to look at the equation and decide what would happen to W as x increases.
Help students to understand that when x gets bigger, the denominator of the fraction on the right had side would get larger, which means the fraction would become smaller, which means that W would decrease. It is important that this is grasped, so you may want to do some simpler examples of such relationships to make it clear.
Tell students that when expressions or equations that include fractions with variables in the numerator or denominator, they are called rational expressions and equations, and that they will be learning how to work with such equations and expressions in this chapter. |
