Functions & Equations
For each of the following problems, consider how you would pose the same problem to your students. Would the wording need to change? Would you need to include more pictures? More detailed pictures? But remember we don't want to do TOO MUCH for the student. If we provide too much information, they will not need to think about what the question is asking.
Consider your problem-solving strategy for each of the following investigations. Is there another strategy that you could use? If so, which strategy would be more appropriate for understanding the concept?
You used equations in elementary school when you worked with simple addition sentences, such as 3 + 7 = 10. We also use equations in algebra, such as 3x + 4 = 19. An equation is a sentence that uses an equal sign (=) to indicate that two expressions represent the same number or value. The expressions on either side of the equal sign can be numbers (like 19) or symbols that represent numbers (like 3x + 4).
In mathematics, there are special equations that represent functions. A function is a special relationship in which each input (or x value) results in one and only one output (or y value). In other words, if we put 3 in an equation and get 5 out, the next time we put 3 in the same equation, we know what we will get if we are working with a function: 5, every time! Thus, the key characteristic of a function is reliability.
Examples of functions are:
- Each student at a school is assigned a unique locker.
- Each person is assigned a unique social security number.
- Each house on a street is assigned a unique address.
- The distance a car travels (d) in 5 hours is a function of the speed of the car (r). So, an equation showing this functional relationship would be: d=5r.