a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

So how are two variables related to each other? Are they siblings? Spouses? Third cousins twice removed? It's common to refer to a function to solve these crazy variable family trees. Make sure students dust off their algebra skills before plunging into these different relationships. Students should already be familiar with linear, quadratic, and exponential functions, but a quick recap wouldn't hurt.

In a linear function, the dependent variable increases (or decreases) at a constant rate as the dependent variable increases. The data will look like a straight line, more or less. Make sure students remember that a linear function takes the form y = mx + b, where m is the slope and b is the intercept.

When data is described by a quadratic function, the scatter plot will look like a curve. In a quadratic function, the change in the dependent variable y and the change in the variable both depend on the independent variable x. We'll end up with a function that looks like y = ax² + bx + c.

For an exponential function, the dependent variable increases faster as the independent variable increases. The typical form of this type of function is y = C^x, where C is some coefficient, commonly 10 or the mathematical constant e. If the weight follows an exponential relationship to the height, it might look something like this:

Students should know that a quick visual glance of the data can help determine the best type of function to fit to the data. They just have to remember the shape of the three types described above: linear, quadratic and exponential. Once a solid relationship has been built (based on mutual trust and understanding), students can use the function to extrapolate and predict more values.