This activity was created for middle school math stations on functions. It is brief (one page), but will give your students the opportunity to each represent and analyze their own functions. They will each identify a variety of functions as increasing, decreasing, linear, nonlinear, find intercepts and slope. This way when they ask each other for help, it cannot be, “What’s the answer to number one?” but rather, “Can you explain how to do number one?” The conversations and explanations that arise are great.
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Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Common Core Math Stations and Games - Pick-a-Card - Functions
by Kimberly Wasylyk
is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License