Graphing and functions
• Sketch graphs showing key features (F-IF.B.4$^\star$, F-IF.C.7$^\star$).
• Interpret key features of graphs in terms of the quantities represented (F-IF.B.4$^\star$, F-IF.C.7$^\star$).
In this unit, students begin their formal study of functions. They are introduced to function notation and gain a more precise understanding of what it means to be a function. They learn how to interpret functions in a given context and how to analyze them using different representations. In this section, they begin by graphing a variety of different functions.
WHAT: The Graphing Stories web site has numerous short videos that capture a change in a quantity such as height, width, volume, or length with respect to time for 15 seconds. Students watch a video a few times, then try to graph the given situation on the grids provided in a worksheet. The videos show the label needed for the vertical axis of the worksheet, e.g., “height, meters.” The videos show elapsed time as a number on the screen but, in general, do not show numerical measurements for the second quantity. However, the videos show “the answer” as a graph with numerical measurements for the second quantity.
WHY: This activity provides students with an opportunity to build on their prior knowledge of graphing before beginning the formal discussion of functions in section 2. The teacher can guide students to observe what determines these functions with questions and comments, for example, “What are the input and output values?” For each time there is only one position, distance, height, etc (F-IF.B.4$^\star$). Also, this activity may broaden students’ repertoires because the graphs include non-linear and piecewise-defined functions. Students model the relationships shown while attending to precision in order to create a realistic graph (F-IF.C.7$^\star$, MP6). Because no measurements are given other than time, attending to precision does not mean using exact measurements for the dependent variable, but rather drawing graphs that correctly indicate qualitative changes (e.g., positive, negative, zero, increasing, decreasing) in the dependent variable.