This task deals with a student error that may occur while students are completing F-IF Average Cost.
- Author:
- Illustrative Mathematics
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The purpose of the task is to explicitly identify a common error made by many students, when they make use of the "identity" f(x+h)=f(x)+f(h). A function f cannot in general be distributed over a sum of inputs.
- Author:
- Illustrative Mathematics
In this task students interpret two graphs that look the same but show very different quantities. The first graph gives information about how fast a car is moving while the second graph gives information about the position of the car. This problem works well to generate a class or small group discussion. Students learn that graphs tell stories and have to be interpreted by carefully thinking about the quantities shown.
- Author:
- Illustrative Mathematics
This real world word problem requires students to use equations and functions.
- Author:
- Illustrative Mathematics
When one end of a wooden board is placed on a bathroom scale and the other end is suspended on a textbook, students can "walk the plank" and record the weight measurement as their distance from the scale changes. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find. An activity sheet and full instructions are included.
This task is meant to be a straight-forward assessment task of graph reading and interpreting skills. This task helps reinforce the idea that when a variable represents time, t=0 is chosen as an arbitrary point in time and positive times are interpreted as times that happen after that.
- Author:
- Illustrative Mathematics
These problems give students the opportunity to construct and compare linear, quadratic, and exponential models.
- Author:
- Illustrative Mathematics
This task addresses knowledge related to interpreting forms of functions derived by factoring or completing the square. It requires students to pay special attention to the information provided by the way the equation is represented as well as the sign of the leading coefficient, which is not written out explicitly, and then to connect this information to the important features of the graph.
- Author:
- Illustrative Mathematics
The purpose of this task is to give students practice interpreting statements using function notation. It can be used as a diagnostic if students seem to be having trouble with function notation, for example interpreting f(x) as the product of f and x.
- Author:
- Illustrative Mathematics
This is a simple task touching on two key points of functions. First, there is the idea that not all functions have real numbers as domain and range values. Second, the task addresses the issue of when a function admits an inverse, and the process of "restricting the domain" in order to achieve an invertible function.
- Author:
- Illustrative Mathematics