This task presents an opportunity to explore a more general and non-algebraic view of functions.
The purpose of this task is to construct and use inverse functions to model a a real-life context. Students choose a linear function to model the given data, and then use the inverse function to interpolate a data point.
This task focuses on the fact that exponential functions are characterized by equal successive quotients over equal intervals. This task can be used alongside F-LE Equal Factors over Equal Intervals.
This task focuses on the fact that linear functions are characterized by constant differences over equal intervals. It could be used alongside to F-LE Equal Differences over Equal Intervals I & II.
This task deals with a student error that may occur while students are completing F-IF Average Cost.
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.
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.
This real world word problem requires students to use equations and functions.
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.
These problems give students the opportunity to construct and compare linear, quadratic, and exponential models.
This problem-based learning module is designed to link a student’s real-life problem to learning targets in the subjects of math, social studies and language arts. The problem being, what route is best for me to buy a vehicle? The students will prepare, research and present findings about their own personal finances relating to buying a vehicle. The students will create two equations based on two purchasing plans they will be comparing. At the conclusion, students will be able to decide which plan is best for them based on research and mathematical practices. Students will present to their peers, teachers, administrators, and most importantly their parents in an attempt to convince them of their chosen plan. This blended module includes teacher led instruction, student led rotations, community stakeholder collaboration and technology integration.
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.
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.
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.