This task is intended strictly for instructional purposes with the goal of building understandings of linear relationships within a meaningful and, hopefully, somewhat familiar context.
Material Type: Activity/Lab
This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents.
Material Type: Activity/Lab
This task presents an opportunity to explore a more general and non-algebraic view of functions.
Material Type: Activity/Lab
This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.
Material Type: Activity/Lab
This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.
Material Type: Activity/Lab
This task can be played as a game where students have to guess the rule and the instructor gives more and more input output pairs. Giving only three input output pairs might not be enough to clarify the rule.
Material Type: Activity/Lab
The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.
Material Type: Activity/Lab
In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable.
Material Type: Activity/Lab
This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.
Material Type: Activity/Lab
This task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation.
Material Type: Activity/Lab
This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions. The task lends itself to an extended discussion comparing the differences that students have found and relating them back to the equation and the graph of the two functions.
Material Type: Activity/Lab
There is a natural (and complicated!) predator-prey relationship between the fox and rabbit populations, since foxes thrive in the presence of rabbits, and rabbits thrive in the absence of foxes. However, this relationship, as shown in the given table of values, cannot possibly be used to present either population as a function of the other. This task emphasizes the importance of the "every input has exactly one output" clause in the definition of a function, which is violated in the table of values of the two populations.
Material Type: Activity/Lab
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.
Material Type: Activity/Lab
This shows how Newton's method (also known as Newton-Raphson) is used to find a root of a function. You can show/hide various parts of the construction, and edit the particular function being considered.
Material Type: Simulation
In this video segment from Cyberchase, Digit must a make a straight line between the two points and then follow the path created.
Material Type: Lecture
In this video segment from Cyberchase, Harry uses tessellations to wallpaper his apartment. ***Access to Teacher's Domain content now requires free login to PBS Learning Media.
Material Type: Lecture
The purpose of this task is to provide students an opportunity to use mathematics addressed in different standards in the same problem.
Material Type: Activity/Lab
The purpose of this task is to provide students with a multi-step problem involving volume and to give them a chance to discuss the difference between exact calculations and their meaning in a context.
Material Type: Activity/Lab
The purpose of this task is to help students understand what is meant by a base and its corresponding height in a triangle and to be able to correctly identify all three base-height pairs.
Material Type: Activity/Lab
This task is primarily about volume and surface area, although it also gives students an early look at converting between measurements in scale models and the real objects they correspond to.
Material Type: Activity/Lab
