Logistic Growth Model, Abstract Version
(View Complete Item Description)The goal of this task is to have students appreciate how the different constants (P0, K, and r) influence the shape of the graph.
Material Type: Activity/Lab
All resources in Wisconsin Digital Learning Collaborative CCSS Math Resources
Points on a Graph
(View Complete Item Description)This task is designed to get at a common student confusion between the independent and dependent variables. This confusion often arises in situations like (b), where students are asked to solve an equation involving a function, and confuse that operation with evaluating the function.
Material Type: Activity/Lab
Domains
(View Complete Item Description)The purpose of this task to help students think about an expression for a function as built up out of simple operations on the variable, and understand the domain in terms of values for which each operation is invalid (e.g., dividing by zero or taking the square root of a negative number).
Material Type: Activity/Lab
How is the Weather?
(View Complete Item Description)This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match.
Material Type: Activity/Lab
Logistic Growth Model, Explicit Version
(View Complete Item Description)This problem introduces a logistic growth model in the concrete setting of estimating the population of the U.S. The model gives a surprisingly accurate estimate and this should be contrasted with linear and exponential models, studied in ``U.S. Population 1790-1860.'' This task requires students to interpret data presented.
Material Type: Activity/Lab
Parabolas and Inverse Functions
(View Complete Item Description)This task assumes students have an understanding of the relationship between functions and equations. Using this knowledge, the students are prompted to try to solve equations in order to find the inverse of a function given in equation form: when no such solution is possible, this means that the function does not have an inverse.
Material Type: Activity/Lab
Graphs of Power Functions
(View Complete Item Description)This task requires students to recognize the graphs of different (positive) powers of x. There are several important aspects to these graphs. First, the graphs of even powers of x all open upward as x grows in the positive or negative direction. The larger the even power, the flatter these graphs look near 0 and the more rapidly they increase once the distance of x from 0 excedes 1.
Material Type: Activity/Lab
Identifying Graphs of Functions
(View Complete Item Description)The goal of this task is to get students to focus on the shape of the graph of the equation y=ex and how this changes depending on the sign of the exponent and on whether the exponential is in the numerator or denominator. It is also intended to develop familiarity, in the case of f and k, with the functions which are used in logistic growth models, further examined in ``Logistic Growth Model, Explicit Case'' and ``Logistic Growth Model, Abstract Verson.''
Material Type: Activity/Lab
Quadratic curve and graph display
(View Complete Item Description)An interactive applet that allows the user to graphically explore the properties of a quadratic equation. Specifically, it is designed to foster an intuitive understanding of the effects of changing the three coefficients in the function. The applet shows a large graph of a quadratic (ax^2 + bx +c) and has three slider controls, one each for the coefficients a,b and c. As the sliders are moved, the graph is redrawn in real time illustrating the effects of these variations. The roots of the equation are shown both graphically and numerically, including the case where the roots are imaginary. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
Material Type: Reading, Simulation
Chess Wager
(View Complete Item Description)Harry and his friend make a wager on a game of chess in this video segment from Cyberchase. ***Access to Teacher's Domain content now requires free login to PBS Learning Media.
Material Type: Lecture
Equation Grapher
(View Complete Item Description)Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.
Material Type: Simulation
Telling a Story with Graphs
(View Complete Item Description)In this task students are given graphs of quantities related to weather. The purpose of the task is to show that graphs are more than a collection of coordinate points, that they can tell a story about the variables that are involved and together they can paint a very complete picture of a situation, in this case the weather.
Material Type: Activity/Lab
The Customers
(View Complete Item Description)The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant real-life context.
Material Type: Activity/Lab
The High School Gym
(View Complete Item Description)In this task students must interpret a function in relation to a given problem.
Material Type: Activity/Lab
The Parking Lot
(View Complete Item Description)The purpose of this task is to investigate the meaning of the definition of function in a real-world context where the question of whether there is more than one output for a given input arises naturally. In more advanced courses this task could be used to investigate the question of whether a function has an inverse.
Material Type: Activity/Lab
The Random Walk
(View Complete Item Description)This task requires interpreting a function in a non-standard context. While the domain and range of this function are both numbers, the way in which the function is determined is not via a formula but by a (pre-determined) sequence of coin flips. In addition, the task provides an opportunity to compute some probabilities in a discrete situation.
Material Type: Activity/Lab
Throwing Baseballs
(View Complete Item Description)This task allows the students to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out algebraically. Specifically, we are asking the students to determine which function has the greatest maximum and the greatest non-negative root.
Material Type: Activity/Lab
Using Function Notation I
(View Complete Item Description)This task deals with a student error that may occur while students are completing F-IF Average Cost.
Material Type: Activity/Lab
Using Function Notation II
(View Complete Item Description)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.
Material Type: Activity/Lab
Warming and Cooling
(View Complete Item Description)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.
Material Type: Activity/Lab