Average Cost
(View Complete Item Description)In this real world problem students solve questions based on the relationship between production costs and price.
Material Type: Activity/Lab
All resources in Oregon Mathematics
Oakland Coliseum
(View Complete Item Description)The primary purpose of this task is to illustrate that the domain of a function is a property of the function in a specific context and not a property of the formula that represents the function. Similarly, the range of a function arises from the domain by applying the function rule to the input values in the domain. A second purpose would be to illicit and clarify a common misconception, that the domain and range are properties of the formula that represent a function.
Material Type: Activity/Lab
The Canoe Trip, Variation 2
(View Complete Item Description)The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function. The canoe context focuses attention on the variables as numbers, rather than as abstract symbols.
Material Type: Activity/Lab
The Canoe Trip, Variation 1
(View Complete Item Description)The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of that context. It can be used as either an assessment or a teaching task.
Material Type: Activity/Lab
The restaurant
(View Complete Item Description)The purpose of this task is to get students thinking about the domain and range of a function representing a particular context. Often when a function is being used to model a context, the expression for the function has a larger domain and range than is reasonable for the context. Asking students to focus on a function for which there is no formula focuses attention on the context itself. Note that in many contexts, there are multiple plausible sets that one could choose for the domain (and/or the range), and the solution to the current task provides such an example.
Material Type: Activity/Lab
Pizza Place Promotion
(View Complete Item Description)This task requires students to use functions to calculate how to best benefit from a pizza promotion.
Material Type: Activity/Lab
If As the Wheel Turns
(View Complete Item Description)In this task, students use trigonometric functions to model the movement of a point around a wheel and, in the case of part (c), through space (F-TF.5). Students also interpret features of graphs in terms of the given real-world context (F-IF.4).
Material Type: Activity/Lab
F-IF Containers
(View Complete Item Description)This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
Material Type: Activity/Lab
Influenza Epidemic
(View Complete Item Description)The purpose of this task is to probe students' ability to correlate symbolic statements about a function using function notation with a graph of the function, and to interpret their answers in terms of the quantities between which the function describes a relationship
Material Type: Activity/Lab
F-IF Lake Sonoma
(View Complete Item Description)This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
Material Type: Activity/Lab
F-BF Model air plane acrobatics
(View Complete Item Description)This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A model airplane pilot is practicing flying her airplane in a big loop for an upcoming competition. At time $t=0$ her airplane is at the bottom of the ...
Material Type: Activity/Lab
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
F-IF The Aquarium
(View Complete Item Description)This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
Material Type: Activity/Lab
F-IF The story of a flight
(View Complete Item Description)This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
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
F-IF Words - Tables - Graphs
(View Complete Item Description)This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
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
Identifying Exponential Functions
(View Complete Item Description)The task is an introduction to the graphing of exponential functions. The first part asks students to use technology to experiment with the two parameters defining an exponential function, with little guidance. Since it is important for the second part, teachers should encourage students to try a wide range of values, and in particular, values of b both less than and greater than 1. The task includes a Desmos app, in which students can make use of sliders to more viscerally see the effect of changing a and b separately.
Material Type: Activity/Lab
Bank Account Balance
(View Complete Item Description)The purpose of this task is to study an example of a function which varies discretely over time. Step functions are often good examples for this type of function. In practice, instead of a step function, bar graphs are sometimes used. Alternatively, Jessie's method of ''smoothing'' over the jumps is also very common.
Material Type: Activity/Lab
Exponential Kiss
(View Complete Item Description)The purpose of this task is twofold: first using technology to study the behavior of some exponential and logarithmic graphs and secondly to manipulate some explicit logarithmic and exponential expressions. Although not asked in the task body, the teacher may wish to prompt students to explain why the two graphs behave as they do as the base b varies: that is, a larger value of b between 1 and 2 makes the exponential graph grow faster and the logarithmic graph grow more slowly as x increases.
Material Type: Activity/Lab