There are many different ways to write exponential expressions that describe the same quantity, in this task the amount of a radioactive substance after t years. Depending on what aspect of the context we need to investigate, one expression of the quantity may be more useful than another. This task contrasts the usefulness of four equivalent expressions. Students first have to confirm that the given expressions for the radioactive substance are equivalent. Then they have to explain the significance of each expression in the context of the situation.

The example of rabbits and foxes was introduced to illustrate two functions of time given in a table. We are now in a position to actually model the data given previously with trigonometric functions and investigate the behavior of this predator-prey situation.

The example of rabbits and foxes was introduced to illustrate two functions of time given in a table. The same situation was used in F-TF Foxes and Rabbits 2 to find trigonometric functions modeling the data in the table. The previous situation was somewhat unrealistic since we were able to find functions that fit the data perfectly. In this task, on the other hand, we do some legitimate modelling, in that we come up with functions that approximate the data well, but do not perfectly match, the given data.

This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed

This task is intended to engage students into considering how margin of error can be estimated from examining the results of repeated simple random sampling.

This lesson unit is intended to help educators assess how well students are able to articulate verbally the relationships between variables arising in everyday contexts, translate between everyday situations and sketch graphs of relationships between variables, and interpret algebraic functions in terms of the contexts in which they arise. Students will also reflect on the domains of everyday functions and in particular whether they should be discrete or continuous.

The vertical line test for functions is the focus of this lesson plan.

Thousands of species of plants and animals face threats that could result in their extinction, while biodiversity conservation actions that could save them are often available. Conservation managers face difficult decisions when there is limited funding for biodiversity conservation. Managers need to decide which projects they should fund to best achieve their objectives, not the least of which is to save the most species. This is particularly important if the benefits of certain conservation actions vary across projects, the costs of these actions for specific projects differ, and the available funding for these actions is considerably less than is needed to support all proposed projects.

It appears from the economic reports that the world uses gasoline on a very short supply and demand scale. The impact of any storm, let alone Hurricane Katrina, affects the costs at the pumps too quickly. Let's restrict our study to the continental United States.

This question examines the algebraic equations for three different spheres. The intersections of each pair of spheres are then studied, both using the equations and thinking about the geometry of the spheres.

Reflective of the modernness of the technology involved, this is a challenging geometric modelling task in which students discover from scratch the geometric principles underlying the software used by GPS systems.

The United States can address its national carbon footprint in two ways: by reducing carbon dioxide emissions or by increasing carbon dioxide consumption (sequestration). Assume that the total U.S. carbon dioxide emissions are capped at 2007-2008 levels indefinitely. What should the U.S. do to increase carbon dioxide consumption to achieve national carbon neutrality with minimal economic and cultural impact? Is it even possible to achieve neutrality? Model your solution to show feasibility, effectiveness, and costs. Prepare a short summary paper for the U.S. Congress to persuade them to adopt your plan.

This task provides a real world context for examining the incredible power of exponential growth/decay.

The purpose of this task is to help students understand the relationship between the factors of a polynomial and the x-intercepts of the graph of the polynomial. By giving students two different polynomials with the same factors the task draws attention to the fact that both polynomials cross the x-axis at the same points. Students are then invited to reflect on why this is so by looking at the structure of the polynomials.

The purpose of this task is to give students an opportunity to see and use the structure of the factored form of a polynomial (MP7).

The task has students use the remainder theorem to deduce a linear factor of a cubic polynomial, and then to completely factor the polynomial. Students will need some procedure (e.g., synthetic or long division, or guess-and-check the coefficients) for determining the quadratic factor. Having the factored form permits students to deduce much about the structure of the graph.

The task is aligned to G-GMD.3 at each part involves either finding the volume of a pyramid or using the volume to find the base or height.

This task is designed to make students think about the meaning of the quantities presented in the context and choose which ones are appropriate for the two different constraints presented. In particular, note that the purpose of the task is to have students generate the constraint equations for each part (though the problem statements avoid using this particular terminology), and not to have students solve said equations.

The goal of this task is to use geometry study the structure of beehives.

The purpose of this task is to assess understanding of how study design dictates whether a conclusion of causation is warranted.