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.

The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.

This short video and interactive assessment activity is designed to teach second graders about capacity comparison problems with illustrations - word problems.

This short video and interactive assessment activity is designed to teach fourth graders about finding the amount of water with illustrations and calculations (metric units).

This short video and interactive assessment activity is designed to teach third graders an overview of capacity IIi (metric units).

This short video and interactive assessment activity is designed to teach second graders about capacity problems with illustrations - word problems.

The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places. Students should be guided to recognize the use of the natural logarithm when the exponential function has the given base of e, as in this problem. Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.

In the task "Carbon 14 Dating'' the amount of Carbon 14 in a preserved plant is studied as time passes after the plant has died. In practice, however, scientists wish to determine when the plant died and, as this task shows, this is not possible with a simple measurement of the amount of Carbon 14 remaining in the preserved plant. The equation for the amount of Carbon 14 remaining in the preserved plant is in many ways simpler here, using 12 as a base.

This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies. This problem is intended for instructional purposes only. It provides an interesting and important example of mathematical modeling with an exponential function.

This exploratory task requires the student to use a property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.

This task lets students explore the concept of independence of events. There are two alternative ways of solving the problem.

In this task, students can see that if the price level increases and peopleŐs incomes do not increase, they arenŐt able to purchase as many goods and services; in other words, their purchasing power decreases.

A catenary is the curve created by a theoretical representation of a hanging chain or cable held at both ends.

This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations.

This simple task assesses whether students can interpret function notation. The four parts of the task provide a logical progression of exercises for advancing understanding of function notation and how to interpret it in terms of a given context.

An interactive applet and associated web page that the definition of the center of a regular polygon. The applet presents a regular polygon, where the user can drag any vertex to resize it, and change the number of sides. The center point is shown to always be the point equidistant from every vertex. 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.

The purpose of this task is to use geometric and algebraic reasoning to model a real-life scenario. In particular, students are in several places (implicitly or explicitly) to reason as to when making approximations is reasonable and when to round, when to use equalities vs. inequalities, and the choice of units to work with (e.g., mm vs. cm).

This short video and interactive assessment activity is designed to teach fourth graders about comparing lengths in centimeters using a ruler.

An interactive applet and associated web page that define and illustrate the central angle of a polygon. The applet shows the angle and users can experiment by changing the number of sides and resizing the polygon. The web page has a description and a formula for the central angle given the number of sides. 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.

An interactive applet and associated web page that demonstrate the central angle of a circle - the angle subtended at the center by two points ion the circle. The applet presents a circle with two points on it that can be dragged. The central angle is shown changing as you drag. 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.