In 1945, Noah Sentz died in a car accident and his estate was handled by the local courts. The state law stated that 1/3 of all assets and property go to the wife and 2/3 of all assets go to the children. There were four children. Over the next four years, three of the four children sold their shares of the assets back to the mother for a sum of $1300 each. The original total assets were mainly 75.43 acres of land. This week, the fourth child has sued the estate for his rightful inheritance from the original probate ruling. The judge has ruled in favor of the fourth son and has determined that he is rightfully due monetary compensation. The judge has picked your group as the jury to determine the amount of compensation.

Use the principles of mathematical modeling to build a model that enables you to determine the compensation. Additionally, prepare a short one-page summary letter to the court that explains your results. Assume the date is November 10, 2003.

1. Identify and analyze the major factors that you consider crucial to limiting the Earth’s carrying capacity for human life under current conditions.

2. Use mathematical modeling to determine the current carrying capacity of the Earth for human life under today’s conditions and technology.

3. What can mankind realistically do to raise the carrying capacity of the Earth for human life in perceived or anticipated future conditions? What would those conditions be?

The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence. In this problem, we considered SSA. Also insufficient is AAA, which determines a triangle up to similarity. Unlike SSA, AAS is sufficient because two pairs of congruent angles force the third pair of angles to also be congruent.

The goal of this task is to examine when two lines in the plane are perpendicular in terms of their slopes.

We read all the time in the sports pages about an athlete being called the G.O.A.T. - the Greatest Of All Time. What does that really mean and how can that truly be determined? For the purpose of this IM2C problem, we consider two types of “sports” – and, we allow “sports” to be defined broadly.

The two triangles in this problem share a side so that only one rigid transformation is required to exhibit the congruence between them. In general more transformations are required and the "Why does SSS work?'' and "Why does SAS work?'' problems show how this works.

For these particular triangles, three reflections were necessary to express how to move from ABC to DEF. Sometimes, however, one reflection or two reflections will suffice. Since any rigid motion will take triangle ABC to a congruent triangle DEF, this shows the remarkable fact that any rigid motion of the plane can be expressed as one reflection, a composition of two reflections, or a composition of three reflections.

This particular sequence of transformations which exhibits a congruency between triangles ABC and DEF used one translation, one rotation, and one reflection.

The purpose of the task is to show that graphs can tell a story about the variables that are involved.

Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

The purpose of this task is to give students practice interpreting statements using function notation. It can be used as a diagnostic if students seem to be having trouble with function notation, for example interpreting f(x) as the product of f and x.

This is a simple task touching on two key points of functions. First, there is the idea that not all functions have real numbers as domain and range values. Second, the task addresses the issue of when a function admits an inverse, and the process of "restricting the domain" in order to achieve an invertible function.

This task is the first in a series that leads students to understand and apply the zero product property to solving quadratic equations. The emphasis is on using the structure of a factorable expression in order to justify the steps in a solution (rather than memorizing steps without understanding).

This task is part of a series of tasks that lead students to understand and apply the zero product property to solving quadratic equations. The emphasis is on using the structure of a factorable expression to help find its solutions (rather than memorizing steps without understanding).

This task is part of a series of tasks that lead students to understand and apply the zero product property to solving quadratic equations. The emphasis is on using the structure of a factorable expression to help find its solutions (rather than memorizing steps without understanding).

This task is the fourth in a series of tasks that leads students to understand The Zero Product Property (ZPP) and apply it to solving quadratic equations. The emphasis is on using the structure of a factorable expression to justify the solution method (rather than memorizing steps without understanding)

Lake Mead, a Colorado River reservoir on the Nevada-Arizona border, is the largest water reservoir in the United States (Figure 1). In the summer of 2021, Lake Mead registered its lowest level on record since its initial filling in the 1930s. Drought, fueled by climate change, along with increasing demand for water by the 25 million people Lake Mead serves, has shrunk this reservoir to approximately 36 percent of its full capacity. On August 16, 2021, the Bureau of Reclamation announced the first-ever water shortage declaration on the Colorado River[1]. Initially, this Tier 1 water shortage declaration results in reduced water deliveries to the states of Arizona, Nevada, and New Mexico with agricultural communities being the first to feel the cuts.

In this task students explore changing areas and patterns of numbers. It is a low floor high ceiling task that can be used with many grade levels. The question posed is : what is the biggest fence that can be made out of 36 pieces of fence?

Our friends at the Monterey Bay Aquarium Research Institute have created an interesting task where they share data they collected from Blue Whales. We send many thanks to the MBARI scientists and the American Museum of Natural History for creating and posting these wonderful resources. This collection of videos, text passages and interactive data graphs will light up minds as students explore data that has been collected to explain what goes on when a Blue Whale is under the surface of the ocean.