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IMP® Sample Activities

The following sample activities are being made available as PDF documents.

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Year 1: The Pit and the Pendulum

This unit opens with an excerpt from The Pit and the Pendulum, by Edgar Allan Poe. In the story, a prisoner is tied down while a pendulum with a sharp blade slowly descends. If the prisoner does not act, he will be killed by the pendulum. When the pendulum has about 12 swings left, the prisoner creates a plan for escape and executes it. Students are presented with the problem of whether the prisoner would have enough time to escape.

In these sequential activities, students explore how changes in data affect mean and standard deviation.

Year 2: Cookies

This unit focuses on graphing systems of linear inequalities and solving systems of linear equations. Although the central problem is in the field of linear programming, the major goal of the unit is for students to learn how to manipulate equations and how to reason using graphs.

In these sequential activities, students begin to examine the relationship between the profit function and the feasible region.

Year 3: Meadows or Malls?

Meadows or Malls?, the third Year 3 unit, extends the concepts of linear programming problems with two variables introduced in the Year 2 unit Cookies. Students develop a strategy for solving linear programming problems in several variables and solve systems of linear equations using the elimination method and matrix algebra. The unit introduces the concepts of identity elements and inverses, and develops the understanding that inverses of matrices are the key to solving linear systems.

In these sequential activities, students use the context of a problem to motivate the definition of multiplication of matrices.

Year 4: The Pollster's Dilemma

In The Pollster's Dilemma, the final unit of the four-year IMP curriculum, students examine the mathematics of sampling and see that the distribution of sampling percentages resembles a normal distribution. They use this idea, which is the essence of the central limit theorem, to find confidence levels and margins of error.

In these sequential activities, students find the probability of each possible sampling percentage for specific sample sizes and see that as the sample grows, the distribution looks more and more like the normal curve. The first activity sets the stage for the second one.

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