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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.
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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.
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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.
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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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