Learning the Basics
Both traditional mathematics curriculums and the Interactive Mathematics Program cover basic high school mathematics content. Here are some examples.
Algebra. Solving systems of linear equations for unknowns is an important skill in traditional algebra classes. In IMP, this topic is presented both in Meadows or Malls? and in a second-year unit called Cookies, which deals with maximizing profits from a bakery. Students don't just learn one method, but develop their own approaches in groups and then share ideas with one another. In Meadows or Malls, they also see how to use matrices and the technology of graphing calculators to solve such systems.
Geometry. Basic concepts in traditional geometry include similar triangles and the Pythagorean theorem. In Shadows, a first-year IMP unit, students learn about similar triangles, develop proportion equations to solve similar triangles, and apply the concept of similarity to predict the lengths of shadows. They also extend their knowledge to see how similarity is used as the foundation of trigonometry.
In Do Bees Build It Best? students develop the Pythagorean theorem experimentally, prove it algebraically or geometrically, and apply it to see why the hexagonal prism of the bees' honeycomb design is the most efficient regular prism possible. Several units later, students apply the Pythagorean theorem to develop other principles, such as the distance formula in coordinate geometry.
Trigonometry. In traditional programs, sine, cosine, and tangent are introduced in the 11th or 12th grade. In IMP, students begin working with these functions in 9th grade (in Shadows), and learn their value and application over the years. Right triangle trigonometry is used in several units in the second and third year.
In a fourth-year unit, High Dive, students extend trigonometry from right triangles to circular functions, defining the trigonometric functions for angles of more than 90 degrees. The problem-solving context in this unit is a circus act in which a performer jumps off a Ferris wheel into a moving tub of water. Not only are students developing and applying general ideas from trigonometry, but they are also learning principles of physics, developing laws for falling objects, and using vectors to find vertical and horizontal elements of velocity.
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