# Units

#### Algebra 1

**THE OVERLAND TRAIL** Students look at mid-19th-century Western migration in terms of the
many linear relationships involved.

**ALL ABOUT ALICE** The unit starts with a model based on Lewis Carroll’s Alice’s Adventures
in Wonderland, through which students develop the basic principles for working with exponents.

**THE PIT AND THE PENDULUM** Exploring an excerpt from this Edgar Allan Poe classic,
students use data from experiments and statistical ideas, such as standard deviation, to develop a
formula for the period of a pendulum.

**COOKIES** In their work to maximize profits for a bakery, students deepen their
understanding of the relationship between equations and inequalities and their graphs.

**FIREWORKS** The central problem of this unit involves sending up a rocket to create a
fireworks display. This unit builds on the algebraic investigations of Year 1, with a special focus on
quadratic expressions, equations, and functions.

#### Geometry

**SHADOWS** Students use principles about similar triangles and basic trigonometry to
develop formulas for finding the length of a shadow.

**GEOMETRY BY DESIGN** Students explore the history of geometry and human design to learn
the concepts of congruence, transformations, geometric construction, and proof.

**DO BEES BUILD IT BEST?** Students study surface area, volume, and trigonometry to answer
the question, “What is the best shape for a honeycomb?”

**ORCHARD HIDEOUT** Students study circles and coordinate geometry to determine how long it
will take before the trees in a circular orchard grow so large that someone standing at the center of
the orchard cannot see out.

#### Algebra 2

**SMALL WORLD, ISN'T IT?** Beginning with a table of population data, students study
situations involving rates of growth, develop the concept of slope, and then generalize this to the idea
of the derivative.

**THE GAME OF PIG** Students develop a mathematical analysis for a complex game based on an
area model for probability.

**HIGH DIVE** Using trigonometry, polar coordinates, and the physics of falling objects,
students model this problem: When should a diver on a Ferris wheel aiming for a moving tub of water be
released in order to create a splash instead of a splat?

**THE WORLD OF FUNCTIONS** In this unit, students explore families of functions in terms of
various representations—tables, graphs, algebraic representations, and situations they can model; they
also explore ways of combining functions using arithmetic operations and composition.

**IS THERE REALLY A DIFFERENCE?** Students build on prior experience with statistical ideas
expanding their understanding of statistical analysis.