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.

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 and logarithms.

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

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.

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.

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.

IS THERE REALLY A DIFFERENCE? Students build on prior experience with statistical ideas from IMP Year 1, expanding their understanding of statistical analysis.

PENNANT FEVER Students use combinatorics to develop the binomial distribution and find the probability that the team leading in the pennant race will ultimately win the pennant.

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 DIVER RETURNS This unit builds upon Year 3’s High Dive 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?" In Year 4, students use vectors modeling horizontal and vertical components of the diver’s initial velocity.

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.

AS THE CUBE TURNS Students study the fundamental geometric transformations—translations, rotations, and reflections—in two and three dimensions, in order to create a display of a cube rotating around an axis in three-dimensional space.

HOW MUCH? HOW FAST? This unit adds integrals to the derivative concepts explored in Year 3. Students solve accumulation problems using a version of the Fundamental Theorem of Calculus. They find that the derivative of the function that describes the amount of accumulation up to a particular time is the rate of accumulation, and that the function describing accumulation is an anti-derivative of the function describing the rate of accumulation.

THE POLLSTER'S DILEMMA The central problem of this unit concerns an election poll, and students use normal distributions and standard deviations to find confidence intervals and see how concepts such as margin of error are used in polling results.