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# Interactive Mathematics Program® Content

## Interactive Mathematics Program Year 1

## Interactive Mathematics Program Year 1

**Provides a broad introduction of to algebra****Helps students develop strong mathematical skills and habits of mind****Improves communication and writing skills**

**PATTERNS **Students develop basic ideas about functions, integers, angles, and polygons. They learn how to work on mathematical investigations and report on their ideas both orally and in writing.

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

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

**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.

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

## Interactive Mathematics Program Year 2

## Interactive Mathematics Program Year 2

**Covers quadratic functions and equations****Deepens students’ conceptual understanding through new contexts****Includes embedded practice**

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

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

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

**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.

## Interactive Mathematics Program Year 3

## Interactive Mathematics Program Year 3

**Extends students’ understanding of material studied in preceding years of the curriculum as they learn and apply new skills****Topics include combinatorics, derivatives, and the algebra of matrices**

**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.

**MEADOWS OR MALLS?** This unit concerns making a decision about land use and builds on skills learned in *Cookies* about graphing systems of linear inequalities and solving systems of linear equations.

**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.

**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?

## Interactive Mathematics Program Year 4

## Interactive Mathematics Program Year 4

**Features widely varied topics, including computer graphics, statistical sampling, and an introduction to accumulation and integrals****Builds on the strong knowledge base of***IMP s*tudents

**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.

**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.

**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.

**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.