#### THE INTERACTIVE MATHEMATICS PROGRAM^{®}(IMP)

*“I would say that IMP is the best high-school curriculum that I know of that really takes the problem-solving approach. . . In all the IMP classes we worked in, watched, and researched, we found great engagement in mathematical thinking and work.*

*I am a big fan!”*

– Jo Boaler, Professor of Mathematics Education at the Stanford Graduate School of Education

**Research-Based, Research-Proven**

- Designed and field tested with support from the National Science Foundation (NSF)
- Identified as “Exemplary” by the U.S. Department of Education: convincing evidence of effectiveness with diverse populations
- Brings the Standards for Mathematical Practice to life

**Students are Active Learners**

- Problem-based learning
- Real-life, compelling contexts including
- The Game of Pig
- The Pit and the Pendulum
- The Pollsters’ Dilemma

- Students experiment, investigate, and communicate

**Total Support for Teachers**

- Options: choose complete Student Edition or individual units
- Online Teachers Guide with calculator guides, technology activities, and assessments
- The CyberPD website with PD videos and just-in-time support

#### Introduction

Introducing IMP^{®}: No other curriculum embeds the CCSSM practices and standards so deeply. Interactive Mathematics Program is an integrated high-school mathematics curriculum designed to challenge students with a four-year sequence of college-preparatory mathematics. The curriculum has demonstrated in schools throughout the country that the successful study of advanced mathematics is an achievable standard for ALL students.

**Interactive Mathematics Program® is an “exemplary” math curriculum.**

IMP is one of three comprehensive high-school mathematics curricula identified as “Exemplary” by the U.S. Department of Education for providing convincing evidence of its effectiveness in multiple schools with diverse populations.

**Interactive Mathematics Program places a strong emphasis on mathematical reasoning.**

In IMP, students rely on mathematical reasoning to solve challenging problems, based on real-world situations as well as meaningful scenarios. With an emphasis on critical thinking, students develop multiple strategies to solve problems.

**Interactive Mathematics Program® is technology-enhanced.**

The IMP curriculum incorporates graphing calculators as an integral part of the development of mathematical ideas. The calculators enable students to see mathematics and problem solving in a different way and allow them to focus on ideas.

#### Projects

#### IMP Year 1

**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.

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

**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.

#### IMP Year 2

**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 BY DESIGN** provides students with historical knowledge about how people created mathematics, and in particular, geometry. Students use the ancient tools of straightedge and compass to do constructions, and ruler and protractor to make accurate drawings. The classical deductive system consisting of Euclid’s postulates and theorems is introduced to prove theorems about triangles and quadrilaterals.

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

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

**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.

#### IMP Year 3

**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.

**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.

**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 from IMP Years 1 and 2, expanding their understanding of statistical analysis.

#### IMP Year 4

**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.

**HOW MUCH? HOW FAST?** This unit adds integrals to the derivative concepts explored in Year 2. 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.

**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.

**KNOW HOW** In this unit, students independently research mathematical concepts and skills that they either have not yet learned or may have forgotten. Students reflect on their future needs for independent learning, and consider what it means to really know something.

#### Videos

Seeing is believing, so, grab the popcorn! The Activate Learning video team has traveled the nation visiting many different schools all engaged with our curricula. Watch to see how ALL of our learners are succeeding in investigation-centered STEM.

IMP / Meaningful Math – Overview – It's About Mathematics

IMP / Meaningful Math- Students Persevere on NYS Geometry Regents Exam

IMP / Meaningful Math- Jo Boaler's Experience

IMP / Meaningful Math- Portfolio Writing

IMP / Meaningful Math – Creating a sustainable model (DE)

IMP / Meaningful Math – The Beauty of Meaningful Math

IMP / Meaningful Math – Student Experiences (DE)

IMP / Meaningful Math – Eight CCSSM Practices