Interactive Mathematics Program
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Interactive Mathematics is a comprehensive high-school mathematics program, identified as Exemplary by the U.S. Department of Education.
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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.

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.

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.

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.

Dr. Dan Fendel is Professor Emeritus at San Francisco State University, having been an active member of the Mathematics Department at SFSU from 1973 to 2006. His career focused on in-service and pre-service training of K-12 teachers in mathematics, and he was one of the two primary authors of the Interactive Mathematics Program, a four-year, integrated, problem-based mathematics curriculum program for high school students. Dr. Fendel also helped create the comprehensive teacher professional development program which accompanies the curriculum. Throughout his career, he spoke regularly at mathematics education conferences, with talks internationally in Mexico, Chile, Israel, and Japan.

Diane Resek is Professor Emerita of Mathematics at San Francisco State University. During her 30 years in the Mathematics Department she taught remedial algebra, math for elementary school teachers, calculus, upper division courses in algebra, and upper division and graduate courses in logic and set theory. Since retiring in 2005, she has worked on inservice programs for secondary and college mathematics teachers. She is presently developing a new curriculum for remedial algebra courses at the college level. Before receiving her PhD in mathematical logic from University of California, Berkeley she worked as a mathematics specialist in elementary schools, developed inservice mathematics programs for pre-school and elementary school teachers, and wrote scripts for educational mathematics films. While teaching at San Francisco State she developed computer using curriculum for middle school and college students, as well as, a college textbook on Proof and Exploration. She has published a number of papers in the area of mathematics education.

Mathematics has always been the educational focus of Lynne’s life. As a mathematics major in college and after receiving her MA in mathematics education from Stanford University, Lynne taught high school mathematics in Massachusetts, Colorado, and California. During the development of the Interactive Mathematics Program®, she taught the first three years of the curriculum in California. She also taught at San Francisco State University and was a member of the Equals staff at the Lawrence Hall of Science, UC Berkeley. At Equals, she focused on professional development for secondary teachers, combining mathematics and equity principles to open challenging mathematics to all students. Fluent in Spanish, Lynne taught mathematics while serving in the Peace Corps in Chile; she conducted mathematics and equity inservices in Costa Rica.

For the past five years, she has been promoting equity in mathematics at the elementary and middle school level, working with parents and teachers in their classrooms and introducing the FAMILY MATH program to school communities.

Sherry Fraser considers herself first and foremost a high school mathematics teacher. She has taught every level of traditional high school mathematics as well as teaching all four years of the Interactive Mathematics Program. She currently serves as Director of the IMP Implementation Center, with her primary focus centered on the professional development of teachers. During her 15 years at the Lawrence Hall of Science, UC Berkeley she was director of the curriculum project SPACES (Solving Problems of Access to Careers in Engineering and Science) and a member of the Equals staff, focusing on increasing the participation of minority and female students in secondary mathematics courses. In addition to working with state and national leaders in math education, she has worked in Australia, New Zealand, England, The Netherlands, Germany, Denmark, and Hungary providing materials and strategies and exchanging ideas for how to involve all students in secondary mathematics.