Inside IMP®
What is IMP?
How does IMP address the Common Core State Standards?
Why is a change needed in mathematics education?
How does IMP differ from traditional high school mathematics courses?
What happens in an IMP classroom?
Does IMP prepare students for college?
IMP Nationwide
IMP Curriculum Content: A Summary
IMP CoDirectors & Advisory Board
What is IMP?
The Interactive Mathematics Program (IMP) is an exciting new way for high school students to learn mathematics.
IMP's fouryear program of problembased mathematics replaces the traditional Algebra IGeometryAlgebra
II/TrigonometryPrecalculus sequence. This new curriculum meets college entrance requirements and prepares
students to use problemsolving skills at school and on the job.
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How does IMP address the Common Core State Standards?
With the use of IMP, teachers can be confident that they will meet the Standards
for Mathematical Practice as outlined in the Common Core State Standards for
Mathematics. Teachers can quickly see that their students will be problem
solvers through the use of "Problems of the Week." Students will
model mathematics and attend to precision by investigating situations and
generalizing the mathematics embedded in each problem. The use of logic and
proof will allow students to practice being persuasive writers as well as
critics of arguments set before them.
The IMP
curriculum consistently employs the Standards for Mathematical Practice
throughout the fouryear program. Students will see the value of these
practices in all the assignments, activities, and investigations that they
perform. These include: Problems of the Week, classroom investigations,
presentations, alternative assessments, and portfolios.
Teachers will also see their teaching
of IMP mirror the eight Standards for Mathematical Practice. Teachers will
discover a multifaceted approach to teaching that reaches all learners.
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Why is a change needed in mathematics education?
As students enter the professions and trades, demands will be placed on them that
focus on their problemsolving and communication skills. Preparing students for
the challenges of business and industry requires a shift in instruction away
from routine manipulation of symbols and procedures toward an indepth,
conceptual understanding of mathematics.
IMP integrates traditional areas of
mathematics with new topics such as probability, statistics, discrete
mathematics, and matrix algebra. It also includes use of graphing calculators
and computers, encourages cooperative learning, and is accessible to all
students.
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How does IMP differ from traditional high school mathematics courses?
Conceptual Understanding The IMP curriculum challenges students to actively explore openended
situations, in a way that closely resembles the inquiry method used by
mathematicians and scientists in their work. While the traditional curriculum
emphasizes rote learning of isolated mathematical skills, IMP calls on
students to experiment with examples, look for and articulate patterns, and
make, test, and prove conjectures.
Updated Mathematics
IMP integrates algebra, geometry, and trigonometry with the additional topics recommended by the national
reports, using calculator and computer technology to enhance student understanding.
ProblemBased Units
The IMP curriculum is problembased, consisting of five to eightweek units bound into a single techbook. The
units are each organized around a central problem or theme. Motivated by this central focus, students solve a
variety of smaller problems, both routine and nonroutine, that develop the underlying skills and concepts
needed to solve the central problem in that unit.
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What happens in an IMP classroom?
Interactive Learning The "interactive" aspect of IMP refers, in part, to the program's
emphasis on students working with each other in collaborative groups. Students
discuss problems, use writing to clarify, and express complex mathematical ides
and present findings to the rest of the class. Students share many different and
valid approaches, expanding everyone's thinking. Together, they tackle problems
that are usually too complex to be solved by any one individual.
Flexible Curriculum The curriculum design offers complex problems that can be explored at many levels
of sophistication. A typical first year IMP class includes accelerated students who
have taken algebra in the 8th grade, those who would begin a college preparatory
sequence in the 9th grade, and students who might have otherwise been excluded from
challenging mathematics classes. A varied collection of supplemental problems gives
teachers the flexibility to meet individual student needs. Special features include
extensions (for students who want to pursue a specific topic in greater depth) and
reinforcement experiences (for student who need to reflect on and synthesize what
they have already learned).
Homework Students complete daily homework assignments that focus on challenging their ability to think
mathematically rather than drilling them on the computation skills. They also work on "Problems
of the Week," openended investigations in which they must write and illustrate their
strategies and solutions to complex problems, and deliver oral presentations to the class.
Assessment IMP Students are evaluated according to a variety of criteria. Student grades are based on
class participation, daily homework assignments, Problems of the Week, portfolios, and unit
assessments, including a twohour semester exam rather than on weekly quizzes and chapter
tests.
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Does IMP prepare students for college?
College Acceptance The curriculum has been accepted as fulfilling mathematics requirements for
admission to the University of California system as well as to other schools
throughout the country. Students who have completed the IMP curriculum have been
admitted to top schools, including Yale University, Stanford University, Howard
University, Carnegie Mellon University, Columbia University, University of Michigan,
and all campuses of the University of California. Click here for a complete list of schools.
Case Study: Comparison of IMP Students'
Progress to Peers in Traditional Mathematics

While a formal, fiveyear evaluation of IMP is
currently
underway, schools with IMP classrooms have conducted
their own research as well. In the Colorado study, sample
SAT tests were given to IMP Year One and Algebra
I
students at the beginning and end of the academic
year (1991–92). The average gain of IMP Year
One students
was significantly higher than that of Algebra I
Students. 
SAT Average Raw Scores*
Eaglecrest High School, Aurora, Colorado

*Average raw scores of IMP Year One students
increased by 2.92,
while average raw scores of Algebra I students
increased by only
1.25. The difference in growth was significant at
the .025 level. 
SAT Performance IMP students studied at the original three California test sites were given sample SAT
tests, and their scores were compared to control groups of students in traditional
mathematics classes. These sample SAT results indicate that although IMP students spend
less time on traditional algebra and geometry skills they are doing as well as, and in
some cases better than, students in traditional mathematics classes.
Studies of IMP classrooms in Colorado, Oregon, and Texas also indicated that IMP students are doing as well as or
better than students in traditional classes on sample SAT and other competency exams.
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IMP Nationwide
In 1989 IMP began as part of a curriculumdevelopment effort funded by the California
Postsecondary
Education
Commission
(CPEC) and the California State Department of Education. With additional
funding from the National Science Foundation, IMP is currently involved in disseminating the curriculum in high
schools in over half the states across the United States and in Canada.
For more information, call 1888698TIME (8463) .
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IMP Curriculum Content: A Summary
Year 1
Revised
to better help you prepare your students for algebrabased standardized tests,
the second edition of Year 1 provides a broader introduction to algebra and
more formal work with linear functions and algebraic symbol manipulation. The
firstyear curriculum contains an introduction to problemsolving strategies,
the use of variables, and the meaning and use of functions and graphs, as well
as concepts from statistics, geometry, and trigonometry. These mathematics
ideas are set in varied contexts, such as the settlement of the American West,
games of chance, Edgar Allan Poe's The Pit and
the Pendulum, and measurement of shadows.
Year 2
Students
work with powerful mathematical ideasincluding the chisquare statistic, the
Pythagorean theorem, linear programming, and quadratic functions—and
learn a variety of approaches to solving equations. Problem contexts include
statistical comparison of populations, the geometry of the honeycomb, and
maximization of profits from a cookie store.
Year 3
Students
extend their understanding of material studied in preceding years of the
curriculum, while learning about and applying new topics such as combinatorics,
derivatives, and the algebra of matrices. A baseball pennant race, population
growth, and decisionmaking on land use provide some of the contexts for the
mathematical concepts.
Year 4
Revised
to complete the fouryear IMP curriculum, the second edition of fourthyear IMP has a more varied
subject matter than a
calculusfocused course, and includes topics such as circular functions,
computer graphics, statistical sampling, and the Fundamental Theorem of
Calculus. Units build on the strong knowledge base of students who have
completed three years in the program; further, the modified unit The Diver Returns completes the
solution of the High Dive problem from Year 3, while the allnew unit How Much? How Fast?
follows up on the Year 3 unit, Small World, Isn't It? by looking at the issue of
accumulation of change. Problem settings in Year 4 include a Ferriswheel
circus act, election polling, and a solar energy collector.
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IMP CoDirectors
Lynne Alper, Sherry Fraser
Mathematics Educators, Interactive Mathematics Program
Professors Dan Fendel, Diane Resek
Mathematics Department, San Francisco State University
IMP Advisory Board
David Blackwell
Professor of Mathematics and Statistics, University of California, Berkeley
Constance Clayton
Professor of Pediatrics, Chief, Division of Community Health Care, Medical College of Pennsylvania
Tom Ferrio
Manager, Professional Calculators, Texas Instruments
Andrew Gleason
Hollis Professor of Mathematics and Natural Philosophy, Department of Mathematics, Harvard University
Milton A. Gordon
President and Professor of Mathematics, California State University, Fullerton
Shirley Hill
Curator's Professor of Education and Mathematics, School of Education, University of Missouri
Steven Leinwand
Mathematics Consultant, Connecticut Department of Education
Art McArdle
Northern California Surveyors Apprentice Committee
Diane Ravitch (1994 only)
Senior Research Scholar, Brookings Institute
Roy Romer (1992–1994 only)
Governor, State of Colorado
Karen Sheingold
Research Director, Educational Testing Service
Theodore R. Sizer
Chairman, Coalition of Essential Schools
Gary D. Watts
Educational Consultant
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* Everybody Counts (National Research Council, 1989), Reshaping School
Mathematics (Mathematical
Sciences Education Board, 1990), Science for All Americans (American Association for
the Advancement of Science, 1989), and Curriculum and Evaluation Standards for School
Mathematics (National Council of Teachers of
Mathematics, 1989)
