General Info | Resources | Research & Reports | Contacts & Connections | Curriculum
General Information
  A Brief Description of IMP
Inside IMP
IMP Success Brochure
IMP Strategies
Common Core Correlations
to IMP
Product & Pricing Info
Professional Development

Resources
  Publications & Articles
Research & Reports
Curriculum Resources
Especially for Parents

Contacts & Connections
  Contact IMP
NSF Funded Curriculum Projects

Introduction and Implementation Strategies for the Interactive Mathematics Program: A Guide for Teacher-Leaders and Administrators


Appendix B:
Concepts and Skills for
the IMP® Curriculum

The Interactive Mathematics Program has developed an integrated four-year high school mathematics sequence, designed to replace the traditional Algebra I - Geometry-Algebra II/Trigonometry-Precalculus sequence.

The following year-by-year lists describe the major topics covered in the IMP curriculum. The lists are formulated in terms of traditional mathematics topic organization, although the topics listed are covered in an integrated fashion, in the context of meaningful larger mathematical problems. Generally, topics taught in a given year are reviewed and extended through the curriculum of subsequent years. The year-by-year content descriptions are followed by a list of performance skills that are an integral part of this curriculum in all four years.

Content for Year 1

From Algebra

  • Using variables and algebraic expressions to represent concrete situations, generalize results, and describe functions
  • Using different representations of functions—symbolic, graphical, situational, and numerical—and understanding the connections between these representations
  • Understanding and using function notation
  • Understanding, modeling, and computing with signed numbers
  • Solving equations using trial and error
  • Interpreting graphs and using graphs to represent situations
  • Relating graphs to their equations, with emphasis on linear relationships
  • Solving pairs of linear equations by graphing
  • Fitting equations to data, both with and without graphing calculators
  • Developing and using principles for equivalent expressions, including the distributive property
  • Understanding and using the distributive property
  • Developing principles for equivalent equations and applying these principles to solve equations
  • Solving linear equations in one variable
  • Discovering and understanding relationships between the algebraic expression defining a linear function and the graph of that function

From Geometry

  • Understanding the meaning of angles and their measurement
  • Developing relationships among angles of polygons, including angle-sum formulas
  • Defining and developing criteria for establishing similarity and congruence
  • Using properties of similar polygons to solve real-world problems

From Trigonometry

  • Using similarity to define right-triangle trigonometric functions
  • Applying right-triangle trigonometry to real-world problems

From Probability and Statistics

  • Developing basic methods for calculating probabilities
  • Constructing area models and tree diagrams
  • Distinguishing between theoretical and experimental probabilities
  • Planning and carrying out simulations
  • Collecting and analyzing data
  • Constructing frequency bar graphs
  • Understanding, calculating, and interpreting expected value
  • Applying the concept of expected value to real-world situations
  • Learning about normal distributions and their properties
  • Calculating mean and standard deviation
  • Using normal distribution, mean, and standard deviation

From Logic

  • Making and testing conjectures
  • Formulating counterexamples
  • Constructing sound logical arguments
  • Understanding the idea of proof
  • Writing proofs
  • Developing and describing algorithms and strategies

Content for Year 2

From Algebra

  • Expressing real-world situations in terms of equations and inequalities
  • Understanding and using the distributive property
  • Developing and using several methods for solving systems of linear equations in two variables
  • Defining and recognizing dependent, inconsistent, and independent pairs of linear equations
  • Solving non-routine equations using graphing calculators
  • Writing and graphing linear inequalities in two variables
  • Developing and using principles of linear programming for two variables
  • Creating linear programming problems with two variables
  • Solving quadratic equations by factoring
  • Studying the number of roots of a quadratic equation and relating this number to the graph of the associated quadratic function
  • Using the method of completing the square to analyze the graphs of quadratic equations and to solve quadratic equations
  • Understanding and using exponential expressions, including zero, negative, and fractional exponents
  • Developing and using laws of exponents
  • Using scientific notation
  • Using the concept of order of magnitude in estimation

From Geometry

  • Developing the meaning of area using both standard and nonstandard units
  • Developing and using several methods for finding areas of polygons, including development of formulas for area of triangles, rectangles, parallelograms, trapezoids, and regular polygons
  • Understanding and finding surface area and volume for three-dimensional solids, including prisms and cylinders
  • Discovering and using the Pythagorean theorem
  • Understanding and explaining a proof of the Pythagorean theorem
  • Finding figures of maximum area for a given perimeter
  • Understanding the relationship between the areas and volumes of similar figures
  • Using and developing methods for creating tessellations

From Trigonometry

  • Applying right triangle trigonometry to area and perimeter problems

From Probability and Statistics

  • Drawing inferences from statistical data
  • Designing, conducting, and interpreting statistical experiments
  • Making and testing statistical hypotheses
  • Formulating null hypotheses and understanding their role in statistical reasoning
  • Understanding and using the χ2 statistic
  • Understanding and appreciating that tests of statistical significance do not lead to definitive conclusions
  • Solving problems that involve conditional probability

From Logic

  • Working with indirect proof and proof by contradiction
  • Using "if, then" statements

Content for Year 3

From Algebra

  • Working with exponential and logarithmic functions and describing their graphs
  • Understanding the relationship between logarithms and exponents
  • Finding that the derivative of an exponential function is proportional to the value of the function
  • Developing general laws of exponents
  • Understanding the meaning and significance of e
  • Approximating data by an exponential function
  • Developing and using the elimination method for solving systems of linear equations in up to four variables
  • Extending the concepts of dependent, inconsistent, and independent systems of linear equations to more than two variables
  • Working with matrices
  • Developing the operations of matrix addition and multiplication in the context of applied problems
  • Understanding the use of matrices in representing systems of linear equations
  • Developing the concepts of identity element and inverse in the context of matrices
  • Understanding the use of matrices and matrix inverses to solve systems of linear equations
  • Relating the existence of matrix inverses to the uniqueness of the solution of corresponding systems of linear equations
  • Using calculators to multiply and invert matrices and to solve systems of linear equations
  • Extending concepts of linear programming to problems with several variables
  • Expressing the physical laws of falling bodies in terms of quadratic functions

From Analytic and Coordinate Geometry

  • Defining slope and understanding its relationship to rate of change and to equations for straight lines
  • Developing equations for straight lines from two points and from point-slope information
  • Developing and applying various formulas from coordinate geometry, including:
    • Distance formula
    • Midpoint formula
    • Equation of a circle with arbitrary center and radius
  • Finding the distance from a point to a line
  • Developing and working with equations of planes in three-dimensional coordinate geometry
  • Defining polar coordinates
  • Studying graphs of polar equations

From Precalculus

  • Understanding and using inverse functions
  • Understanding the meaning of the derivative of a function at a point and its relationship to instantaneous rate of change
  • Approximating the value of a derivative at a given point

From Geometry

  • Developing the relationship of the area and circumference of a circle to its radius
  • Understanding the definition and significance of using regular polygons to approximate the area and circumference of a circle
  • Discovering and justifying locus descriptions of various geometric entities, such as perpendicular bisectors and angle bisectors
  • Developing properties of parallel lines
  • Studying the possible intersections of lines and planes

From Trigonometry

  • Applying right-triangle trigonometry to real-world situations
  • Extending the right-triangle trigonometric functions to circular functions
  • Using trigonometric functions to work with polar coordinates
  • Defining radian measure
  • Graphing the sine and cosine functions and variations of these functions
  • Working with inverse trigonometric functions
  • Developing and using various trigonometric formulas, including:
    • The Pythagorean identity
    • Formulas for the sine and cosine of a sum of angles
    • The law of sines and the law of cosines

From Probability and Statistics

  • Developing and applying principles for finding the probability for a sequence of events
  • Developing methods for the systematic listing of possibilities for complex problems
  • Developing the meaning of combinatorial and permutation coefficients in the context of real-world situations, and understanding the distinction between combinations and permutations
  • Developing principles for computing combinatorial and permutation coefficients
  • Understanding and using Pascal's triangle
  • Developing and applying the binomial distribution

From Logic

  • Using "if and only if" in describing sets of points fitting given criteria
  • Defining and using the concept of the converse of a statement

Content for Year 4

From Algebra

  • Proving and using the quadratic formula
  • Expressing the physical laws of falling bodies in terms of quadratic functions

From Analytic and Coordinate Geometry

  • Expressing geometric transformations—translations, rotations, and reflections—in analytic terms
  • Using matrices to represent geometric transformations
  • Developing an analytic expression for projection onto a plane from a point perspective
  • Representing a line in 3-dimensional space algebraically

From Precalculus

  • Studying and using families of functions from several perspectives:
    • Through their algebraic representations
    • In relationship to their graphs
    • As tables of values
    • In terms of real-world situations that they describe
  • Studying the effect of changing parameters on functions in a given family
  • Working with end behavior and asymptotes of rational functions
  • Working with the algebra of functions, including composition and inverse functions
  • Defining the least-squares approximation and using a calculator's regression capability to do curve-fitting
  • Extending the number system to include complex numbers to solve certain quadratic equations

From Trigonometry

  • Extending the right-triangle trigonometric functions to circular functions
  • Defining radian measure

From Calculus

  • Estimating derivatives from graphs, and developing formulas for derivatives of some basic functions
  • Understanding accumulation as the antiderivative of a corresponding rate function

From Probability and Statistics

  • Using the binomial distribution to model a polling situation
  • Distinguishing between sampling with replacement and sampling without replacement
  • Understanding the central limit theorem as a statement about approximating a binomial distribution by a normal distribution
  • Using area estimates to understand and use a normal distribution table
  • Extending the concepts of mean and standard deviation from sets of data to probability distributions
  • Developing formulas for mean and standard deviation for binomial sampling situations
  • Using the normal approximation for binomial sampling to assess the significance of poll results
  • Working with the concepts of confidence interval, confidence level, and margin of error
  • Understanding the relationship between poll size and margin of error

From Programming

  • Using loops
  • Writing and interpreting programs
  • Using a graphing calculator to create programs involving animation

Click here to see a grid that shows how the Interactive Mathematics Program curriculum fits the NCTM standards.


<--page
Table of Contents


©2012 It's About Time Interactive. All rights reserved.