Math Content by Unit

The following table lists the important clusters of related concepts, skills, procedures, and ways of thinking in each Unit of CMP3

Grade 6

  • Prime Time: Factors and Multiples

    Number theory, including factors, multiples, primes, composites, prime factorization; order of operations, distributive property.
  • Comparing Bits and Pieces: Ratios, Rational Numbers and Equivalence

    Ratio, unit rate, rate tables, rational numbers, decimals, percents, equivalence, absolute value, number line.
  • Let’s Be Rational: Understanding Fraction Operations

    Addition, subtraction, multiplication, division of fractions, fact families.
  • Covering and Surrounding: Two Dimensional Measurement

    Area and perimeter relationships, area and perimeter of polygons, surface area and volume of rectangular prisms.
  • Decimal Ops: Computing with Decimals and Percents

    Addition, subtraction, multiplication and division of decimals, estimation; solutions for a % of b = c
  • Variables and Patterns: Focus on Algebra

    Variables, variable expressions, equations, inequalities; representations of relationships in tables, graphs, equations.
  • Data About Us: Statistics and Data Analysis

    Analysis of data distributions, including shape, measures of center (mean, median, mode) and variability (range, inter quartile range, mean absolute deviation).

Grade 7

  • Shapes and Designs: Two Dimensional Geometry

    Polygons, measurement of angles, angle sum of polygons, conditions for unique triangle, parallel lines and transversals.
  • Accentuate the Negative: Integers and Rational Numbers

    Addition, subtraction, multiplication and division of rational numbers, absolute value, opposites, order of operations, distributive property.
  • Stretching and Shrinking: Understanding Similarity

    Enlarging a figure, effect of scale factors on perimeter and area, coordinate rules, ratios between and within similar figures; using similarity to find measures.
  • Comparing and Scaling: Ratios, Rates, Percent, Proportions

    Ratios, unit rate, rate tables, constant of proportionality, solving proportions, Inc. markups, discounts, commission, measurement, conversion.
  • Moving Straight Ahead: Linear Relationships

    Representing linear relationships in graphs, tables, equations; solving linear equations; slope, intercept, writing equation for linear relationship given points.
  • What Do You Expect: Probability and Expected Value

    Probability models, experimental and theoretical probability, analysis of compound events.
  • Filing and Wrapping: Three Dimensional Measurement

    Area circumference of circle; volume and surface area of rectangular and polygonal prisms, cylinders; volume of pyramids, cones, spheres; plane sections of prisms, pyramids; effect of scaling on surface area and volume.
  • Samples and Populations: Making Comparisons and Predictions

    Sampling plans, effect of sample size, predicting population statistics, simulations, comparing sample statistics to draw inferences about two populations.

Grade 8

  • Thinking With Mathematical Models: Linear and Inverse Variations

    Linear models and equations, inverse variation models and equations, variability of numerical and categorical data
  • Looking for Pythagoras: The Pythagorean Theorem

    Pythagorean Theorem and converse, square roots, cube roots, irrational and real numbers, equation of circle.
  • Growing, Growing, Growing: Exponential Functions

    Representing exponential growth with tables, graphs, equations; rules for exponents, scientific notation; Exponential Decay; growth/decay factors and rates.
  • Say it with Symbols: Making Sense of Symbols

    Equivalent expressions, solving linear and quadratic equations; identify and represent linear, exponential and quadratic functions.
  • Butterflies, Pinwheels and Wallpaper: Symmetry and Transformations

    Symmetry, transformations, congruence, similarity, coordinate proofs.
  • It's in the System: Systems of Linear Equations and Inequalities

    Solving linear systems graphically and algebraically, systems of functions and inequalities, solving systems of linear inequalities.

Algebra

  • Thinking With Mathematical Models: Linear and Inverse Variations

    Linear models and equations, inverse variation models and equations, variability of numerical and categorical data
  • Looking for Pythagoras: The Pythagorean Theorem

    Pythagorean Theorem and converse, square roots, cube roots, irrational and real numbers, equation of circle.
  • Growing, Growing, Growing: Exponential Functions

    Representing exponential growth with tables, graphs, equations; rules for exponents, scientific notation; Exponential Decay; growth/decay factors and rates.
  • Frogs and Fleas and Painted Cubes: Quadratic Functions

    Representing quadratic functions, factoring quadratic expressions, patterns of change, effect of parameters.
  • Say it with Symbols: Making Sense of Symbols

    Equivalent expressions, solving linear and quadratic equations; identify and represent linear, exponential and quadratic functions.
  • Butterflies, Pinwheels and Wallpaper: Symmetry and Transformations

    Symmetry, transformations, congruence, similarity, coordinate proofs.
  • It's in the System: Systems of Linear Equations and Inequalities

    Solving linear systems graphically and algebraically, systems of functions and inequalities, solving systems of linear inequalities.
  • Function Junction: Families of Functions

    Function notation, inverses, arithmetic/ geometric sequences, transformations on functions; completing the square, quadratic formula, polynomial expressions/ functions /equations.

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CMP3 Grade 8 and Algebra I Pathways

Appendix A of the Common Core State Standards for Mathematics (CCSSM) and the PARCC Model Content Framework for Mathematics both suggest required standards that an Algebra I course would comprise. Connected Mathematics 3 (CMP3) is aligned with both sets of recommendations and is also a good fit for Algebra 1 courses designed by local school districts. Therefore, CMP3 students completing all 23 units in Grades 6, 7, and 8 will be prepared to take college-level courses, including calculus, by their senior year of high school.

CMP3 offers two paths through Grade 8: Grade 8 and Grade 8 and Algebra I.

Grade 8 Units

  • Thinking with Mathematical Models
  • Looking for Pythagoras
  • Growing, Growing, Growing
  • Butterflies, Pinwheels, and Wallpaper
  • Say It With Symbols
  • It’s in the System

Algebra I  Grade 8 Units

  • Thinking with Mathematical Models
  • Looking for Pythagoras
  • Growing, Growing, Growing
  • Frogs, Fleas, and Painted Cubes
  • Butterflies, Pinwheels, and Wallpaper
  • Say It With Symbols
  • It’s in the System
  • Function Junction

CCSSM and PARCC include studying exponential functions in Algebra I standards, but not in the Grade 8 standards. However, Growing, Growing, Growing is included in Grade 8 to contrast linear functions with nonlinear functions, a Grade 8 standard. Exponential functions are a natural choice to include in Grade 8 because the multiplicities constant growth patterns of exponential functions provide a contrast to the additive constant growth patterns of linear functions. This contrast strengthens students’ understanding of linear functions. In addition, Growing, Growing, Growing provides a platform for developing the rules of exponents and the use of scientific notation, both of which are part of the Grade 8 standards.

Furthermore, a few CMP3 Problems in some units will go further than the Grade 8 standards require. This is done to deepen the algebraic understanding for students studying Algebra I. One example appears in Thinking With Mathematical Models. While investigating patterns of association in bivariate data, students extend their understanding to correlation coefficients, part of the Algebra I standards.