Core Curriculum Content Standards
4.1.A: Number Sense
4.1.A.2: Compare and order rational and irrational numbers.
4.1.B: Numerical Operations
4.1.B.4: Understand and apply the laws of exponents to simplify expressions involving numbers raised to powers.
4.2.A: Geometric Properties
4.2.A.2: Draw perspective views of 3D objects on isometric dot paper, given 2D representations (e.g., nets or projective views).
4.2.A.3: Apply the properties of geometric shapes.
4.2.A.3.1: Parallel lines – transversal, alternate interior angles, corresponding angles
4.2.A.3.2a: Conditions for congruence
4.2.A.3.2c: Triangle Inequality
4.2.A.3.3: Minimal conditions for a shape to be a special quadrilateral
4.2.A.3.4: Circles – arcs, central and inscribed angles, chords, tangents
4.2.A.4: Use reasoning and some form of proof to verify or refute conjectures and theorems.
4.2.A.4.1: Verification or refutation of proposed proofs
4.2.A.4.2: Simple proofs involving congruent triangles
4.2.B: Transforming Shapes
4.2.B.1: Determine, describe, and draw the effect of a transformation, or a sequence of transformations, on a geometric or algebraic object, and, conversely, determine whether and how one object can be transformed to another by a transformation or a sequence of transformations.
4.2.B.2: Recognize three-dimensional figures obtained through transformations of two-dimensional figures (e.g., cone as rotating an isosceles triangle about an altitude), using software as an aid to visualization.
4.2.B.4: Generate and analyze iterative geometric patterns.
4.2.B.4.2: Patterns in areas and perimeters of self-similar figures
4.2.B.4.3: Outcome of extending iterative process indefinitely
4.2.C: Coordinate Geometry
4.2.C.1: Use coordinate geometry to represent and verify properties of lines.
4.2.C.1.1: Distance between two points
4.2.C.1.2: Midpoint and slope of a line segment
4.2.C.1.4: Lines with the same slope are parallel
4.2.C.1.5: Lines that are perpendicular have slopes whose product is –1
4.2.C.2: Show position and represent motion in the coordinate plane using vectors.
4.2.C.2.1: Addition and subtraction of vectors
4.2.E: Measuring Geometric Objects
4.2.E.1: Use techniques of indirect measurement to represent and solve problems.
4.2.E.1.1: Similar triangles
4.2.E.1.2: Pythagorean theorem
4.2.E.1.3: Right triangle trigonometry (sine, cosine, tangent)
4.2.E.2: Use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures.
4.2.E.2.1: Approximation of area using grids of different sizes
4.2.E.2.2: Finding which shape has minimal (or maximal) area, perimeter, volume, or surface area under given conditions using graphing calculators, dynamic geometric software, and/or spreadsheets
4.2.E.2.3: Estimation of area, perimeter, volume, and surface area
4.3.A.1: Use models and algebraic formulas to represent and analyze sequences and series.
4.3.A.1.1: Explicit formulas for nth terms
4.3.B: Functions and Relationships
4.3.B.1: Understand relations and functions and select, convert flexibly among, and use various representations for them, including equations or inequalities, tables, and graphs.
4.3.B.2: Analyze and explain the general properties and behavior of functions of one variable, using appropriate graphing technologies.
4.3.B.2.1: Slope of a line or curve
4.3.B.2.2: Domain and range
4.3.B.2.6: Estimating roots of equations
4.3.B.2.7: Intersecting points as solutions of systems of equations
4.3.B.2.8: Rates of change
4.3.B.3: Understand and perform transformations on commonly-used functions.
4.3.B.3.1: Translations, reflections, dilations
4.3.B.3.2: Effects on linear and quadratic graphs of parameter changes in equations
4.3.B.4: Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions.
4.3.B.4.1: Linear vs. non-linear
4.3.C.1: Use functions to model real-world phenomena and solve problems that involve varying quantities.
4.3.C.1.1: Linear, quadratic, exponential, periodic (sine and cosine), and step functions (e.g., price of mailing a first-class letter over the past 200 years)
4.3.C.1.2: Direct and inverse variation
4.3.C.1.3: Absolute value
4.3.C.1.4: Expressions, equations and inequalities
4.3.C.1.5: Same function can model variety of phenomena
4.3.C.1.7: Applications in mathematics, biology, and economics (including compound interest)
4.3.C.2: Analyze and describe how a change in an independent variable leads to change in a dependent one.
4.3.C.3: Convert recursive formulas to linear or exponential functions (e.g., Tower of Hanoi and doubling).
4.3.D.1: Evaluate and simplify expressions.
4.3.D.1.1: Add and subtract polynomials
4.3.D.1.2: Multiply a polynomial by a monomial or binomial
4.3.D.1.3: Divide a polynomial by a monomial
4.3.D.2: Select and use appropriate methods to solve equations and inequalities.
4.3.D.2.1: Linear equations – algebraically
4.3.D.2.2: Quadratic equations – factoring (when the coefficient of x² is 1) and using the quadratic formula
4.3.D.2.3: All types of equations using graphing, computer, and graphing calculator techniques
4.4.A: Data Analysis
4.4.A.1: Use surveys and sampling techniques to generate data and draw conclusions about large groups.
4.4.A.1.1: Advantages/disadvantages of sample selection methods (e.g., convenience sampling, responses to survey, random sampling)
4.4.A.3: Design a statistical experiment, conduct the experiment, and interpret and communicate the outcome.
4.4.A.4: Estimate or determine lines of best fit (or curves of best fit if appropriate) with technology, and use them to interpolate within the range of the data.
4.4.A.5: Analyze data using technology, and use statistical terminology to describe conclusions.
4.4.A.5.2: Correlation coefficient
4.4.B.2: Use concepts and formulas of area to calculate geometric probabilities.
4.4.B.3: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models, and solve problems using these models.
4.4.B.4: Determine probabilities in complex situations.
4.4.B.4.3: Dependent and independent events
4.4.B.5: Estimate probabilities and make predictions based on experimental and theoretical probabilities.
4.4.B.6: Understand and use the "law of large numbers" (that experimental results tend to approach theoretical probabilities after a large number of trials).
4.4.C: Discrete Mathematics-Systematic Listing and Counting
4.4.C.1: Calculate combinations with replacement (e.g., the number of possible ways of tossing a coin 5 times and getting 3 heads) and without replacement (e.g., number of possible delegations of 3 out of 23 students).
4.4.C.4: Recognize and explain relationships involving combinations and Pascal’s Triangle, and apply those methods to situations involving probability.
Correlation last revised: 11/13/2008