Core Curriculum Content Standards

4.1.A: Number Sense

4.1.A.2: Compare and order rational and irrational numbers.

Comparing and Ordering Decimals

Comparing and Ordering Fractions

Comparing and Ordering Rational 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.

Dividing Exponential Expressions

Multiplying Exponential Expressions

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).

3D and Orthographic Views - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

4.2.A.3: Apply the properties of geometric shapes.

4.2.A.3.1: Parallel lines – transversal, alternate interior angles, corresponding angles

Investigating Angle Theorems - Activity A

Triangle Angle Sum - Activity A

4.2.A.3.2a: Conditions for congruence

Congruence in Right Triangles

Proving Triangles Congruent

4.2.A.3.2c: Triangle Inequality

4.2.A.3.3: Minimal conditions for a shape to be a special quadrilateral

Classifying Quadrilaterals - Activity B

4.2.A.3.4: Circles – arcs, central and inscribed angles, chords, tangents

Chords and Arcs

Inscribing Angles

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

Biconditional Statement

Conditional Statement

Proving Triangles Congruent

4.2.A.4.2: Simple proofs involving congruent triangles

Biconditional Statement

Conditional Statement

Congruence in Right Triangles

Proving Triangles Congruent

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.

Dilations

Reflections

Rotations, Reflections and Translations

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.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Rotations, Reflections and Translations

Surface and Lateral Area of Pyramids and Cones

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

Arithmetic and Geometric Sequences

Geometric Sequences

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

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

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

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

4.2.E.1.2: Pythagorean theorem

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

4.2.E.1.3: Right triangle trigonometry (sine, cosine, tangent)

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

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

Area of Parallelograms - Activity A

Rectangle: Perimeter and Area

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

Minimize Perimeter

Perimeter, Circumference, and Area - Activity B

Rectangle: Perimeter and Area

4.2.E.2.3: Estimation of area, perimeter, volume, and surface area

Minimize Perimeter

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Rectangle: Perimeter and Area

4.3.A: Patterns

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

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

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.

Exponential Functions - Activity A

Introduction to Functions

Linear Functions

Logarithmic Functions: Translating and Scaling

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

Functions Involving Square Roots

Introduction to Functions

4.3.B.2.3: Intercepts

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

4.3.B.2.4: Continuity

Cosine Function

Exponential Functions - Activity A

Functions Involving Square Roots

Sine Function

Tangent Function

4.3.B.2.5: Maximum/minimum

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

4.3.B.2.6: Estimating roots of equations

Polynomials and Linear Factors

Roots of a Quadratic

4.3.B.2.7: Intersecting points as solutions of systems of equations

Solving Linear Systems by Graphing

Systems of Linear Equations - Activity A

4.3.B.2.8: Rates of change

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

4.3.B.3: Understand and perform transformations on commonly-used functions.

4.3.B.3.1: Translations, reflections, dilations

Absolute Value with Linear Functions - Activity B

Reflections of a Linear Function

Reflections of a Quadratic Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

4.3.B.3.2: Effects on linear and quadratic graphs of parameter changes in equations

Linear Functions

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

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

Cosine Function

Cubic Function Activity

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Functions Involving Square Roots

General Form of a Rational Function

Linear Functions

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Point-Slope Form of a Line - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Sine Function

Slope-Intercept Form of a Line - Activity A

Tangent Function

Unit Circle

Using Tables, Rules and Graphs

4.3.C: Modeling

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)

Cosine Function

Exponential Functions - Activity A

Linear Functions

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

Sine Function

Sine, Cosine and Tangent

Tangent Function

Translating and Scaling Sine and Cosine Functions - Activity A

4.3.C.1.2: Direct and inverse variation

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

4.3.C.1.3: Absolute value

Inequalities Involving Absolute Values

Quadratic and Absolute Value Functions

4.3.C.1.4: Expressions, equations and inequalities

4.3.C.1.5: Same function can model variety of phenomena

Exponential Growth and Decay - Activity B

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.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

4.3.C.3: Convert recursive formulas to linear or exponential functions (e.g., Tower of Hanoi and doubling).

Arithmetic Sequences

Arithmetic and Geometric Sequences

Exponential Functions - Activity A

Geometric Sequences

Linear Functions

4.3.D: Procedures

4.3.D.1: Evaluate and simplify expressions.

4.3.D.1.1: Add and subtract polynomials

Addition of Polynomials - Activity A

4.3.D.1.2: Multiply a polynomial by a monomial or binomial

Polynomials and Linear Factors

4.3.D.1.3: Divide a polynomial by a monomial

Dividing Exponential Expressions

Dividing Polynomials Using Synthetic Division

4.3.D.2: Select and use appropriate methods to solve equations and inequalities.

4.3.D.2.1: Linear equations – algebraically

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Equations By Graphing Each Side

Solving Two-Step Equations

4.3.D.2.2: Quadratic equations – factoring (when the coefficient of x² is 1) and using the quadratic formula

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

4.3.D.2.3: All types of equations using graphing, computer, and graphing calculator techniques

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

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.

Geometric Probability - Activity A

Probability Simulations

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.

Describing Data Using Statistics

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: Probability

4.4.B.2: Use concepts and formulas of area to calculate geometric probabilities.

Geometric Probability - Activity A

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.

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

4.4.B.4: Determine probabilities in complex situations.

4.4.B.4.3: Dependent and independent events

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

4.4.B.5: Estimate probabilities and make predictions based on experimental and theoretical probabilities.

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Polling: City

Probability Simulations

Theoretical and Experimental Probability

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).

Geometric Probability - Activity A

Polling: City

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).

Binomial Probabilities

Permutations and Combinations

4.4.C.4: Recognize and explain relationships involving combinations and Pascal’s Triangle, and apply those methods to situations involving probability.

Binomial Probabilities

Permutations and Combinations

Correlation last revised: 11/13/2008