4.1: All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways.

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: All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

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

Triangle Inequalities

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

Finding Patterns

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

Slope - Activity B

4.2.C.1.4: Lines with the same slope are parallel

Slope - Activity B

4.2.C.1.5: Lines that are perpendicular have slopes whose product is –1

Slope - Activity B

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

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: All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

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

Slope - Activity B

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

Using Algebraic Equations

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)

Simple and 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 ax²+bx+c
Modeling the Factorization of x²+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: All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.

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)

Polling: Neighborhood

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

Correlation

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