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.

4.1.12 A: Number Sense

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

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

4.1.12 B: Numerical Operations

4.1.12 B.1: Extend understanding and use of operations to real numbers and algebraic procedures.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Multiplying Exponential Expressions

4.1.12 B.2: Develop, apply, and explain methods for solving problems involving rational and negative exponents.

Exponents and Power Rules

4.1.12 B.3: Perform operations on matrices.

4.1.12 B.3.1: Addition and subtraction

Translations

4.1.12 B.4: Understand and apply the laws of exponents to simplify expressions involving numbers raised to powers.

Dividing Exponential Expressions
Exponents and Power Rules
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.

4.2.12 A: Geometric Properties

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

4.2.12 A.3.1: Parallel lines - transversal, alternate interior angles, corresponding angles

Constructing Congruent Segments and Angles
Similar Figures
Triangle Angle Sum

4.2.12 A.3.2: Triangles

4.2.12 A.3.2.a: Conditions for congruence

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Proving Triangles Congruent

4.2.12 A.3.2.c: Triangle Inequality

Triangle Inequalities

4.2.12 A.3.2.d: Special right triangles

Cosine Function
Sine Function
Tangent Function

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

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

4.2.12 A.3.4: Circles - arcs, central and inscribed angles, chords, tangents

Chords and Arcs
Inscribed Angles

4.2.12 A.4: Use reasoning and some form of proof to verify or refute conjectures and theorems.

4.2.12 A.4.1: Verification or refutation of proposed proofs

Biconditional Statements

4.2.12 A.4.2: Simple proofs involving congruent triangles

Congruence in Right Triangles
Proving Triangles Congruent

4.2.12 A.5: Perform basic geometric constructions using a variety of methods (e.g., straightedge and compass, patty/tracing paper, or technology).

4.2.12 A.5.1: Perpendicular bisector of a line segment

Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

4.2.12 A.5.2: Bisector of an angle

Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

4.2.12 A.5.3: Perpendicular or parallel lines

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Parallel, Intersecting, and Skew Lines

4.2.12 B: Transforming Shapes

4.2.12 B.1: Determine, describe, and draw the effect of a transformation, or a sequence of transformations, on a geometric or algebraic representation, and, conversely, determine whether and how one representation can be transformed to another by a transformation or a sequence of transformations.

Dilations
Reflections
Rotations, Reflections, and Translations
Translations

4.2.12 C: Coordinate Geometry

4.2.12 C.1: Use coordinate geometry to represent and verify properties of lines and line segments.

4.2.12 C.1.1: Distance between two points

Points in the Coordinate Plane

4.2.12 C.1.3: Finding the intersection of two lines

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)

4.2.12 C.2: Show position and represent motion in the coordinate plane using vectors.

4.2.12 C.2.1: Addition and subtraction of vectors

Adding Vectors
Vectors

4.2.12 C.3: Find an equation of a circle given its center and radius and, given an equation of a circle in standard form, find its center and radius.

Circles

4.2.12 E: Measuring Geometric Objects

4.2.12 E.1: Use techniques of indirect measurement to represent and solve problems.

4.2.12 E.1.1: Similar triangles

Similarity in Right Triangles

4.2.12 E.1.2: Pythagorean theorem

Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Tangent Function

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

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine
Tangent Function

4.2.12 E.2: Use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of 3D figures.

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

Area of Triangles

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

4.3.12 A: Patterns

4.3.12 A.1: Use models and algebraic formulas to represent and analyze sequences and series.

4.3.12 A.1.1: Explicit formulas for nth terms

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

4.3.12 B: Functions and Relationships

4.3.12 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
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

4.3.12 B.2: Analyze and explain the general properties and behavior of functions or relations, using algebraic and graphing techniques.

4.3.12 B.2.1: Slope of a line

Cat and Mouse (Modeling with Linear Systems)
Introduction to Functions
Point-Slope Form of a Line
Slope

4.3.12 B.2.2: Domain and range

Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Logarithmic Functions
Radical Functions

4.3.12 B.2.3: Intercepts

Cat and Mouse (Modeling with Linear Systems)
Logarithmic Functions
Points, Lines, and Equations
Polynomials and Linear Factors
Roots of a Quadratic
Slope-Intercept Form of a Line

4.3.12 B.2.7: Solutions of systems of equations

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

4.3.12 B.2.8: Solutions of systems of linear inequalities using graphing techniques

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

4.3.12 B.2.9: Rates of change

Cat and Mouse (Modeling with Linear Systems)
Distance-Time and Velocity-Time Graphs
Translating and Scaling Functions

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

4.3.12 B.3.1: Translations, reflections, dilations

Absolute Value with Linear Functions
Introduction to Exponential Functions
Translating and Scaling Sine and Cosine Functions
Translations

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

Absolute Value with Linear Functions
Translating and Scaling Functions
Zap It! Game

4.3.12 B.3.3: Using graphing calculators or computers for more complex functions

Absolute Value with Linear Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations

4.3.12 B.4: Understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions.

4.3.12 B.4.1: Linear vs. non-linear

Linear Functions

4.3.12 C: Modeling

4.3.12 C.1: Use functions to model real-world phenomena and solve problems that involve varying quantities.

4.3.12 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)

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
Compound Interest
Cosine Function
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Sine Function
Slope-Intercept Form of a Line
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

4.3.12 C.1.2: Direct and inverse variation

Determining a Spring Constant
Direct and Inverse Variation

4.3.12 C.1.3: Absolute value

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Rational Numbers, Opposites, and Absolute Values

4.3.12 C.1.4: Expressions, equations and inequalities

Absolute Value Equations and Inequalities
Compound Interest
Linear Functions
Linear Inequalities in Two Variables
Solving Equations on the Number Line
Using Algebraic Equations

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

Determining a Spring Constant
Estimating Population Size

4.3.12 C.1.7: Applications in mathematics, biology, and economics (including compound interest)

Compound Interest
Estimating Population Size
Unit Conversions

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

Arithmetic Sequences
Geometric Sequences

4.3.12 D: Procedures

4.3.12 D.1: Evaluate and simplify expressions.

4.3.12 D.1.1: Add and subtract polynomials

Addition and Subtraction of Functions
Addition of Polynomials

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

Factoring Special Products

4.3.12 D.1.3: Divide a polynomial by a monomial

Dividing Polynomials Using Synthetic Division

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

4.3.12 D.2.1: Linear equations and inequalities - algebraically

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Systems of Linear Inequalities (Slope-intercept form)

4.3.12 D.2.2: Quadratic equations - factoring (including trinomials when the coefficient of x2 is 1) and using the quadratic formula

Modeling the Factorization of x²+bx+c
Roots of a Quadratic

4.3.12 D.2.3: Literal equations

Area of Triangles
Solving Formulas for any Variable

4.3.12 D.2.4: All types of equations and inequalities using graphing, computer, and graphing calculator techniques

Absolute Value Equations and Inequalities
Compound Inequalities
Linear Inequalities in Two Variables
Point-Slope Form of a Line
Quadratic Inequalities
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form)

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.

4.4.12 A: Data Analysis

4.4.12 A.1: Use surveys and sampling techniques to generate data and draw conclusions about large groups.

4.4.12 A.1.1: Advantages/disadvantages of sample selection methods (e.g., convenience sampling, responses to survey, random sampling)

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Populations and Samples

4.4.12 A.2: Evaluate the use of data in real-world contexts.

4.4.12 A.2.1: Accuracy and reasonableness of conclusions drawn

Box-and-Whisker Plots

4.4.12 A.2.2: Correlation vs. causation

Correlation

4.4.12 A.2.4: Statistical claims based on sampling

Polling: City

4.4.12 A.3: Design a statistical experiment, conduct the experiment, and interpret and communicate the outcome.

Polling: Neighborhood

4.4.12 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.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

4.4.12 A.5: Analyze data using technology, and use statistical terminology to describe conclusions.

4.4.12 A.5.1: Measures of dispersion: variance, standard deviation, outliers

Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Real-Time Histogram

4.4.12 A.5.2: Correlation coefficient

Correlation

4.4.12 A.5.3: Normal distribution (e.g., approximately 95% of the sample lies between two standard deviations on either side of the mean)

Polling: City

4.4.12 A.6: Distinguish between randomized experiments and observational studies.

Polling: Neighborhood

4.4.12 B: Probability

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

Geometric Probability

4.4.12 B.3: Model situations involving probability with simulations (using spinners, dice, calculators and computers) and theoretical models, and solve problems using these models.

Binomial Probabilities
Geometric Probability
Theoretical and Experimental Probability

4.4.12 B.4: Determine probabilities in complex situations.

4.4.12 B.4.1: Conditional events

Independent and Dependent Events

4.4.12 B.4.3: Dependent and independent events

Binomial Probabilities
Independent and Dependent Events

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

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

4.4.12 B.6: Understand and use the "law of large numbers" (that experimental results tend to approach theoretical probabilities after a large number of trials).

Theoretical and Experimental Probability

4.4.12 C: Discrete Mathematics-Systematic Listing and Counting

4.4.12 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

4.4.12 C.2: Apply the multiplication rule of counting in complex situations, recognize the difference between situations with replacement and without replacement, and recognize the difference between ordered and unordered counting situations.

Binomial Probabilities
Permutations and Combinations

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

Binomial Probabilities