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

Correlation last revised: 5/18/2018

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