Core Curriculum Content Standards

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.

4.1.12 B.3: Perform operations on matrices.

4.1.12 B.3.1: Addition and subtraction

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

4.2.12 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

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

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

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.

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

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

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

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

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 *x*^{2}+*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)

4.4.12 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

4.4.12 A.2.2: Correlation vs. causation

4.4.12 A.2.4: Statistical claims based on sampling

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

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

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)

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

4.4.12 B: Probability

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

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).

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.

Correlation last revised: 5/18/2018

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