L1: Based on their knowledge of the properties of arithmetic, students understand and reason about numbers, number systems, and the relationships between them. They represent quantitative relationships using mathematical symbols, and interpret relationships from those representations.

L1.1: Number Systems and Number Sense

L1.1.2: Explain why the multiplicative inverse of a number has the same sign as the number, while the additive inverse of a number has the opposite sign.

Solving Formulas for any Variable

L1.1.6: Explain the importance of the irrational numbers square root of 2 and square root of 3 in basic right triangle trigonometry; the importance of π because of its role in circle relationships; and the role of e in applications such as continuously compounded interest.

Square Roots

L1.2: Representations and Relationships

L1.2.3: Use vectors to represent quantities that have magnitude and direction; interpret direction and magnitude of a vector numerically, and calculate the sum and difference of two vectors.

Vectors

L1.2.4: Organize and summarize a data set in a table, plot, chart, or spreadsheet; find patterns in a display of data; understand and critique data displays in the media.

Arithmetic and Geometric Sequences
Describing Data Using Statistics
Geometric Sequences

L1.3: Counting and Probabilistic Reasoning

L1.3.1: Describe, explain, and apply various counting techniques (e.g., finding the number of different 4-letter passwords; permutations; and combinations); relate combinations to Pascal’s triangle; know when to use each technique.

Binomial Probabilities
Permutations
Permutations and Combinations

L1.3.2: Define and interpret commonly used expressions of probability (e.g., chances of an event, likelihood, odds).

Estimating Population Size
Geometric Probability - Activity A

L1.3.3: Recognize and explain common probability misconceptions such as “hot streaks” and “being due.”

Binomial Probabilities

L2: Students calculate fluently, estimate proficiently, and describe and use algorithms in appropriate situations (e.g., approximating solutions to equations.) They understand the basic ideas of iteration and algorithms.

L2.1: Calculation Using Real and Complex Numbers

L2.1.1: Explain the meaning and uses of weighted averages (e.g., GNP, consumer price index, grade point average).

Describing Data Using Statistics
Mean, Median and Mode

L2.1.4: Know that the complex number i is one of two solutions to x² = -1.

Points in the Complex Plane - Activity A

L2.1.5: Add, subtract, and multiply complex numbers; use conjugates to simplify quotients of complex numbers.

Points in the Complex Plane - Activity A

L2.2: Sequences and Iteration

L2.2.1: Find the nth term in arithmetic, geometric, or other simple sequences.

Arithmetic Sequences

L2.2.2: Compute sums of finite arithmetic and geometric sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

L2.2.3: Use iterative processes in such examples as computing compound interest or applying approximation procedures.

Simple and Compound Interest

L4: Students understand mathematical reasoning as being grounded in logic and proof and can distinguish mathematical arguments from other types of arguments. They can interpret arguments made about quantitative situations in the popular media. Students know the language and laws of logic and can apply them in both mathematical and everyday settings. They write proofs using direct and indirect methods and use counterexamples appropriately to show that statements are false.

L4.1: Mathematical Reasoning

L4.1.1: Distinguish between inductive and deductive reasoning, identifying and providing examples of each.

Biconditional Statement
Conditional Statement

L4.1.2: Differentiate between statistical arguments (statements verified empirically using examples or data) and logical arguments based on the rules of logic.

Biconditional Statement
Conditional Statement

L4.2: Language and Laws of Logic

L4.2.1: Know and use the terms of basic logic (e.g., proposition, negation, truth and falsity, implication, if and only if, contrapositive, and converse).

Conditional Statement

L4.2.3: Use the quantifiers “THERE EXISTS” and “ALL” in mathematical and everyday settings and know how to logically negate statements involving them.

Biconditional Statement
Conditional Statement

L4.3: Proof

L4.3.3: Explain the difference between a necessary and a sufficient condition within the statement of a theorem; determine the correct conclusions based on interpreting a theorem in which necessary or sufficient conditions in the theorem or hypothesis are satisfied.

Conditional Statement

A1: Students recognize, construct, interpret, and evaluate expressions. They fluently transform symbolic expressions into equivalent forms. They determine appropriate techniques for solving each type of equation, inequality, or system of equations, apply the techniques correctly to solve, justify the steps in the solutions, and draw conclusions from the solutions. They know and apply common formulas.

A1.1: Construction, Interpretation, and Manipulation of Expressions (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric)

A1.1.1: Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables.

Using Algebraic Equations
Using Algebraic Expressions

A1.1.3: Factor algebraic expressions using, for example, greatest common factor, grouping, and the special product identities (e.g., differences of squares and cubes).

Factoring Special Products
Modeling the Factorization of x²+bx+c

A1.1.4: Add, subtract, multiply, and simplify polynomials and rational expressions (e.g., multiply (x – 1) (1 – x² + 3); simplify (9x - x³)/(x + 3))

Addition of Polynomials - Activity A

A1.1.5: Divide a polynomial by a monomial.

Dividing Exponential Expressions
Dividing Polynomials Using Synthetic Division

A1.1.6: Transform exponential and logarithmic expressions into equivalent forms using the properties of exponents and logarithms including the inverse relationship between exponents and logarithms.

Dividing Exponential Expressions

A1.2: Solutions of Equations and Inequalities (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric)

A1.2.1: Write equations and inequalities with one or two variables to represent mathematical or applied situations, and solve.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
Using Algebraic Equations

A1.2.2: Associate a given equation with a function whose zeros are the solutions of the equation.

Linear Functions
Polynomials and Linear Factors
Using Algebraic Equations

A1.2.3: Solve (and justify steps in the solutions) linear and quadratic equations and inequalities, including systems of up to three linear equations with three unknowns; apply the quadratic formula appropriately.

Quadratic Inequalities - Activity A
Roots of a Quadratic
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

A1.2.4: Solve absolute value equations and inequalities, (e.g. solve l x - 3 l ≤ 6), and justify steps in the solution.

Inequalities Involving Absolute Values
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

A1.2.6: Solve power equations (e.g., (x + 1)³ = 8) and equations including radical expressions (e.g., the square root of (3x - 7) = 7), justify steps in the solution, and explain how extraneous solutions may arise.

Simplifying Radicals - Activity A

A1.2.8: Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable, and justify steps in the solution.

Solving Formulas for any Variable

A1.2.9: Know common formulas (e.g., slope, distance between two points, quadratic formula, compound interest, distance = velocity x time), and apply appropriately in contextual situations.

Distance Formula - Activity A
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Roots of a Quadratic
Slope - Activity B

A2: Students understand functions, their representations, and their attributes. They perform transformations, combine and compose functions, and find inverses. Students classify functions and know the characteristics of each family. They work with functions with real coefficients fluently.

A2.1: Definitions, Representations, and Attributes of Functions

A2.1.1: Recognize whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a function; and identify its domain and range.

Functions Involving Square Roots
Introduction to Functions
Linear Functions
Logarithmic Functions: Translating and Scaling

A2.1.2: Read, interpret, and use function notation, and evaluate a function at a value in its domain.

Logarithmic Functions: Translating and Scaling

A2.1.3: Represent functions in symbols, graphs, tables, diagrams, or words, and translate among representations.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Introduction to Functions
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Polynomials and Linear Factors
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
Using Algebraic Equations
Using Algebraic Expressions
Using Tables, Rules and Graphs

A2.1.4: Recognize that functions may be defined by different expressions over different intervals of their domains; such functions are piecewise-defined (e.g., absolute value and greatest integer functions).

Quadratic and Absolute Value Functions

A2.1.5: Recognize that functions may be defined recursively, and compute values of and graph simple recursively defined functions (e.g., f(0) = 5, and f(n) = f(n-1) + 2).

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A2.1.6: Identify the zeros of a function and the intervals where the values of a function are positive or negative, and describe the behavior of a function, as x approaches postive or negative infinity, given the symbolic and graphical representations.

Polynomials and Linear Factors

A2.1.7: Identify and interpret the key features of a function from its graph or its formula(e), (e.g. slope, intercept(s), asymptote(s), maximum and minimum value(s), symmetry, average rate of change over an interval, and periodicity).

Cosine Function
Cubic Function Activity
Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Fourth-Degree Polynomials - Activity A
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Sine Function
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Using Tables, Rules and Graphs

A2.2: Operations and Transformations

A2.2.1: Combine functions by addition, subtraction, multiplication, and division.

Addition and Subtraction of Polynomials

A2.2.2: Apply given transformations (e.g., vertical or horizontal shifts, stretching or shrinking, or reflections about the x- and y-axes) to basic functions, and represent symbolically.

Absolute Value with Linear Functions - Activity B
Logarithmic Functions: Translating and Scaling
Reflections of a Linear Function
Reflections of a Quadratic Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

A2.2.3: Recognize whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs (e.g., f(x) = x³ and g(x) = x to the 1/3 power).

Introduction to Functions

A2.3: Families of Functions (linear, quadratic, polynomial, rational, power, exponential, logarithmic, and trigonometric)

A2.3.1: Identify a function as a member of a family of functions based on its symbolic, or graphical representation; recognize that different families of functions have different asymptotic behavior at infinity, and describe these behaviors.

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
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Roots of a Quadratic
Sine Function
Slope-Intercept Form of a Line - Activity A
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle
Using Algebraic Equations

A2.3.2: Describe the tabular pattern associated with functions having constant rate of change (linear); or variable rates of change.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

A2.4: Lines and Linear Functions

A2.4.1: Write the symbolic forms of linear functions (standard [i.e., Ax + By = C, where B ≠ 0], point-slope, and slope-intercept) given appropriate information, and convert between forms.

Defining a Line with Two Points
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Using Tables, Rules and Graphs

A2.4.2: Graph lines (including those of the form x = h and y = k) given appropriate information.

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

A2.4.3: Relate the coefficients in a linear function to the slope and x- and y-intercepts of its graph.

Linear Functions
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Using Tables, Rules and Graphs

A2.4.4: Find an equation of the line parallel or perpendicular to given line, through a given point; understand and use the facts that non-vertical parallel lines have equal slopes, and that non-vertical perpendicular lines have slopes that multiply to give -1.

Point-Slope Form of a Line - Activity A
Slope - Activity B

A2.5: Exponential and Logarithmic Functions

A2.5.1: Write the symbolic form and sketch the graph of an exponential function given appropriate information. (e.g., given an initial value of 4 and a rate of growth of 1.5, write f(x) = 4 (1.5) to the x power).

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B

A2.5.2: Interpret the symbolic forms and recognize the graphs of exponential and logarithmic functions (e.g., f(x) = 10 to the x power, f(x) = log x, f(x) = e to the x power, f(x) = ln x); recognize the logarithmic function as the inverse of the exponential function.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

A2.5.3: Apply properties of exponential and logarithmic functions (e.g., a ot the x+y power = a to the x power times a to the y power; log(ab)= log a + log b).

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

A2.5.4: Understand and use the fact that the base of an exponential function determines whether the function increases or decreases and understand how the base affects the rate of growth or decay.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life

A2.5.5: Relate exponential and logarithmic functions to real phenomena, including half-life and doubling time.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

A2.6: Quadratic Functions

A2.6.1: Write the symbolic form and sketch the graph of a quadratic function given appropriate information (e.g., vertex, intercepts, etc.).

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

A2.6.2: Identify the elements of a parabola (vertex, axis of symmetry, direction of opening) given its symbolic form or its graph, and relate these elements to the coefficient(s) of the symbolic form of the function.

Holiday Snowflake Designer
Parabolas - Activity A
Quadratics in Factored Form

A2.6.3: Convert quadratic functions from standard to vertex form by completing the square.

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

A2.6.4: Relate the number of real solutions of a quadratic equation to the graph of the associated quadratic function.

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

A2.6.5: Express quadratic functions in vertex form to identify their maxima or minima, and in factored form to identify their zeros.

Modeling the Factorization of x²+bx+c
Parabolas - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

A2.7: Power Functions (including roots, cubics, quartics, etc.)

A2.7.2: Express direct and inverse relationships as functions (e.g., y = kx to the n power and y = kx to the -n power, n > 0) and recognize their characteristics (e.g., in y = x³, note that doubling x results in multiplying y by a factor of 8).

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

A2.7.3: Analyze the graphs of power functions, noting reflectional or rotational symmetry.

Holiday Snowflake Designer

A2.8: Polynomial Functions

A2.8.1: Write the symbolic form and sketch the graph of simple polynomial functions.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors

A2.8.2: Understand the effects of degree, leading coefficient, and number of real zeros on the graphs of polynomial functions of degree greater than 2.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions

A2.8.3: Determine the maximum possible number of zeros of a polynomial function, and understand the relationship between the x-intercepts of the graph and the factored form of the function.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors

A2.9: Rational Functions

A2.9.1: Write the symbolic form and sketch the graph of simple rational functions.

General Form of a Rational Function
Rational Functions

A2.9.2: Analyze graphs of simple rational functions (e.g., f(x) = (2x + 1)/(x - 1); g(x) = x/(x² - 4)) and understand the relationship between the zeros of the numerator and denominator and the function’s intercepts, asymptotes, and domain.

General Form of a Rational Function
Rational Functions

A2.10: Trigonometric Functions

A2.10.1: Use the unit circle to define sine and cosine; approximate values of sine and cosine (e.g., sin 3, or cos 0.5); use sine and cosine to define the remaining trigonometric functions; explain why the trigonometric functions are periodic.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

A2.10.3: Use the unit circle to determine the exact values of sine and cosine, for integer multiples of pi/6 and pi/4.

Cosine Function
Sine Function
Sine, Cosine and Tangent
Tangent Function
Unit Circle

A2.10.4: Graph the sine and cosine functions; analyze graphs by noting domain, range, period, amplitude, and location of maxima and minima.

Cosine Function
Sine Function
Sine, Cosine and Tangent
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

A2.10.5: Graph transformations of basic trigonometric functions (involving changes in period, amplitude, and midline) and understand the relationship between constants in the formula and the transformed graph.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

A3: Students construct or select a function to model a real-world situation in order to solve applied problems. They draw on their knowledge of families of functions to do so.

A3.1: Models of Real-world Situations Using Families of Functions.

A3.1.1: Identify the family of function best suited for modeling a given real-world situation (e.g., quadratic functions for motion of an object under the force of gravity; exponential functions for compound interest; trigonometric functions for periodic phenomena. In the example above, recognize that the appropriate general function is exponential (P = P0a to the t power)

Cosine Function
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Simple and Compound Interest
Sine Function
Tangent Function

A3.1.2: Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers. In the example above, substitute the given values P0 = 300 and a = 1.02 to obtain P = 300(1.02) to the t power.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Tangent Function
Using Algebraic Equations

G1: Students represent basic geometric figures, polygons, and conic sections and apply their definitions and properties in solving problems and justifying arguments, including constructions and representations in the coordinate plane. Students represent three-dimensional figures, understand the concepts of volume and surface area, and use them to solve problems. They know and apply properties of common three-dimensional figures.

G1.1: Lines and Angles; Basic Euclidean and Coordinate Geometry

G1.1.1: Solve multi-step problems and construct proofs involving vertical angles, linear pairs of angles supplementary angles, complementary angles, and right angles.

Biconditional Statement
Conditional Statement
Investigating Angle Theorems - Activity A

G1.1.2: Solve multi-step problems and construct proofs involving corresponding angles, alternate interior angles, alternate exterior angles, and same-side (consecutive) interior angles.

Biconditional Statement
Conditional Statement
Investigating Angle Theorems - Activity A

G1.1.3: Perform and justify constructions, including midpoint of a line segment and bisector of an angle, using straightedge and compass.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

G1.1.4: Given a line and a point, construct a line through the point that is parallel to the original line using straightedge and compass; given a line and a point, construct a line through the point that is perpendicular to the original line; justify the steps of the constructions.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

G1.2: Triangles and Their Properties

G1.2.1: Prove that the angle sum of a triangle is 180° and that an exterior angle of a triangle is the sum of the two remote interior angles.

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

G1.2.2: Construct and justify arguments and solve multi-step problems involving angle measure, side length, perimeter, and area of all types of triangles.

Classifying Triangles
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B

G1.2.3: Know a proof of the Pythagorean Theorem and use the Pythagorean Theorem and its converse to solve multi-step problems.

Biconditional Statement
Conditional Statement
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

G1.2.5: Solve multi-step problems and construct proofs about the properties of medians, altitudes, and perpendicular bisectors to the sides of a triangle, and the angle bisectors of a triangle; using a straightedge and compass, construct these lines.

Biconditional Statement
Concurrent Lines, Medians, and Altitudes
Conditional Statement
Constructing Congruent Segments and Angles

G1.3: Triangles and Trigonometry

G1.3.1: Define the sine, cosine, and tangent of acute angles in a right triangle as ratios of sides; solve problems about angles, side lengths, or areas using trigonometric ratios in right triangles.

Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
Unit Circle

G1.3.3: Determine the exact values of sine, cosine, and tangent for 0°, 30°, 45°, 60°, and their integer multiples, and apply in various contexts.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle

G1.4: Quadrilaterals and Their Properties

G1.4.1: Solve multi-step problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids.

Area of Parallelograms - Activity A
Biconditional Statement
Conditional Statement
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area
Special Quadrilaterals

G1.4.2: Solve multi-step problems and construct proofs involving quadrilaterals (e.g., prove that the diagonals of a rhombus are perpendicular) using Euclidean methods or coordinate geometry.

Biconditional Statement
Classifying Quadrilaterals - Activity B
Conditional Statement
Special Quadrilaterals

G1.4.3: Describe and justify hierarchical relationships among quadrilaterals, (e.g. every rectangle is a parallelogram).

Area of Parallelograms - Activity A
Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals

G1.4.4: Prove theorems about the interior and exterior angle sums of a quadrilateral.

Parallelogram Conditions
Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

G1.5: Other Polygons and Their Properties

G1.5.1: Know and use subdivision or circumscription methods to find areas of polygons (e.g., regular octagon, non-regular pentagon).

Area of Parallelograms - Activity A

G1.5.2: Know, justify, and use formulas for the perimeter and area of a regular n-gon and formulas to find interior and exterior angles of a regular n-gon and their sums.

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B
Polygon Angle Sum - Activity A
Rectangle: Perimeter and Area
Triangle Angle Sum - Activity A

G1.6: Circles and Their Properties

G1.6.1: Solve multi-step problems involving circumference and area of circles.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

G1.6.2: Solve problems and justify arguments about chords (e.g., if a line through the center of a circle is perpendicular to a chord, it bisects the chord) and lines tangent to circles (e.g., a line tangent to a circle is perpendicular to the radius drawn to the point of tangency).

Chords and Arcs

G1.6.3: Solve problems and justify arguments about central angles, inscribed angles and triangles in circles.

Chords and Arcs
Inscribing Angles

G.1.7.1: Find an equation of a circle given its center and radius; given the equation of a circle, find its center and radius.

Circles

G1.7: Conic Sections and Their Properties

G1.7.2: Identify and distinguish among geometric representations of parabolas, circles, ellipses, and hyperbolas; describe their symmetries, and explain how they are related to cones.

Circles
Ellipse - Activity A
Holiday Snowflake Designer
Hyperbola - Activity A
Parabolas - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones

G1.7.3: Graph ellipses and hyperbolas with axes parallel to the x- and y-axes, given equations.

Ellipse - Activity A
Hyperbola - Activity A

G1.8: Three- Dimensional Figures

G1.8.1: Solve multi-step problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

G1.8.2: Identify symmetries of pyramids, prisms, cones, cylinders, hemispheres, and spheres.

Holiday Snowflake Designer
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones

G2: Students use and justify relationships between lines, angles, area and volume formulas, and 2- and 3-dimensional representations. They solve problems and provide proofs about congruence and similarity.

G2.1: Relationships Between Area and Volume Formulas

G2.1.1: Know and demonstrate the relationships between the area formula of a triangle, the area formula of a parallelogram, and the area formula of a trapezoid.

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B

G2.1.2: Know and demonstrate the relationships between the area formulas of various quadrilaterals (e.g., explain how to find the area of a trapezoid based on the areas of parallelograms and triangles).

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B

G2.1.3: Know and use the relationship between the volumes of pyramids and prisms (of equal base and height) and cones and cylinders (of equal base and height).

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

G2.2: Relationships Between Two-dimensional and Three-dimensional Representations

G2.2.1: Identify or sketch a possible 3-dimensional figure, given 2-dimensional views (e.g., nets, multiple views); create a 2-dimensional representation of a 3-dimensional figure.

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

G2.2.2: Identify or sketch cross-sections of 3-dimensional figures; identify or sketch solids formed by revolving 2-dimensional figures around lines.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

G2.3: Congruence and Similarity

G2.3.1: Prove that triangles are congruent using the SSS, SAS, ASA, and AAS criteria, and for right triangles, the hypotenuse-leg criterion.

Congruence in Right Triangles
Proving Triangles Congruent

G2.3.2: Use theorems about congruent triangles to prove additional theorems and solve problems, with and without use of coordinates.

Congruence in Right Triangles
Proving Triangles Congruent

G2.3.3: Prove that triangles are similar by using SSS, SAS, and AA conditions for similarity.

Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

G2.3.4: Use theorems about similar triangles to solve problems with and without use of coordinates.

Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

G2.3.5: Know and apply the theorem stating that the effect of a scale factor of k relating one two dimensional figure to another or one three dimensional figure to another, on the length, area, and volume of the figures is to multiply each by k, k², and k³, respectively.

Area of Parallelograms - Activity A
Perimeters and Areas of Similar Figures
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Similar Figures - Activity A
Similar Polygons

G3: Students will solve problems about distance-preserving transformations and shape-preserving transformations. The transformations will be described synthetically and, in simple cases, by analytic expressions in coordinates.

G3.1: Distance-preserving Transformations: Isometries

G3.1.1: Define reflection, rotation, translation, and glide reflection and find the image of a figure under a given isometry.

Reflections
Rotations, Reflections and Translations
Translations

G3.1.2: Given two figures that are images of each other under an isometry, find the isometry and describe it completely.

Dilations
Reflections
Rotations, Reflections and Translations

G3.1.3: Find the image of a figure under the composition of two or more isometries, and determine whether the resulting figure is a reflection, rotation, translation, or glide reflection image of the original figure.

Reflections
Rotations, Reflections and Translations
Translations

G3.2: Shape-preserving Transformations: Dilations and Isometries

G3.2.1: Know the definition of dilation, and find the image of a figure under a given dilation.

Dilations

G3.2.2: Given two figures that are images of each other under some dilation, identify the center and magnitude of the dilation.

Dilations

S1: Students plot and analyze univariate data by considering the shape of distributions and analyzing outliers; they find and interpret commonly-used measures of center and variation; and they explain and use properties of the normal distribution.

S1.1: Producing and Interpreting Plots

S1.1.1: Construct and interpret dot plots, histograms, relative frequency histograms, bar graphs, basic control charts, and box plots with appropriate labels and scales; determine which kinds of plots are appropriate for different types of data; compare data sets and interpret differences based on graphs and summary statistics.

Box-and-Whisker Plots
Histograms
Line Plots
Populations and Samples

S1.1.2: Given a distribution of a variable in a data set, describe its shape, including symmetry or skewness, and state how the shape is related to measures of center (mean and median) and measures of variation (range and standard deviation) with particular attention to the effects of outliers on these measures.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

S1.2: Measures of Center and Variation

S1.2.1: Calculate and interpret measures of center including: mean, median, and mode; explain uses, advantages and disadvantages of each measure given a particular set of data and its context.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

S1.2.2: Estimate the position of the mean, median, and mode in both symmetrical and skewed distributions, and from a frequency distribution or histogram.

Describing Data Using Statistics
Histograms
Line Plots
Mean, Median and Mode
Populations and Samples

S1.2.3: Compute and interpret measures of variation, including percentiles, quartiles, interquartile range, variance, and standard deviation.

Box-and-Whisker Plots

S1.3: The Normal Distribution

S1.3.2: Describe characteristics of the normal distribution, including its shape and the relationships among its mean, median, and mode.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

S2: Students plot and interpret bivariate data by constructing scatterplots, recognizing linear and nonlinear patterns, and interpreting correlation coefficients; they fit and interpret regression models, using technology as appropriate.

S2.1: Scatterplots and Correlation

S2.1.1: Construct a scatterplot for a bivariate data set with appropriate labels and scales.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

S2.1.2: Given a scatterplot, identify patterns, clusters, and outliers; recognize no correlation, weak correlation, and strong correlation.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

S2.1.3: Estimate and interpret Pearson’s correlation coefficient for a scatterplot of a bivariate data set; recognize that correlation measures the strength of linear association.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

S2.1.4: Differentiate between correlation and causation; know that a strong correlation does not imply a cause-and-effect relationship; recognize the role of lurking variables in correlation.

Correlation
Solving Using Trend Lines

S2.2: Linear Regression

S2.2.1: For bivariate data which appear to form a linear pattern, find the least squares regression line by estimating visually and by calculating the equation of the regression line; interpret the slope of the equation for a regression line.

Correlation
Slope - Activity B
Solving Using Trend Lines

S2.2.2: Use the equation of the least squares regression line to make appropriate predictions.

Correlation
Solving Using Trend Lines

S3: Students understand and apply sampling and various sampling methods, examine surveys and experiments, identify bias in methods of conducting surveys, and learn strategies to minimize bias. They understand basic principles of good experimental design.

S3.1: Data Collection and Analysis

S3.1.2: Identify possible sources of bias in data collection and sampling methods and simple experiments; describe how such bias can be reduced and controlled by random sampling; explain the impact of such bias on conclusions made from analysis of the data; and know the effect of replication on the precision of estimates.

Polling: Neighborhood

S3.1.3: Distinguish between an observational study and an experimental study, and identify, in context, the conclusions that can be drawn from each.

Geometric Probability - Activity A
Probability Simulations

S4: Students understand probability and find probabilities in various situations, including those involving compound events, using diagrams, tables, geometric models and counting strategies; they apply the concepts of probability to make decisions.

S4.1: Probability

S4.1.1: Understand and construct sample spaces in simple situations (e.g., tossing two coins, rolling two number cubes and summing the results).

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

S4.1.2: Define mutually exclusive events, independent events, dependent events, compound events, complementary events and conditional probabilities; and use the definitions to compute probabilities.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

S4.2: Application and Representation

S4.2.1: Compute probabilities of events using tree diagrams, formulas for combinations and permutations, Venn diagrams, or other counting techniques.

Binomial Probabilities
Permutations
Permutations and Combinations

S4.2.2: Apply probability concepts to practical situations, in such settings as finance, health, ecology, or epidemiology, to make informed decisions.

Binomial Probabilities
Geometric Probability - Activity A