MA1N1: Students will represent and operate with complex numbers.

MA1N1.a: Write square roots of negative numbers in imaginary form.

Square Roots

MA1N1.b: Write complex numbers in the form a + bi.

Points in the Complex Plane - Activity A

MA1A1: Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MA1A1.b: Graph the basic functions f(x) = x to the power n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
General Form of a Rational Function
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Radical Functions
Rational Functions
Roots of a Quadratic

MA1A1.c: Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

Function Machines 2 (Functions, Tables, and Graphs)
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

MA1A1.d: Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

Functions Involving Square Roots
Parabolas - Activity A
Polynomials and Linear Factors

MA1A1.e: Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Fourth-Degree Polynomials - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Functions Involving Square Roots
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Sine Function
Tangent Function
Using Tables, Rules and Graphs

MA1A1.f: Recognize sequences as functions with domains that are sets of whole numbers.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences

MA1A1.g: Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Linear Functions
Quadratics in Factored Form
Radical Functions
Roots of a Quadratic
Slope - Activity B

MA1A1.h: Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

Cosine Function
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Sine Function
Tangent Function

MA1A1.i: Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side

MA1A2: Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MA1A2.a: Simplify algebraic and numeric expressions involving square root.

Operations with Radical Expressions
Simplifying Radicals - Activity A
Square Roots

MA1A2.b: Perform operations with square roots.

Operations with Radical Expressions
Simplifying Radicals - Activity A
Square Roots

MA1A2.c: Add, subtract, multiply, and divide polynomials.

Addition of Polynomials - Activity A
Dividing Polynomials Using Synthetic Division

MA1A2.e: Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below. (x + y)² = x² + 2xy + y²; (x ? y)² = x² ? 2xy + y²; (x + y)(x ? y) = x² ? y²; (x + a)(x + b) = x² + (a + b)x + ab; (x + y)³ = x³ + 3x²y + 3xy² + y³; (x ? y)³ = x³ ? 3x²y + 3xy² ? y³

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MA1A2.f: Use area and volume models for polynomial arithmetic.

Addition of Polynomials - Activity A

MA1A3: Students will analyze quadratic functions in the forms f(x) = ax² + bx + c and f(x) = a(x ? h)² + k.

MA1A3.a: Convert between standard and vertex form.

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

MA1A3.b: Graph quadratic functions as transformations of the function f(x) = x².

Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Reflections of a Quadratic Function
Roots of a Quadratic
Translating and Scaling Functions

MA1A3.c: Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

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

MA1A3.d: Explore arithmetic series and various ways of computing their sums.

Arithmetic Sequences
Arithmetic and Geometric Sequences

MA1A3.e: Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Quadratics in Factored Form
Roots of a Quadratic

MA1A4: Students will solve quadratic equations and inequalities in one variable.

MA1A4.b: Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Roots of a Quadratic

MA1A4.c: Analyze the nature of roots using technology and using the discriminant.

Roots of a Quadratic

MA1A4.d: Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

Linear Inequalities in Two Variables - Activity A
Quadratic Inequalities - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MA1A5: Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MA1A5.a: Write absolute value functions as piecewise functions.

Quadratic and Absolute Value Functions

MA1A5.b: Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

Polynomials and Linear Factors

MA1A5.c: Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MA1G1: Students will investigate properties of geometric figures in the coordinate plane.

MA1G1.a: Determine the distance between two points.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

MA1G1.b: Determine the distance between a point and a line.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

MA1G1.d: Understand the distance formula as an application of the Pythagorean theorem.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

MA1G3: Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MA1G3.a: Determine the sum of interior and exterior angles in a polygon.

Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

MA1G3.b: Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

Triangle Inequalities

MA1G3.c: Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

Congruence in Right Triangles
Proving Triangles Congruent

MA1G3.d: Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

MA1G3.e: Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

Concurrent Lines, Medians, and Altitudes

MA1G4: Students will understand the properties of circles.

MA1G4.a: Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

Chords and Arcs

MA1G4.b: Understand and use properties of central, inscribed, and related angles.

Chords and Arcs
Inscribing Angles

MA1G4.c: Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

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

MA1D1: Students will determine the number of outcomes related to a given event.

MA1D1.b: Calculate and use simple permutations and combinations.

Binomial Probabilities
Permutations
Permutations and Combinations

MA1D2: Students will use the basic laws of probability.

MA1D2.b: Find the probabilities of dependent events.

Compound Independent and Dependent Events

MA1D3: Students will relate samples to a population.

MA1D3.a: Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

Box-and-Whisker Plots
Line Plots
Mean, Median and Mode
Populations and Samples

MA1D3.b: Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

Line Plots
Mean, Median and Mode
Polling: City

MA1D3.c: Understand that a random sample is used to improve the chance of selecting a representative sample.

Polling: Neighborhood

MA1D4: Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

Line Plots

MA1D5: Students will determine an algebraic model to quantify the association between two quantitative variables.

MA1D5.a: Gather and plot data that can be modeled with linear and quadratic functions.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Quadratics in Factored Form
Roots of a Quadratic