MM1A1: Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MM1A1.b: Graph the basic functions f(x) = x to the n power, 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
Translating and Scaling Functions

MM1A1.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)
Functions Involving Square Roots
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

MM1A1.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.

Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A

MM1A1.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
Translating and Scaling Functions
Using Tables, Rules and Graphs

MM1A1.f: Recognize sequences as functions with domains that are whole numbers.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MM1A1.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 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Functions Involving Square Roots
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Roots of a Quadratic
Slope - Activity B

MM1A1.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

MM1A1.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).

Solving Equations By Graphing Each Side

MM1A2: Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MM1A2.a: Simplify algebraic and numeric expressions involving square root.

Operations with Radical Expressions
Simplifying Radicals - Activity A
Square Roots

MM1A2.b: Perform operations with square roots.

Operations with Radical Expressions
Simplifying Radicals - Activity A
Square Roots

MM1A2.c: Add, subtract, multiply, and divide polynomials.

Addition of Polynomials - Activity A
Dividing Polynomials Using Synthetic Division

MM1A2.f: 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

MM1A2.g: Use area and volume models for polynomial arithmetic.

Addition of Polynomials - Activity A

MM1A3: Students will solve simple equations.

MM1A3.a: Solve quadratic equations in the form ax² + bx + c = 0 where a = 1 by using factorization and finding square roots where applicable.

Roots of a Quadratic

MM1A3.b: Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

Square Roots

MM1G1: Students will investigate properties of geometric figures in the coordinate plane.

MM1G1.a: Determine the distance between two points.

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

MM1G1.b: Determine the distance between a point and a line.

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

MM1G1.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

MM1G1.e: Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

Area of Parallelograms - Activity A

MM1G3: Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MM1G3.a: Determine the sum of interior and exterior angles in a polygon.

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

MM1G3.b: Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

Classifying Triangles
Triangle Angle Sum - Activity A
Triangle Inequalities

MM1G3.c: Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

Congruence in Right Triangles
Proving Triangles Congruent

MM1G3.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

MM1G3.e: Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

Concurrent Lines, Medians, and Altitudes

MM1D1: Students will determine the number of outcomes related to a given event.

MM1D1.b: Calculate and use simple permutations and combinations.

Binomial Probabilities
Permutations
Permutations and Combinations

MM1D2: Students will use the basic laws of probability.

MM1D2.b: Find the probabilities of dependent events.

Compound Independent and Dependent Events

MM1D3: Students will relate samples to a population.

MM1D3.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

MM1D3.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

MM1D3.c: Understand that a random sample is used to improve the chance of selecting a representative sample.

Polling: Neighborhood

MM1D4: Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

Line Plots