M3.1: Solving problems

M3.1.A: Select and justify functions and equations to model and solve problems.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations on the Number Line

M3.1.B: Solve problems that can be represented by systems of equations and inequalities.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

M3.1.D: Solve problems that can be represented by exponential and logarithmic functions and equations.

Compound Interest
Exponential Functions
Introduction to Exponential Functions

M3.1.E: Solve problems that can be represented by inverse variations of the forms f(x) = a/x + b, f(x) = a/x² + b, and f(x) = a/(bx+c).

Direct and Inverse Variation

M3.2: Transformations and functions

M3.2.A: Sketch results of transformations and compositions of transformations for a given two-dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axes or the line y = x.

Dilations
Rotations, Reflections, and Translations
Translations

M3.2.B: Determine and apply properties of transformations.

Circles
Dilations
Reflections
Rotations, Reflections, and Translations
Translations

M3.2.D: Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.

Holiday Snowflake Designer

M3.2.E: Construct new functions using the transformations f(x - h), f(x) + k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s).

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Exponential Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

M3.3: Functions and modeling

M3.3.A: Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.

Exponential Functions
Logarithmic Functions

M3.3.B: Graph an exponential function of the form f(x) = ab to the x power and its inverse logarithmic function.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

M3.3.C: Solve exponential and logarithmic equations.

Exponential Functions

M3.3.D: Plot points, sketch, and describe the graphs of functions of the form f (x) = a times the square root of x - c + d, and solve related equations.

Radical Functions

M3.3.E: Plot points, sketch, and describe the graphs of functions of the form f(x) = a/x² + b and f(x) = a/(bx + c), and solve related equations.

Compound Interest
Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Logarithmic Functions
Rational Functions

M3.3.F: Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.

Graphs of Polynomial Functions
Translating and Scaling Functions

M3.4: Quantifying variability

M3.4.A: Calculate and interpret measures of variability and standard deviation and use these measures and the characteristics of the normal distribution to describe and compare data sets.

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

M3.4.B: Calculate and interpret margin of error and confidence intervals for population proportions.

Polling: City
Polling: Neighborhood

M3.5: Three-dimensional geometry

M3.5.A: Describe the intersections of lines in the plane and in space, of lines and planes, and of planes in space.

Cat and Mouse (Modeling with Linear Systems)
Concurrent Lines, Medians, and Altitudes
Parallel, Intersecting, and Skew Lines
Solving Equations by Graphing Each Side

M3.5.B: Describe prisms, pyramids, parallelepipeds, tetrahedra, and regular polyhedra in terms of their faces, edges, vertices, and properties.

Pyramids and Cones
Surface and Lateral Areas of Pyramids and Cones

M3.5.D: Apply formulas for surface area and volume of three-dimensional figures to solve problems.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

M3.6: Algebraic properties

M3.6.A: Explain how whole, integer, rational, real, and complex numbers are related, and identify the number system(s) within which a given algebraic equation can be solved.

Points in the Complex Plane
Solving Algebraic Equations II
Solving Equations on the Number Line

M3.6.C: Add, subtract, multiply, and divide polynomials.

Addition and Subtraction of Functions
Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c

M3.6.D: Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
Using Algebraic Equations

M3.7: Additional Key Content

M3.7.A: Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles.

Chords and Arcs
Inscribed Angles

M3.7.B: Determine the equation of a circle that is described geometrically in the coordinate plane and, given equations for a circle and a line, determine the coordinates of their intersection(s).

Circles

M3.7.C: Explain and perform constructions related to the circle.

Inscribed Angles