IM1.1: Algebra and Functions

IM1.1.1: Determine whether a relation represented by a table, graph, words or equation is a function or not a function. Translate among tables, graphs, words and equations.

Introduction to Functions
Linear Functions

IM1.1.2: Identify the domain and range of relations represented by tables, graphs, words and equations.

Introduction to Functions
Using Algebraic Equations
Using Algebraic Expressions

IM1.1.3: Translate among various representations of linear functions like tables, graphs, words and equations.

Arithmetic Sequences
Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations
Using Algebraic Expressions
Using Tables, Rules and Graphs

IM1.1.4: Graph linear equations and show that they have constant rates of change.

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

IM1.1.5: Determine the slope, x-intercept and y-intercept of a line given its graph, its equation or two points on the line. Then determine the equation of a line given sufficient information.

Defining a Line with Two Points
Function Machines 2 (Functions, Tables, and Graphs)
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

IM1.1.6: Write, interpret and translate among equivalent forms of equations for linear functions (i.e., slope-intercept, point-slope and standard). Recognize that equivalent forms reveal more or less information about a given situation.

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

IM1.1.7: Solve problems that can be modeled using linear equations and inequalities, interpret the solutions and determine whether the solutions are reasonable.

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

IM1.1.8: Graph a linear inequality in two variables.

Linear Inequalities in Two Variables - Activity A

IM1.1.9: Understand the relationship between a solution of a pair of linear equations in two variables and the graphs of the corresponding lines. Solve pairs of linear equations in two variables by graphing, substitution or elimination.

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

IM1.1.10: Graph with and without technology the solution set for a pair of linear inequalities in two variables. Use the graph to find the solution set.

Inequalities Involving Absolute Values
Modeling Linear Systems - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

IM1.1.11: Solve problems that can be modeled using pairs of linear equations containing two variables, interpret the solutions and determine whether the solutions are reasonable.

Modeling Linear Systems - Activity A

IM1.1.12: Graph quadratic functions.

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
Roots of a Quadratic

IM1.1.13: Solve quadratic equations in the real number system with real number solutions by factoring, by completing the square and by using the quadratic formula.

Factoring Special Products
Roots of a Quadratic

IM1.1.15: Analyze and describe the relationships among the solutions of a quadratic equation, the zeros of a quadratic function, the x-intercepts of a graph of a quadratic function and the factors of a quadratic expression.

Polynomials and Linear Factors
Quadratics in Factored Form
Roots of a Quadratic

IM1.1.16: Sketch and interpret linear and non-linear graphs representing given situations and identify independent and dependent variables.

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Modeling Linear Systems - Activity A
Using Tables, Rules and Graphs

IM1.1.19: Simplify radical expressions involving square roots.

Simplifying Radicals - Activity A

IM1.1.20: Solve equations that contain radical expressions on only one side of the equation and identify extraneous roots when they occur.

Simplifying Radicals - Activity A

IM1.2: Geometry and Measurement

IM1.2.1: Find the length of line segments in one- or two-dimensional coordinate systems, the slopes of line segments in two-dimensional coordinate systems, and the point that is a given fractional distance from one end of the segment to another.

Slope - Activity B
Distance Formula - Activity A

IM1.2.2: Justifying the method used, find and use the sum of the measures of interior and exterior angles of convex polygons.

Triangle Angle Sum - Activity A

IM1.2.4: Solve problems involving congruent and similar polygons.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

IM1.2.5: Predict and describe the results of translations, reflections and rotations on polygons. Describe a motion or series of motions that will show that two shapes are congruent.

Reflections
Rotations, Reflections and Translations
Translations

IM1.2.6: Deduce formulas relating lengths and sides, perimeters, and areas of regular polygons. Understand how limiting cases of such formulas lead to expressions for the circumference and area of a circle.

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

IM1.2.9: Develop simple geometric proofs (i.e., direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry) using two-column, paragraphs and flow charts formats. Provide reasons for each statement in the proofs.

Biconditional Statement
Conditional Statement
Simplifying Trigonometric Expressions

IM1.3: Data Analysis and Probability

IM1.3.1: Organize and display data using appropriate methods to detect patterns and departures from patterns. Summarize the data using measures of center (i.e., mean, median) and spread (i.e., range, percentiles, variance, standard deviation). Compare data sets using graphs and summary statistics.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode
Populations and Samples
Solving Using Trend Lines

IM1.3.2: Distinguish between random and non-random sampling methods, identify possible sources of bias in sampling, describe how such bias can be controlled and reduced, evaluate the characteristics of a good survey and well-designed experiment, design simple experiments or investigations to collect data to answer questions of interest and make inferences from sample results.

Polling: Neighborhood

IM1.4: Discrete Mathematics

IM1.4.3: Define arithmetic and geometric sequences recursively.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

IM1.4.4: Determine the number of ways events can occur using permutations, combinations and the Fundamental Counting Principle.

Binomial Probabilities
Permutations
Permutations and Combinations