#### 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.

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

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

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

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.

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.

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

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

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.

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.

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.

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.

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.

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

IM1.1.19: Simplify radical expressions involving square roots.

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

#### 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.

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

IM1.2.4: Solve problems involving congruent and 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.

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.

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.

#### 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.

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.

#### IM1.4: Discrete Mathematics

IM1.4.3: Define arithmetic and geometric sequences recursively.

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

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.