### 1: The student understands and applies the concepts and procedures of mathematics.

#### 1.1: Understand and apply concepts and procedures from number sense.

1.1.1: Understand the concept and symbolic representation of real numbers, including rational exponents.

1.1.1.a: Explain the meaning of the square root of a number, including why negative numbers have no real square roots.

1.1.5: Understand the concept and symbolic representation of rational numbers including absolute values.

1.1.5.d: Perform arithmetic operations with expressions involving absolute value.

1.1.6: Complete multi-step computations of real numbers in all forms, including rational exponents and scientific notation, using order of operations and properties of operations.

1.1.6.a: Compute using rational numbers.

#### 1.2: Understand and apply concepts and procedures from measurement.

1.2.2: Understand and apply rate and other derived units of measure.

1.2.2.a: Use vectors to represent velocity and direction: multiply a vector by a scalar and adds vectors both algebraically and graphically.

1.2.2.b: Solve problems involving rates such as speed, density, population density, or flow rates.

1.2.5: Recognize and apply the basic right triangle trigonometric relationships of sine, cosine, and tangent to solve problems.

1.2.5.a: Use sine, cosine or tangent to find unknown distances and angles.

1.2.5.c: Recognize the dependence of definitions of the trigonometric relations (sine, cosine and tangent) on the properties of similar triangles.

1.2.5.d: Use sine, cosine or tangent in a right triangle to solve problems about measure of angles.

1.2.5.e: Interpret and use the identity sin_(theta)+ cos_(theta) = 1 for angles between 0¡ and 90¡; recognize this identity as a special representation of the Pythagorean Theorem.

#### 1.3: Understand and apply concepts and procedures from geometric sense.

1.3.1: Make and test conjectures about 2-D figures (polygons and circles) and 3-D figures (spheres, right prisms and pyramids, right circular cylinders and cones), or figures constructed from these shapes.

1.3.1.b: Recall and interpret definitions and basic properties of congruent and similar triangles, circles, quadrilaterals, polygons, parallel, perpendicular, and intersecting lines, and associated angle relationships.

1.3.1.c: Analyze properties of circles and spheres.

1.3.2: Use properties of and relationships between 2-D or 3-D figures to draw and justify conclusions about a situation represented with such figures with or without a coordinate system.

1.3.2.a: Inductively generate a conjecture and deductively support it.

1.3.2.b: Apply and justify the applicability of transformations, congruence, similarity, ratios, and proportions in problem-solving situations.

1.3.2.c: Distinguish between area and perimeter of 2-D figures, surface area, and volume of 3-D figures.

1.3.2.d: Calculate the area and perimeter of circles, triangles, quadrilaterals, and regular polygons.

1.3.2.e: Use the Pythagorean Theorem (or distance formula) in 2-D and 3-D situations when appropriate to compute unknown distances.

1.3.2.f: Calculate the volume and surface area of spheres, right rectangular prisms, and right circular cylinders.

1.3.3: Represent the relevant features of a physical situation using 2-D figures with and without a coordinate system.

1.3.3.a: Use basic 2-D figures such as circles or polygons to represent objects essential to a situation.

1.3.3.d: Solve problems involving the coordinate plane such as the distance between two points, the midpoint of a segment, or slopes of perpendicular or parallel lines.

#### 1.4: Understand and apply concepts and procedures from probability and statistics.

1.4.2: Use empirical/ experimental and theoretical probability to investigate, represent, solve, and interpret the solutions to problems involving uncertainty (probability) or counting techniques.

1.4.2.a: Describe and apply the concepts of complementary, mutually exclusive, independent, and compound events.

1.4.2.b: Describe and apply procedures for computing and comparing theoretical probabilities and empirical/experimental results.

1.4.2.c: Describe and apply procedures for counting techniques such as the Fundamental Counting Principle, permutations, and combinations.

1.4.3: Understand and apply the key characteristics of a normal distribution.

1.4.3.a: Know and interpret the key characteristics of a normal distribution such as shape, center (mean), and spread (standard deviation).

1.4.4: Develop and evaluate inferences and predictions that are based on data.

1.4.4.a: Use measures of central tendency (mean, median, mode) and spread (range, quartiles) to summarize data, draw inferences, make predictions, and justify conclusions.

1.4.4.b: Develop and conduct an investigation drawing appropriate conclusions through the use of statistical measures of center, frequency, and spread, combined with graphical displays.

1.4.5: Create and evaluate the suitability of linear models for a data set.

1.4.5.c: Recognize when arguments based on data confuse correlation with causation.

1.4.5.d: Recognize that the correlation coefficient is a number between -1 and +1 that measures the strength of the linear relationship between two variables: usually estimate the correlation coefficient (e.g., positive or negative, closer to 0, 0.5, or 1.0) of a scatter plot.

1.4.6: Develop informative tables, plots, and graphic displays to accurately represent and study data.

1.4.6.a: Use and interprets circle graphs, bar graphs, histograms, box-and-whisker plots, scatter plots, stem and leaf, and line graphs.

1.4.6.b: Analyze data displays to evaluate the reasonableness of claims, reports, studies, and conclusions.

1.4.6.c: Justify the use of appropriate graphical displays to accurately represent and study data.

1.4.6.d: Determine trends, predicted values and possible causes of skewed and clustered distributions.

#### 1.5: Understand and apply concepts and procedures from algebraic sense.

1.5.1: Represent, analyze, and interpret basic functions (linear, quadratic, cubic, exponential, and reciprocal) and piecewise-defined functions (varying over subintervals of the domain) using and translating among words, tables, graphs, and symbols.

1.5.1.a: Evaluate functions to generate a graph.

1.5.1.b: Describe relationships between the algebraic features of a function and the features of its graph and/or its tabular representation.

1.5.1.c: Use simple transformations (horizontal and vertical shifts, reflections about axes, shrinks and stretches to create the graphs of new functions using linear, quadratic, and/ or absolute value functions.

1.5.1.d: Algebraically construct new functions using addition and subtraction (e.g., profit function).

1.5.1.e: Describe whether a relation, given verbal, symbolic, tabular, or graphical form is a function.

1.5.1.f: Identify and analyze the general forms of linear, quadratic, reciprocal (y=k/x), exponential, or trigonometric functions.

1.5.1.g: Identify patterns in the function's rate of change, identifying intervals of increase, decrease, constancy, and, if possible, relate them to the function's description in words or graphically (using graphing calculator).

1.5.1.h: Identify y-intercepts and zeros using symbols, graphs, and tables.

1.5.1.i: Identify extrema and trends using graphs and tables.

1.5.2: Determine an equation or rule for linear and non-linear functions represented in a patterns, tables, graphs, or models.

1.5.2.a: Determine an equation from a set of ordered pairs.

1.5.2.c: Write an equation or rule to describe a sequence.

1.5.2.d: Write an equation for a line given a graph of the line.

1.5.2.e: Write a rule for a recursive geometric pattern.

1.5.2.f: Write an expression, equation, or inequality with two variables representing a linear and/or non-linear model of a real-world problem.

1.5.2.g: Write an equation for a reasonable line to describe a set of bivariate data from a table or scatter plot.

1.5.3: Recognize functional relationships presented in words, tables, graphs and symbols.

1.5.3.a: Recognize whether a relationship given in a symbolic, graphical, or tabular form is a function.

1.5.3.b: Determine the domain of the function.

1.5.3.c: Understand and interpret function notation, particularly as it relates of graphic displays of data.

1.5.4: Recognize and use appropriate concepts, procedures, definitions, and properties to simplify expressions and solve equations.

1.5.4.b: Explain the distinction between expression and equation.

1.5.4.d: Know what it means to have a solution to an equation.

1.5.4.e: Use properties of equality to solve an equation through a series of equivalent equations.

1.5.4.h: Find an equation of a circle given its center and radius and, given an equation of a circle, finds its center and radius.

1.5.5: Combine and simplify algebraic expressions that contain polynomials, rational expressions, radicals, or rational exponents.

1.5.5.a: Find the sum, difference, or product of two polynomials, then simplifies the result.

1.5.5.b: Factor out the greatest common factor from polynomials of any degree.

1.5.5.c: Factor quadratic polynomials with integer coefficients into a product of linear terms.

1.5.5.d: Simplify quotients of polynomials given in factored form, or in a form which can be factored.

1.5.6: Solve various types of equations and inequalities numerically, graphically, and algebraically; interpret solutions algebraically and in the context of the problem; distinguish between exact and approximate answers.

1.5.6.a: Solve linear equations in one variable.

1.5.6.b: Solve linear inequalities in one variable, including those involving "and" and "or."

1.5.6.c: Solve systems of linear equations in two variables.

1.5.6.d: Solve linear inequalities in two variables (graphically only).

1.5.6.f: Use a variety of strategies to solve quadratic equations including those with irrational solutions and recognize when solutions are non-real.

1.5.6.i: Solve rational equations in one variable that can be transformed into an equivalent linear or quadratic equation (limited to monomial or binomial denominators).

1.5.6.j: Solve literal equations (formulas) for a particular variable.

### 2: The student uses mathematics to define and solve problems.

#### 2.2: Construct solutions.

2.2.4: Use logical reasoning and mathematical knowledge to obtain and justify mathematically correct solutions.

2.2.4.f: Use a variety of approaches - inductive and deductive, estimations, generalizations, formal, and/or informal methods of proof - to justify solutions.

### 3: The student uses mathematical reasoning.

#### 3.1: Analyze information.

3.1.1: Model situations and relationships using a variety of basic functions (linear, quadratic, logarithmic, cubic, exponential, and reciprocal) and piecewise-defined functions.

3.1.1.b: Determine and interprets the meaning of rates of change, intercepts, zeros, extrema, and trends.

### 4: The student communicates knowledge and understanding in both everyday and mathematical language.

#### 4.2: Organize, represent, and share information.

4.2.2: Summarize and interpret mathematical information which may be in oral or written formats.

4.2.2.a: Summarize and interprets many different types of graphs.

### 5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-world situations.

#### 5.1: Relate concepts and procedures within mathematics.

5.1.1: Understand the importance of mathematics as a language. (aligns with CRS 3.2) Make connections by using multiple representations--analytic, numeric, and geometric.

5.1.1.b: Use multiple representations to demonstrate understanding of links between math and other disciplines, and real world situations.

5.1.1.d: Transfer mathematical vocabulary, concepts, and procedures to other disciplinary contexts and the real world.

5.1.2: Abstract mathematical models from word problems, geometric problems, and applications.

5.1.2.b: Describe geometric objects and shapes algebraically.

#### 5.3: Relate mathematical concepts and procedures to real-world situations.

5.3.1: Use mathematical ideas and strategies to analyze relationships within mathematics and in other disciplines and real life situations.

5.3.1.b: Recognize patterns and apply mathematical concepts and procedures in other subject areas and real world situations.

Correlation last revised: 1/20/2017

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