### 1: Number, Number Sense and Operations

#### 1.C: Apply properties of operations and the real number system, and justify when they hold for a set of numbers.

1.C.1: Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication.

#### 1.E: Compare, order and determine equivalent forms of real numbers.

1.E.2: Compare, order and determine equivalent forms for rational and irrational numbers.

#### 1.I: Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.

1.I.5: Estimate the solutions for problem situations involving square and cube roots.

### 2: Measurement

#### 2.D: Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates.

2.D.1: Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second.

2.D.3: Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively.

2.D.5: Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system.

### 4: Patterns, Functions and Algebra

#### 4.A: Generalize and explain patterns and sequences in order to find the next term and the nth term.

4.A.2: Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.

#### 4.B: Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations.

4.B.1: Define function with ordered pairs in which each domain element is assigned exactly one range element.

4.B.3: Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.

#### 4.C: Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.

4.C.2: Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.

#### 4.D: Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.

4.D.7: Use formulas to solve problems involving exponential growth and decay.

4.D.11: Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only).

#### 4.E: Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.

4.E.4: Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words.

4.E.5: Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum.

#### 4.F: Solve and graph linear equations and inequalities.

4.F.8: Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point.

#### 4.G: Solve quadratic equations with real roots by graphing, formula and factoring.

4.G.10: Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology.

#### 4.H: Solve systems of linear equations involving two variables graphically and symbolically.

4.H.9: Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.

#### 4.I: Model and solve problem situations involving direct and inverse variation.

4.I.13: Model and solve problems involving direct and inverse variation using proportional reasoning.

4.I.14: Describe the relationship between slope and the graph of a direct variation and inverse variation.

### 5: Data Analysis and Probability

#### 5.A: Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.

5.A.2: Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit.

5.A.3: Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers.

#### 5.F: Construct convincing arguments based on analysis of data and interpretation of graphs.

5.F.6: Make inferences about relationships in bivariate data, and recognize the difference between evidence of relationship (correlation) and causation.

#### 5.G: Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.

5.G.5: Describe characteristics and limitations of sampling methods, and analyze the effects of random versus biased sampling; e.g., determine and justify whether the sample is likely to be representative of the population.

#### 5.H: Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes.

5.H.7: Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations.

#### 5.I: Design an experiment to test a theoretical probability, and record and explain results.

5.I.8: Describe, create and analyze a sample space and use it to calculate probability.

#### 5.J: Compute probabilities of compound events, independent events, and simple dependent events.

5.J.9: Identify situations involving independent and dependent events, and explain differences between, and common misconceptions about probabilities associated with those events.

#### 5.K: Make predictions based on theoretical probabilities and experimental results.

5.K.10: Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events.

### 6: Mathematical Processes

#### 6.F: Use precise mathematical language and notations to represent problem situations and mathematical ideas.

Correlation last revised: 8/29/2016

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