### 1: The Real Number System

#### 1: Extend the properties of exponents to rational exponents.

N.RN.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

### 3: The Complex Number System

#### 3: Perform arithmetic operations with complex numbers.

N.CN.1: Know there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 with 𝘢 and 𝘣 real.

N.CN.2: Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

#### 4: Use complex numbers in polynomial identities and equations.

N.CN .7: Solve quadratic equations with real coefficients that have complex solutions.

### 4: Seeing Structure in Expressions

#### 5: Interpret the structure of expressions

A.SSE.2: Use the structure of an expression to identify ways to rewrite it.

#### 6: Write expressions in equivalent forms to solve problems

A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A.SSE.3.c: Use the properties of exponents to transform expressions for exponential functions.

### 5: Arithmetic with Polynomials and Rational Expressions

#### 7: Understand the relationship between zeros and factors of polynomials

A.APR.2: Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹).

A.APR.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

### 6: Creating Equations

#### 10: Create equations that describe numbers or relationships

A.CED.1: Create equations and inequalities in one variable and use them to solve problems.

### 7: Reasoning with Equations and Inequalities

#### 11: Understand solving equations as a process of reasoning and explain the reasoning

A.REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A.REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

#### 12: Solve equations and inequalities in one variable

A.REI.4: Solve equations and inequalities in one variable

A.REI.4.b: Solve quadratic equations by inspection (e.g., for 𝘹² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝘢 ± 𝘣𝘪 for real numbers 𝘢 and 𝘣.

#### 13: Solve systems of equations

A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

#### 14: Represent and solve equations and inequalities graphically

A.REI.11: Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

### 8: Interpreting Functions

#### 16: Interpret functions that arise in applications in terms of the context

F.IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F.IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

#### 17: Analyze functions using different representations

F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.7.c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F.IF.7.e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.8.b: Use the properties of exponents to interpret expressions for exponential functions.

### 9: Building Functions

#### 18: Build a function that models a relationship between two quantities

F.BF.1: Write a function that describes a relationship between two quantities.

F.BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.BF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

#### 19: Build new functions from existing functions

F.BF.3: Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

### 10: Linear, Quadratic, and Exponential Models

#### 20: Construct and compare linear, quadratic, and exponential models and solve problems

F.LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

F.LE.4: For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology.

#### 21: Interpret expressions for functions in terms of the situation they model

F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context.

### 11: Trigonometric Functions

#### 23: Model periodic phenomena with trigonometric functions

F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

### 12: Expressing Geometric Properties with Equations

#### 25: Translate between the geometric description and the equation for a conic section

G.GPE.2: Derive the equation of a parabola given a focus and directrix.

### 13: Interpreting Categorical and Quantitative Data

#### 27: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

S.ID.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S.ID.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

### 14: Making Inferences and Justifying Conclusions

#### 29: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

S.IC.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

S.IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

### 15: Conditional Probability and the Rules of Probability

#### 30: Understand independence and conditional probability and use them to interpret data

S.CP.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

S.CP.2: Understand that two events 𝘈 and 𝘉 are independent if the probability of 𝘈 and 𝘉 occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

S.CP.3: Understand the conditional probability of 𝘈 given 𝘉 as 𝘗(𝘈 and 𝘉)/𝘗(𝘉), and interpret independence of 𝘈 and 𝘉 as saying that the conditional probability of 𝘈 given 𝘉 is the same as the probability of 𝘈, and the conditional probability of 𝘉 given 𝘈 is the same as the probability of 𝘉.

Correlation last revised: 5/8/2018

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