### N: Number Sense, Properties, and Operations

#### N.1: The complex number system includes real numbers and imaginary numbers

N.1.a: Show that between any two rational numbers there are an infinite number of rational numbers, and that between any two irrational numbers there are also an infinite number of irrational numbers

#### N.2: Formulate, represent, and use algorithms with real numbers flexibly, accurately, and efficiently

N.2.b: Use technology to perform operations (addition, subtraction, multiplication, and division) on numbers written in scientific notation

#### N.3: Systematic counting techniques are used to describe and solve problems

N.3.a: Use combinatorics (Fundamental Counting Principle, permutations and combinations) to solve problems in real-world contexts

### P: Patterns, Functions, and Algebraic Structures

#### P.1: Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables

P.1.a: Determine when a relation is a function using a table, a graph, or an equation

P.1.b: Demonstrate the relationship between all representations of linear functions using point-slope, slope-intercept, and standard form of a line

P.1.c: Represent linear, quadratic, absolute value, power, exponential, logarithmic, rational, trigonometric (sine and cosine), and step functions in a table, graph, and equation and convert from one representation to another

P.1.d: Determine the inverse (expressed graphically or in tabular form) of a function from a graph or table

P.1.e: Categorize sequences as arithmetic, geometric, or neither and develop formulas for the general terms related to arithmetic and geometric sequences

#### P.2: Graphs and tables are used to describe the qualitative behavior of common types of functions

P.2.a: Evaluate a function at a given point in its domain given an equation (including function notation), a table, and a graph

P.2.b: Identify the domain and range of a function given an equation (including function notation), a table, and a graph

P.2.c: Identify intercepts, zeros (or roots), maxima, minima, and intervals of increase and decrease, and asymptotes of a function given an equation (including function notation), a table, and a graph

P.2.d: Make qualitative statements about the rate of change of a function, based on its graph or table

#### P.3: Parameters influence the shape of the graphs of functions

P.3.a: Apply transformations (translation, reflection, dilation) to a parent function, f(x)

P.3.b: Interpret the results of these transformations verbally, graphically, and symbolically

#### P.4: Expressions, equations, and inequalities can be expressed in multiple, equivalent forms

P.4.a: Perform and justify steps in generating equivalent expressions by identifying properties used including the commutative, associative, inverse, identity, and distributive properties

P.4.c: Solve equations for one variable in terms of the others

#### P.5: Solutions to equations, inequalities and systems of equations are found using a variety of tools

P.5.a: Find solutions to quadratic and cubic equations and inequalities by using appropriate algebraic methods such as factoring, completing the square, graphing or using the quadratic formula

P.5.b: Find solutions to equations involving power, exponential, rational and radical functions

P.5.c: Solve systems of linear equations and inequalities with two variables

#### P.6: Quantitative relationships in the real world can be modeled and solved using functions

P.6.a: Represent, solve, and interpret problems in various contexts using linear, quadratic, and exponential function

P.6.b: Represent, solve, and interpret problems involving direct and inverse variations and a combination of direct and inverse variation

P.6.c: Analyze the impact of interest rates on a personal financial plan

### D: Data Analysis, Statistics, and Probability

#### D.1: Statistical methods take variability into account, supporting informed decision-making through quantitative studies designed to answer specific questions

D.1.a: Formulate appropriate research questions that can be answered with statistical analysis

D.1.b: Determine appropriate data collection methods to answer a research question

D.1.c: Explain how data might be analyzed to provide answers to a research question

#### D.2: The design of an experiment or sample survey is of critical importance to analyzing the data and drawing conclusions

D.2.a: Identify the characteristics of a well-designed and well-conducted survey

D.2.b: Identify the characteristics of a well-designed and well-conducted experiment

#### D.3: Visual displays and summary statistics condense the information in data sets into usable knowledge

D.3.a: Identify and choose appropriate ways to summarize numerical or categorical data using tables, graphical displays, and numerical summary statistics (describing shape, center and spread) and accounting for outliers when appropriate

D.3.b: Define and explain how sampling distributions (developed through simulation) are used to describe the sample-to-sample variability of sample statistics

D.3.d: When the relationship between two numerical variables is reasonably linear, apply the least-squares criterion for line fitting, use Pearson's correlation coefficient as a measure of strength, and interpret the slope and y-intercept in the context of the problem

#### D.4: Randomness is the foundation for using statistics to draw conclusions when testing a claim or estimating plausible values for a population characteristic

D.4.a: Define and explain the meaning of significance (both practical and statistical)

D.4.c: Determine the margin of error associated with an estimate of a population characteristic

#### D.5: Probability models outcomes for situations in which there is inherent randomness, quantifying the degree of certainty in terms of relative frequency of occurrence

D.5.b: Apply and solve problems using the concepts of independence and conditional probability

D.5.d: Evaluate and interpret probabilities using a normal distribution

D.5.e: Find and interpret the expected value and standard deviation of a discrete random variable X

### S: Shape, Dimension, and Geometric Relationships

#### S.1: Attributes of two- and three-dimensional objects are measurable and can be quantified

S.1.b: Justify, interpret, and apply the use of formulas for the surface area, and volume of cones, pyramids, and spheres including real-world situations

S.1.c: Solve for unknown quantities in relationships involving perimeter, area, surface area, and volume

#### S.2: Objects in the plane and their parts, attributes, and measurements can be analyzed deductively

S.2.a: Classify polygons according to their similarities and differences

S.2.c: Know and apply properties of angles including corresponding, exterior, interior, vertical, complementary, and supplementary angles to solve problems. Justify the results using two-column proofs, paragraph proofs, flow charts, or illustrations

#### S.3: Objects in the plane can be transformed, and those transformations can be described and analyzed mathematically

S.3.b: Represent transformations (reflection, translation, rotation, and dilation) using Cartesian coordinates

S.3.c: Develop arguments to establish what remains invariant and what changes after a transformation (reflection, translation, rotation, and dilations). Justify these conjectures using two-column proofs, paragraph proofs, flow charts, and/or illustrations

#### S.4: Right triangles are central to geometry and its applications

S.4.a: Apply right triangle trigonometry (sine, cosine, and tangent) to find indirect measures of lengths and angles

S.4.b: Apply the Pythagorean theorem and its converse to solve real-world problems

S.4.c: Determine the midpoint of a line segment and the distance between two points in the Cartesian coordinate plane

Correlation last revised: 5/9/2018

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