#### S.1: Number Sense, Properties, and Operations

S.1.GLE.1: The complex number system includes real numbers and imaginary numbers

S.1.GLE.1.IQ: Inquiry Questions:

S.1.GLE.1.IQ.2: Are there more complex numbers than real numbers?

S.1.GLE.1.IQ.4: Why are complex numbers important?

S.1.GLE.1.N: Nature of Mathematics:

S.1.GLE.1.N.2: Mathematics involves making and testing conjectures, generalizing results, and making connections among ideas, strategies, and solutions.

S.1.GLE.2: Quantitative reasoning is used to make sense of quantities and their relationships in problem situations

S.1.GLE.2.RA: Relevance and Application:

S.1.GLE.2.RA.2: The reading, interpreting, and writing of numbers in scientific notation with and without technology is used extensively in the natural sciences such as representing large or small quantities such as speed of light, distance to other planets, distance between stars, the diameter of a cell, and size of a micro?organism.

S.1.GLE.2.RA.3: Fluency with computation and estimation allows individuals to analyze aspects of personal finance, such as calculating a monthly budget, estimating the amount left in a checking account, making informed purchase decisions, and computing a probable paycheck given a wage (or salary), tax tables, and other deduction schedules.

S.1.GLE.2.N: Nature of Mathematics:

S.1.GLE.2.N.1: Using mathematics to solve a problem requires choosing what mathematics to use; making simplifying assumptions, estimates, or approximations; computing; and checking to see whether the solution makes sense.

S.1.GLE.2.N.2: Mathematicians reason abstractly and quantitatively.

#### S.2: Patterns, Functions, and Algebraic Structures

S.2.GLE.1: Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables

S.2.GLE.1.IQ: Inquiry Questions:

S.2.GLE.1.IQ.1: Why are relations and functions represented in multiple ways?

S.2.GLE.1.IQ.2: How can a table, graph, and function notation be used to explain how one function family is different from and/or similar to another?

S.2.GLE.1.IQ.3: What is an inverse?

S.2.GLE.1.IQ.4: How is ?inverse function? most likely related to addition and subtraction being inverse operations and to multiplication and division being inverse operations?

S.2.GLE.1.IQ.6: How could you visualize a function with four variables, such as x² + y² + z² + w² = 1?

S.2.GLE.1.IQ.8: How do symbolic transformations affect an equation, inequality, or expression?

S.2.GLE.1.RA: Relevance and Application:

S.2.GLE.1.RA.1: Knowledge of how to interpret rate of change of a function allows investigation of rate of return and time on the value of investments.

S.2.GLE.1.RA.3: The ability to analyze a function for the intercepts, asymptotes, domain, range, and local and global behavior provides insights into the situations modeled by the function. For example, epidemiologists could compare the rate of flu infection among people who received flu shots to the rate of flu infection among people who did not receive a flu shot to gain insight into the effectiveness of the flu shot.

S.2.GLE.1.RA.6: Comprehension of slope, intercepts, and common forms of linear equations allows easy retrieval of information from linear models such as rate of growth or decrease, an initial charge for services, speed of an object, or the beginning balance of an account.

S.2.GLE.1.N: Nature of Mathematics:

S.2.GLE.1.N.1: Mathematicians use multiple representations of functions to explore the properties of functions and the properties of families of functions.

S.2.GLE.1.N.2: Mathematicians model with mathematics.

S.2.GLE.2: Quantitative relationships in the real world can be modeled and solved using functions

S.2.GLE.2.IQ: Inquiry Questions:

S.2.GLE.2.IQ.2: What phenomena can be modeled with particular functions?

S.2.GLE.2.IQ.3: Which financial applications can be modeled with exponential functions? Linear functions?

S.2.GLE.2.IQ.4: What elementary function or functions best represent a given scatter plot of two-variable data?

S.2.GLE.2.RA: Relevance and Application:

S.2.GLE.2.RA.1: The understanding of the qualitative behavior of functions allows interpretation of the qualitative behavior of systems modeled by functions such as time-distance, population growth, decay, heat transfer, and temperature of the ocean versus depth.

S.2.GLE.2.RA.2: The knowledge of how functions model real-world phenomena allows exploration and improved understanding of complex systems such as how population growth may affect the environment, how interest rates or inflation affect a personal budget, how stopping distance is related to reaction time and velocity, and how volume and temperature of a gas are related.

S.2.GLE.2.N: Nature of Mathematics:

S.2.GLE.2.N.1: Mathematicians use their knowledge of functions to create accurate models of complex systems.

S.2.GLE.2.N.3: Mathematicians reason abstractly and quantitatively.

S.2.GLE.2.N.4: Mathematicians construct viable arguments and critique the reasoning of others.

S.2.GLE.2.N.5: Mathematicians model with mathematics.

S.2.GLE.3: Expressions can be represented in multiple, equivalent forms

S.2.GLE.3.IQ: Inquiry Questions:

S.2.GLE.3.IQ.1: When is it appropriate to simplify expressions?

S.2.GLE.3.IQ.2: The ancient Greeks multiplied binomials and found the roots of quadratic equations without algebraic notation. How can this be done?

S.2.GLE.3.RA: Relevance and Application:

S.2.GLE.3.RA.2: The manipulation of expressions and solving formulas are techniques used to solve problems in geometry such as finding the area of a circle, determining the volume of a sphere, calculating the surface area of a prism, and applying the Pythagorean Theorem.

S.2.GLE.3.N: Nature of Mathematics:

S.2.GLE.3.N.1: Mathematicians abstract a problem by representing it as an equation. They travel between the concrete problem and the abstraction to gain insights and find solutions.

S.2.GLE.3.N.2: Mathematicians construct viable arguments and critique the reasoning of others.

S.2.GLE.3.N.3: Mathematicians model with mathematics.

S.2.GLE.4: Solutions to equations, inequalities and systems of equations are found using a variety of tools

S.2.GLE.4.IQ: Inquiry Questions:

S.2.GLE.4.IQ.1: What are some similarities in solving all types of equations?

S.2.GLE.4.IQ.2: Why do different types of equations require different types of solution processes?

S.2.GLE.4.IQ.4: How are order of operations and operational relationships important when solving multivariable equations?

S.2.GLE.4.RA: Relevance and Application:

S.2.GLE.4.RA.1: Linear programming allows representation of the constraints in a real-world situation identification of a feasible region and determination of the maximum or minimum value such as to optimize profit, or to minimize expense.

S.2.GLE.4.RA.2: Effective use of graphing technology helps to find solutions to equations or systems of equations.

S.2.GLE.4.N: Nature of Mathematics:

S.2.GLE.4.N.3: Mathematicians construct viable arguments and critique the reasoning of others.

#### S.3: Data Analysis, Statistics, and Probability

S.3.GLE.1: Visual displays and summary statistics condense the information in data sets into usable knowledge

S.3.GLE.1.IQ: Inquiry Questions:

S.3.GLE.1.IQ.1: What makes data meaningful or actionable?

S.3.GLE.1.RA: Relevance and Application:

S.3.GLE.1.RA.1: Facility with data organization, summary, and display allows the sharing of data efficiently and collaboratively to answer important questions such as is the climate changing, how do people think about ballot initiatives in the next election, or is there a connection between cancers in a community?

S.3.GLE.1.N: Nature of Mathematics:

S.3.GLE.1.N.1: Mathematicians create visual and numerical representations of data to reveal relationships and meaning hidden in the raw data.

S.3.GLE.1.N.2: Mathematicians reason abstractly and quantitatively.

S.3.GLE.1.N.3: Mathematicians model with mathematics.

S.3.GLE.2: Statistical methods take variability into account supporting informed decisions making through quantitative studies designed to answer specific questions

S.3.GLE.2.IQ: Inquiry Questions:

S.3.GLE.2.IQ.3: When should sampling be used? When is sampling better than using a census?

S.3.GLE.2.IQ.4: Can the practical significance of a given study matter more than statistical significance? Why is it important to know the difference?

S.3.GLE.2.IQ.5: Why is the margin of error in a study important?

S.3.GLE.2.N: Nature of Mathematics:

S.3.GLE.2.N.2: Mathematicians are skeptical of apparent trends. They use their understanding of randomness to distinguish meaningful trends from random occurrences.

S.3.GLE.2.N.3: Mathematicians construct viable arguments and critique the reasoning of others.

S.3.GLE.2.N.4: Mathematicians model with mathematics.

S.3.GLE.3: Probability models outcomes for situations in which there is inherent randomness

S.3.GLE.3.IQ: Inquiry Questions:

S.3.GLE.3.IQ.1: Can probability be used to model all types of uncertain situations? For example, can the probability that the 50th president of the United States will be female be determined?

S.3.GLE.3.IQ.2: How and why are simulations used to determine probability when the theoretical probability is unknown?

S.3.GLE.3.RA: Relevance and Application:

S.3.GLE.3.RA.1: Comprehension of probability allows informed decision-making, such as whether the cost of insurance is less than the expected cost of illness, when the deductible on car insurance is optimal, whether gambling pays in the long run, or whether an extended warranty justifies the cost.

S.3.GLE.3.RA.2: Probability is used in a wide variety of disciplines including physics, biology, engineering, finance, and law. For example, employment discrimination cases often present probability calculations to support a claim.

S.3.GLE.3.N: Nature of Mathematics:

S.3.GLE.3.N.2: Mathematicians explore randomness and chance through probability.

S.3.GLE.3.N.3: Mathematicians construct viable arguments and critique the reasoning of others.

S.3.GLE.3.N.4: Mathematicians model with mathematics.

#### S.4: Shape, Dimension, and Geometric Relationships

S.4.GLE.1: Objects in the plane can be transformed, and those transformations can be described and analyzed mathematically

S.4.GLE.1.IQ: Inquiry Questions:

S.4.GLE.1.IQ.3: What does it mean for two things to be the same? Are there different degrees of "sameness?"

S.4.GLE.1.RA: Relevance and Application:

S.4.GLE.1.RA.1: Comprehension of transformations aids with innovation and creation in the areas of computer graphics and animation.

S.4.GLE.1.N: Nature of Mathematics:

S.4.GLE.1.N.2: Mathematicians construct viable arguments and critique the reasoning of others.

S.4.GLE.2: Concepts of similarity are foundational to geometry and its applications

S.4.GLE.2.IQ: Inquiry Questions:

S.4.GLE.2.IQ.4: Do perfect circles naturally occur in the physical world?

S.4.GLE.2.N: Nature of Mathematics:

S.4.GLE.2.N.2: Mathematicians construct viable arguments and critique the reasoning of others.

S.4.GLE.3: Objects in the plane can be described and analyzed algebraically

S.4.GLE.3.IQ: Inquiry Questions:

S.4.GLE.3.IQ.1: What does it mean for two lines to be parallel?

S.4.GLE.3.RA: Relevance and Application:

S.4.GLE.3.RA.1: Knowledge of right triangle trigonometry allows modeling and application of angle and distance relationships such as surveying land boundaries, shadow problems, angles in a truss, and the design of structures.

S.4.GLE.3.N: Nature of Mathematics:

S.4.GLE.3.N.2: Mathematicians make sense of problems and persevere in solving them.

S.4.GLE.3.N.3: Mathematicians construct viable arguments and critique the reasoning of others.

S.4.GLE.4: Attributes of two- and three-dimensional objects are measurable and can be quantified

S.4.GLE.4.IQ: Inquiry Questions:

S.4.GLE.4.IQ.1: How might surface area and volume be used to explain biological differences in animals?

S.4.GLE.4.IQ.3: How can surface area be minimized while maximizing volume?

S.4.GLE.4.RA: Relevance and Application:

S.4.GLE.4.RA.1: Understanding areas and volume enables design and building. For example, a container that maximizes volume and minimizes surface area will reduce costs and increase efficiency. Understanding area helps to decorate a room, or create a blueprint for a new building.

S.4.GLE.4.N: Nature of Mathematics:

S.4.GLE.4.N.1: Mathematicians use geometry to model the physical world. Studying properties and relationships of geometric objects provides insights in to the physical world that would otherwise be hidden.

S.4.GLE.4.N.2: Mathematicians make sense of problems and persevere in solving them.

S.4.GLE.4.N.3: Mathematicians construct viable arguments and critique the reasoning of others.

S.4.GLE.4.N.4: Mathematicians model with mathematics.

S.4.GLE.5: Objects in the real world can be modeled using geometric concepts

S.4.GLE.5.N: Nature of Mathematics:

S.4.GLE.5.N.2: Mathematicians make sense of problems and persevere in solving them.

S.4.GLE.5.N.3: Mathematicians reason abstractly and quantitatively.

Correlation last revised: 9/24/2019

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