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?

Points in the Complex Plane
Roots of a Quadratic

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

Points in the Complex Plane
Roots of a Quadratic

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.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Biconditional Statements
Geometric Sequences
Unit Conversions

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.

Unit Conversions

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.

Household Energy Usage
Percent of Change

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.

Estimating Population Size

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

Biconditional Statements
Conditional Statements

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?

Introduction to Functions
Linear Functions

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?

Absolute Value with Linear Functions
Exponential Functions
Radical Functions

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

Conditional Statements
Direct and Inverse Variation
Logarithmic Functions
Solving Algebraic Equations I
Solving Two-Step Equations

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?

Logarithmic Functions

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

Linear Functions
Points, Lines, and Equations

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

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations

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.

Cat and Mouse (Modeling with Linear Systems)
Slope

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.

Cat and Mouse (Modeling with Linear Systems)
General Form of a Rational Function
Introduction to Exponential Functions
Rational Functions
Slope-Intercept Form of a Line

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.

Cat and Mouse (Modeling with Linear Systems)
Slope-Intercept Form of a Line

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.

Introduction to Functions

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

Determining a Spring Constant
Estimating Population Size

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?

Linear Functions

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

Compound Interest
Exponential Functions

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

Zap It! Game

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.

General Form of a Rational Function

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.

Linear Functions

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.

Linear Functions

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

Biconditional Statements
Conditional Statements

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

Biconditional Statements

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

Determining a Spring Constant
Estimating Population Size

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?

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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?

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

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.

Area of Triangles
Circles
Circumference and Area of Circles
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones
Tangent Function

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.

Solving Equations on the Number Line
Using Algebraic Equations

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

Biconditional Statements

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

Determining a Spring Constant
Estimating Population Size

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?

Circles

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

Circles
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line

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

Solving Algebraic Equations II

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.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

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

Circles
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

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

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

Biconditional Statements

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?

Box-and-Whisker Plots

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?

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Stem-and-Leaf Plots

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.

Box-and-Whisker Plots
Correlation
Stem-and-Leaf Plots

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

Biconditional Statements
Conditional Statements

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

Determining a Spring Constant
Estimating Population Size

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?

Polling: City
Populations and Samples

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?

Polling: City
Polling: Neighborhood
Populations and Samples

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

Polling: City
Polling: Neighborhood

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.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

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

Biconditional Statements

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

Determining a Spring Constant
Estimating Population Size

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?

Probability Simulations
Theoretical and Experimental Probability

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

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

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.

Household Energy Usage
Percent of Change
Probability Simulations
Theoretical and Experimental Probability

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.

Estimating Population Size

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

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

Probability Simulations
Theoretical and Experimental Probability

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

Biconditional Statements

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

Determining a Spring Constant
Estimating Population Size

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?"

Constructing Congruent Segments and Angles
Solving Algebraic Equations II
Solving Two-Step Equations
Using Algebraic Equations

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.

Rotations, Reflections, and Translations
Translations

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

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

Biconditional Statements

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?

Circles

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

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

Biconditional Statements

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?

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Parallel, Intersecting, and Skew Lines

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.

Sine, Cosine, and Tangent Ratios

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

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

Estimating Population Size

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

Biconditional Statements

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?

Prisms and Cylinders

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

Surface and Lateral Areas of Prisms and Cylinders

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.

Area of Parallelograms
Perimeter and Area of Rectangles
Prisms and Cylinders

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.

Estimating Population Size

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

Estimating Population Size

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

Biconditional Statements

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

Determining a Spring Constant
Estimating Population Size

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.

Estimating Population Size

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

Biconditional Statements
Conditional Statements