3126.1: Mathematical Processes

3126.1.1: Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.

 Biconditional Statements
 Conditional Statements
 Estimating Population Size

3126.1.2: Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

 Estimating Population Size

3126.1.4: Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.

 Using Algebraic Equations
 Using Algebraic Expressions

3126.1.5: Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.

 Estimating Population Size
 Unit Conversions

3126.1.6: Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.

 Biconditional Statements

3126.2: Number & Operations

3126.2.1: Understand the capabilities and the limitations of calculators and computers in solving problems.

 Estimating Population Size

3126.2.2: Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II

3126.2.4: Develop facility with simplification of complex algebraic expressions involving exponential notation, logarithmic notation, rational notation, and radicals.

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

3126.2.5: Be able to calculate vector arithmetic and vector length.

 Adding Vectors
 Vectors

3126.3: Algebra

3126.3.1: Develop an understanding of functions as elements that can be operated upon to get new functions: addition, subtraction, multiplication, division, and composition of functions.

 Addition and Subtraction of Functions

3126.3.3: Analyze the graph of a function, given either a sketch or a symbolic description.

 Exponential Functions
 Introduction to Exponential Functions
 Points, Lines, and Equations
 Radical Functions
 Translating and Scaling Functions

3126.3.4: Identify or analyze the distinguishing properties of exponential, polynomial, logarithmic, trigonometric, and rational functions from tables, graphs, and equations.

 Compound Interest
 Exponential Functions
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Logarithmic Functions
 Polynomials and Linear Factors
 Quadratics in Factored Form
 Quadratics in Vertex Form
 Rational Functions

3126.3.5: Apply appropriate techniques to analyze mathematical models and functions constructed from verbal information; interpret the solution obtained in written form using appropriate units of measurement.

 Function Machines 3 (Functions and Problem Solving)
 Linear Functions

3126.3.8: Understand the properties of conic sections (whether displayed in equation or graphical form) and apply conic sections to model real-world phenomena.

 Addition and Subtraction of Functions
 Circles
 Ellipses
 Hyperbolas

3126.3.10: Derive and use the formulas for the general term and summation of finite or infinite arithmetic and geometric series, if they exist.

 Arithmetic Sequences
 Geometric Sequences

3126.4: Geometry & Measurement

3126.4.1: Understand basic right triangle trigonometry and use it to solve problems.

 Cosine Function
 Sine Function
 Sine, Cosine, and Tangent Ratios
 Tangent Function

3126.4.4: Apply trigonometric identities to rewrite expressions and solve equations.

 Simplifying Trigonometric Expressions
 Sum and Difference Identities for Sine and Cosine

3126.4.7: Interpret transformations of trigonometric functions.

 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions

3126.4.8: Understand the geometric interpretation of vectors and their use in real life analysis of problems.

 Adding Vectors
 Vectors

3126.4.9: Develop an understanding of the graphic representation of vectors and vector arithmetic.

 Adding Vectors
 Vectors

3126.5: Data Analysis, Statistics, & Probability

3126.5.1: Create scatter plots, analyze patterns and describe relationships that exist in a set of linear and non-linear paired data to model real-world phenomena and make predictions.

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines

3136.1: Mathematical Processes

3136.1.1: Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.

 Biconditional Statements
 Conditional Statements
 Estimating Population Size

3136.1.2: Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

 Estimating Population Size

3136.1.4: Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.

 Using Algebraic Equations
 Using Algebraic Expressions

3136.1.5: Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.

 Estimating Population Size
 Unit Conversions

3136.1.6: Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.

 Biconditional Statements

3136.2: Exploring Data

3136.2.1: Understand histograms, parallel box plots, and scatterplots, and use them to compare display data.

 Box-and-Whisker Plots
 Correlation
 Histograms
 Real-Time Histogram
 Trends in Scatter Plots

3136.2.2: Summarize distributions of univariate data.

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Populations and Samples
 Real-Time Histogram

3136.2.4: Explore categorical data.

 Box-and-Whisker Plots

3136.3: Sampling & Experimentation

3136.3.1: Understand the differences among various kinds of studies and which types of inferences can be legitimately drawn from each.

 Correlation
 Describing Data Using Statistics
 Polling: City
 Polling: Neighborhood

3136.3.2: Select a method to collect data and plan and conduct surveys and experiments.

 Polling: Neighborhood

3136.3.3: Analyze results and make conclusions from observational studies, experiments, and surveys.

 Correlation
 Describing Data Using Statistics
 Polling: City
 Polling: Neighborhood
 Real-Time Histogram

3136.4: Anticipating Patterns

3136.4.1: Understand and apply basic concepts of probability.

 Probability Simulations
 Theoretical and Experimental Probability

3136.4.2: Design appropriate probability models.

 Probability Simulations
 Theoretical and Experimental Probability

3136.4.3: Understand the normal distribution.

 Polling: City
 Populations and Samples

3136.4.4: Describe the sampling distribution of a statistic and define the standard error of a statistic.

 Polling: City
 Polling: Neighborhood
 Populations and Samples

3136.5: Statistical Inference

3136.5.1: Develop and evaluate inferences and predictions that are based on data.

 Box-and-Whisker Plots
 Polling: City
 Real-Time Histogram

3136.5.2: Understand and use confidence intervals.

 Polling: City

Correlation last revised: 5/24/2018

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