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Advanced Functions and Modeling

1 The learner will analyze data and apply probability concepts to solve problems.

1.01. Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, and logarithmic functions of bivariate data to solve problems.

1.01.b. Check models for goodness-of-fit; use the most appropriate model to draw conclusions and make predictions.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

1.02. Summarize and analyze univariate data to solve problems.

1.02.a. Apply and compare methods of data collection.

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

1.02.b. Apply statistical principles and methods in sample surveys.

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

1.02.c. Determine measures of central tendency and spread.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

1.02.e. Interpret graphical displays of univariate data.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

1.03. Use theoretical and experimental probability to model and solve problems.

1.03.b. Calculate and apply permutations and combinations.

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

Discrete Mathematics

2 The learner will analyze data and apply probability concepts to solve problems.

2.01. Describe data to solve problems.

2.01.a. Apply and compare methods of data collection.

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

2.01.b. Apply statistical principles and methods in sample surveys.

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

2.01.c. Determine measures of central tendency and spread.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

2.01.e. Interpret graphical displays of data.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

2.02. Use theoretical and experimental probability to model and solve problems.

2.02.b. Calculate and apply permutations and combinations.

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

Math 1

NC.M1.A-APR. Algebra: Arithmetic with Polynomial Expressions

Perform arithmetic operations on polynomials.

NC.M1.A-APR.1. Build an understanding that operations with polynomials are comparable to operations with integers by adding and subtracting quadratic expressions and by adding, subtracting, and multiplying linear expressions.

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

NC.M1.A-CED. Algebra: Creating Equations

Create equations that describe numbers or relationships.

NC.M1.A-CED.1. Create equations and inequalities in one variable that represent linear, exponential, and quadratic relationships and use them to solve problems.

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

NC.M1.A-CED.2. Create and graph equations in two variables to represent linear, exponential, and quadratic relationships between quantities.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

NC.M1.A-CED.3. Create systems of linear equations and inequalities to model situations in context.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

NC.M1.A-CED.4. Solve for a quantity of interest in formulas used in science and mathematics using the same reasoning as in solving equations.

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

NC.M1.A-REI. Algebra: Reasoning with Equations and Inequalities

Solve equations and inequalities in one variable.

NC.M1.A-REI.3. Solve linear equations and inequalities in one variable.

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

Solve systems of equations.

NC.M1.A-REI.5. Explain why replacing one equation in a system of linear equations by the sum of that equation and a multiple of the other produces a system with the same solutions.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

NC.M1.A-REI.6. Use tables, graphs, or algebraic methods (substitution and elimination) to find approximate or exact solutions to systems of linear equations and interpret solutions in terms of a context.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

Represent and solve equations and inequalities graphically

NC.M1.A-REI.11. Build an understanding of why the x-coordinates of the points where the graphs of two linear, exponential, and/or quadratic equations y = (x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) and approximate solutions using graphing tec

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

NC.M1.A-REI.12. Represent the solutions of a linear inequality or a system of linear inequalities graphically as a region of the plane.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

NC.M1.F-BF. Functions: Building Functions

Build a function that models a relationship between two quantities.

NC.M1.F-BF.2. Translate between explicit and recursive forms of arithmetic and geometric sequences and use both to model situations.

Flip Charts Arithmetic & Sequences

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

NC.M1.F-IF. Functions: Interpreting Functions

Understand the concept of a function and use function notation.

NC.M1.F-IF.1. Build an understanding that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range by recognizing that:

NC.M1.F-IF.1a. If f is a function and x is an element of its domain, then (x) denotes the output of f corresponding to the input x.

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

NC.MI.F-IF.3. Recognize that recursively and explicitly defined sequences are functions whose domain is a subset of the integers, the terms of an arithmetic sequence are a subset of the range of a linear function, and the terms of a geometric sequence are a subset of t

Flip Charts Arithmetic & Sequences

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

Interpret functions that arise in applications in terms of the context.

NC.M1.F-IF.4. Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities, including: intercepts; intervals where the function is increasing, decreasing, positive, or negative; an

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

NC.M1.F-IF.6. Calculate and interpret the average rate of change over a specified interval for a function presented numerically, graphically, and/or symbolically.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

Analyze functions using different representations.

NC.M1.F-IF.7. Analyze linear, exponential, and quadratic functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features, including: domain and range; rate of change; intercepts; intervals

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

NC.M1.F-IF.8. Use equivalent expressions to reveal and explain different properties of a function.

NC.M1.F-IF.8b. Interpret and explain growth and decay rates for an exponential function.

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

NC.M1.G-GPE. Geometry: Expressing Geometric Properties with Equations

Use coordinates to prove simple geometric theorems algebraically.

NC.M1.G-GPE.4. Use coordinates to solve geometric problems involving polygons algebraically

NC.M1.G-GPE.4a. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

NC.M1.G-GPE.4b. Use coordinates to verify algebraically that a given set of points produces a particular type of triangle or quadrilateral.

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

NC.M1.G-GPE.5. Use coordinates to prove the slope criteria for parallel and perpendicular lines and use them to solve problems.

NC.M1.G-GPE.5a. Determine if two lines are parallel, perpendicular, or neither.

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

NC.M1.N-RN. Number and Quantity: The Real Number System

Extend the properties of exponents to rational exponents.

NC.M1.N-RN.2. Rewrite algebraic expressions with integer exponents using the properties of exponents.

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

NC.M1.S-ID. Statistics and Probability: Interpreting Categorical and Quantitative Data

Summarize, represent, and interpret data on two categorical and quantitative variables.

NC.M1.S-ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

NC.M1.S-ID.6a. Fit a least squares regression line to linear data using technology. Use the fitted function to solve problems.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

NC.M1.S-ID.6b. Assess the fit of a linear function by analyzing residuals.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Interpret linear models.

NC.M1.S-ID.8. Analyze patterns and describe relationships between two variables in context. Using technology, determine the correlation coefficient of bivariate data and interpret it as a measure of the strength and direction of a linear relationship. Use a scatter plo

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

Math 2

NC.M2.A-APR. Algebra: Arithmetic with Polynomial and Rational Expressions

Perform arithmetic operations on polynomials

NC.M2.A-APR.1. Extend the understanding that operations with polynomials are comparable to operations with integers by adding, subtracting, and multiplying polynomials.

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

NC.M2.A-CED. Algebra: Creating Equations

Create equations that describe numbers or relationships.

NC.M2.A-CED.1. Create equations and inequalities in one variable that represent quadratic, square root, inverse variation, and right triangle trigonometric relationships and use them to solve problems.

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

NC.M2.A-CED.3. Create systems of linear, quadratic, square root, and inverse variation equations to model situations in context.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

NC.M2.A-REI. Algebra: Reasoning with Equations and Inequalities

Solve systems of equations.

NC.M2.A-REI.7. Use tables, graphs, and algebraic methods to approximate or find exact solutions of systems of linear and quadratic equations, and interpret the solutions in terms of a context.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

Represent and solve equations and inequalities graphically.

NC.M2.A-REI.11. Extend the understanding that the x-coordinates of the points where the graphs of two square root and/or inverse variation equations y = (x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) and approximate solutions using graphing tech

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

NC.M2.F-IF. Functions: Interpreting Functions

Analyze functions using different representations.

NC.M2.F-IF.7. Analyze quadratic, square root, and inverse variation functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features, including: domain and range; intercepts; intervals wher

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

NC.M2.G-CO. Geometry: Congruence

Experiment with transformations in the plane.

NC.M2.G-CO.2. Experiment with transformations in the plane.

NC.M2.G-CO.2b. Compare rigid motions that preserve distance and angle measure (translations, reflections, rotations) to transformations that do not preserve both distance and angle measure (e.g. stretches, dilations).

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

NC.M2.G-CO.2c. Understand that rigid motions produce congruent figures while dilations produce similar figures.

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

NC.M2.G-CO.3. Given a triangle, quadrilateral, or regular polygon, describe any reflection or rotation symmetry i.e., actions that carry the figure onto itself. Identify center and angle(s) of rotation symmetry. Identify line(s) of reflection symmetry.

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

NC.M2.G-CO.4. Verify experimentally properties of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

NC.M2.G-CO.5. Given a geometric figure and a rigid motion, find the image of the figure. Given a geometric figure and its image, specify a rigid motion or sequence of rigid motions that will transform the pre-image to its image.

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Understand congruence in terms of rigid motions.

NC.M2.G-CO.6. Determine whether two figures are congruent by specifying a rigid motion or sequence of rigid motions that will transform one figure onto the other.

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Prove geometric theorems.

NC.M2.G-CO.9. Prove theorems about lines and angles and use them to prove relationships in geometric figures including:

NC.M2.G-CO.9b. When a transversal crosses parallel lines, alternate interior angles are congruent.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

NC.M2.G-CO.9c. When a transversal crosses parallel lines, corresponding angles are congruent.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

NC.M2.G-SRT. Geometry: Similarity, Right Triangles, and Trigonometry

Understand similarity in terms of similarity transformations.

NC.M2.G-SRT.1. Verify experimentally the properties of dilations with given center and scale factor:

NC.M2.G-SRT.1a. When a line segment passes through the center of dilation, the line segment and its image lie on the same line. When a line segment does not pass through the center of dilation, the line segment and its image are parallel.

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

NC.M2.G-SRT.1b. The length of the image of a line segment is equal to the length of the line segment multiplied by the scale factor.

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

NC.M2.G-SRT.1c. The distance between the center of a dilation and any point on the image is equal to the scale factor multiplied by the distance between the dilation center and the corresponding point on the pre-image.

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

NC.M2.G-SRT.1d. Dilations preserve angle measure.

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

NC.M2.G-SRT.2. Understand similarity in terms of transformations.

NC.M2.G-SRT.2a. Determine whether two figures are similar by specifying a sequence of transformations that will transform one figure into the other.

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

NC.M2.G-SRT.2b. Use the properties of dilations to show that two triangles are similar when all corresponding pairs of sides are proportional and all corresponding pairs of angles are congruent.

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

NC.M2.G-SRT.3. Use transformations (rigid motions and dilations) to justify the AA criterion for triangle similarity.

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

NC.M2.N-RN. Number and Quantity: The Real Number System

Extend the properties of exponents to rational exponents.

NC.M2.N-RN.2. Rewrite expressions with radicals and rational exponents into equivalent expressions using the properties of exponents.

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

Use properties of rational and irrational numbers.

NC.M2.N-RN.3. Use the properties of rational and irrational numbers to explain why:

NC.M2.N-RN.3b. The sum of a rational number and an irrational number is irrational.

Flip Charts Math Grade 8

Flip Charts The Real Numbers

NC.M2.N-RN.3c. The product of a nonzero rational number and an irrational number is irrational.

Flip Charts Math Grade 8

Flip Charts The Real Numbers

NC.M2.S-CP. Statistics and Probability: Conditional Probability and the Rules for Probability

Understand independence and conditional probability and use them to interpret data.

NC.M2.S-CP.3. Develop and understand independence and conditional probability.

NC.M2.S-CP.3b. Understand that event A is independent from event B if the probability of event A does not change in response to the occurrence of event B. That is P(A|B)=P(A).

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

NC.M2.S-CP.4. Represent data on two categorical variables by constructing a two-way frequency table of data. Interpret the two-way table as a sample space to calculate conditional, joint and marginal probabilities. Use the table to decide if events are independent.

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

NC.M2.S-CP.5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

NC.M2.S-CP.8. Apply the general Multiplication Rule P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in context. Include the case where A and B are independent: P(A and B) = P(A) P(B).

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

Math 3

NC.M3.A-CED. Algebra: Creating Equations

Create equations that describe numbers or relationships.

NC.M3.A-CED.1. Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically.

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

NC.M3.A-CED.2. Create and graph equations in two variables to represent absolute value, polynomial, exponential and rational relationships between quantities.

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

NC.M3.A-CED.3. Create systems of equations and/or inequalities to model situations in context.

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

NC.M3.A-REI. Algebra: Reasoning with Equations and Inequalities

Understand solving equations as a process of reasoning and explain the reasoning.

NC.M3.A-REI.2. Solve and interpret one variable rational equations arising from a context, and explain how extraneous solutions may be produced.

Flip Charts Math Grade 8

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

Represent and solve equations and inequalities graphically.

NC.M3.A-REI.11. Extend an understanding that the x-coordinates of the points where the graphs of two equations y = (x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) and approximate solutions using a graphing technology or successive approximations

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

NC.M3.A-SSE. Algebra: Seeing Structure in Expressions

Write expressions in equivalent forms to solve problems.

NC.M3.A-SSE.3c. Write an equivalent form of an exponential expression by using the properties of exponents to transform expressions to reveal rates based on different intervals of the domain.

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

NC.M3.F-BF. Functions: Building Functions

Build a function that models a relationship between two quantities.

NC.M3.F-BF.1. Write a function that describes a relationship between two quantities.

NC.M3.F-BF.1a. Build polynomial and exponential functions with real solution(s) given a graph, a description of a relationship, or ordered pairs (include reading these from a table).

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

NC.M3.F-IF. Functions: Interpreting Functions

Analyze functions using different representations.

NC.M3.F-IF.7. Analyze piecewise, absolute value, polynomials, exponential, rational, and trigonometric functions (sine and cosine) using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

NC.M3.G-GMD. Geometry: Geometric Measurement & Dimension

Explain volume formulas and use them to solve problems.

NC.M3.G-GMD.3. Use the volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.

Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

NC.M3.S-IC. Statistics and Probability: Making Inference and Justifying Conclusions

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

NC.M3.S-IC.3. Recognize the purposes of and differences between sample surveys, experiments, and observational studies and understand how randomization should be used in each.

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

Mathematical Practice

MP.1. Make sense of problems and persevere in solving them.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

MP.2. Reason abstractly and quantitatively.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

Pre-Calculus

2 The learner will use relations and functions to solve problems.

2.01. Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise-defined, and greatest integer) to model and solve problems; justify results.

2.01.b. Interpret the constants, coefficients, and bases in the context of the problem.

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions