NY-8.NS: The Number System

1.1: Know that there are numbers that are not rational, and approximate them by rational numbers.

NY-8.NS.1: Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion eventually repeats. Know that other numbers that are not rational are called irrational.

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

NY-8.NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.

Circumference and Area of Circles
Square Roots

NY-8.EE: Expressions, Equations, and Inequalities

2.1: Work with radicals and integer exponents.

NY-8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

NY-8.EE.2: Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Know square roots of perfect squares up to 225 and cube roots of perfect cubes up to 125. Know that the square root of a non-perfect square is irrational.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

NY-8.EE.3: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

Number Systems
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

NY-8.EE.4: Perform multiplication and division with numbers expressed in scientific notation, including problems where both standard decimal form and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

2.2: Understand the connections between proportional relationships, lines, and linear equations.

NY-8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation

NY-8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

2.3: Analyze and solve linear equations and pairs of simultaneous linear equations.

NY-8.EE.7: Solve linear equations in one variable.

NY-8.EE.7.a: Recognize when linear equations in one variable have one solution, infinitely many solutions, or no solutions. Give examples and show which of these possibilities is the case by successively transforming the given equation into simpler forms.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations

NY-8.EE.7.b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms.

Modeling and Solving Two-Step Equations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations by Graphing Each Side

NY-8.EE.8: Analyze and solve pairs of simultaneous linear equations.

NY-8.EE.8.a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Recognize when the system has one solution, no solution, or infinitely many solutions.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

NY-8.EE.8.b: Solve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases by inspection.

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

NY-8.EE.8.c: Solve real-world and mathematical problems involving systems of two linear equations in two variables with integer coefficients.

Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

NY-8.F: Functions

3.1: Define, evaluate, and compare functions.

NY-8.F.1: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations

NY-8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Function Machines 2 (Functions, Tables, and Graphs)
Graphs of Polynomial Functions
Linear Functions
Quadratics in Polynomial Form

NY-8.F.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and non-linear.

Absolute Value with Linear Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

3.2: Use functions to model relationships between quantities.

NY-8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Arithmetic Sequences
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line
Translating and Scaling Functions

NY-8.F.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described in a real-world context.

Arithmetic Sequences
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Linear Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions

3.2.3.1: e.g., where the function is increasing or decreasing or when the function is linear or non-linear

Arithmetic Sequences
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Linear Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions

NY-8.G: Geometry

4.1: Understand congruence and similarity using physical models, transparencies, or geometry software.

NY-8.G.1: Verify experimentally the properties of rotations, reflections, and translations.

NY-8.G.1.a: Verify experimentally lines are mapped to lines, and line segments to line segments of the same length.

Circles
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Similar Figures
Translations

NY-8.G.1.b: Verify experimentally angles are mapped to angles of the same measure.

Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

NY-8.G.1.c: Verify experimentally parallel lines are mapped to parallel lines.

Reflections
Rotations, Reflections, and Translations
Similar Figures

NY-8.G.2: Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane.

Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

NY-8.G.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Dilations
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

NY-8.G.4: Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, two two-dimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that maps the similarity between them on the coordinate plane.

Congruence in Right Triangles
Dilations
Proving Triangles Congruent
Similar Figures

NY-8.G.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Investigating Angle Theorems
Isosceles and Equilateral Triangles
Polygon Angle Sum
Similar Figures
Similarity in Right Triangles
Triangle Angle Sum

4.2: Understand and apply the Pythagorean Theorem.

NY-8.G.6: Understand a proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

NY-8.G.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

NY-8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Circles
Distance Formula
Pythagorean Theorem

4.3: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

NY-8.G.9: Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real-world problems.

Prisms and Cylinders
Pyramids and Cones

NY-8.SP: Statistics and Probability

5.1: Investigate patterns of association in bivariate data.

NY-8.SP.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

NY-8.SP.2: Understand that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

NY-8.SP.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots