Next Generation Learning Standards

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.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

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.

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

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.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

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

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.

Isosceles and Equilateral Triangles

Polygon Angle Sum

Similar Figures

Similarity in Right Triangles

Triangle Angle Sum

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.

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.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

Trends in Scatter Plots

Correlation last revised: 1/22/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.