The Number System  eTAP Lesson 

Know that there are numbers that are not rational, and approximate them by rational numbers.  
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.
NY.MATH.8.NS.1 
Operations with Decimals Rational & Irrational Numbers 
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.
NY.MATH.8.NS.2 
Integers and the Number Line 
Expressions, Equations, and Inequalities  eTAP Lesson 
Work with radicals and integer exponents.  
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
NY.MATH.8.EE.1 
Raising Numbers to Various Powers Rules of Exponents 
Use square root and cube root symbols to represent solutions to equations of the form x2= pand 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 nonperfect square is irrational.
NY.MATH.8.EE.2 
Roots and Radicals Completing the Square Squares and Square Roots Perfect Square Trinomial 
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.
NY.MATH.8.EE.3 
Base Ten Exponents 
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.
NY.MATH.8.EE.4 

Understand the connections between proportional relationships, lines, and linear equations.  
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
NY.MATH.8.EE.5 
Ratios and Proportions Setting Up and Solving Equations 
Use similar triangles to explain why the slope mis the same between any two distinct points on a nonvertical 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.
NY.MATH.8.EE.6 
Slope Intercept Form of Equations Slope of a Line 
Analyze and solve linear equations and pairs of simultaneous linear equations.  
Solve linear equations in one variable. 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.
NY.MATH.8.EE.7a 
Basic Operations Simultaneous Equations With Strange Solutions Changing Words into Math 
Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms.
NY.MATH.8.EE.7b 
Factoring with the Distributive Property The Substitution Method 
Analyze and solve pairs of simultaneous linear equations. 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.
NY.MATH.8.EE.8a 
Why Do We Need Two Equations? Graphing Systems of Inequalities When to do What Summary 
Analyze and solve pairs of simultaneous linear equations. Solve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases by inspection.
NY.MATH.8.EE.8b 
Solving Equations When Several Terms and Procedures are Involved 
Analyze and solve pairs of simultaneous linear equations. Solve realworld and mathematical problems involving systems of two linear equations in two variables with integer coefficients.simultaneous linear equations.
NY.MATH.8.EE.8c 
Simultaneous Equations The Addition  Subtraction Method Summary 
Functions  eTAP Lesson 
Define, evaluate, and compare functions.  
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.
NY.MATH.8.F.1 
Summary What is a Function? 
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
NY.MATH.8.F.2 
Visually Representing Numerical Data 
Interpret the equation y= mx+ bas defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and nonlinear.
NY.MATH.8.F.3 
Slope of a Line Slope Intercept Form of Equations 
Use functions to model relationships between quantities.  
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.
NY.MATH.8.F.4 
Functions as Graphs in the Coordinate System Seeking Trends with Line Graphs 
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 realworld context.
NY.MATH.8.F.5 
Graphing Data Splitting up the Whole with Pie Graphs Comparing Categories with Bar Graphs 
Geometry  eTAP Lesson 
Understand congruence and similarity using physical models, transparencies, or geometry software.  
Verify experimentally the properties of rotations, reflections, and translations.
NY.MATH.8.G.1 
Tessellations Using Translations, Rotations, and Glide Reflections 
Know that a twodimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two twodimensional 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.
NY.MATH.8.G.2 
SSS and SAS Congruencies ASA Congruencies AAS and HL Congruencies 
Describe the effect of dilations, translations, rotations,and reflections on twodimensional figures using coordinates.
NY.MATH.8.G.3 
Transformations 
Know that a twodimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, two twodimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations. Given two similar twodimensional figures, describe a sequence that maps the similarity between them on the coordinate plane.
NY.MATH.8.G.4 
Similar Triangles Symmetry Expressing Relationships Between Figures 
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 angleangle criterion for similarity of triangles.
NY.MATH.8.G.5 
Corresponding Parts Lines and Angles 
Understand and apply the Pythagorean Theorem.  
Understand a proof of the Pythagorean Theorem and its converse.
NY.MATH.8.G.6 
Historical Beginnings Other Commonly Used Functions – Cosine and Tangent 
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.
NY.MATH.8.G.7 
The Application of Equation Rules to Formulas Indirect Measurement with Similar Triangles 
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
NY.MATH.8.G.8 
The Theorem of Pythagoras Distance Calculations Other Functions in a Right Triangle – Secant, Cosecant, and Cotangent 
Solve realworld and mathematical problems involving volume of cylinders, cones, and spheres.  
Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and realworld problems.
NY.MATH.8.G.9 
Cones Cylinders Solids with Curved Surfaces 
Statistics and Probability  eTAP Lesson 
Investigate patterns of association in bivariate data.  
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.
NY.MATH.8.SP.1 
Paired Data Sets and Scatterplots 
Understandthat 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.
NY.MATH.8.SP.2 
Correlations Graphing in One Quadrant 
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
NY.MATH.8.SP.3 
Regression Models and Least Square Methods 