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Five District Partnership 1 Grade 8 Math Year-Long Plan Overview Standards Shorthand Description Sept-Oct Nov-Dec Jan-Feb Mar-Apr May-June 8.NS.1 Rational numbers & decimal expansions X 8.NS.2 Irrational numbers X 8.EE.1 Integer exponents X 8.EE.2 Square and cube roots X 8.EE.3 Scientific notation X 8.EE.4 Scientific notation operations X 8.EE.5 Graph & compare proportional relationships & interpret slope X 8.EE.6 Slope and similar triangle X 8.EE.7a Linear equations: number of solutions X 8.EE.7b Linear equations: solve multi-step X 8.EE.8a Point of intersection of linear equations X R 8.EE.8b Solve systems of linear equations X R 8.EE.8c Solve contextual problems using linear equations X R 8.F.1 Functions: Graphing & definition X 8.F.2 Compare functions in different representations X R 8.F.3 Linear & non-linear functions X 8.F.4 Model with functions, slope, and initial value X R 8.F.5 Describe functions from a graph X X 8.G.1a Transformation properties X 8.G.1b Transformation angles taken to angles X 8.G.1c Transformations: parallel lines taken to parallel lines X 8.G.2 Congruency & transformations X 8.G.3 Transformations & coordinates X 8.G.4 Similarity & transformations X 8.G.5 Angles & similar triangles X 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. X X 8.G.7 Pythagorean theorem in 2D &3D shapes X X 8.G.8 Pythagorean theorem distance in coordinate plan X X 8.G.9 Volume: cones, cylinders, and spheres X 8.SP.1 Scatter plots & descriptions X 8.SP.2 Trend lines X 8.SP.3 Linear equations on scatterplots X 8.SP.4 Two-way tables X R Last revised: June 23, 2014 The Five District Partnership Grade 8 Math

Five District Partnership 2 Grade 8 Math Overview: The Number System Know that there are numbers that are not rational, and approximate them by rational numbers. Expressions and Equations Work with radicals and integer exponents. Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. STANDARDS FOR MATHEMATICAL PRACTICE Functions Define, evaluate, and compare functions. Use functions to model relationships between quantities. Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean Theorem. Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure. 8. Look for an express regularity in repeated reasoning. Statistics and Probability Investigate patterns of association in bivariate data. Last revised: June 23, 2014 The Five District Partnership Grade 8 Math

Five District Partnership 3 Grade 8 Math Sept-Oct 28 Teaching Days A1: 10/15-10/17 Standards Covered: PARCC emphasis: Assessed on A1? 8.NS.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal Major expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 8.NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately Major on a number line diagram, and estimate the value of expressions (e.g., p2). 8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. Major 8.EE.2: Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a Major positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. 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 Major quantities, and to express how many times as much one is than the other. 8.EE.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific Major notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 8.G.6: Explain a proof of the Pythagorean Theorem and its converse. No 8.G.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical Major problems in two and three dimensions. 8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Major Unit Name Time Frame Notes Unit 1 5 Days Unit 2 8 Days Unit 3 8 Days Unit 4 7 Days Not assessed until A2 Resources Notes EngageNY Module 1 8.EE.1, 8.EE.3, 8.EE.4 EngageNY Module 4 8.EE.5, 8.EE.6, 8.EE.7, 8.EE.8 EngageNY Module 7 8.NS.1, 8.NS.2, 8.EE.2, 8.G.6, 8.G.7, 8.G.8 Exponents and Scientific Notation 8.EE.1, 8.EE.2, 8.EE.3, 8.EE.4, SMP.1, SMP.4, SMP.5, SMP.6 Number Sense 8.NS.1, 8.NS.2 Pythagorean Theorem 8.G.7, 8.G.8 Last revised: June 23, 2014 The Five District Partnership Grade 8 Math

Unit of Study 1 Grade 8 Topic: Number Sense Approximate Time Frame: 5 Days *pretest recommended to determine time needed, if any, on each objective ANET: A1 8.NS.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. For example, by truncating the decimal expansion of 2 show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. - understand that every rational number has a decimal expansion (terminating and repeating) -convert a decimal expansion into a rational number -explain the difference between rational and irrational numbers -evaluate square roots of rational and irrational numbers -evaluate cube roots of small perfect cubes -estimate irrational numbers -locate rational and irrational numbers on a number line -use rational approximations of irrational numbers to compare irrational numbers Focus SMP's 7, 8 Major 5, 7, 8 Major Vocabulary: ratio, rational number, irrational number, square roots, cube roots, repeating decimal, terminating decimal, real numbers Standards for Mathematical Practice: EngageNY Module 7 Number Sense 8.NS.1, 8.NS.2, 8.EE.2, 8.G.6, 8.G.7, 8.G.8 8.NS.1, 8.NS.2

Unit of Study 2 Grade 8 Topic: Expressions Approximate Time Frame: 8 Days Emphasis on Scientific Notation ANET: A1 -know and apply the properties of integer exponents to generate an equivalent expression (includes negative and zero exponents) Focus SMP's 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. 7 Major For example, 3 2 x 3-5 = 3-3 = 1 / 3 3 = 1 / 27 8.EE.3 Use numbers expressed in the form of a single digit -use numbers in scientific notation to express large and small numbers times an integer power of 10 to estimate very large or very -express how many times as much one number is in scientific notation than the other small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10 8 and the population of the world as 7 x 10 9, and determine that the world population is more than 10 times larger. 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. -choose appropriate units of measurement for very large and small quantities -interpret scientific notation that has been generated by technology (ex/ know that when a calculator reads 3.4 E 3 it means 3.4 X 10 3 ) -perform operations with numbers which are written in scientific notation 4 Major 6, 7, 8 Major integer, expression, equivalent, properties of exponents, scientific notation Standards for Mathematical Practice: EngageNY Module 1 Exponents and Scientific Notation 8.EE.1, 8.EE.3, 8.EE.4 8.EE.1, 8.EE.3, 8.EE.4, SMP.1, SMP.5, SMP.6, SMP.7

Unit of Study 3 Grade 8 Topic: Pythagorean Theorem Approximate Time Frame: 8 Days ANET: A1 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. 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. 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 =P and x 3 =P, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational -explain a proof of the Pythagorean Theorem and its converse **Not assessed until A4 -apply the Pythagorean theorem to determine unknown side lengths in right triangles -apply the Pythagorean theorem to solve real world and mathematical problems in two and three dimensions -apply the Pythagorean Theorem to find the distance between two points on a coordinate system -use square and cube root symbols to represent solutions to equations (ex/ x 2 = 5 then x = 5) -evaluate the roots of small perfect squares and cubes -know that non-perfect square roots are irrational Focus SMP's 1,2,3 Major 1,2,3 Major 1,2,3 Major 1,2,3 Major Vocabulary: Pythagorean Theorem, right triangle, converse, two-dimensional, three-dimensional, hypotenuse, distance Standards for Mathematical Practice: EngageNY Module 7 Pythagorean Theorem 8.NS.1, 8.NS.2, 8.EE.2, 8.G.6, 8.G.7, 8.G.8 8.G.7, 8.G.8, SMP.1, SMP.2, SMP.3

Unit of Study 4 Grade 8 Topic: Equations Approximate Time Frame: 7 Days **during A1 time frame ANET: A2 8.EE.7.a Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). I can solve, write, and explain: -linear equations in one variable that have one solution (x=a) -linear equations in one variable that have no solutions (a=b) -linear equations in one variable that have infinite solutions (a=a) Focus SMP's 3, 6 Major 8.EE.7.b 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 collecting like terms. I can solve, write, and explain: -linear equations with rational number coefficients -linear equations that require combining like terms -linear equations that require expanding expressions using the Distributive Property -linear equations with variables on both sides -solve for a given variable in terms of another -synthesize linear equations with one solution, infinitely many solutions or no solutions 3, 6, 7 Major Vocabulary: expression, equation, variable, coefficient, solution, like terms, Distributive Property, linear equation Standards for Mathematical Practice: EngageNY Module 4 Linear & Non-linear Functions 8.EE.5, 8.EE.6, 8.EE.7, 8.EE.8 8.EE.7a, 8.EE.7b, 8.F.1, 8.F.2, 8.F.3, 8.F.4, 8.F.5, SMP.1, SMP.4, SMP.5, SMP.6

Five District Partnership 4 Grade 8 Math Nov-Dec 30 Teaching days A2: 12/9-12/12 Standards Covered: PARCC emphasis: Assessed on A2? 8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional Major relationships represented in different ways. 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. 8.EE.7a: Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely Major many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 8.EE.7b: Solve linear equations in one variable. Solve linear equations with rational number coefficients, including equations Major whose solutions require expanding expressions using the distributive property and collecting like terms. 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 Major ordered pairs consisting of an input and the corresponding output. 8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, Major or by verbal descriptions). 8.F.3: Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that Major are not linear. 8.F.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value Supporting 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. 8.F.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Supporting Unit Name Time Frame Notes Unit 4 0 days *taught before A1 Unit 5 20 Days Unit 6 10 Days ANet Review Standards 8.EE.3, 8.G.7 Resources Notes EngageNY Module 4 8.EE.5, 8.EE.6, 8.EE.7, 8.EE.8 EngageNY Module 5 8.F.1, 8.F.2, 8.F.3, 8.G.9 EngageNY Module 6 8.F.4, 8.F.5, 8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4 Last revised: June 23, 2014 The Five District Partnership Grade 8 Math

Unit of Study 5 Grade 8 Topic: Linear Functions Approximate Time Frame: 20 Days ANET: A2 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. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. -graph proportional relationships -compare two proportional relationships represented in different ways (verbal descriptions, graphs, tables, equations) -interpret the unit rate as slope when the relationship is proportional Focus SMP's 1, 5, 7 Major 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. 8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.3 Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4), and (3,9), which are not on a straight line. 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. 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Standards for Mathematical Practice: (not limited to but must include) EngageNY Module 4 EngageNY Module 5 EngageNY Module 6 Proportion, Lines, and Equations -derive the equation y=mx through the origin and y=mx+b through the y-intercept -show, using similar triangles, that the slope is the same between any 2 points in a linear relationship -determine and interpret the rate of change from a description, two (x,y) points, a table, or a graph -compare 2 functions given in different forms -write the equation of a line given a point and a slope, two points, a table, a graph, or a description -know equations written in y=mx+b form are linear, anything else is non-linear -give examples of non-linear functions and explain why they are non-linear -understand that non linear relationships have points that do not lie in a straight line when graphed -construct a function to model a linear pattern -create the equation, table or graph of a real life linear situation -explain a linear situation from a table, graph, or equation (rate of change and y-intercept in context) -determine and interpret the rate of change and the initial value from a description, two (x,y) points, a table, and a graph -describe a relationship as increasing, decreasing, linear, or nonlinear from an equation, table, or graph sketch a graph that fits features described verbally Vocabulary linear function, rate of change, slope, initial value, Y-intercept, table, graph, equation, proportional, similar, points, origin, slope-intercept form, function 8.EE.5, 8.EE.6, 8.EE.7, 8.EE.8 8.F.1, 8.F.2, 8.F.3, 8.G.9 8.F.4, 8.F.5, 8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4 8.EE.5, 8.EE.6, 8.F.1, 8.F.2, 8.F.3, SMP.1, SMP.2, SMP.3, SMP.4, SMP.6 2, 3, 5, 7, 8 Additional 2, 5 Additional 2, 3, 6, 7 Additional 2, 4 Additional 2, 5, 7 Additional

Unit of Study 6 Grade 8 Topic: Functions Approximate Time Frame: 10 Days ANET: A2 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. -explain what a function is -determine if a table, graph, or ordered pairs is a function -understand that a graph of a function is the ordered pairs generated by inputs and their corresponding outputs **function notation is not required in grade 8** Focus SMP's 2, 5 Major 8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. -compare properties of two functions each in a different form; algebraically, graphically, numerically, and verbally 2, 5 Major 8.F.3 Interpret the equation y=mx+b as defining a linear -give examples of functions that are not linear (the graph contains points not on a straight line) function whose graph is a straight line; give examples of - interpret y = mx + b as a graph with a straight line functions that are not linear. For example, the function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4), and (3,9) which are not on a straight line. 8.F.5Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. -describe qualitatively the functional relationship between two quantities by analyzing a graph (increasing/decreasing, linear/nonlinear) -sketch a graph that exhibits the qualitative features of a function that has been described verbally 2, 3, 6, 7 Major 2, 5, 7 Supporting Vocabulary: domain, range, input, output, ordered pairs, graph model Standards for Mathematical Practice: (not limited to but must include) EngageNY Module 5 EngageNY Module 6 Linear & Non-Linear Functions Proportions, Lines, and Equations 8.F.1, 8.F.2, 8.F.3, 8.G.9 8.F.4, 8.F.5, 8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4 8.F.1, 8.F.2, 8.F.3, 8.F.4, 8.F.5, SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.6 8.EE.5, 8.EE.6, 8.F.1, 8.F.2, 8.F.3, SMP.1, SMP.2, SMP.3, SMP.4, SMP.6

Five District Partnership 5 Grade 8 Math Jan-Feb 32 Teaching Days A3 : 2/10-2/13 Standards Covered: PARCC emphasis: Assessed on A3? 8.EE.8a: Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear Major equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. 8.EE.8b: Analyze and solve pairs of simultaneous linear equations. Solve systems of two linear equations in two variables Major algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. 8.EE.8c: Analyze and solve pairs of simultaneous linear equations. Solve real-world and mathematical problems leading to two Major linear equations in two variables. 8.SP.4: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. Supporting Unit Name Time Frame Notes Unit 7 20 days Unit 8 10 days **use only 3 of these days in A3 to teach 6.SP.4, the other 7 days are in A4 ANet Review Standards 8.EE.7, 8.EE.7a, 8.EE.7b, 8.F.1, 8.F.2, 8.F.4 There are 9 days extra for this review Resources Notes System of Equations 8.EE.8, SMP.1, SMP.4, SMP.5, SMP.6, SMP.7, SMP.8 Scatterplots 8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4 EngageNY Module 4 8.EE.5, 8.EE.6, 8.EE.7, 8.EE.8 EngageNY Module 6 8.F.4, 8.F.5, 8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4 Last revised: June 23, 2014 The Five District Partnership Grade 8 Math

Unit of Study 7 Grade 8 Topic: Systems of Equations Approximate Time Frame: 20 Days ANET: A3 8.EE.8.a. Analyze and solve pairs of simultaneous linear equations. -analyze and solve systems with no solutions or infinitely many solutions Understand that solutions to a system of two linear equations in two -understand that solutions to a system of two linear equations in two variables correspond to the points of variables correspond to points of intersection of their graphs, intersection because points of intersection satisfy both equations simultaneously. -estimate solutions by graphing 8.EE.8.b. Analyze and solve pairs of simultaneous linear equations. -solve linear systems graphically Solve systems of two linear equations in two variables algebraically, -solve linear systems algebraically (includes substitution, elimination, etc.) and estimate solutions by graphing the equations. Solve simple cases -solve simple cases by inspection by inspection. For example, 3x + 2Y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. Focus SMP's 2, 3, 5, 6, 7 Major 1, 3, 5, 6, 7 Major 8.EE.8.c. Analyze and solve pairs of simultaneous linear equations. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. -solve real-world and mathematical problems involving a system of linear equations -show that a point of intersection satisfies a system by evaluating each linear equation at that point 1, 2, 3, 5, 6, 7 Major Vocabulary: systems of equations, simultaneously, point of intersection, parallel lines, perpendicular lines Standards for Mathematical Practice: EngageNY Module 4 Systems of equations 8.EE.5, 8.EE.6, 8.EE.7, 8.EE.8 8.EE.8

Unit of Study 8 Grade 8 Topic: Probability and Statistics Approximate Time Frame: 10 Days (3 before A3, 7 after) ANET: A3/A4 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. 8.SP.2 Know 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. -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 **assessed on A4 -for scatter plots that suggest a linear association, informally fit a straight line -assess the graph model fit by judging the closeness of the points to the line of best fit **assessed on A4 8.SP.3 Use the equation of a linear model to solve problems -interpret the slope and y-intercept of the line of best fit in the context of the problem in the context of bivariate measurement data, interpreting the -use the equation of a line of best fit to make predictions in the context of the problem slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning **assessed on A4 that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. -display frequencies and relative frequencies in a two-way table 8.SP.4 Understand that patterns of association can also be -construct and interpret a two-way table summarizing data on two variables seen in bivariate categorical data by displaying frequencies -use relative frequencies to describe any associations between the variables and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two **NOTE** this is the only standards which is assessed on A3 so teach this first in your unit categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Focus SMP's 3, 5, 7 Supporting 2, 5, 7 Supporting 2, 5, 7 Supporting 2, 4, 5, 7 Supporting Vocabulary: bivariate, scatter plot, patterns, clustering, outliers, frequencies, two-way table, positive association, negative association, categorical variables, categorical data Standards for Mathematical Practice: (not limited to but must include) EngageNY Module 6 Scatter plots 8.F.4, 8.F.5, 8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4 8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4

Five District Partnership 6 Grade 8 Math March-April 30 Teaching days A4: 4/13-4/17 Standards Covered: PARCC emphasis: Assessed on A4? 8.G.1a: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line Major segments to line segments of the same length. 8.G.1b: Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same Major measure. 8.G.1c: Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines. Major 8.G.2: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a Major sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.3: Describe the effects of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Major 8.G.4: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a Major sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. 8.G.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created Major when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles 8.G.9: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical Additional problems. 8.SP.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two Supporting quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.SP.2: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots Supporting 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. 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. Supporting Unit Name Time Frame Notes Unit 8 10 days 7 days to teach 8.SP.1, 8.SP.2, 8.SP.3 Unit 9 10 days Unit 10 6 Days Unit 11 7 Days ANet Review Standards 8.EE.1, 8.EE.4, 8.EE.8b, 8.EE.8c, 8.G.6, 8.G.7 8.G.6 can be assessed as an OR question Resources Notes EngageNY Module 2 8.G.1, 8.G.2, 8.G.5, 8.G.6, 8.G.7 EngageNY Module 3 8.G.3, 8.G.4, 8.G.5, 8.G.6, 8.G.7 EngageNY Module 6 8.F.4, 8.F.5, 8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4 Last revised: June 23, 2014 The Five District Partnership Grade 8 Math

Unit of Study 9 Grade 8 Topic: Transformations Approximate Time Frame: 10 Days ANET: A4 8.G.1 verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. -use properties of translations, rotations, and reflections on line segments, angles, parallel lines, and geometric figures -verify transformations by experimenting to observe properties of figures after transformations occur -understand that if a figure is formed by a series of rotations, reflections, and translations that it is congruent to the original figure -if given two congruent figures, describe the sequence of rotations, reflections, and translations that have occurred Focus SMP's 3, 5, 8 Major 2, 3, 5, 6, 7 Major 8.G.3 Describe the effect of dilations, translation, rotations, and reflections on two-dimensional figures using coordinates. 8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. -describe the effect of dilations, translations, rotations, and reflections on two dimensional figures using coordinates -understand that if a figure is formed by a series of rotations, reflections, and translations that it is congruent to the original figure -given two similar figures, describe a sequence of rotations, reflections, translations, and dilations that has occurred, showing how they are similar 2, 3, 5 Major 2, 3, 5, 6, 7 Major Vocabulary: rotation, reflection, translation, dilation, lines, segments, angles, similar, congruent, coordinates Standards for Mathematical Practice: (not limited to but must include) EngageNY Module 2 EngageNY Module 3 Rotations/Reflections 8.G.1, 8.G.2, 8.G.5, 8.G.6, 8.G.7 8.G.3, 8.G.4, 8.G.5, 8.G.6, 8.G.7 88.SP.1, 8.SP.2, 8.SP.3, 8.SP.4

Unit of Study 10 Grade 8 Topic: Angles Approximate Time Frame: 6 Days ANET: A4 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. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. -use informal arguments to establish facts about the angle sum and exterior angles of triangles -use informal arguments to establish facts about the angles created when parallel lines are cut by a transversal -use informal arguments to establish facts about the angle-angle criterion for similarity of triangles Focus SMP's 3, 5, 6 Major Vocabulary interior angles, exterior angles, transversal, AA property, similar, congruent, vertical angles, corresponding angles, alternate exterior angle, alternate interior angle Standards for Mathematical Practice: (not limited to but must include) EngageNY Module 2 EngageNY Module 3 8.G.1, 8.G.2, 8.G.5, 8.G.6, 8.G.7 8.G.3, 8.G.4, 8.G.5, 8.G.6, 8.G.7

Unit of Study 11 Grade 8 Topic: Volume Approximate Time Frame: 7 Days ANET: A4 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. -KNOW the formulas for the volume of cones, cylinders, and spheres -use the formulas for the volume of cones, cylinders, and spheres to solve real world and mathematical problems Focus SMP's 1, 5 Additional Vocabulary volume, cone, cylinder, sphere, area, dimensions Standards for Mathematical Practice: (not limited to but must include) EngageNY Module 5 8.F.1, 8.F.2, 8.F.3, 8.G.9

Five District Partnership 8 Grade 8 Math May-June Suggested Standards to be reinforced Standards Covered: 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. 8.EE.8a: 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. 8.EE.8b: Analyze and solve pairs of simultaneous linear equations. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. 8.EE.8c: Analyze and solve pairs of simultaneous linear equations. Solve real-world and mathematical problems leading to two linear equations in two variables. 8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 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. Unit Name PARCC emphasis: Major Major Major Major Supporting Established Goals/Standards Notes Last revised: June 23, 2014 The Five District Partnership Grade 8 Math