Grade 8 Big Ideas SY

Transcription

1 Topics and Chapters/Units Days in Cycle Dates Grade 8 Big Ideas SY Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4 September 5 - October 31 BM Window Nov 1-17 November 2 - January 26 BM Window Jan 29-Feb 13 January 30 - May 8 BM Window May 9-25 May 10 - June 12 Total Days: 39 Including 1 Half Day Total Days: 50 Days Including 4 Half Days Total Days Before PSSA: 50 Including 9 Half Days Total Days in Cycle: 60 Including 13 Half Days Total Days: 22 Including 1 Half Day Big Ideas 1: Equations , 2.7*: Transformations Extension: Graphing and Writing Linear Equations Big Ideas *: Graphing and Writing Linear Equations 5: Systems of Linear Equations 6: Functions 7.1, 7.2: Real Numbers Big Ideas : Real Numbers and the Pythagorean Theorem 9: Data Analysis and Displays 10: Exponents and Scientific Notation Big Ideas 2.6: Transformations 3: Angles and Triangles 8: Volume and Similar Solids Remediate and Extend *Note: Lesson 2.6 does not contain eligible content for the 8 th Grade PSSA and so can be covered after the PSSA. *Note: Chapter 3 and 4-7 do not contain eligible content for the 8 th Grade PSSA and so can be covered after the PSSA. A benchmark cycle is defined as the time allotted to teach the content that is on each benchmark, and assumes the benchmark is taken in the first week of the window. This means that though it is fine to give the test later in the window, you should be moving on to new content as of the above listed dates, or you will fall behind. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

2 Table of Contents Benchmark Cycle 1 Standards... 3 Benchmark Cycle 1 Scope and Sequence... 5 Benchmark Cycle 2 Standards... 8 Benchmark Cycle 2 Scope and Sequence Benchmark Cycle 3 Standards Benchmark Cycle 3 Scope and Sequence Cycle 4 Standard Cycle 4 Scope and Sequence PA Core Standards and Eligible Content by Cycle Document Information Page THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

3 Benchmark Cycle 1 Standards PA Core Standard PA Eligible Content Common Core Standard B.3 Analyze and solve linear equations and pairs of simultaneous linear equations A.2 Understand and apply congruence, similarity, and geometric transformations using various tools. M08.B-E Write and identify 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). M08.B-E Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. M08.C-G Identify and apply properties of rotations, reflections, and translations. Example: Angle measures are preserved in rotations, reflections, and translations. M08.C-G Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them. 8.EE.7. Solve linear equations in one variable. a. 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). 8.EE.7. Solve linear equations in one variable. b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 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. M08.C-G Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures, using coordinates. 8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

4 2.2.8.B.2 Understand the connections between proportional relationships, lines, and linear equations. M08.C-G Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them. M08.B-E Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Example: Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. M08.B-E Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. M08.B-E 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.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. 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. 8.EE.6. Use similar triangles to explain why the slope m is 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

5 9/5 9/20 2 Days Per Lesson + 4 Days Benchmark Cycle 1 Scope and Sequence Suggested Dates Chapter 1: Solving Equations Section Lesson Title Lesson Goal(s) 1.1 Solving Simple Equations - Solve simply equations using addition, subtraction, multiplication, or division Eligible Content M08.B-E M08.B-E Solving Multi-Step Equations Solving Equations with Variables on Both Sides Rewriting Equations and Formulas - Use inverse operations to solve multi-step equations - Use the Distributive Property to solve multi-step equations - Solve equations with variables on both sides - Determine whether equations have no solution or infinitely many solutions - Rewrite equations to solve for one variable in terms of the other variable(s) M08.B-E M08.B-E M08.B-E M08.B-E M08.B-E THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

6 9/25 10/17 2 Days Per Lesson + 4 Days Suggested Dates Chapter 2: Transformations Section Lesson Title Lesson Goal(s) 2.1 Congruent Figures 2.2 Translations 2.3 Reflections 2.4 Rotations 2.5 Similar Figures 2.7 Dilations - Name corresponding angles and corresponding sides of congruent figures - Identify congruent figures - Identify translations - Translate figures in the coordinate plane - Identify reflections - Reflect figures in the x-axis or y-axis of the coordinate plane - Identify rotations - Rotate figures in the coordinate plane - Use more than one transformation to find images of figures - Name corresponding angles and sides of similar figures - Identify similar figures - Find unknown measures of similar figures - Identify dilations - Dilate figures in the coordinate plane - Use more than one transformation to find images of figures Eligible Content M08.C-G M08.C-G M08.C-G M08.C-G M08.C-G M08.C-G M08.C-G M08.C-G M08.C-G M08.C-G Preparing for: M08.C-G M08.C-G M08.C-G THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

7 10/18 10/31 2 Days Per Lesson + 4 Days Suggested Dates Chapter 4: Graphing and Writing Linear Equations Section Lesson Title Lesson Goal(s) 4.1 Graphing Linear Equations 4.2 Slope of a Line 4.2 Extension Slopes of Parallel and Perpendicular Lines - Understand that lines represent solutions of linear equations - Graph linear equations - Find slopes of lines by using two points - Find slopes of lines from tables - Identify parallel and perpendicular lines Benchmark 1 Window: 11/1 11/17 Eligible Content M08.B-E M08.B-E M08.B-E M08.B-E M08.B-E THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

8 Benchmark Cycle 2 Standards PA Core Standard PA Eligible Content Common Core Standard B.2 Understand the connections between proportional relationships, lines, and linear equations B.3 Analyze and solve linear equations and pairs of simultaneous linear equations C.1 Define, evaluate, and compare functions. M08.B-E Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Example: Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. M08.B-E Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. M08.B-E 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. M08.B-E Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. M08.B-E Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. Example: 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. M08.B-F Determine whether a relation is a function. 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. 8.EE.6. Use similar triangles to explain why the slope m is 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. 8.EE.8. Analyze and solve pairs of simultaneous linear equations. 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. 8.EE.8. Analyze and solve pairs of simultaneous linear equations. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

9 2.2.8.C.2 Use concepts of functions to model relationships between quantities. M08.B-F 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. M08.B-F Compare properties of two functions each represented in a different way (i.e., algebraically, graphically, numerically in tables, or by verbal descriptions). 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. M08.B-F 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. M08.B-F 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.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.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 = s2 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

10 2.4.8.B.1 Analyze and/or interpret bivariate data displayed in multiple representations. M08.B-F 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 or determine a graph that exhibits the qualitative features of a function that has been described verbally. M08.D-S 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 correlation, linear association, and nonlinear association. M08.D-S For scatter plots that suggest a linear association, identify a line of best fit by judging the closeness of the data points to the line. M08.D-S Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Example: In a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 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. 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. 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. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

11 2.4.8.B.2 Understand that patterns of association can be seen in bivariate data utilizing frequencies E.1 Distinguish between rational and irrational numbers using their properties B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions. M08.D-S 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 associations between the two variables. Example: Given data on whether students have a curfew on school nights and whether they have assigned chores at home, is there evidence that those who have a curfew also tend to have chores? M08.A-N Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths). M08.B-E 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 perfect squares (up to and including 12 2 ) and cube roots of perfect cubes (up to and including 5 3 ) without a calculator. Example: If x 2 = 25 then x = ± 25 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. 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? 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.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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

12 11/02 11/22 2 Days Per Lesson Days Benchmark Cycle 2 Scope and Sequence Suggested Dates Chapter 4: Graphing and Writing Linear Equations Section Lesson Title Lesson Goal(s) Graphing Proportional Relationships Graphing Linear Equations in Slope- Intercept Form - Write and graph proportional relationships - Find slopes and y-intercepts of graphs of linear equations - Graph linear equations written in slope-intercept form Eligible Content M08.B-E M08.B-E M08.B-E M08.B-E M08.B-E Graphing Linear Equations in Standard Form - Graph linear equations written in standard form M08.B-E M08.B-E Writing Equations in Slope- Intercept Form - Write equations of lines in slope-intercept form M08.B-F THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

13 11/27 12/15 2 Days per Lesson Days Suggested Dates Chapter 5: Systems of Linear Equations Section Lesson Title Lesson Goal(s) Solving Systems of Linear Equations by Graphing Solving Systems of Linear Equations by Substitution - Write and solve systems of linear equations by graphing - Solve real-life problems - Write and solve systems of linear equations by substitution - Solve real-life problems Eligible Content M08.B-E M08.B-E M08.B-E M08.B-E M08.B-E Solving Systems of Linear Equations by Elimination - Write and solve systems of linear equations by elimination - Solve real-life problems M08.B-E M08.B-E Solving Special Systems of Linear Equations - Solve systems of linear equations with no solution or infinitely many solutions M08.B-E M08.B-E THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

14 12/18 01/17 2 Days per Lesson + 5 Days Suggested Dates Chapter 6: Functions Section Lesson Title Lesson Goal(s) Eligible Content 6.1 Relations and Functions - Represent a relation as ordered pairs or a mapping diagram - Determine whether a relation is a function M08.B-F Representations of Functions - Write function rules - Use input-output tables to represent functions - Use graphs to represent functions M08.B-F Linear Functions - Understand that the equation y = mx + b defines a linear function - Write linear functions using graphs or tables - Compare linear functions M08.B-F M08.B-F M08.B-F Comparing Linear and Nonlinear Functions - Identify linear and nonlinear functions from tables or graphs - Compare linear and nonlinear functions M08.B-F Analyzing and Sketching Graphs - Analyze the relationship between two quantities using graphs - Sketch graphs to represent the relationship between two quantities M08.B-F THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

15 01/18 01/26 2 Days Per Lesson + 3 Days Suggested Dates Chapter 7: Real Numbers and The Pythagorean Theorem Section Lesson Title Lesson Objective(s) Eligible Content 7.1 Finding Square Roots 7.2 Finding Cube Roots* - Find square roots of perfect squares - Evaluate expressions involving square roots - Use square roots to solve equations - Find cube roots of perfect cubes - Evaluate expressions involving cube roots - Use cube roots to solve equations M08.B-E M08.B-E M08.A-N Benchmark 2 Window 01/29 02/13 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

16 Benchmark Cycle 3 Standards PA Core Standard PA Eligible Content Common Core Standard E.1 Distinguish between rational and irrational numbers using their properties E.4 Estimate irrational numbers by comparing them to rational numbers B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions. M08.A-N Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths). M08.A-N Convert a terminating or repeating decimal into a rational number (limit repeating decimals to thousandths). M08.A-N Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144). Example: 5 is between 2 and 3 but closer to 2 M08.A-N Use rational approximations of irrational numbers to compare and order irrational numbers. M08.A-N Locate/identify rational and irrational numbers at their approximate locations on a number line. M08.B-E Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided. Example: = 3 3 = 1/3 3 = 1/27 M08.B-E 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 perfect squares (up to and including 12 2 ) and cube roots of perfect cubes (up to and including 5 3 ) without a calculator. Example: If x 2 = 25 then x = ± 25 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 (e.g., π2). 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. 8.EE.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, = 3 3 = 1/3 3 = 1/27. 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

17 2.2.8.B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions A.3 Understand and apply the Pythagorean Theorem to solve problems. M08.B-E Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10, and express how many times larger or smaller one number is than another. Example: Estimate the population of the United States as and the population of the world as , and determine that the world population is more than 20 times larger than the United States population. M08.B-E Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Express answers in 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 (e.g., interpret 4.7EE9 displayed on a calculator as ). M08.C-G Apply the converse of the Pythagorean theorem to show a triangle is a right triangle. M08.C-G Apply the Pythagorean theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. (Figures provided for problems in three dimensions will be consistent with Eligible Content in grade 8 and below.) M08.C-G Apply the Pythagorean theorem to find the distance between two points in a coordinate system. 8.EE.3. Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very 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 times 10 8 and the population of the world as 7 times 10 9, and determine that the world population is more than 20 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. 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

18 2.4.8.B.1 Analyze and/or interpret bivariate data displayed in multiple representations B.2 Understand that patterns of association can be seen in bivariate data utilizing frequencies. M08.D-S 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 correlation, linear association, and nonlinear association. M08.D-S For scatter plots that suggest a linear association, identify a line of best fit by judging the closeness of the data points to the line. M08.D-S Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Example: In a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. M08.D-S 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 associations between the two variables. Example: Given data on whether students have a curfew on school nights and whether they have assigned chores at home, is there evidence that those who have a curfew also tend to have chores? 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. 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. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 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. 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? THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

19 01/30 02/16 2 Days per Lesson Days Benchmark Cycle 3 Scope and Sequence Suggested Dates Chapter 7: Real Numbers and The Pythagorean Theorem Section Lesson Title Lesson Objective(s) 7.3 The Pythagorean Theorem 7.4 Approximating Square Roots 7.4 Extension Repeating Decimals 7.5 Using the Pythagorean Theorem - Provide geometric proof of the Pythagorean Theorem - Use the Pythagorean Theorem to find missing side lengths of right triangles - Solve real-life problems - Define irrational numbers - Approximate square roots - Approximate values of expressions involving irrational numbers - Write repeating decimals as fractions - Use the converse of the Pythagorean Theorem to identify right triangles - Use the Pythagorean Theorem to find distances in a coordinate plane - Solve real-life problems Eligible Content M08.B-E M08.C-G M08.C-G M08.C-G M08.B-E M08.A-N M08.A-N M08.A-N M08.A-N M08.A-N M08.A-N M08.B-E M08.C-G M08.C-G M08.C-G THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

20 02/20 03/07 2 Days per Lesson + 4 Days Suggested Dates Chapter 9: Data Analysis and Displays Section Lesson Title Lesson Objective(s) 9.1 Scatter Plots 9.2 Lines of Fit 9.3 Two-Way Tables - Construct and interpret scatter plots - Describe patterns in scatter plots - Find lines of fit - Use lines of fit to solve problems Eligible Content M08.D-S M08.D-S M08.D-S M08.B-F Read two-way tables - Make and interpret two-way tables M08.D-S Choosing a Data Display - Choose appropriate data displays - Identify and analyze misleading data displays M08.D-S THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

21 03/08 04/13 2 Days per Lesson Days and ELA PSSA Week Suggested Dates Chapter 10: Exponents and Scientific Notation Section Lesson Title Lesson Objective(s) 10.1 Exponents 10.2 Product of Powers Property - Write expressions using integer exponents - Evaluate expressions involving integer exponents - Multiply powers with the same base - Find a power of a power - Find a power of a product Eligible Content M08.B-E M08.B-E M08.B-E Quotient of Powers Property 10.4 Zero and Negative Exponents 10.5 Reading Scientific Notation 10.6 Writing Scientific Notation - Divide powers with the same base - Simplify expressions involving the quotient of powers - Evaluate expressions involving numbers with zero as an exponent - Evaluate expressions involving negative integer exponents - Identify numbers written in scientific notation - Write numbers in standard form - Compare numbers in scientific notation - Write large and small numbers in scientific notation - Perform operations with numbers written in scientific notation M08.B-E M08.B-E M08.B-E M08.B-E M08.B-E M08.B-E Operations in Scientific Notation - Add, subtract, multiply and divide numbers in scientific notation M08.B-E Math PSSA 4/16 4/20 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

22 04/25 05/08 2 Days Per Lesson + 6 Days Suggested Dates Chapter 8: Surface Area and Volume Section Lesson Title Lesson Objective 8.1 Volumes of Cylinders 8.2 Volumes of Cones 8.3 Volumes of Spheres - Find the volumes of cylinders - Find the heights of cylinders given the volumes - Solve real-life problems - Find the volumes of cones - Find the heights of cones given the volumes - Solve real-life problems - Find the volumes of spheres - Find the radii of spheres given the volumes - Solve real-life problems Eligible Content M08.C-G M08.C-G M08.C-G *Note: Chapter 8 Content will not be assessed on Benchmark 3 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

23 Cycle 4 Standard PA Core Standard PA Eligible Content Common Core Standard A.1 Apply the concepts of volume of cylinders, cones, and spheres to solve realworld and mathematical problems. M08.C-G Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. Formulas will be provided. 8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

24 05/10 05/25 2 Days Per Lesson + 2 Days Cycle 4 Scope and Sequence Suggested Dates Chapter 8: Surface Area and Volume Section Lesson Title Lesson Objective 8.4 Surface Area and Volumes of Similar Solids 3.1 Parallel Lines and Transversals 3.2 Angles of Triangles 3.3 Angles of Polygons - Identify similar solids - Use properties of similar solids to find missing measures - Understand the relationship between surface areas of similar solids - Understand the relationship between volumes of similar solids - Solve real-life problems - Identify the angles formed when parallel lines are cut by a transversal - Find the measures of angles formed when parallel lines are cut by a transversal - Understand that the sum of the interior angle measures of a triangle is 180 o - Find the measures of interior and exterior angles of triangles - Find the sum of the interior angle measures of polygons - Understand that the sum of the exterior angle measures of a polygon is 360 o - Find the measures of interior and exterior angles of polygons Eligible Content M08.C-G M07.C-G Not assessed in PA Not assessed in PA THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

25 Remediation and Extension Options 5/29-6/12 11 Days Option 1: Revisit 3-Act Math Lessons (6-8 env) Each Topic featured a 3-Act Mathematical Modeling lesson that you may or may not have had time to do with your students. During the remainder of the year, you can revisit key ideas from 6 th grade and provide students with opportunities to engage authentically in the Standards for Mathematical Practice through a series of 3-Act Lessons. You can also find more lessons at this link: Option 2: Reteach Based on Common Core-identified focal areas. Option 3: Miscellaneous (Financial Literacy, Quantitative Reasoning, Statistics, etc.) You taught many topics this year. The topics below are identified as the most critical for 8 th grade. If you want to revisit something, one or more of these topics would be a good idea. 8.EE.A Work with radicals and integer exponents. 8.EE.B Understand the connections between proportional relationships, lines, and linear equations. 8.EE.C Analyze and solve linear equations and pairs of simultaneous linear equations. 8.F.A Define, evaluate, and compare functions. 8.F.B Use functions to model relationships between quantities. 8.G.A Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.B Understand and apply the Pythagorean Theorem. The Federal Reserve Bank of Philadelphia has posted free lesson plans for elementary teachers (including K) on financial literacy at: Many of these lessons are tied to early children s literature, as well. In addition, Census.gov has a number of data analysis activities, using real U.S. Census data, at: THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

26 PA Core Standards and Eligible Content by Cycle PA Core Standard CC E.1 Distinguish between rational and irrational numbers using their properties. PA Eligible Content M08.A-N Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths). M08.A-N Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths). Cycle 1 Cycle 2 Cycle 3 Cycle 4 CC E.4 Estimate irrational numbers by comparing them to rational numbers CC B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions. M08.A-N Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144). M08.A-N Use rational approximations of irrational numbers to compare and order irrational numbers. M08.A-N Locate/identify rational and irrational numbers at their approximate locations on a number line. M08.B-E Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided. M08.B-E 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 perfect squares (up to and including 12 2 ) and cube roots of perfect cubes (up to and including 5 3 ) without a calculator. M08.B-E Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10 and express how many times larger or smaller one number is than another. M08.B-E Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Express answers in 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 (e.g., interpret 4.7EE9 displayed on a calculator as ). THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

27 CC B.2 Understand the connections between proportional relationships, lines, and linear equations. CC B.3 Analyze and solve linear equations and pairs of simultaneous linear equations. CC C.1 Define, evaluate, and compare functions. CC C.2 Use concepts of functions to model relationships between quantities. M08.B-E Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. M08.B-E Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. M08.B-E 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. M08.B-E Write and identify 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). M08.B-E Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. M08.B-E Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs because points of intersection satisfy both equations simultaneously. M08.B-E Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection. M08.B-E Solve real-world and mathematical problems leading to two linear equations in two variables. M08.B-F Determine whether a relation is a function. M08.B-F Compare properties of two functions, each represented in a different way (i.e., algebraically, graphically, numerically in tables, or by verbal descriptions). M08.B-F 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. M08.B-F 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

28 CC A.1 Apply the concepts of volume of cylinders, cones, and spheres to solve real world and mathematical problems. CC A.2 Understand and apply congruence, similarity, and geometric transformations using various tools. M08.B-F 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 or determine a graph that exhibits the qualitative features of a function that has been described verbally. M08.C-G Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. Formulas will be provided. M08.C-G Identify and apply properties of rotations, reflections, and translations. M08.C-G Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them. CC A.3 Understand and apply the Pythagorean Theorem to solve problems. CC B.1 Analyze and/or interpret bivariate data displayed in multiple representations. M08.C-G Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. M08.C-G Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them. M08.C-G Apply the converse of the Pythagorean theorem to show a triangle is a right triangle. M08.C-G Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (Figures provided for problems in three dimensions will be consistent with Eligible Content in grade 8 and below.) M08.C-G Apply the Pythagorean theorem to find the distance between two points in a coordinate system. M08.D-S 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 correlation, linear association, and nonlinear association. M08.D-S For scatter plots that suggest a linear association, identify a line of best fit by judging the closeness of the data points to the line. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

29 CC B.2 Understand that patterns of association can be seen in bivariate data utilizing frequencies. M08.D-S Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. M08.D-S 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 associations between the two variables. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

30 Document Information Page Overview of Contents of Document The Cover Page lays out the Topics taught within each Cycle as well as the corresponding dates. The Benchmark Cycle Standards pages that precede each cycle outline all of the standards that are taught within that cycle. These are, therefore, all of the standards that may be on that Cycle s Benchmark. The Benchmark Cycle Scope and Sequence pages provide suggested pacing that allows for 1 day per lesson plus some flex days. We recommend proactively using the flex days for: reviewing pre-requisite content, splitting lessons over multiple days, assessing, reteaching, and doing projects. Of course, some of these will also be taken by field trips and other school activities. The PA Core Standards and Eligible Content by Cycle page lists all of the standards and indicates in which cycle(s) they are taught. What is a Cycle? We want to offer clarity on what appears on each benchmark. Additionally, there should be sufficient time to teach that content before it is tested. Because each school administers the benchmark on a different day, not necessarily corresponding with the last day of the Term, we have created Cycles. Each Cycle contains the content that is to be taught and tested on a given benchmark. Please refer to the dates on the Cover Page to ensure you are aware of the beginning and ending dates for each Cycle. What If I Fall Behind? We trust you to make decisions about what is best for your students. This pacing will prepare you for the Benchmarks and PSSA, but it is a suggested, not mandated, pacing. You may also wish to move at a faster pace. Do not feel you should slow down to match this guide. If you are concerned about content that you may not reach before the PSSA, consider implementing number talks and other short routines and games. For example, a lot of Geometry vocabulary and concepts could be taught through Which Once Doesn t Belong. Rather than pushing to cover content, or using test prep resources, content can be infused through short but meaningful structures. The table below is purely for informational purposes. We used the PSSA Mathematics Blueprint to calculate what percent of tested content you will cover, based on how much of the book you teach before the test. Again, we recommend depth and understanding over coverage, but we wanted to provide this information for your planning purposes. Percent of PSSA if Chapters 1-10 Are Taught Percent of PSSA if Chapters 1-9 Are Taught Percent of PSSA if Chapters 1-8 Are Taught Percent of PSSA if Chapters 1-10 except 8 Are Taught 100% 89% 74% 96.4% THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY