Grade 8 Big Ideas + HMH Algebra SY

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1 Topics and Chapters/Units Days in Dates Grade 8 Big Ideas + HMH Algebra SY Benchmark 1 Benchmark 2 Benchmark 3 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 : 60 Including 13 Half Days Total Days: 22 Including 1 Half Day 8 th Grade(Big Ideas) : Equations 6.1, 6.2, 6.5: Functions : : Graphing and Writing Linear Equations Algebra 1 (HMH) 2.4, 2.5: Algebraic Models 13.3, 13.4: Absolute Value Equations and Inequalities 3.3: Functions and Models 8 th Grade(Big Ideas) : Graphing and Writing Linear Equations 6.3, 6.4: Functions : Systems of Linear Equations : Data Analysis and Displays Algebra 1 (HMH) 7.3: Linear Inequalities in Two Variables 9.1, 9.3: One-Variable Data Distributions 12.2: Graphing Systems of Linear Inequalities 8 th Grade(Big Ideas) , 2.7*: Transformations : Real Numbers and the Pythagorean Theorem Algebra 1 (HMH) 14.2: Simplifying Radicals** : Adding and Subtracting Polynomials : Multiplying Polynomials 21.1: Solving Equations by Factoring x 2 + bx + c*** *Note: Lessons 2.5 and 2.6 do not contain eligible content or PA Core content and so can be covered after the PSSA and Keystone **Note: Integer exponents and index 2 radicals only ***Note: Factoring only; no solving 8 th Grade(Big Ideas) 2.5, 2.6: Transformations 8 Volume and Similar Solids 10.7: Operations in Scientific Notation Remediate and Extend 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 1 Standards (8th Grade)... 3 Benchmark 1 Standards (Algebra 1)... 5 Benchmark 1 Scope and Sequence... 6 Benchmark 2 Standards (8 th Grade)... 9 Benchmark 2 Standards (Algebra 1) Benchmark 2 Scope and Sequence Benchmark 3 Standards (8 th Grade) Benchmark 3 Standards (Algebra 1) Benchmark 3 Scope and Sequence Standards (8 th Grade) Scope and Sequence th Grade Standards and Eligible Content by Quarter Algebra Eligible Content by Quarter Document Information Page THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

3 Benchmark 1 Standards (8th Grade) PA Core Standard PA Eligible Content Common Core Standard B.3 Analyze and solve linear equations and pairs of simultaneous linear equations C.1 Define, evaluate, and compare functions C.2 Use concepts of functions to model relationships between quantities B.2 Understand the connections between proportional relationships, lines, and linear equations. 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-F Determine whether a relation is a function. 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.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. 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.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. 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.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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

4 PA Core Standard PA Eligible Content Common Core Standard 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.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 Benchmark 1 Standards (Algebra 1) PA Eligible Content A Write, solve, and/or apply a linear equation (including problem situations). A Use and/or identify an algebraic property to justify any step in an equation-solving process. Note: Linear equations only A Interpret solutions to problems in the context of the problem situation. Note: Linear equations only. A Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). A Identify or graph the solution set to a linear inequality on a number line. A Interpret solutions to problems in the context of the problem situation. Note: Linear inequalities only. A Identify, describe, and/or use constant rates of change. A Apply the concept of linear rate of change (slope) to solve problems. PA Core High School Standards CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multi-step problems. CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

6 9/5 10/04 2 Days Per Lesson + 4 Days Benchmark 1 Scope and Sequence Suggested Dates Chapter. Section Lesson Title Unit 1: Equations and Inequalities 1.1 Solving Simple Equations - Solve one-step equations 1.2 Solving Multi-Step Equations - Solve multi-step equations 1.3 Solving Equations with Variables on Both Sides Lesson Goal(s) - Solve equations with variables on both sides 1.4 Rewriting Equations and Formulas - Solve literal equations Eligible Content M08.B-E M08.B-E A A M08.B-E M08.B-E A A M08.B-E M08.B-E A A M08.B-E A (HMH) Solving Absolute Value Equations - Solve absolute value equations A (HMH) 2.5 (HMH) 13.4 (HMH) Creating and Solving Inequalities Creating and Solving Compound Inequalities Solving Absolute Value Inequalities - Use a verbal or tabular model to write an inequality - Solve inequalities - Check solutions for reasonableness - Write compound inequalities - Solve and graph compound inequalities - Solve absolute value inequalities algebraically or graphically - Use absolute value inequalities to solve real-life problems A A A A A A A A Please Note: Blue Chapter. Section (1.3) labels correspond to the 8 th Grade Big Ideas text. Black Chapter. Section (13.3) labels correspond to the HMH Algebra 1 text. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

7 10/05 10/20 2 Days Per Lesson + 2 Days Unit 2: Introduction to Functions Suggested Dates Chapter. Section Lesson Title 6.1 Relations and Functions Lesson Goal(s) - Represent a relation as ordered pairs or a mapping diagram - Determine whether a relation is a function Eligible Content M08.B-F A A Representations of Functions - Represent functions as equations, input-output tables and graphs M08.B-F Analyzing and Sketching Graphs - Use graphs without numbers to show the relationship between quantities M08.B-F Supplement (1 Day) Define Domain and Range A (HMH) Modeling with Functions - Use function notation - Represent dependent and independent variables with function notation A Please Note: Blue Chapter. Section (1.3) labels correspond to the 8 th Grade Big Ideas text. Black Chapter. Section (13.3) labels correspond to the HMH Algebra 1 text. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

8 10/23 10/31 2 Days per Lesson +.5 Day Suggested Dates Chapter. Section Lesson Title Unit 3: Linear Functions Lesson Goal(s) 4.1 Graphing Linear Equations Graph linear equations 4.2 Slope of a Line Find the slope of a line 4.3 Graphing Proportional Relationships Graph proportional relationships Benchmark 1 Window: 11/1 11/17 Eligible Content M08.B-E A M08.B-E M08.B-E A M08.B-E M08.B-E M08.B-E A Please Note: Blue Chapter. Section (1.3) labels correspond to the 8 th Grade Big Ideas text. Black Chapter. Section (13.3) labels correspond to the HMH Algebra 1 text. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

9 Benchmark 2 Standards (8 th Grade) 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. 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. 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

10 PA Core Standard PA Eligible Content Common Core Standard C.1 Define, evaluate, and compare functions 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

11 PA Core Standard PA Eligible Content Common Core Standard 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

12 PA Core Standard PA Eligible Content Common Core Standard B.2 Understand that patterns of association can be seen in bivariate data utilizing frequencies. 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.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

13 Benchmark 2 Standards (Algebra 1) PA Eligible Content A Identify, describe, and/or use constant rates of change. A Apply the concept of linear rate of change (slope) to solve problems. A Write or identify a linear equation when given the graph of the line, two points on the line, or the slope and a point on the line. Note: Linear equation may be in point-slope, standard, and/or slope-intercept form. PA Core High School Standards CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable. A Determine the slope and/or y-intercept represented by a linear equation or graph. A Create, interpret, and/or use the equation, graph, or table of a linear function. A Translate from one representation of a linear function to another (i.e., graph, table, and equation). A Write and/or solve a system of linear equations (including problem situations) using CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multi-step problems. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables. CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

14 PA Eligible Content graphing, substitution, and/or elimination. Note: Limit systems to two linear equations. A Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations. A Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities. A Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities. A Estimate or calculate to make predictions based on a circle, line, bar graph, measure of central tendency, or other representation. A Analyze data, make predictions, and/or answer questions based on displayed data (box-andwhisker plots, stem-and-leaf plots, scatter plots, measures of central tendency, or other representations). A Make predictions using the equations or graphs of best-fit lines of scatter plots. A Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal, or percent. PA Core High School Standards CC B.3 Analyze and solve linear equations and pairs of simultaneous linear equations. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. C.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable. CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data. CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies. CC B.3 Investigate chance processes and develop, use, and evaluate probability models. CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments. CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

15 11/02 12/01 2 Days per Lesson Days (some are Report Card Conference half days) Benchmark 2 Scope and Sequence Suggested Dates Chapter. Section Lesson Title Graphing Linear Equations in Slope-Intercept Form Graphing Linear Equations in Standard Form Writing Equations in Slope- Intercept Form Writing Equations in Point-Slope Form Unit 3: Linear Functions (Continued) Lesson Goal(s) Graph the equation of a line written in slope-intercept form Graph a linear equation in standard form Write an equation in slope-intercept form Write an equation of a line given a slope and a point or two points 6.3 Linear Functions Write a linear function from a graph or a table of values 6.4 Comparing Linear and Nonlinear Functions Compare linear and nonlinear functions Eligible Content M08.B-E M08.B-E A M08.B-E M08.B-E A M08.B-F A M08.B-F A A M08.B-F M08.B-F M08.B-F A M08.B-F Please Note: Blue Chapter. Section (1.3) labels correspond to the 8 th Grade Big Ideas text. Black Chapter. Section (13.3) labels correspond to the HMH Algebra 1 text. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

16 12/04 12/22 2 Days per Lesson Days Unit 4: Systems Suggested Dates Chapter. Section Lesson Title Solving Systems of Linear Equations by Graphing Solving Systems of Linear Equations by Substitution Solving Systems of Linear Equations by Elimination Lesson Goal(s) Solve a system of linear equations by graphing Solve a system of linear equations by substitution Solve a system of linear equations by elimination Eligible Content M08.B-E M08.B-E M08.B-E A A M08.B-E M08.B-E A A M08.B-E M08.B-E A A Solving Special Systems of Linear Equations Solve a system of linear equations with no solution or infinitely many solutions M08.B-E M08.B-E A (HMH) 12.2 (HMH) Linear Inequalities in Two Variables Graphing Systems of Linear Inequalities -Write linear inequalities in two variables - Graph linear inequalities in two variables - Check solutions of systems of linear inequalities - Graph systems of linear inequalities - Write systems of linear inequalities A A A A Please Note: Blue Chapter. Section (1.3) labels correspond to the 8 th Grade Big Ideas text. Black Chapter. Section (13.3) labels correspond to the HMH Algebra 1 text. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

17 01/03 01/26 2 Days per Lesson+ 4 Days Suggested Dates Chapter. Section 9.1 Scatter Plots Lesson Title Unit 5: Probability, Data Analysis and Displays Lesson Objective(s) Make a scatter plot and describe the relationship between the data 9.2 Lines of Fit Identify a line of fit for a scatter plot 9.3 Two-Way Tables 9.4 Choosing a Data Display Construct and Analyze Two-Way Tables Choose and construct an appropriate data display Eligible Content M08.D-S M08.D-S M08.D-S M08.B-F A A A M08.D-S M08.D-S (HMH) 9.3 (HMH) Measures of Center and Spread Histograms and Box and Whisker Plots* Probability (2 Day Supplementary / Review Lesson) - Use the mean and median to describe and compare the center of data sets* - Use the range, interquartile range, or standard deviate to describe and compare spreads of data sets* *Note: These objectives are not part of PA 8 th Grade Eligible Content and so are only assessed on the Keystone - Estimate statistics and compare distributions using histograms - Use box-and-whisker plots to represent and compare data sets **Note: Box and Whisker Plots were shifted to Grade 6 (from Grade 8) in the PA Core, so students may not have prior knowledge. - Find probabilities of compound events - Find probability and represent it as a fraction, decimal or percent A A A A A Benchmark 2 Window: 1/29 2/13 Please Note: Blue Chapter. Section (1.3) labels correspond to the 8 th Grade Big Ideas text. Black Chapter. Section (13.3) labels correspond to the HMH Algebra 1 text THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

18 Benchmark 3 Standards (8 th Grade) PA Core Standard PA Eligible Content Common Core Standard A.2 Understand and apply congruence, similarity, and geometric transformations using various tools E.1 Distinguish between rational and irrational numbers using their properties. 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. 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.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). 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. 8.G.3. Describe the effect of dilations, translations, 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. 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

19 PA Core Standard PA Eligible Content Common Core Standard 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 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 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. 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. 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

20 PA Core Standard PA Eligible Content Common Core Standard A.3 Understand and apply the Pythagorean Theorem to solve problems. 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.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

21 Benchmark 3 Standards (Algebra 1) PA Eligible Content A Compare and/or order any real numbers. Note: Rational and irrational may be mixed. A Simplify square roots (e.g., 24 = 2 6). A Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from 10 to 10. A Use estimation to solve problems. A Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial. A Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials are limited to the form ax 2 + bx + c where a is equal to 1 after factoring out all monomial factors. A Simplify/reduce a rational algebraic expression. A Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. PA Core High School Standards CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems. C.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context. CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials. CC.2.2.HS.D.5 Use polynomial identities to solve problems. CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms. CC E.3 Develop and/or apply number theory concepts to find common factors and multiples. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

22 01/30 02/16 2 Days Per Lesson Days (including Report Card Conference Days) Benchmark 3 Scope and Sequence Unit 6: Geometric Transformations Suggested Dates Chapter. Section 2.1 Congruent Figures Lesson Title Lesson Objective(s) Eligible Content 2.2 Translations Identify translations Define congruent figures and determine if two figures are congruent 2.3 Reflections Identify and draw reflections 2.4 Rotations Identify and draw rotations 2.7 Dilations Draw dilations in the coordinate plane 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 M08.C-G M08.C-G THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

23 02/20 04/13 2 Days per Lesson +4.5 Days and ELA PSSA Week Suggested Dates Chapter. Section Unit 8: Real Numbers and The Pythagorean Theorem Lesson Title Lesson Goal(s) Eligible Content 7.1 Finding Square Roots Find square roots 7.2 Finding Cube Roots Find cube roots 7.3 The Pythagorean Theorem 7.4 Approximating Square Roots Approximate square roots 7.4 Extension Repeating Decimals 7.5 Using the Pythagorean Theorem Use the Pythagorean Theorem to solve for side lengths of right triangles Write repeating decimals as fractions 10.1 Exponents Write and evaluate powers 10.2 Product of Powers Property Use the converse of the Pythagorean Theorem and the distance formula - Use the Product of Powers Property - Use the Power of a Power Property - Use the Power of a Product Property M08.B-E M08.B-E M08.A-N A 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 A M08.A-N M08.A-N M08.B-E M08.C-G M08.C-G M08.C-G A M08.B-E A M08.B-E A Quotient of Powers Property Use the Quotient of Powers Property to simplify expressions 10.4 Zero and Negative Exponents Evaluate and simplify expressions with negative and zero exponents M08.B-E A M08.B-E A THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

24 (see above) Suggested Dates Chapter. Section 10.5 Reading Scientific Notation Unit 8: Real Numbers and The Pythagorean Theorem Lesson Title Lesson Goal(s) Eligible Content Read numbers in scientific notation and write them in standard form 10.6 Writing Scientific Notation Write numbers in scientific notation 14.2 (HMH) Simplifying Expressions with Rational Exponents and Radicals - Use properties of exponents to simplify expressions *Note: Limited to integer exponents and index 2 radicals on the Keystone. Not assessed on the 8 th Grade PSSA. M08.B-E M08.B-E A M08.B-E M08.B-E A A A A Math PSSA 4/16 4/20 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

25 04/23 05/11 1 Day Per Lesson + 4 Days (Includes Science PSSA days and Report Card Conference Half Days) Unit 9: Polynomials and Factoring Suggested Date Chapter. Section Lesson Title Lesson Objective(s) Eligible Content 17.1 (HMH) Understanding Polynomial Expressions - Distinguish between monomials and polynomials - Classify polynomials A (HMH) Adding Polynomial Expressions - Add polynomials A (HMH) 18.1 (HMH) 18.2 (HMH) Subtracting Polynomial Expressions Multiplying Polynomials by Monomials Multiplying Polynomial Expressions - Subtract polynomials A Multiply binomials by monomials A Multiply binomials A (HMH) Special Products of Binomials - Use the square of a binomial pattern - Use the sum and difference pattern A (HMH) Factoring x 2 + bx + c - Factor x 2 + bx + c A GCF and LCM of Monomials (1 Day Supplementary Lesson) A Keystone Exam Window 5/14 5/25 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

26 4 Standards (8 th Grade) 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 B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions. 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.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 ). 8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

27 5/21-6/12 2 Days Per Lesson 4 Scope and Sequence Unit 10: Surface Area, Volume and Similarity Suggested Dates Chapter. Section Lesson Title Lesson Objective Eligible Content 8.1 Volumes of Cylinders - Calculate the surface area of cylinders, cones and spheres M08.C-G Volumes of Cones 8.3 Volumes of Spheres - Identify and use the correct formula to find the volume of cylinders - Recognize the relationship between the formulas for volume of a rectangular prism and the volume of a cylinder - Find the volume of a cone - Recognize the relationship between volume of a cylinder and volume of a cone M08.C-G M08.C-G Surface Area and Volumes of Similar Solids Find the surface areas and volumes of similar solids M08.C-G Parallel Lines and Transversals Find measures of angles formed by parallel lines and a transversal M07.C-G Angles of Triangles Find interior and exterior angle measures of triangles 3.3 Angles of Polygons Find interior and exterior angle measures of polygons Not assessed in PA Not assessed in PA 10.7 Operations with Numbers in Scientific Notation Add, subtract, multiply and divide numbers in scientific notation M08.B-E THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

28 8 th Grade Standards and Eligible Content by Quarter 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) 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