Topics and Chapters/Units Total Teaching Days Dates Grade 7 envisionmath2.0 2017-2018 SY Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4 September 5 - October 31 BM Window Opens November 1 November 2 - January 26 BM Window Opens January 29 January 30 - May 8 BM Window Opens May 9 May 10 - June 12 Total Days: 39 Including 1 Half Day Total Days: 50 Including 4 Half Days Total Days Before PSSA: 50 Including 9 Half Days Total Days in Cycle: 60 Including 13 Half Days; Excluding Week of Math PSSA Total Days: 22 Including 1 Half Day envisionmath2.0 (Pearson) 1: Integers and Rational Numbers 2: Analyze and Use Proportional Relationships envisionmath2.0 (Pearson) 3: Analyze and Solve Percent Problems 4: Generate Equivalent Expressions 5-1 5-3: Solve Problems Using Equations and Inequalities envisionmath2.0 (Pearson) 5-4 5-7: Solve Problems Using Equations and Inequalities (cont d) 8: Solve Problems Involving Geometry + 2 PA Lessons (see below) 6: Use Sampling to Draw Inferences About Populations 7-1 7-3: Probability* *Note: Topic 7 will not be assessed on Benchmark 3. envisionmath2.0 (Pearson) 7: Probability Remediate and Extend Supplementary Lessons PA-1: Describe Triangle Properties PA-2: Angles, Lines and Transversals. Note: A cycle is defined as the time allotted to teach the content that is on each benchmark, and assumes the benchmark is taken on the first day 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 2017-2018 1
Table of Contents Benchmark Cycle 1 Standards... 3 Benchmark Cycle 1 Scope and Sequence... 5 Benchmark Cycle 2 Standards... 7 Benchmark Cycle 2 Scope and Sequence... 10 Benchmark Cycle 3 Standards... 13 Benchmark Cycle 3 Scope and Sequence... 17 Cycle 4 Standards... 21 Cycle 4 Scope and Sequence... 23 PA Core Standards and Eligible Content... 25 Document Information Page... 28 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 2
Benchmark Cycle 1 Standards PA Core Standard PA Eligible Content Common Core Standard CC.2.1.7.E.1 Apply and extend previous understandings of operations with fractions to operations with rational numbers. M07.A-N.1.1.1 Apply properties of operations to add and subtract rational numbers, including real-world contexts. M07.A-N.1.1.2 Represent addition and subtraction on a horizontal or vertical number line. 7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. d. Apply properties of operations as strategies to add and subtract rational numbers. CC.2.1.7.D.1 Analyze proportional relationships and use them to model and solve real world and mathematical problems. M07.A-N.1.1.3 Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats. M07.A-R.1.1.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. M07.A-R.1.1.2 Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin). M07.A-R.1.1.3 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. M07.A-R.1.1.4 Represent proportional relationships by equations. M07.A-R.1.1.5 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate. 7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers. 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2. Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 3
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. CC.2.2.7.B.3 Model and solve real world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems. M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. 7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. 7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. d. Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 4
9/5 10/10 2 Days Per Lesson + 3 Days Benchmark Cycle 1 Scope and Sequence Topic 1: Integers and Rational Numbers Suggested Dates Topic- Lesson 1-1 Lesson Title Relate Integers and Their Opposites 1-2 Understand Rational Numbers 1-3 Add Integers 1-4 Subtract Integers 1-5 Add and Subtract Rational Numbers 1-6 Multiply Integers 1-7 Multiply Rational Numbers 1-8 Divide Integers 1-9 Divide Rational Numbers 1-10 Solve Problems with Rational Numbers Lesson Objective(s) - Understand how integers, their opposites, and absolute values are related - Apply this understanding to models (number lines) and use these to solve real-world problems - Identify rational numbers - Convert rational numbers expressed as fractions to terminating or repeating decimals - Add positive and negative integers - Model integer addition in real-life applications - Understand subtraction of integers as addition the additive inverse, p q = p + (-q) - Use addition and subtraction rules to solve real-world problems - Add and subtract positive and negative rational numbers - Use number lines to model addition and subtraction as a movement or distance between rational numbers - Multiply positive and negative integers - Use models and mathematical properties to develop a deep understanding of and fluency with multiplying integers - Multiply with rational numbers - Apply operations with rational numbers to real-world contexts - Use the relationship between multiplication and division to divide integers - Determine which quotients of integers are equivalent - Understand how the signs of integers in multiplication sentence relate to the signs in a related division sentence - Extend their knowledge about multiplying rational numbers and dividing integers to division of rational numbers - Decide which operations to use to solve problems with rational numbers Eligible Content M06.A-N.3.2.1 Preparing for: M07.A-N.1.1.1 M07.A-N.1.1.2 Preparing for: M07.A-N.1.1.1 M07.A-N.1.1.1 M07.A-N.1.1.1 M07.A-N.1.1.2 M07.A-N.1.1.1 M07.A-N.1.1.2 M07.A-N.1.1.3 M07.A-N.1.1.3 M07.A-N.1.1.3 M07.A-N.1.1.3 M07.A-N.1.1.1 M07.A-N.1.1.3 M07.B-E.2.1.1 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 5
10/11 10/31 2 Days Per Lesson + 2.5 Days Topic 2: Analyze and Use Proportional Relationships Suggested Dates Topic- Lesson 2-1 2-2 2-3 2-4 Lesson Title Connect Ratios, Rates and Unit Rates Determine Unit Rates with Ratios of Fractions Understand Proportional Relationships: Equivalent Ratios Describe Proportional Relationships: Constant of Proportionality 2-5 Graph Proportional Relationships 2-6 Apply Proportional Reasoning to Solve Problems Lesson Objective(s) - Use ratios and rates to describe the relationship between two quantities - Find equivalent ratios and use unit rates to solve multi-step problems - Find unit rates with ratios of fractions - Use unit rates to solve multi-step problems - Determine whether quantities are proportional by testing for equivalent ratios - Use the constant of proportionality to write equations that represent proportional relationships - Use equations to solve problems involving proportional relationships - Use a graph to recognize proportionality - Identify a constant of proportionality from a graph - Interpret a point on a graph of a proportional relationship - Explain whether a situation represents a proportional relationship - Use representations to find entry points into problems Eligible Content M07.A-R.1.1.1 M07.A-R.1.1.6 M07.A-R.1.1.1 M07.A-R.1.1.6 M07.A-R.1.1.2 M07.A-R.1.1.3 M07.A-R.1.1.4 M07.A-R.1.1.2 M07.A-R.1.1.3 M07.A-R.1.1.5 M07.A-R.1.1.2 M07.A-R.1.1.6 Benchmark 1 Window: 11/1 11/17 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 6
Benchmark Cycle 2 Standards PA Core Standard PA Eligible Content Common Core Standard CC.2.2.7.B.1 Apply properties of operations to generate equivalent expressions. CC.2.2.7.B.3 Model and solve real world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. M07.B-E.1.1.1 Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. M07.B-E.2.2.1 Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. 7.EE.4 Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 7
CC.2.1.7.D.1 Analyze proportional relationships and use them to model and solve real world and mathematical problems. M07.B-E.2.3.1 Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem. M07.B-E.2.2.2 Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality. M07.A-R.1.1.2 Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin). M07.A-R.1.1.3 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. M07.A-R.1.1.4 Represent proportional relationships by equations. M07.A-R.1.1.5 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.EE.4. Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. 7.RP.2. Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 8
M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 9
11/02 12/01 2 Days per Lesson + 4.5 Days (includes Report Card Conference Half Days) Benchmark Cycle 2 Scope and Sequence Topic 3: Analyze and Solve Percent Problems Suggested Dates Topic- Lesson 3-1 Lesson Title Lesson Objective(s) Eligible Content Compare Proportional Relationships 3-2 Connect Percent and Proportion - Understand that equivalent ratios can be used to model percent problems - Analyze percents of numbers in a real-world context - Write a proportion to model a percent situation - Use a percent proportion to find an unknown part, whole, or percent M07.A-R.1.1.2 M07.A-R.1.1.3 M07.A-R.1.1.4 M07.A-R.1.1.5 M07.A-R.1.1.4 3-3 Represent and Use the Percent Equation - Represent proportional relationships using percents - Use the percent equation to represent and solve percent problems M07.A-R.1.1.4 3-4 Solve Percent Change and Percent Error Problems - Calculate percent change and percent error - Understand the percent equation and how it leads to the percent change formula M07.A-R.1.1.6 3-5 Solve Markup and Markdown Problems - Understand and calculate percent markups and markdowns M07.A-R.1.1.6 3-6 Solve Simple Interest Problems - Understand what simple interest is and how it is calculated - Solve problems involving simple interest M07.A-R.1.1.6 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 10
12/04 01/10 2 Days per Lesson + 4 Days Topic 4: Generate Equivalent Expressions Suggested Dates Topic- Lesson 4-1 Lesson Title Write and Evaluate Algebraic Expressions 4-2 Generate Equivalent Expressions 4-3 Simplify Expressions 4-4 Expand Expressions 4-5 Factor Expressions 4-6 Add Expressions 4-7 Subtract Expressions 4-8 Analyze Equivalent Expressions Lesson Objective(s) Eligible Content - Write and evaluate algebraic expressions M07.B-E.2.1.1 - Write equivalent expressions by using properties and by combining like terms - Identify equivalent expressions - Identify and combine like terms - Simplify expressions using like terms - Apply the Distributive Property to expand linear expressions - Use area models to solidify their understanding of the Distributive Property - Find common factors of linear expressions using the Distributive Property Recognize factoring is the opposite of expanding expressions - Add expressions with rational coefficients using the Commutative and Associative Properties - Add expressions that represent real-world situations - Identify the similarity of the procedure between subtracting integers and subtracting linear expressions - Simplify linear expressions involving subtraction - Write equivalent expressions by combining like terms, using the Distributive Property, and performing other mathematical operations - Use equivalent expressions to examine relationships between quantities and interpret information in real-world problems M07.B-E.1.1.1 M07.B-E.1.1.1 M07.B-E.1.1.1 M07.B-E.1.1.1 M07.B-E.1.1.1 M07.B-E.1.1.1 M07.B-E.1.1.1 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 11
01/11 01/26 2 Days per Lesson + 3 Days Topic 5: Solve Problems Using Equations and Inequalities (5-1 5-3) Suggested Dates Topic- Lesson Lesson Title Lesson Objective(s) Eligible Content 5-1 Write Two-Step Equations - Analyze word problems to write two-step equations - Interpret the quantities in an equation M07.B-E.2.2.1 M07.B-E.2.3.1 5-2 Solve Two-Step Equations - Solve a problem using a two-step equation - Compare algebraic and arithmetic solutions M07.B-E.2.1.1 M07.B-E.2.2.1 5-3 5-4 Solve Equations Using the Distributive Property Solve Inequalities Using Addition or Subtraction - Solve equations using the Distributive Property - Graph the solution of inequalities on a number line - Solve inequalities using the Addition and Subtraction Properties of Inequality M07.B-E.2.1.1 M07.B-E.2.2.1 M07.B-E.2.3.1 M07.B-E.2.2.2 M07.B-E.2.3.1 Benchmark 2 Window 01/29-2/13 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 12
Benchmark Cycle 3 Standards PA Core Standard PA Eligible Content Common Core Standard CC.2.1.7.E.1 Apply and extend previous understandings of operations with fractions to operations with rational numbers. CC.2.2.7.B.3 Model and solve realworld and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. CC.2.3.7.A.2 Visualize and represent geometric figures and describe the relationships between them. M07.A-N.1.1.3 Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats. M07.B-E.2.2.2 Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality. M07.B-E.2.3.1 Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem. M07.C-G.1.1.1 Solve problems involving scale drawings of geometric figures, including finding length and area. 7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers. 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 13
M07.C-G.1.1.2 Identify or describe the properties of all types of triangles based on angle and side measures. M07.C-G.1.1.3 Use and apply the triangle inequality theorem. M07.C-G.1.1.4 Describe the two-dimensional figures that result from slicing three-dimensional figures. NO MATCH 8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. 7.G.3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids CC.2.3.7.A.1 Solve real world and mathematical problems involving angle measure, area, surface area, circumference, and volume. M07.C-G.2.1.1 Identify and use properties of supplementary, complementary, and adjacent angles in a multi- step problem to write and solve simple equations for an unknown angle in a figure. 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. M07.C-G.2.1.2 Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding). 8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 14
CC.2.4.7.B.1 Draw inferences about populations based on random sampling concepts. CC.2.4.7.B.2 Draw informal comparative inferences about two populations. M07.C-G.2.2.1 Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided. M07.C-G.2.2.2 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided. M07.D-S.1.1.1 Determine whether a sample is a random sample given a real-world situation. M07.D-S.1.1.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. M07.D-S.2.1.1 Compare two numerical data distributions using measures of center and variability. 7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 15
CC.2.4.7.B.2 Draw informal comparative inferences about two populations. M07.D-S.2.1.1 Compare two numerical data distributions using measures of center and variability. 7.SP.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 16
01/30 02/09 2 Days Per Lesson + 3 days Benchmark Cycle 3 Scope and Sequence Topic 5: Solve Problems Using Equations and Inequalities (5-4 5-7) Suggested Dates Topic. Lesson Lesson Title Lesson Objective(s) Eligible Content 5-5 Solve Inequalities Using Multiplication or Division - Write inequalities and solve them using the Multiplication and Division Properties of Inequality - Graph the solutions of inequalities on a number line M07.B-E.2.2.2 M07.B-E.2.3.1 5-6 Solve Two-Step Inequalities 5-7 Solve Multi-Step Inequalities - Solve an inequality by multiplying or dividing by a negative rational number - Write a two-step inequality to solve a problem - Solve a two-step inequality - Reinforce skills learned in previous lessons and apply that knowledge to solving multi-step inequalities - Explore the relationship between two-step inequalities and multi-step inequalities - Apply the Distributive Property to simplify and solve multi-step inequalities M07.B-E.2.2.2 M07.B-E.2.3.1 M07.B-E.2.2.2 M07.B-E.2.3.1 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 17
02/12 03/23 2 Days per Lesson + 4 Days Suggested Dates Topic- Lesson 8-1 Lesson Title Solve Problems Involving Scale Drawings 8-2 Draw Geometric Figures 8-3 PA-1 8-4 PA-2 8-5 8-6 Draw Triangles with Given Conditions Describe Triangle Properties Solve Problems Using Angle Relationships Angles, Lines and Transversals Solve Problems Involving Circumference of a Circle Solve Problems Involving Area of a Circle 8-7 Describe Cross Sections 8-8 8-9 Solve Problems Involving Surface Area Solve Problems Involving Volume Unit 8: Solve Problems Involving Geometry Lesson Objective(s) Eligible Content - Use a scale drawing as a representation of actual lengths and area M07.C-G.1.1.1 - Draw geometric shapes with given conditions - Name and classify quadrilaterals according to their properties - Sketch and construct triangles with given conditions - Determine the number of triangles that can be formed given side lengths and angle measures - Determine measures of interior angles of triangles - Describe a triangle using angle measures and side lengths - Use the Triangle Inequality Theorem to determine whether three side lengths can form a triangle - Find the measure of angles using angle relationships - Recognize the relationship between different angles formed by intersecting lines and rays - Identify relationships among angles formed by parallel lines and a transversal - Determine the measures of angles formed by parallel lines and a transversal - Calculate the circumference, radius, or diameter of a circle - Recognize the relationship between the circumference of a circle, diameter of a circle, and - Find the area of a circle - Use the area of a circle to find the radius and diameter - Solve problems involving the area of a circle - Describe and sketch cross sections of right rectangular prisms and right rectangular pyramids - Solve problems involving cross sections - Find the surface area of 2-dimensional composite shapes - Find the surface area of 3-dimensional composite shapes - Calculate the volume of various three-dimensional figures composed of prisms - Solve problems involving the volume of three-dimensional figures No PA Alignment M07.C-G.1.1.2 M07.C-G.1.1.3 M07.C-G.1.1.2 M07.C-G.1.1.3 M07.C-G.2.1.1 M08.C-G.2.1.2 M07.C-G.2.2.1 M07.C-G.2.2.1 M07.C-G.2.1.4 M07.C-G.2.2.2 M07.C-G.2.2.2 M07.A-N.1.1.3 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 18
03/26 4/13 2 Days per Lesson + ELA PSSA Days Topic 6: Use Sampling to Draw Inferences About Populations Suggested Dates Topic- Lesson Lesson Title 6-1 Populations and Samples 6-2 Draw Inferences from Data 6-3 6-4 Make Comparative Inferences About Populations Make More Comparative Inferences About Populations Lesson Objective(s) - Understand the difference between a population and a sample - Establish whether a sample is representative of a population - Generate random samples that represent the entire population - Make qualitative and quantitative inferences from a sample data set - Make estimates about a population based on a sample data set, and assess whether the inferences are valid - Use box plots to compare and make inferences about populations - Use the median and interquartile range (IQR) of data sets to informally compare and make inferences about two populations - Use the mode, range, mean and mean absolute deviation (MAD) to compare populations Eligible Content M07.D-S.1.1.1 M07.D-S.1.1.2 M07.D-S.2.1.1 M07.D-S.2.1.1 Math PSSA 4/16 4/20 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 19
04/23 05/08 2 Days Per Lesson + 2 Days Topic 7: Probability Suggested Date Topic- Lesson 7-1 7-2 7-3 Lesson Title Understand Likelihood and Probability Understand Theoretical Probability Understand Experimental Probability Lesson Objective(s) - Use probability to describe the likelihood that an event will occur - Relate probability to mathematical fairness - Understand theoretical probability and how it can be used - Use theoretical probability to predict an outcome - Compare theoretical and experimental probability - Use experimental probability to make predictions - Explain difference between theoretical and experimental probability Eligible Content M07.D-S.3.1.1 M07.D-S.3.1.1 M07.D-S.3.2.2 M07.D-S.3.2.1 Benchmark 3 Window 5/9 5/25 *Note: Topic 7(Probability) will not be assessed on Benchmark 3. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 20
Cycle 4 Standards PA Core Standard PA Eligible Content Common Core Standard CC.2.4.7.B.3 Investigate chance processes and develop, use, and evaluate probability models. M07.D-S.3.1.1 Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (i.e., a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event). M07.D-S.3.2.1 Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability. M07.D-S.3.2.2 Find the probability of a simple event, including the probability of a simple event not occurring. M07.D-S.3.2.3 Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. Preparing for 7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 21
(e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. c. Design and use a simulation to generate frequencies for compound events. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 22
04/23 05/18 2 Days Per Lesson + 4 Days (does not include half days) for assessment and responding to student needs Cycle 4 Scope and Sequence Topic 7: Probability Suggested Date Topic- Lesson 7-1 7-2 7-3 Lesson Title Understand Likelihood and Probability Understand Theoretical Probability Understand Experimental Probability 7-4 Use Probability Models 7-5 7-6 Determine Outcomes of Compound Events Find Probabilities of Compound Events 7-7 Simulate Compound Events Lesson Objective(s) - Use probability to describe the likelihood that an event will occur - Relate probability to mathematical fairness - Understand theoretical probability and how it can be used - Use theoretical probability to predict an outcome - Compare theoretical and experimental probability - Use experimental probability to make predictions - Explain difference between theoretical and experimental probability - Develop a probability model - Use a probability model to evaluate a situation - Use a probability model to make an estimate - Use a tree diagram, a table, or an organized list to represent the sample space for a compound event - Organize information about a compound event on a table, a tree diagram, or an organized list - Find the probability of a compound event - Use different tools to simulate a compound event - Model a real-world situation involving a compound event and predict its outcome using a simulation Eligible Content M07.D-S.3.1.1 M07.D-S.3.1.1 M07.D-S.3.2.2 M07.D-S.3.2.1 M07.D-S.3.1.1 M07.D-S.3.2.1 M07.D-S.3.2.2 M07.D-S.3.2.3 M07.D-S.3.2.3 M07.D-S.3.2.3 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 23
Option 1: Revisit 3-Act Math Lessons (6-8 env) 5/21 6/12 15 Days Remediate and Extend by Preparing for Grade 8 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: https://whenmathhappens.com/3-act-math/. Option 2: Reteach Based on Common Coreidentified focal areas. You taught many topics this year. The four below are identified as the most critical for 7 th grade. If you want to revisit something, one or more of these topics would be a good idea. 7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7.EE.A Use properties of operations to generate equivalent expressions. 7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations Option 3: Pre-Teach Based on 7 th Grade Needs You can check in with your 8 th grade teacher to ask what content you could pre-teach or what content they would like you to revisit. The first two Topics in 8 th grade are: 1) Real Numbers 2) Analyze and Solve Linear Equations You can access the 8 th grade Teacher s Guide and materials online for reference. Option 4: Financial Literacy The Federal Reserve Bank of Philadelphia has posted free lesson plans for elementary teachers (including K) on financial literacy at: https://philadelphiafed.org/education/teachers/lesson-plans. 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: https://www.census.gov/schools/activities/math.html. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 24
PA Core Standards and Eligible Content PA Core Standard CC.2.1.7.D.1 Analyze proportional relationships and use them to model and solve real-world and mathematical problems. PA Eligible Content M07.A-R.1.1.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. M07.A-R.1.1.2 Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin). Cycle 1 Cycle 2 Cycle 3 Cycle 4 M07.A-R.1.1.3 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. M07.A-R.1.1.4 Represent proportional relationships by equations. M07.A-R.1.1.5 Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r), where r is the unit rate. M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems. CC.2.1.7.E.1 Apply and extend previous understandings of operations with fractions to operations with rational numbers. M07.A-N.1.1.1 Apply properties of operations to add and subtract rational numbers, including real-world contexts. M07.A-N.1.1.2 Represent addition and subtraction on a horizontal or vertical number line. M07.A-N.1.1.3 Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 25
CC.2.2.7.B.1 Apply properties of operations to generate equivalent expressions. CC.2.2.7.B.3 Model and solve real world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. M07.B-E.1.1.1 Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. M07.B-E.2.1.1 Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. M07.B-E.2.2.1 Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. M07.B-E.2.2.2 Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers, and graph the solution set of the inequality. CC.2.2.7.B.3 Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. M07.B-E.2.3.1 Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem. CC.2.3.7.A.1 Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume. M07.C-G.2.1.1 Identify and use properties of supplementary, complementary, and adjacent angles in a multi- step problem to write and solve simple equations for an unknown angle in a figure. M07.C-G.2.1.2 Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding). M07.C-G.2.2.1 Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). Formulas will be provided. M07.C-G.2.2.2 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Formulas will be provided. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 26
CC.2.3.7.A.2 Visualize and represent geometric figures and describe the relationships between them. CC.2.4.7.B.1 Draw inferences about populations based on random sampling concepts. CC.2.4.7.B.2 Draw informal comparative inferences about two populations. M07.C-G.1.1.1 Solve problems involving scale drawings of geometric figures, including finding length and area. M07.C-G.1.1.2 Identify or describe the properties of all types of triangles based on angle and side measures. M07.C-G.1.1.3 Use and apply the triangle inequality theorem. M07.C-G.1.1.4 Describe the two-dimensional figures that result from slicing three-dimensional figures. M07.D-S.1.1.1 Determine whether a sample is a random sample given a realworld situation. M07.D-S.1.1.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. M07.D-S.2.1.1 Compare two numerical data distributions using measures of center and variability. CC.2.4.7.B.3 Investigate chance processes and develop, use, and evaluate probability models. M07.D-S.3.1.1 Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible (i.e., a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event). M07.D-S.3.2.1 Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability. M07.D-S.3.2.2 Find the probability of a simple event, including the probability of a simple event not occurring. M07.D-S.3.2.3 Find probabilities of independent compound events using organized lists, tables, tree diagrams, and simulation. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 27
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 if Topics 1-8 Are Taught Percent if Topics 1-6 and 8 Are Taught Percent if Topics 1-7 Are Taught Percent if Topics 1-6 Are Taught 100% 91.2% 80% 71.2% THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 28
The Standards for Mathematical Practice are: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Additional Key Considerations in Mathematics You should try to infuse these Standards into your lessons regularly. Rather than thinking of them as a box to check, think about how you are providing students with opportunities to develop as mathematical thinkers and doers. The Common Core has identified the following as the four critical areas for Grade 7: 7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7.EE.A Use properties of operations to generate equivalent expressions. 7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations These do not necessarily reflect what is most tested on the PSSA, but it is the content that is most essential as you prepare students for 8th grade. The School District of Philadelphia s Vision for Mathematics Teaching and Learning: Our Guiding Principles: All students think mathematically, and they will be empowered to own, share, and do mathematics. Equitable Discourse Rich + Meaningful Tasks Purpose-Driven Work Questioning and Curiosity Valuing Diverse Thinking If you have any questions or would like more information, please contact us at math@philasd.org. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 29