Topics and Chapters/Units Days in Cycle Dates Grade 7 Big Ideas 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 Big Ideas 1: Integers 2: Rational Numbers 3.1, 3.2*: Expressions and Equations *Note: The 3.2 Lesson Extension does not include PA eligible content for 7 th grade and so can be done following the PSSA. Big Ideas 3.3 3.5: Expressions and Equations 4: Inequalities 5: Ratios and Proportions 6.1 6.4: Percents Big Ideas 6.5 6.7: Percents 7: Constructions and Scale Drawings 8: Circles and Area 9: Surface Area and Volume Big Ideas 10: Probability and Statistics 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 2017-2018 1
Table of Contents Benchmark Cycle 1 Standards... 3 Benchmark Cycle 1 Scope and Sequence... 4 Benchmark Cycle 2 Standards... 7 Benchmark Cycle 2 Scope and Sequence... 9 Benchmark Cycle 3 Standards... 12 Benchmark Cycle 3 Scope and Sequence... 15 Cycle 4 Standards... 19 Cycle 4 Scope and Sequence... 21 Document Information Page... 26 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. 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.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. 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. 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. 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 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 3
9/5 9/26 2 Days Per Lesson + 4 Days Benchmark Cycle 1 Scope and Sequence Suggested Dates Chapter 1: Integers Section Lesson Title Lesson Goal(s) 1.1 Integers and Absolute Value 1.2 Adding Integers - Define the absolute value of a number - Find absolute values of numbers - Add integers - Show that the sum of a number and its opposite is 0 Eligible Content M06.A-N.3.2.1 Preparing for: M07.A-N.1.1.1 M07.A-N.1.1.2 M07.A-N.1.1.1 1.3 Subtracting Integers - Subtract Integers M07.A-N.1.1.1 M07.A-N.1.1.2 1.4 Multiplying Integers - Multiply integers M07.A-N.1.1.3 1.5 Dividing Integers - Divide Integers M07.A-N.1.1.3 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 4
9/27 10/12 2 Days Per Lesson + 3 Days Suggested Dates Chapter 2: Rational Numbers Section Lesson Title Lesson Goal(s) 2.1 Rational Numbers 2.2 Adding Rational Numbers - Understand that a rational number is an integer divided by an integer - Convert rational numbers to decimals - Add rational numbers Eligible Content Preparing for: M07.A-N.1.1.1 M07.A-N.1.1.1 M07.A-N.1.1.2 2.3 Subtracting Rational Numbers - Subtract rational numbers M07.A-N.1.1.1 M07.A-N.1.1.2 2.4 Multiplying and Dividing Rational Numbers - Multiply and divide rational numbers M07.A-N.1.1.3 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 5
10/13 10/31 2 Days per Lesson + 2.5 Days Suggested Dates Chapter 3: Expressions and Equations Section Lesson Title Lesson Goal(s) 3.1 Algebraic Expressions 3.2 3.3 Adding and Subtracting Linear Expressions Solving Equations Using Addition or Subtraction - Apply properties of operations to simplify algebraic expressions - Apply properties of operations to add and subtract linear expressions - Write simple equations - Solve equations using addition or subtraction Eligible Content M07.B-E.1.1.1 M07.B-E.2.1.1 M07.B-E.1.1.1 M07.B-E.2.2.1 M07.B-E.2.3.1 3.4 Solving Equations Using Multiplication or Division - Solve equations using multiplication or dividion M07.B-E.2.2.1 M07.B-E.2.3.1 3.5 Solving Two-Step Equations - Solve two-step equations M07.B-E.2.2.1 M07.B-E.2.3.1 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.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. M07.A-R.1.1.6 Use proportional relationships to solve multi-step ratio and percent problems. 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.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. 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 8
11/02 11/22 2 Days per Lesson + 3.5 Days Benchmark Cycle 2 Scope and Sequence Suggested Dates Chapter 4: Inequalities Section Lesson Title Lesson Goal(s) 4.1 Writing and Graphing Inequalities 4.2 Solving Inequalities Using Addition or Subtraction - Write and graph inequalities - Use substitution to check whether a number is a solution to an inequality - Solve inequalities using addition or subtraction Eligible Content M07.B-E.2.2.2 M07.B-E.2.3.1 M07.B-E.2.2.2 M07.B-E.2.3.1 4.3 Solving Inequalities Using Multiplication or Division - Solve inequalities using multiplication or division M07.B-E.2.2.2 M07.B-E.2.3.1 4.4 Solving Two-Step Inequalities - Solve multi-step inequalities 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 9
11/27 12/22 2 Days per Lesson + 5.5 Days Suggested Dates Chapter 5: Ratios and Proportions Section Lesson Title Lesson Goal(s) Eligible Content 5.1 Ratios and Rates 5.2 Proportions - Find ratios, rates and unit rates - Find ratios and rates involving ratios of fractions - Use equivalent ratios to determine whether two ratios form a proportion - Use the Cross Products Property to determine whether two ratios form a proportion M07.A-R.1.1.1 M07.A-R.1.1.2 5.2 Extension Graphing Proportional relationships - Use graphs to determine whether two ratios form a proportion - Interpret graphs of proportional relationships M07.A-R.1.1.2 5.3 Writing Proportions - Write proportions - Solve proportions using mental math M07.A-R.1.1.4 5.4 Solving Proportions - Solve proportions using multiplication or the Cross Products Property - Use a point on a graph to write and solve proportions M07.A-R.1.1.6 5.5 Slope - Find the slopes of lines - Interpret the slopes of lines as rates M07.A-R.1.1.5 5.6 Direct Variation - Identify direct variation from graphs or equations - Use direct variation models to solve problems M07.A-R.1.1.5 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 10
01/03 01/26 2 Days per Lesson + 3 Days Suggested Dates Chapter 6: Percents Section Lesson Title Lesson Goal(s) 6.1 Percents and Decimals 6.2 Comparing and Ordering Fractions, Decimals, and Percents - Write percents as decimals - Write decimals as percents - Compare and order fractions, decimals, and percents Eligible Content Preparing for: M07.A-R.1.1.6 Preparing for: M07.A-R.1.1.6 6.3 The Percent Proportion - Use the percent proportion to find parts, wholes, and percents M07.A-R.1.1.6 6.4 The Percent Equation - Use the percent equation to find parts, wholes, and percents M07.A-R.1.1.6 6.5 Percents of Increase and Decrease - Find percents of increase - Find percents of decrease M07.A-R.1.1.6 6.6 Discounts and Markups - Use percent of discounts to find prices of items - Use percents of markups to find selling prices of items M07.A-R.1.1.6 6.7 Simple Interest - Use the simple interest formula to find interest earned or paid, annual interest rates and amounts paid on loans M07.A-R.1.1.6 Benchmark 2 Window 01/26 02/13 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 11
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 real world 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 realworld 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 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.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 12
CC.2.3.7.A.2 Visualize and represent geometric figures and describe the relationships between them. CC.2.3.7.A.1 Solve real world and mathematical problems involving angle measure, area, surface area, circumference, and volume. 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.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). 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 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. 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. 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. 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 13
CC.2.4.7.B.3 Investigate chance processes and develop, use, and evaluate probability models. 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.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). 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.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. 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. 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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 14
01/30 02/23 2 Days per Lesson + 2.5 Days Benchmark Cycle 3 Scope and Sequence Suggested Dates Chapter 7: Constructions and Scale Drawings Section Lesson Title Lesson Objective(s) 7.1 Adjacent and Vertical Angles 7.2 7.3 7.3 Extension 7.4 Complementary and Supplementary Angles Triangles Angle Measures of Triangles Quadrilaterals 7.5 Scale Drawings Supplemental Lesson Angles formed by Parallel Lines Cut by a Transversal - Identify adjacent and vertical angles - Find angle measures using adjacent and vertical angles - Classify pairs of angles as complementary, supplementary, or neither - Find angle measures using complementary and supplementary angles - Construct triangles with given angle measurements - Construct triangles with given side lengths* *Note: Construction is not assessed on the PSSA. Students must be familiar, however, with angles in triangles and the Triangle Inequality Theorem. - Understand that the sum of the angle measures of any triangle is 180 o - Find missing angle measures in triangles - Understand that the sum of the angle measures of any quadrilateral is 360 o - Find missing angle measures in quadrilaterals - Construct quadrilaterals* *Note: Construction is not assessed on the PSSA. Students must be familiar, however, with angles in quadrilaterals. - Use scale drawings to find actual distances - Find scale factors - Use scale drawings to find actual perimeters and areas - Recreate scale drawings at a different scale Eligible Content M07.C-G.2.1.1 M07.C-G.1.1.1 M07.C-G.1.1.2 M07.C-G.1.1.1 M07.C-G.1.1.2 M07.C-G.1.1.1 M07.C-G.1.1.1 M07.C-G.2.2.2 M07.C-G.1.1.1 M07.C-G.2.1.2 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 15
02/26 03/09 2 Days per Lesson + 3 Days Suggested Dates Chapter 8: Circles and Area Section Lesson Title Lesson Objective(s) 8.1 Circles and Circumference - Describe a circle in terms of radius and diameter - Understand the concept of pi - Find circumferences of circles and perimeters of semicircles Eligible Content M07.C-G.2.2.1 8.3 Areas of Circles - Find areas of circles and semicircles M07.C-G.2.2.1 8.4 Areas of Composite Figures - Find areas of composite figures by separating them into familiar figures M.07.C-G.2.2.2 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 16
03/12 04/13 2 Days per Lesson + 2 Days and ELA PSSA Week Suggested Dates Chapter 9: Surface Area and Volume Section Lesson Title Lesson Objective(s) 9.1 Surface Areas of Prisms - Use two-dimensional nets to represent three-dimensional solids - Find surface areas of rectangular and triangular prisms Eligible Content M.07.C-G.2.2.2 Preparing for M.07.C-G.1.1.4 9.2 Surface Areas of Pyramids - Find surface areas of regular pyramids M.07.C-G.2.2.2 Preparing for M.07.C-G.1.1.4 9.3 Surface Areas of Pyramids - Find surface areas of cylinders M.07.C-G.2.2.2 Preparing for M.07.C-G.1.1.4 9.4 Volumes of Prisms 9.5 Volumes of Pyramids - Find volumes of prisms - Find volumes of pyramids M.07.C-G.2.2.2 Preparing for M.07.C-G.1.1.4 M.07.C-G.2.2.2 Preparing for M.07.C-G.1.1.4 9.5 Extension Cross Sections of Three- Dimensional Figures - Describe the intersections of planes and solids M.07.C-G.1.1.4 Math PSSA 4/16 4/20 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 17
04/23 05/08 2 Days Per Lesson + 2 Days Suggested Dates Chapter 10: Probability and Statistics Section Lesson Title Lesson Objective 10.1 Outcomes and Events - Identify and count the outcomes of experiments 10.2 Probability 10.3 Experimental and Theoretical Probability - Understand the concept of probability and the relationship between probability and likelihood - Find probabilities of events - Find relative frequencies - Use experimental probabilities to make predictions - Use theoretical probabilities to find quantities - Compare experimental and theoretical probabilities Eligible Content M07.D-S.3.1.1 M07.D-S.3.2.2 M07.D-S.3.1.1 M07.D-S.3.2.1 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 18
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. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 19
b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (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 20
05/10 06/01 2 Days Per Lesson + 2.5 Days Cycle 4 Scope and Sequence Suggested Dates Chapter 10: Probability and Statistics Section Lesson Title Lesson Objective 10.4 Compound Events 10.5 10.5 Extension Independent and Dependent Events Simulations 10.6 Samples and Populations 10.6 Extension Generating Multiple Samples 10.7 Comparing Populations - Use tree diagrams tables, or a formula to find the number of possible outcomes - Find probabilities of compound events - Identify independent and dependent events - Use formulas to find probabilities of independent and dependent events - Determine when samples are representative of populations - Use data from random samples to make predictions about populations - Use multiple samples to make predictions about populations - Use measures of center and variation to compare populations - Use random samples to compare populations 8.2 Perimeters of Composite Figures - Find perimeters of composite figures Eligible Content M07.D-S.3.2.3 M07.D-S.3.1.1 M07.D-S.3.2.2 M07.D-S.3.2.3 Not Assessed in PA M07.D-S.1.1.1 M07.D-S.1.1.2 M07.D-S.1.1.1 M07.D-S.1.1.2 M07.D-S.1.1.1 M07.D-S.1.1.2 Not Assessed in PA THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 21
Option 1: Reteach Based on Common Coreidentified focal areas. 6/04 6/12 7 Days Remediate and Extend by Preparing for Grade 8 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 2: 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 3: 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 22
PA Core Standards and Eligible Content by Cycle 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 23
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. CC.2.3.7.A.1 Solve realworld and mathematical problems involving angle measure, area, surface area, circumference, and volume. 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.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 24
CC.2.3.7.A.2 Visualize and represent geometric figures and describe the relationships between them. 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. 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. CC.2.4.7.B.3 Investigate chance processes and develop, use, and evaluate probability models. 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. 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 25
Document Information Page Overview of Contents of Document The Cover Page lays out the Topics taught within each Cycle as well as the corresponding dates. The Benchmark Cycle Standards pages that precede each cycle outline all of the standards that are taught within that cycle. These are, therefore, all of the standards that may be on that Cycle s Benchmark. The Benchmark Cycle Scope and Sequence pages provide suggested pacing that allows for 1 day per lesson plus some flex days. We recommend proactively using the flex days for: reviewing pre-requisite content, splitting lessons over multiple days, assessing, reteaching, and doing projects. Of course, some of these will also be taken by field trips and other school activities. The PA Core Standards and Eligible Content by Cycle page lists all of the standards and indicates in which cycle(s) they are taught. What is a Cycle? We want to offer clarity on what appears on each benchmark. Additionally, there should be sufficient time to teach that content before it is tested. Because each school administers the benchmark on a different day, not necessarily corresponding with the last day of the Term, we have created Cycles. Each Cycle contains the content that is to be taught and tested on a given benchmark. Please refer to the dates on the Cover Page to ensure you are aware of the beginning and ending dates for each Cycle. What If I Fall Behind? We trust you to make decisions about what is best for your students. This pacing will prepare you for the Benchmarks and PSSA, but it is a suggested, not mandated, pacing. You may also wish to move at a faster pace. Do not feel you should slow down to match this guide. If you are concerned about content that you may not reach before the PSSA, consider implementing number talks and other short routines and games. For example, a lot of Geometry vocabulary and concepts could be taught through Which Once Doesn t Belong. Rather than pushing to cover content, or using test prep resources, content can be infused through short but meaningful structures. The table below is purely for informational purposes. We used the PSSA Mathematics Blueprint to calculate what percent of tested content you will cover, based on how much of the book you teach before the test. Again, we recommend depth and understanding over coverage, but we wanted to provide this information for your planning purposes. Percent of Eligible Content if Chapters 1-10 Are Taught Percent of Eligible Content if Chapters 1-9 Are Taught Percent of Eligible Content if Chapters 1-8 Are Taught Percent of Eligible Content if Chapters 1-7 Are Taught 100% 85.5% 83% 81.5% THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 26
Additional Key Considerations in Mathematics 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 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 27