Grade 6 Big Ideas Math SY

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1 Topics Total Teaching Days Dates of Cycle Grade 6 Big Ideas Math SY Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4 September 5 - October 31 BM Window Nov 1-17 November 2 - January 26 BM Window Jan 29-Feb 13 January 30 - May 8 BM Window May 9-25 May 10 - June 12 Total Days: 39 Including 1 Half Day Total Days: 50 Days Including 4 Half Days Total Days Before PSSA: 50 Including 9 Half Days Total Days in Cycle: 60 Including 13 Half Days; Excluding Week of Math PSSA Total Days: 22 Including 1 Half Day 1 Numerical Expressions and Factors 2 Fractions and Decimals 3 Algebraic Expressions and Properties ( ) 3 Algebraic Expressions and Properties ( ) *5 Ratios and Rates 6 Integers and the Coordinate Plane Equations and Inequalities Equations and Inequalities 9 Statistical Measures 10 Data Displays 4 Areas of Polygons 8 Surface Area and Volume Note: A Benchmark 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. *We decided to move Units 4 and 8 to the end because they have lesson heavily tested content. Their content is also related, so it made sense to do them back-to-back. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

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

3 PA Common Core Standard CC E.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. CC E.2 Identify and choose appropriate processes to compute fluently with multi-digit numbers. CC E.3 Develop and/or apply number theory concepts to find common factors and multiples. CC B.1 Apply and extend previous understandings of arithmetic to algebraic expressions. Benchmark Cycle 1 Standards PA Eligible Content M06.A-N Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions. Example 1: Given a story context for (2/3) (3/4), explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = (a/b) (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4- foot pieces can be cut from a 15 1/2-foot board? M06.A-N Solve problems involving operations (+,,, and ) with whole numbers, decimals (through thousandths), straight computation, or word problems. M06.A-N Find the greatest common factor to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express as 4(9+2) M06.B-E Write and evaluate numerical expressions involving whole-number exponents. M06.B-E Write algebraic expressions from verbal descriptions. Example: Express the description five less than twice a number as 2y 5. Common Core State Standard 6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?. 6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm. 6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2). 6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

4 PA Common Core Standard CC B.1 Apply and extend previous understandings of arithmetic to algebraic expressions. PA Eligible Content M06.B-E Identify parts of an expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient, quantity). Example: Describe the expression 2(8 + 7) as a product of two factors. M06.B-E Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems. Example: Evaluate the expression b2 5 when b = 4. Common Core State Standard 6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. 6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s 3 and A = 6 s 2 to find the volume and surface area of a cube with sides of length s = 1/2. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

5 9/5 9/29 2 Days Per Lesson + 3 Days (Do the Extension) Benchmark Cycle 1 Scope and Sequence Suggested Dates Unit- Lesson 1-1 Whole Number Operations 1-2 Powers and Exponents 1-3 Multiply Fractions 1-4 Prime Factorization 1-5 Greatest Common Factor 1-6 Least Common Multiple Lesson Title Lesson Focus Eligible Content - Determine which operation to perform. - Divide multi-digit numbers. - Write expressions as powers. - Find values of powers. - Evaluate numerical expressions with whole-number exponents. - Use divisibility rules to find prime factorizations of numbers. - Use diagrams to identify common factors. - Find greatest common factors. - Use diagrams to identify common multiples. - Find least common multiples. M06.A-N M06.B-E M06.B-E M06.A-N M06.A-N M06.B-E M06.A-N Ext Adding and Subtracting Fractions - Use least common multiples to add/subtract fractions. M06.A-N THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

6 10/2-10/20 2 Days Per Lesson + 3 Days Suggested Dates Unit- Lesson 2-1 Multiplying Fractions 2-2 Dividing Fractions 2-3 Dividing Mixed Numbers Lesson Title Lesson Focus Eligible Content 2-4 Adding and Subtracting Decimals 2-5 Multiplying Decimals 2-6 Dividing Decimals - Use models to multiply fractions. - Multiply fractions by fractions. - Write reciprocals of numbers. - Use models to divide fractions. - Divide fractions by fractions. - Use models to divide mixed numbers. - Divide mixed numbers. - Use models to add and subtract decimals. - Add and subtract decimals. - Use models to multiply decimals. - Multiply decimals. - Use models to divide decimals. - Divide decimals. M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

7 10/23-10/31 1 Day Per Lesson Days Suggested Dates Unit- Lesson Lesson Title Lesson Focus Eligible Content 3-1 Algebraic Expressions - Use order of operations to evaluate algebraic expressions. M06.B-E Writing Expressions - Use variables to represent numbers in algebraic expressions. - Write algebraic expressions. M06.B-E Benchmark 1 Window: 11/1 11/17 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

8 Benchmark Cycle 2 Standards PA Common Core Standard CC D.1 Understand ratio concepts and use ratio reasoning to solve problems. PA Eligible Content M06.A-R Use ratio language and notation (such as 3 to 4, 3:4, ¾) to describe a ratio relationship between two quantities. Example 1: The ratio of girls to boys in a math class is 2:3 because for every 2 girls there are 3 boys. Example 2: For every five votes candidate A received, candidate B received four votes. M06.A-R Find the unit rate a/b associated with a ratio a:b (with b 0) and use rate language in the context of a ratio relationship. Example 1: This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar. Example 2: We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. M06.A-R Construct tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios. M06.A-R Solve unit rate problems including those involving unit pricing and constant speed. Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Common Core State Standard 6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. 6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. 6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

9 PA Common Core Standard CC D.1 Understand ratio concepts and use ratio reasoning to solve problems. CC B.1 Apply and extend previous understandings of arithmetic to algebraic expressions. CC B.2 Understand the process of solving a one variable equation or inequality and apply to real world and mathematical problems. PA Eligible Content M06.A-R Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percentage. M06.B-E Identify parts of an expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient, quantity). Example: Describe the expression 2(8 + 7) as a product of two factors. M06.B-E Apply the properties of operations to generate equivalent expressions. Example 1: Apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x. Example 2: Apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y). Example 3: Apply properties of operations to y + y + y to produce the equivalent expression 3y. M06.B-E Use substitution to determine whether a given number in a specified set makes an equation or inequality true. M06.B-E Write algebraic expressions to represent real-world or mathematical problems. Common Core State Standard 6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. 6.EE.A.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

10 PA Common Core Standard CC B.2 Understand the process of solving a one variable equation or inequality and apply to real world and mathematical problems. CC B.3 Represent and analyze quantitative relationships between dependent and independent variables. PA Eligible Content M06.B-E Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. M06.B-E Write an equation to express the relationship between the dependent and independent variables. Example: In a problem involving motion at a constant speed of 65 units, write the equation d = 65t to represent the relationship between distance and time. M06.B-E Analyze the relationship between the dependent and independent variables using graphs and tables and/or relate these to an equation. Common Core State Standard unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. CC E.3 Develop and/or apply number theory concepts to find common factors and multiples. CC E.4 Apply and extend previous understandings of numbers to the system of rational numbers. M06.A-N Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express as 4(9 + 2). M06.A-N Represent quantities in real-world contexts using positive and negative numbers, explaining the meaning of 0 in each situation (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge). 6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2). 6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

11 PA Common Core Standard CC E.4 Apply and extend previous understandings of numbers to the system of rational numbers. PA Eligible Content M06.A-N Determine the opposite of a number and recognize that the opposite of the opposite of a number is the number itself (e.g., ( 3) = 3; 0 is its own opposite). M06.A-N Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane. M06.A-N Write, interpret, and explain statements of order for rational numbers in real-world contexts. Example: Write 3 C > 7 C to express the fact that 3 C is warmer than 7 C. M06.A-N Interpret the absolute value of a rational number as its distance from 0 on the number line and as a magnitude for a positive or negative quantity in a realworld situation. Example: For an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars, and recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. Common Core State Standard negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. 6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6.NS.C.7 Understand ordering and absolute value of rational numbers. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 o C > -7 o C to express that -3 o C is warmer than -7 o C 6.NS.C.7 Understand ordering and absolute value of rational numbers. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write -30 = 30 to describe the size of the debt in dollars. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

12 PA Common Core Standard PA Eligible Content M06.A-N Solve real-world and mathematical problems by plotting points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Common Core State Standard 6.NS.C.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

13 11/2-11/14 2 Days Per Lesson + 1 Day (Do the Extension) Benchmark Cycle 2 Scope and Sequence Suggested Dates Unit- Lesson Lesson Title Lesson Focus Eligible Content 3-3 Properties of Addition and Multiplication - Use properties of operations to generate equivalent expressions. M06.B-E The Distributive Property - Use the Distributive Property to find products. - Use the Distributive Property to simplify algebraic expressions. M06.A-N M06.B-E M06.B-E Ext Factoring Expressions - Use the Distributive Property to produce equivalent expressions. M06.A-N M06.B-E THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

14 11/15-12/13 2 Days Per Lesson + 3 Whole and 4 Half Days (Skip 5-7) Suggested Dates Unit- Lesson 5-1 Ratios 5-2 Ratio Tables 5-3 Rates Lesson Title Lesson Focus Eligible Content 5-4 Comparing and Graphing Ratios 5-5 Percents 5-6 Solving Percent Problems 5-7 Converting Measures - Understand the concept of a ratio. - Use ratios to describe the relationship between two quantities. - Use ratio tables to find equivalent ratios. - Understand the concepts of rates and unit rates. - Write unit rates. - Compare ratios. - Compare unit rates. - Graph ordered pairs to compare ratios and rates. - Write percents as fractions with denominators of Write fractions as percents. - Find percents of numbers. - Find the whole given the part and the percent. - Use conversion factors (rates) to convert units of measurement. M06.A-R M06.A-R M06.A-R M06.A-R M06.A-R M06.A-R M06.A-R M06.A-R M06.A-R M06.A-R RP.3.d THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

15 12/14-1/11 2 Days per Lesson + 2Days (Do the Extension) Suggested Dates Unit- Lesson 6-1 Integers Lesson Title Lesson Focus Eligible Content 6-2 Comparing and Ordering Integers 6-3 Fractions and Decimals on the Number Line 6-4 Absolute Value 6-5 The Coordinate Plane 6-5 Ext Reflecting Points in the Coordinate Plane - Understand positive and negative integers and use them to describe real-life situations. - Graph integers on a number line. - Use a number line to compare positive and negative integers. - Use a number line to order positive and negative integers for real-life situations. - Understand positive and negative numbers to use them to describe real-life situations. - Graph numbers on a number line. - Find the absolute value of numbers. - Use absolute value to compare numbers in real-life situations. - Describe the locations of points in the coordinate plane. - Plot points in the coordinate plane given ordered pairs. - Find distances between points in the coordinate plane. - Understand reflections of points in the coordinate plane. M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N M06.A-N THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

16 1/12-1/26 2 Days Per Lesson + 2 Days Suggested Dates Unit- Lesson Lesson Title Lesson Focus Eligible Content 7-1 Writing Equations in 1 Variable - Write word sentences as equations. M06.B-E Solving Equations Using Addition or Subtraction Solving Equations Using Multiplication or Division Writing Equations in Two Variables - Use addition or subtraction to solve equations. - Use substitution to check answers. - Use multiplication or division to solve equations. - Use substitution to check answers. - Identify independent and dependent variables. - Write equations in two variables. - Use tables and graphs to analyze the relationship between two variables. M06.B-E M06.B-E M06.B-E M06.B-E M06.A-R M06.B-E M06.B-E Benchmark 2 Window: 1/29 2/13 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

17 Benchmark Cycle 3 Standards PA Common Core Standard CC B.2 Understand the process of solving a one variable equation or inequality and apply to real world and mathematical problems. CC B.1 Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions. PA Eligible Content M06.B-E Use substitution to determine whether a given number in a specified set makes an equation or inequality true. M06.B-E Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem and/or represent solutions of such inequalities on number lines. M06.D-S Display numerical data in plots on a number line, including line plots, histograms, and boxand-whisker plots. M06.D-S Determine quantitative measures of center (e.g., median, mean, mode) and variability (e.g., range, interquartile range, mean absolute deviation). M06.D-S Describe any overall pattern and any deviations from the overall pattern with reference to the context in which the data were gathered. M06.D-S Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Common Core State Standard 6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.B.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. 6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

18 PA Common Core Standard CC A.1 Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume. PA Eligible Content M06.C-G Determine the area of triangles and special quadrilaterals (i.e., square, rectangle, parallelogram, rhombus, and trapezoid). Formulas will be provided. M06.C-G Determine the area of irregular or compound polygons. Example: Find the area of a room in the shape of an irregular polygon by composing and/or decomposing. M06.C-G Given coordinates for the vertices of a polygon in the plane, use the coordinates to find side lengths and area of the polygon (limited to triangles and special quadrilaterals). Formulas will be provided. Common Core State Standard 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 6.G.A.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

19 1/30-2/12 2 Days per Lesson + 4 Days Benchmark Cycle 3 Scope and Sequence Suggested Dates Unit- Lesson Lesson Title Lesson Focus Eligible Content 7-5 Writing and Graphing Inequalities Solving Inequalities Using Addition or Subtraction Solving Inequalities Using Multiplication or Division - Write word sentences as inequalities. - Use a number line to graph the solution set of inequalities. - Use inequalities to represent real-life situations. - Use addition or subtraction to solve inequalities. - Use a number line to graph the solution set of inequalities. - Use multiplication or division to solve inequalities. - Use a number line to graph the solution set of inequalities. M06.B-E M06.B-E M06.B-E M06.B-E M06.B-E M06.B-E THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

20 2/13-3/6 2 Days Per Lesson + 2 Whole and 3 Half Days Suggested Dates Unit- Lesson Lesson Title Lesson Focus Eligible Content 9-1 Introduction to Statistics - Recognize statistical questions. - Use dot plots to display numerical data. M06.D-S Mean - Understand the concept of the mean of data sets. - Find the mean of data sets. - Compare and interpret the mean of data sets. M06.D-S M06.D-S Measures of Center - Understand the concept of measures of center. - Find the median and mode of data sets. M06.D-S M06.D-S Measures of Variation - Find the range of data sets. - Find the interquartile range of data sets. - Check for outliers in data sets. M06.D-S M06.D-S Mean Absolute Deviation - Understand the meaning of mean absolute deviation. - Find the mean absolute deviation of data sets. M06.D-S M06.D-S THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

21 3/7-3/23 2 Days Per Lesson Days (Do the Extension) Suggested Dates Unit- Lesson Lesson Title Lesson Focus Eligible Content 10-1 Stem-and-Leaf Plots - Make and interpret stem-and-leaf plots. M06.D-S Histograms - Make histograms. - Use histograms to analyze data. M06.D-S Shapes of Distributions - Describe shapes of distributions. M06.D-S Ext Choosing Appropriate Measures 10-4 Box-and-Whisker Plots - Choose appropriate measures of center and variation to represent data sets. - Make and interpret box-and-whisker plots. - Compare box-and-whisker plots. M06.D-S M06.D-S M06.D-S M06.D-S THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

22 3/26-4/13 7 Whole Days + ELA PSSA Week (Do the Extension) Suggested Dates Unit- Lesson Lesson Title 4-1 Areas of Parallelograms Lesson Focus - Find areas of parallelograms. Eligible Content M06.C-G Areas of Triangles - Find areas of triangles. M06.C-G Areas of Trapezoids - Find areas of trapezoids. M06.C-G Ext Areas of Composite Figures - Find areas of composite figures. M06.C-G Polygons in the Coordinate Plane - Draw polygons in the coordinate place. - Find distances in the coordinate plane. M06.C-G /16 4/20 MATH PSSA THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

23 4/23-5/7 2 Days Per Lesson + 1 Whole and 4 Half Days (8.3 is an unnecessary extension of standard) Topic 8 will not be on the benchmark, so its standards are included in Cycle 4. You can start it now, though, to save more time in Cycle 4 for additional extension, projects, and remediation. Suggested Unit. Lesson Title Lesson Focus Eligible Content Dates Lesson 8.1 Three-Dimensional Figures - Draw three-dimensional figures. - Find the number of faces, edges, and vertices of solids. M06.C-G Surface Area of Prisms 8.3 Surface Area of Pyramids 8.4 Volumes of Rectangular Prisms - Use nets to represent prisms. - Find the surface area of prisms. - Use nets to represent pyramids. - Find the surface area of pyramids. - Find the volume of prisms with fractional edge lengths by using models. - Find the volume of prisms by using formulas. M06.C-G M06.C-G M06.C-G M06.C-G M06.C-G Benchmark 3 Window: 5/9 5/25 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

24 Cycle 4 Standards PA Common Core Standard CC A.1 Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume. PA Eligible Content M06.C-G Determine the volume of right rectangular prisms with fractional edge lengths. Formulas will be provided. M06.C-G Represent three-dimensional figures using nets made of rectangles and triangles. M06.C-G Determine the surface area of triangular and rectangular prisms (including cubes). Formulas will be provided. Common Core State Standard 6.G.A.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.A.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

25 Cycle 4 Scope and Sequence Remediation and Extension Options 5/24-6/ Days You have a lot of days remaining in the year so below are some suggestions for ways to spend your time. You may also want to access additional content resources on the curriculum engine or math@philasd.org for suggestions on how to maximize this time. Option 1: 3-Act Math Activities Option 2: Reteach Based on the Major Work of the Grade Option 3: Pre-teach Based on 7 th Grade Needs Option 4: Financial Literacy During the remainder of the year, consider offering students opportunities to engage authentically in the Standards for Mathematical Practice through a series of Three-Act modeling activities. You can find some at: orhttps://whenmathhappens.com/3-act-math/ You taught many topics this year. The four below are identified as the most critical for 6 th grade. If you want to revisit something, one or more of these topics would be a good idea. 6.RP.A Understand ratio concepts and use ratio reasoning to solve problems. 6.NS.A Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.NS.C Apply and extend previous understandings of numbers to the system of rational numbers. 6.EE.A Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.B Reason about and solve one-variable equations and inequalities. 6.EE.C Represent and analyze quantitative relationships between dependent and independent variables. You can check in with your 7 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 7 th grade are: 1) Integers 2) Rational Numbers You can access the 7 th grade Teacher s Guide and materials online for reference. The Federal Reserve Bank of Philadelphia has posted free lesson plans for elementary teachers (including K) on financial literacy at: Many of these lessons are tied to early children s literature, as well. In addition, Census.gov has a number of data analysis activities, using real U.S. Census data, at: THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

26 PA Core Standards and Eligible Content by Cycle PA Common Core Standard CC D.1 Understand ratio concepts and use ratio reasoning to solve problems. CC E.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions. CC E.2 Identify and choose appropriate processes to compute fluently with multi-digit numbers. PA Eligible Content M06.A-R Use ratio language and notation (such as 3 to 4, 3:4, 3/4) to describe a ratio relationship between two quantities. Example 1: The ratio of girls to boys in a math class is 2:3 because for every 2 girls there are 3 boys. Example 2: For every five votes candidate A received, candidate B received four votes. M06.A-R Find the unit rate a/b associated with a ratio a:b (with b 0) and use rate language in the context of a ratio relationship. Example 1: This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. Example 2: We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. M06.A-R Construct tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and/or plot the pairs of values on the coordinate plane. Use tables to compare ratios. M06.A-R Solve unit rate problems including those involving unit pricing and constant speed. Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? M06.A-R Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percentage. M06.A-N Interpret and compute quotients of fractions (including mixed numbers), and solve word problems involving division of fractions by fractions. Example 1: Given a story context for (2/3) (3/4), explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = (a/b) (d/c) = ad/bc.) Example 2: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Example 3: How many 2 1/4-foot pieces can be cut from a 15 1/2-foot board? M06.A-N Solve problems involving operations (+,,, and ) with whole numbers, decimals (through thousandths), straight computation, or word problems. Cycle 1 Cycle 2 Cycle 3 Cycle 4 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

27 PA Common Core Standard CC E.3 Develop and/or apply number theory concepts to find common factors and multiples. PA Eligible Content M06.A-N Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. M06.A-N Apply the distributive property to express a sum of two whole numbers, 1 through 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Example: Express as 4(9 + 2). Cycle 1 Cycle 2 Cycle 3 Cycle 4 CC E.4 Apply and extend previous understandings of numbers to the system of rational numbers. CC E.4 Apply and extend previous understandings of numbers to the system of rational numbers. M06.A-N Represent quantities in real-world contexts using positive and negative numbers, explaining the meaning of 0 in each situation (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge). M06.A-N Determine the opposite of a number and recognize that the opposite of the opposite of a number is the number itself (e.g., ( 3) = 3; 0 is its own opposite). M06.A-N Locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and other rational numbers on a coordinate plane. M06.A-N Write, interpret, and explain statements of order for rational numbers in real-world contexts. Example: Write 3 C > 7 C to express the fact that 3 C is warmer than 7 C. M06.A-N Interpret the absolute value of a rational number as its distance from 0 on the number line and as a magnitude for a positive or negative quantity in a real-world situation. Example: For an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars, and recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. M06.A-N Solve real-world and mathematical problems by plotting points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

28 PA Common Core Standard CC B.1 Apply and extend previous understandings of arithmetic to algebraic expressions. CC B.2 Understand the process of solving a one-variable equation or inequality and apply it to real-world and mathematical problems. CC B.3 Represent and analyze quantitative relationships between dependent and independent variables PA Eligible Content M06.B-E Write and evaluate numerical expressions involving whole-number exponents. M06.B-E Write algebraic expressions from verbal descriptions. Example: Express the description five less than twice a number as 2y 5. M06.B-E Identify parts of an expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient, quantity). Example: Describe the expression 2(8 + 7) as a product of two factors. M06.B-E Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems. Example: Evaluate the expression b 2 5 when b = 4. M06.B-E Apply the properties of operations to generate equivalent expressions. Example 1: Apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x. Example 2: Apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y). Example 3: Apply properties of operations to y + y + y to produce the equivalent expression 3y. M06.B-E Use substitution to determine whether a given number in a specified set makes an equation or inequality true. M06.B-E Write algebraic expressions to represent real-world or mathematical problems. M06.B-E Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. M06.B-E Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem and/or represent solutions of such inequalities on number lines. M06.B-E Write an equation to express the relationship between the dependent and independent variables. Example: In a problem involving motion at a constant speed of 65 units, write the equation d = 65t to represent the relationship between distance and time. M06.B-E Analyze the relationship between the dependent and independent variables using graphs and tables and/or relate these to an equation. Cycle 1 Cycle 2 Cycle 3 Cycle 4 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

29 CC A.1 Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume. CC B.1 Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions. M06.C-G Determine the area of triangles and special quadrilaterals (i.e., square, rectangle, parallelogram, rhombus, and trapezoid). Formulas will be provided. M06.C-G Determine the area of irregular or compound polygons. Example: Find the area of a room in the shape of an irregular polygon by composing and/or decomposing. M06.C-G Determine the volume of right rectangular prisms with fractional edge lengths. Formulas will be provided. M06.C-G Given coordinates for the vertices of a polygon in the plane, use the coordinates to find side lengths and area of the polygon (limited to triangles and special quadrilaterals). Formulas will be provided. M06.C-G Represent three-dimensional figures using nets made of rectangles and triangles. M06.C-G Determine the surface area of triangular and rectangular prisms (including cubes). Formulas will be provided. M06.D-S Display numerical data in plots on a number line, including line plots, histograms, and box-and-whisker plots. M06.D-S Determine quantitative measures of center (e.g., median, mean, mode) and variability (e.g., range, interquartile range, mean absolute deviation). M06.D-S Describe any overall pattern and any deviations from the overall pattern with reference to the context in which the data were gathered. M06.D-S Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

30 Document Information Page Overview of Contents of Document The Cover Page lays out the Topics taught within each Cycle as well as the corresponding dates. The Benchmark Cycle Standards pages that precede each cycle outline all of the standards that are taught within that cycle. These are, therefore, all of the standards that may be on that Cycle s Benchmark. The Benchmark Cycle Scope and Sequence pages provide suggested pacing that allows for 1 day per lesson plus some flex days. We recommend proactively using the flex days for: reviewing pre-requisite content, splitting lessons over multiple days, assessing, reteaching, and doing projects. Of course, some of these will also be taken by field trips and other school activities. The PA Core Standards and Eligible Content by Cycle page lists all of the standards and indicates in which cycle(s) they are taught. What is a Cycle? We want to offer clarity on what appears on each benchmark. Additionally, there should be sufficient time to teach that content before it is tested. Because each school administers the benchmark on a different day, not necessarily corresponding with the last day of the Term, we have created Cycles. Each Cycle contains the content that is to be taught and tested on a given benchmark. Please refer to the dates on the Cover Page to ensure you are aware of the beginning and ending dates for each Cycle. What If I Fall Behind? We trust you to make decisions about what is best for your students. This pacing will prepare you for the Benchmarks and PSSA, but it is a suggested, not mandated, pacing. You may also wish to move at a faster pace. Do not feel you should slow down to match this guide. If you are concerned about content that you may not reach before the PSSA, consider implementing number talks and other short routines and games. For example, a lot of Geometry vocabulary and concepts could be taught through Which Once Doesn t Belong. Rather than pushing to cover content, or using test prep resources, content can be infused through short but meaningful structures. The table below is purely for informational purposes. We used the PSSA Mathematics Blueprint to calculate what percent of tested content you will cover, based on how much of the book you teach before the test. Again, we recommend depth and understanding over coverage, but we wanted to provide this information for your planning purposes. Percent if Units 10, 4, and 8 are not covered Percent if Units 4 and 8 are not Covered Percent if all but Unit 8 is Covered (Unit 9 and 10 overlap in their content. It s difficult to gauge how much students can master with just Unit 9 but not 10) THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY