Grade 4 Math Expressions SY

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1 Grade 4 Math Expressions SY Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4 Dates of Cycle 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 Teaching Days Total Days: 39 Including 1 Half Day Total Days: 50 Days Including 4 Half Days Total Days Before PSSA: 50 Including 9 Half Days Total Days in Cycle: 60 Including 13 Half Days Total Days: 22 Including 1 Half Day Topics 1 Place Value and Multi-digit Addition and Subtraction Multiplication with Whole Numbers Multiplication with Whole Numbers 3 Division with Whole Numbers 4 Equations and Word Problems Measurement Measurement 6 Fraction Concepts and Operations 7 Fractions and Decimals Geometry Geometry 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. 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... 7 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 Benchmark Cycle 1 Standards PA Common Core Standard PA Eligible Content Common Core State Standard CC B.1 Apply placevalue concepts to show an understanding of multi digit whole numbers. M04.A-T Demonstrate an understanding that in a multi-digit whole number (through 1,000,000), a digit in one place represents ten times what it represents in the place to its right. Example: Recognize that in the number 770, the 7 in the hundreds place is ten times the 7 in the 4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value and division. CC B.2 Use place value understanding and properties of operations to perform multi digit arithmetic. tens place. M04.A-T Read and write whole numbers in expanded, standard, and word form through 1,000,000. M04.A-T Compare two multi-digit numbers through 1,000,000 based on meanings of the digits in each place, using >, =, and < symbols. M04.A-T Round multi-digit whole numbers (through 1,000,000) to any place. M04.A-T Add and subtract multi-digit whole numbers (limit sums and subtrahends up to and including 1,000,000). 4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.A.3 Use place value understanding to round multidigit whole numbers to any place. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. CC A.1 Solve problems involving measurement and conversions from a larger unit to a smaller unit. M04.A-T Multiply a whole number of up to four digits by a one-digit whole number and multiply 2 twodigit numbers. M04.D-M Use the four operations to solve word problems involving distances, intervals of time (such as elapsed time), liquid volumes, masses of objects; money, including problems involving simple fractions or decimals; and problems that require expressing 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

4 CC A.1 Represent and solve problems involving the four operations. measurements given in a larger unit in terms of a smaller unit. M04.B-O Solve multi-step word problems posed with whole numbers using the four operations. Answers will be either whole numbers or have remainders that must be interpreted yielding a final answer that is a whole number. Represent these problems using equations with a symbol or letter standing for the unknown quantity. M04.B-O Identify the missing symbol (+,,,, =, ) that makes a number sentence true (single-digit divisor only). a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding (not included). THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

5 9/27-10/6 1 Day Per Lesson + 2 Days 9/19-9/26 1 Day Per Lesson + 1 Day 9/5 9/18 1 Day Per Lesson + 4 Days Benchmark Cycle 1 Scope and Sequence Suggested Dates Unit 1: Place Value and Multidigit Addition and Subtraction Unit- Lesson Lesson Title Lesson Focus Eligible Content BIG IDEA 1: Place Value to One Million 1-1 Place Value to Thousands Identify the place value of numbers through thousands. 1-2 Place Value Patterns Read, write, and model numbers to the thousands. M04.A-T Round Numbers Compare and round multi-digit whole numbers. M04.A-T Numbers to One Million Identify the place value of numbers to one million. M04.A-T Compare and Round 1-5 Compare and round multi-digit whole numbers. M04.B-O Greater Numbers PA-1 Use Symbols in Number Sentences BIG IDEA 2: Addition with Greater Numbers Make New Groups for 1-6 Add four-digit numbers. M04.B-O Addition M04.A-T Add Greater Numbers Add multi-digit numbers. M04.A-T Estimation and Mental 1-8 Add using estimation and mental math. M04.D-M Math BIG IDEA 3: Subtraction with Greater Numbers 1-9 Subtract from Subtract multi-digit whole numbers Thousands Subtraction Undoes Addition Subtract Greater Numbers Practice Addition and Subtraction Problem Solving with Greater Numbers Focus on Mathematical Practices Learn about the inverse relationship between addition and subtraction. Use methods for ungrouping to subtract two whole numbers. Practice adding and subtracting multi-digit numbers while solving two-step word problems. Use addition and subtraction to solve word problems. Solve real world problems involving addition and subtraction. M04.B-O M04.A-T M04.A-T M04.D-M THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

6 10/13-10/31 1 Day Per Lesson Days 10/9-10/12 1 Day Per Lesson + 1 Days Suggested Dates Unit 2: Multiplication with Whole Numbers Unit- Lesson Lesson Title Lesson Objective BIG IDEA 1: Multiplication with Tens and Hundreds 2-1 Arrays and Area Models Use area models for multiplication of ones and tens. 2-2 Connect Place Value and Multiplication Use place value understanding to multiply tens. 2-3 Mental Math and Multiply with multiples of ten by using patterns, place value reasoning, Multiplication and factoring. BIG IDEA 2: Multiply by One-Digit Numbers 2-4 Model One-Digit by Two-Digit Multiplication Represent one-digit by two-digit multiplication using area models. 2-5 Estimate Products Use rounding to estimate products and solve real world problems. 2-6 Use Place Value to Learn strategies for multiplying one-digit and two-digit numbers: Place Multiply Value Sections Method and Expanded Notation Method. 2-7 Algebraic Notation Method Use the Distributive Property to multiply two-digit by one-digit numbers. 2-8 Compare Methods of Use different methods of multiplication to multiply a two-digit number One-Digit by Two-Digit by a one-digit number. Multiplication 2-9 Discuss Different Compare and analyze methods of multiplication Methods One-Digit by Three-Digit Multiplication Multistep Word Problems Apply methods they have learned to multiply a three-digit number by a one-digit number. Solve real world problems. Benchmark 1 Window: 11/1 11/17 Eligible Content M04.A-T M04.A-T M04.B-O M04.A-T M04.A-T M04.A-T M04.A-T M04.D-M THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

7 Benchmark Cycle 2 Standards PA Common Core Standard CC B.1 Apply placevalue concepts to show an understanding of multi digit whole numbers. CC B.2 Use place value understanding and properties of operations to perform multi digit arithmetic. PA Eligible Content M04.A-T Read and write whole numbers in expanded, standard, and word form through 1,000,000. M04.A-T Compare two multi-digit numbers through 1,000,000 based on meanings of the digits in each place, using >, =, and < symbols. M04.A-T Round multi-digit whole numbers (through 1,000,000) to any place. M04.A-T Add and subtract multi-digit whole numbers (limit sums and subtrahends up to and including 1,000,000). M04.A-T Multiply a whole number of up to four digits by a one-digit whole number and multiply 2 twodigit numbers. M04.A-T Divide up to four-digit dividends by onedigit divisors with answers written as whole-number quotients and remainders. M04.A-T Estimate the answer to addition, subtraction, and multiplication problems using whole numbers through six digits (for multiplication, no more than 2 digits 1 digit, excluding powers of 10). Common Core State Standard 4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

8 CC A.1 Represent and solve problems involving the four operations. CC A.2 Develop and/or apply number theory concepts to find factors and multiples. CC A.4 Generate and analyze patterns using one rule. M04.B-O Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. Example 1: Interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Example 2: Know that the statement 24 is 3 times as many as 8 can be represented by the equation 24 = 3 8 or 24 = 8 3. M04.B-O Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Example: Know that 3 4 can be used to represent that Student A has 4 objects and Student B has 3 times as many objects not just 3 more objects. M04.B-O Solve multi-step word problems posed with whole numbers using the four operations. Answers will be either whole numbers or have remainders that must be interpreted yielding a final answer that is a whole number. Represent these problems using equations with a symbol or letter standing for the unknown quantity. M04.B-O Find all factor pairs for a whole number in the interval 1 through 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the interval 1 through 100 is a multiple of a given one-digit number. Determine whether a given whole number in the interval 1 through 100 is prime or composite. M04.B-O Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Example 1: Given the rule add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms alternate between odd and even numbers. Example 2: Given the rule increase the number of sides 4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 4.OA.B.4 Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. 4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

9 CC A.1 Solve problems involving measurement and conversions from a larger unit to a smaller unit. CC A.4 Represent and interpret data involving fractions using information provided in a line plot. by 1 and starting with a triangle, observe that the tops of the shapes alternate between a side and a vertex. M04.B-O Determine the missing elements in a function table (limit to +,, or and to whole numbers or money). M04.D-M Know relative sizes of measurement units within one system of units including standard units (in., ft, yd, mi; oz., lb; and c, pt, qt, gal), metric units (cm, m, km; g, kg; and ml, L), and time (sec, min, hr, day, wk, mo, and yr). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. A table of equivalencies will be provided. Example 1: Know that 1 kg is 1,000 times as heavy as 1 g. Example 2: Express the length of a 4-foot snake as 48 in. M04.D-M Use the four operations to solve word problems involving distances, intervals of time (such as elapsed time), liquid volumes, masses of objects; money, including problems involving simple fractions or decimals; and problems that require expressing measurements given in a larger unit in terms of a smaller unit. M04.D-M Make a line plot to display a data set of measurements in fractions of a unit (e.g., intervals of 1/2, 1/4, or 1/8). M04.D-M Solve problems involving addition and subtraction of fractions by using information presented in line plots (line plots must be labeled with common denominators, such as 1/4, 2/4, 3/4). odd and even numbers. Explain informally why the numbers will continue to alternate in this way. 4.MD.A.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),... 4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

10 11/13-11/28 1 Day Per Lesson + 3 Half Days 11/2-11/9 1 Day Per Lesson + 1 Days Benchmark Cycle 2 Scope and Sequence Suggested Dates Unit 2 Continued: Multiplication with Whole Numbers Unit- Lesson Lesson Title Lesson Objective Eligible Content BIG IDEA 3: Multiplication with Two-Digit Numbers 2-12 Two-Digit by Two-Digit Represent two-digit by two-digit multiplication, using area Multiplication models Different Methods for Two-Digit Use different methods of two-digit by two-digit M04.B-O Multiplication multiplication. M04.A-T Check Products of Two-Digit M04.A-T Use estimation to check products of two-digit numbers. Numbers M04.A-T Practice Multiplication Multiply two-digit numbers with fewer steps to solve real world problems. BIG IDEA 4: Multiplication with Thousands 2-16 Multiply One-Digit and Four-Digit Numbers Multiply four-digit numbers by one-digit numbers Use the Shortcut Method Multiply four-digit numbers by one-digit numbers and use estimation to check answers Practice Multiplying Use multi-digit multiplication to solve real world problems. PA-2 Why estimation is Useful PA-3 Explore Estimation Strategies PA-4 Estimate Sums, Differences, and Products 2-19 Focus on Mathematical Practices Solve real world problems involving multiplication. M04.B-O M04.A-T M04.A-T M04.A-T M04.A-T M04.A-T M04.D-M THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

11 12/11-12/19 1 Day Per Lesson + 2 Days 11/29-12/8 1 Day Per Lesson Days Suggested Dates Unit- Lesson 3-1 Divide with Remainders Unit 3: Division with Whole Numbers Lesson Title Lesson Objective Eligible Content BIG IDEA 1: Dividing Whole Numbers Divide with remainders and use multiplication patterns to divide with zeros. 3-2 Relate 3-Digit Multiplication to Division Use multiplication methods to divide. 3-3 Discuss 2-Digit and 4-Digit Quotients Divide with 2-digit and 4-digit quotients. 3-4 Digit-by-Digit Method Use the Digit-by-Digit Method to divide. 3-5 Relate Three Methods Divide with 4-digit dividends. 3-6 Divide by Any Method Solve division problems by using any method. BIG IDEA 2: Division Issues and Word Problems 3-7 Just-Under Quotient Digits Determine the correct-size multiplier for a division quotient. 3-8 Estimate to Check Quotients Use rounding and estimation to check quotients. 3-9 Make Sense of Remainders Learn different ways to interpret remainders in division Mixed Problem Solving Solve word problems with mixed operations Focus on Mathematical Practices Solve real world problems involving division. M04.A-T M04.B-O M04.A-T M04.A-T THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

12 1/16-1/23 1 Day Per Lesson + 2 Days 1/10-1/12 1 Day Per Lesson 1/3-1/9 1 Day Per Lesson + 1 Day 12/20-12/22 1 Day Per Lesson Suggested Dates Unit 4: Equations and Word Problems Unit- Lesson Lesson Title Lesson Objective Eligible Content BIG IDEA 1: Reasoning and Solving Problems 4-1 Properties and Algebraic Notation Use properties and the Order of Operations to simplify expressions and solve equations. M04.A-T Situation and Solution Equations M04.A-T Write addition and subtraction equations to solve problems. for Addition and Subtraction M04.A-T Situation and Solution Equations Write multiplication and division equations to solve M04.D-M for Multiplication and Division problems. BIG IDEA 2: Comparison Word Problems 4-4 Multiplication Comparisons Write multiplication and division equations to solve comparison problems. M04.B-O Discuss Comparison Problems Compare & solve addition & multiplication comparison probs M04.B-O Graphs and Comparison Problems Answer comparison questions about pictograph & bar graph M04.D-M PA-5 Convert Data Displays BIG IDEA 3: Problems with More Than One Step 4-7 Solve Two-Step Problems Use equations to solve two-step word problems involving all four operations. 4-8 Solve Multistep Problems Use equations to solve multistep word problems involving all four operations. M04.B-O Practice with Multistep Problems Use addition, subtraction, multiplication, and division to solve problems that involve more than one step. BIG IDEA 4: Analyzing Patterns 4-10 Factors and Prime Numbers Identify factors, multiples, and prime and composite M04.B-O numbers. M04.B-O M04.B-O Analyze Patterns Analyze and extend number or shape patterns. M04.B-O M04.B-O PA-6 Investigate a Function Table M04.B-O M04.A-T Focus on Mathematical Practices Write equations and solve real-world problems. M04.A-T M04.A-T THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

13 1/24-1/26 1 Day Per Lesson Suggested Dates Unit- Lesson Unit 5: Measurement Lesson Title Lesson Objective Eligible Content BIG IDEA 1: Converting Measurements 5-1 Measure Length Explore the system of metric units of length. 5-2 Metric Measures of Liquid Volume and Mass Recognize and measure metric units of liquid volume and mass. 5-3 Units of Time Solve problems involving different units of time. M04.D-M M04.D-M M04.D-M M04.D-M Benchmark 2 Window: 1/29 2/13 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

14 Benchmark Cycle 3 Standards PA Common Core Standard CC C.1 Extend the understanding of fractions to show equivalence and ordering. CC C.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. PA Eligible Content M04.A-F Recognize and generate equivalent fractions. M04.A-F Compare two fractions with different numerators and different denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the symbols >, =, or < and justify the conclusions. M04.A-F Add and subtract fractions with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; answers do not need to be simplified; and no improper fractions as the final answer). M04.A-F Decompose a fraction or a mixed number into a sum of fractions with the same denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100), recording the decomposition by an equation. Justify decompositions (e.g., by using a visual fraction model). Example 1: 3/8 = 1/8 + 1/8 + 1/8 OR 3/8 = 1/8 + 2/8 Example 2: 2 1/12 = /12 = 12/ /12 + 1/12 M04.A-F Add and subtract mixed numbers with a common denominator (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100; no regrouping with subtraction; fractions do not need to be simplified; and no improper fractions as the final answers). Common Core State Standard 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model. 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. (Note: Not exact match) 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

15 CC C.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. CC C.3 Connect decimal notation to fractions, and compare decimal fractions (base 10 M04.A-F Solve word problems involving addition and subtraction of fractions referring to the same whole or set and having like denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100). M04.A-F Multiply a whole number by a unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 5 (1/4) = 5/4 M04.A-F Multiply a whole number by a non-unit fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100 and final answers do not need to be simplified or written as a mixed number). Example: 3 (5/6) = 15/6 M04.A-F Solve word problems involving multiplication of a whole number by a fraction (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100). M04.A-F Add two fractions with respective denominators 10 and 100. Example: Express 3/10 as 30/100, and add 3/10 + 4/100 = 30/ /100 = 34/100. of operations and the relationship between addition and subtraction. 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models & equations to represent the problem. 4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 (1/4), recording the conclusion by the equation 5/4 = 5 (1/4). (Note: Not exact match) 4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 (2/5) as 6 (1/5), recognizing this product as 6/5. (In general, n (a/b) = (n a)/b.) (Note: Not exact match) 4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? 4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

16 denominator, e.g., 19/100). CC C.3 Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100). CC A.1 Solve problems involving measurement and conversions from a larger unit to a smaller unit. M04.A-F Use decimal notation for fractions with denominators 10 or 100. Example: Rewrite 0.62 as 62/100 and vice versa. M04.A-F Compare two decimals to hundredths using the symbols >, =, or <, and justify the conclusions. M04.D-M Know relative sizes of measurement units within one system of units including standard units (in., ft, yd, mi; oz., lb; and c, pt, qt, gal), metric units (cm, m, km; g, kg; and ml, L), and time (sec, min, hr, day, wk, mo, and yr). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. A table of equivalencies will be provided. Example 1: Know that 1 kg is 1,000 times as heavy as 1 g. Example 2: Express the length of a 4-foot snake as 48 in. M04.D-M Use the four operations to solve word problems involving distances, intervals of time (such as elapsed time), liquid volumes, masses of objects; money, including problems involving simple fractions or decimals; and problems that require expressing measurements given in a larger unit in terms of a smaller unit. M04.D-M Apply the area and perimeter formulas for rectangles in real-world and mathematical problems (may include finding a missing side length). Whole numbers only. The formulas will be provided. denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/ NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. 4.MD.A.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),... 4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

17 CC A.4 Represent and interpret data involving fractions using information provided in a line plot. M04.D-M Identify time (analog or digital) as the amount of minutes before or after the hour. Example 1: 2:50 is the same as 10 minutes before 3:00. Example 2: Quarter past six is the same as 6:15. M04.D-M Make a line plot to display a data set of measurements in fractions of a unit (e.g., intervals of 1/2, 1/4, or 1/8). M04.D-M Solve problems involving addition and subtraction of fractions by using information presented in line plots (line plots must be labeled with common denominators, such as 1/4, 2/4, 3/4). viewing the area formula as a multiplication equation with an unknown factor. 4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. CC A.2 Translate information from one type of data display to another. CC A.6 Measure angles and use properties of adjacent angles to solve problems. M04.D-M Translate information from one type of display to another (table, chart, bar graph, or pictograph). M04.D-M Measure angles in whole-number degrees using a protractor. With the aid of a protractor, sketch angles of specified measure. 4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "onedegree angle," and can be used to measure angles. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

18 4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. CC A.6 Measure angles and use properties of adjacent angles to solve problems. CC A.1 Draw lines and angles and identify these in two dimensional figures. M04.D-M Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. (Angles must be adjacent and non-overlapping.) M04.C-G Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. 4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

19 2/5-2/9 1 Day Per Lesson + 2 Days 1/30-2/2 1 Day Per Lesson + 1 Day Benchmark Cycle 3 Scope and Sequence Suggested Dates Unit- Lesson PA-7 Unit 5 Continued: Measurement Lesson Title Lesson Objective Eligible Content Describing Times on Different Clocks 5-4 Customary Measures of Length 5-5 Customary Measures of Weight and Liquid Volume BIG IDEA 1: Converting Measurements Convert among customary units of length and measure segments to the nearest 1/8 inch. Convert customary units of weight and liquid volume. BIG IDEA 2: Perimeter and Area 5-6 Perimeter and Area of Rectangles Find perimeter and area of rectangles. 5-7 Solve Measurement Problems Solve real world measurement word problems involving all four operations. 5-8 Focus on Mathematical Practices Solve real world problems involving measurement. M04.D-M M04.D-M M04.D-M M04.D-M M04.D-M M04.D-M M04.D-M M04.D-M THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

20 2/28-3/6 1 Day Per Lesson + 1 Days 2/21-2/27 1 Day Per Lesson + 2 Days 2/12-2/20 1 Day Per Lesson + 3 Half Days Suggested Dates Unit- Lesson Unit 6: Fraction Concepts and Operations Lesson Title Lesson Objective Eligible Content BIG IDEA 1: Fractions with Like Denominators 6-1 Understand Fractions Understand fractions as sums of unit fractions. M04.A-F Fractions that Add to One Find pairs of fractions that add to one Add and Subtract Fractions with Like Denominators Add and subtract fractions with like denominators. BIG IDEA 2: Mixed Numbers with Like Denominators Mixed Numbers & Fractions Convert between mixed numbers and fractions greater than Greater Than 1 1. Add and Subtract Mixed Numbers with Like Denominators Add and subtract mixed numbers with like denominators. Practice with Fractions and Mixed Solve problems involving addition and subtraction of fractions Numbers and mixed numbers. BIG IDEA 3: Multiply Fractions and Whole Numbers Multiply a Fraction by a Whole Number Practice Multiplying a Fraction by a Whole Number Multiply a fraction by a whole number. Solve problems involving multiplying a fraction by a whole number. 6-9 Mixed Practice Practice operations with fractions and mixed numbers Focus on Mathematical Practices Solve real world problems involving fractions. M04.A-F M04.A-F M04.A-F M04.D-M M04.A-F M04.A-F M04.A-F M04.A-F M04.A-F M04.A-F M04.A-F M04.A-F M04.A-F M04.A-F M04.A-F M04.A-F M04.A-F M04.D-M THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

21 3/22-4/6 1 Day Per Lesson + 3 Days 3/13-3/21 1 Day Per Lesson Days 3/7-3/12 1 Day Per Lesson + 1 Day Suggested Dates Unit- Lesson Unit 7: Fractions and Decimals Lesson Title Lesson Objective Eligible Content BIG IDEA 1: Fractions and Decimals 7-1 Compare Fractions Compare non-unit fractions. 7-2 Fractions on the Number Line Use the number-line model to compare fractions. 7-3 Fractions of Different-Size Wholes Equivalent Fractions Using Multiplication Equivalent Fractions Using Division Compare Fractions with Unlike Denominators Learn that the size of a fraction depends on the size of the whole. BIG IDEA 2: Equivalent Fractions Find equivalent fractions using multiplication. Find equivalent fractions using division. Compare fractions with unlike denominators. 7-7 Fractions and Line Plots Make and use line plots to display fractional data. BIG IDEA 3: Understanding Decimals 7-8 Relate Fractions and Decimals Model related fractions, decimals, and mixed numbers. 7-9 Explore Decimal Numbers Recognize equivalent tenths and hundredths and model decimal numbers in tenths and hundredths Compare Decimals to Hundredths Write and compare decimals in tenths and in hundredths Decimals Greater Than 1 Read, write, and model decimals greater than Compare Decimals Greater Than 1 Compare decimal numbers Focus on Mathematical Practices Solve real world problems involving fractions and decimals. M04.A-F M04.A-F M04.A-F M04.A-F M04.D-M M04.D-M M04.A-F M04.A-F M04.A-F M04.A-F M04.D-M M04.D-M M04.D-M THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

22 4/9-4/13 ELA PSSA Week Suggested Dates Unit- Lesson 8-1 Points, Rays, and Angles Unit 8: Geometry Lesson Title Lesson Objective Eligible Content BIG IDEA 1: Geometry 8-2 Measuring Angles Draw and measure angles. Draw and describe points, rays, angles, and other simple geometric figures. 8-3 Circles and Angles Identify, measure, and draw angles in a circle. 4.MD.5 4.MD.5.a 4.MD.5.b M04.D-M M04.D-M M04.C-G /16 4/20 MATH PSSA THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

23 4/23-5/8 Science PSSA Week + 4 Whole and 3 Half Days The rest of Unit 8 will not be on the benchmark, so its standards are included in Cycle 4. To ensure you have time in Cycle 4 to finish the unit and to review and extend content before the end of the year, it is recommended that you continue Unit 8 now. Unit 8 Continued: Geometry Suggested Dates Unit- Lesson Lesson Title Lesson Objective Eligible Content BIG IDEA 2: Triangles and Angle Measurements 8-4 Name Triangles Draw and classify triangles by their angles and sides. 8-5 Compose and Decompose Angles Find unknown angle measures. 8-6 Real World Problems Add and subtract angle measures in real world situations. M04.D-M M04.D-M M04.C-G M04.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 Draw lines and angles and identify these in two dimensional figures. CC A.2 Classify twodimensional figures by properties of their lines and angles. CC A.3 Recognize symmetric shapes and draw lines of symmetry. CC A.4 Generate and analyze patterns using one rule. PA Eligible Content M04.C-G Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. M04.C-G Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. M04.C-G Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into mirroring parts. Identify line-symmetric figures and draw lines of symmetry (up to two lines of symmetry). M04.B-O Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Example 1: Given the rule add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms alternate between odd and even numbers. Example 2: Given the rule increase the number of sides by 1 and starting with a triangle, observe that the tops of the shapes alternate between a side and a vertex. Common Core State Standard 4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. 4.G.A.3 Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. 4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

25 CC A.6 Measure angles and use properties of adjacent angles to solve problems. M04.D-M Measure angles in whole-number degrees using a protractor. With the aid of a protractor, sketch angles of specified measure. 4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "onedegree angle," and can be used to measure angles. 4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. CC A.6 Measure angles and use properties of adjacent angles to solve problems. M04.D-M Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. (Angles must be adjacent and non-overlapping.) 4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

26 5/9-5/23 1 Day Per Lesson Days Cycle 4 Scope and Sequence Suggested Dates Unit- Lesson 8-7 Lesson Title Lesson Objective Eligible Content Parallel and Perpendicular Lines and Line Segments BIG IDEA 3: Analyzing Quadrilaterals Identify and draw parallel and perpendicular figures. 8-8 Classify Quadrilaterals Name and classify quadrilaterals based on sides and angles. 8-9 Decompose Quadrilaterals and Triangles 8-10 Classify Polygons 8-11 Line Symmetry Decompose quadrilaterals and triangles into other figures. BIG IDEA 4: Analyzing Polygons Sort triangles and quadrilaterals by a number of different rules. Draw lines of symmetry and determine when figures have line symmetry Focus on Mathematical Practices Solve real world problems involving geometric figures. M04.C-G M04.C-G M04.B-O M04.C-G M04.C-G M04.C-G THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY

27 Remediation and Extension Options 5/24-6/12 13 Days Option 1: Re-teach Based on Major Work of 3 rd Grade Option 2: Pre-Teach Content for Next Year Option 3: Three-Act Math Activities Option 4: Financial Literacy You taught many topics this year. The clusters below represent the major work of 3 rd grade, so if you want to revisit something, one or more of these topics would be a good idea. 4.OA.A Use the four operations with whole numbers to solve problems. 4.NBT.A Generalize place value understanding for multi-digit whole numbers. 4.NBT.B Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NF.A Extend understanding of fraction equivalence and ordering. 4.NF.B Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4.NF.C Understand decimal notation for fractions, and compare decimal fractions. You can check in with your 5 th grade teacher to ask what content you could pre-teach or what content they would like you to revisit. The first two Units in 5 th grade are: 1) Addition and Subtraction with Fractions 2) Addition and Subtraction with Decimals You can access the 5 th grade Teacher s Guide and materials online for reference. 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: 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