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1 NYC Go Math! Grade 5GO Math! Scope and SequenceThis document contains a high-level scope and sequence for the GO Math! program intended to give teachers an overview of where instructional time will be spent across the year through use of GO Math!. It provides a suggested sequence of instruction and assessments, including where NYCDOE Periodic Assessments can be used to gauge students understanding of concepts and skills taught at benchmark moments throughout the year. Based on the Common Core Standards, Go Math! is divided into critical areas that offer a focused and coherent study of the key concepts and skills for each grade. For each critical area, you will see the following: Essential Ideas: The key topics of the unit; chapters and lessons are built around achieving understanding and mastery of these topics.

2 Standards: The standards listed show the main standards covered throughout the Critical Area. Instruction is focused on achieving a thorough knowledge of these standards. Mathematical Practices: While all practices are integrated into each Critical Area, the practices listed are ones that receive particular emphasis. Essential Questions: The essential question for each chapter is listed, showing the goal of each chapter . Assessment Opportunities: This listing highlights the assessments that ensure teachers can gauge student success on mastering the standards covered in the Critical 5: Suggested Sequence for the GO Math! programSuggested Amount of Time (in days)Critical Area 1: Fluency with Whole Numbers and Decimals59 daysNYCDOE Fall Benchmark Assessment Critical Area 2: Operations with Fractions31 daysCritical Area 3: Geometry and Measurement32 daysNYCDOE Spring Benchmark AssessmentState Examination11 The GO Math!

3 Program is paced to ensure that all pre-test and post-test standards are completely and fully covered prior to testing. As the transition to the PARCC assessments progresses, schools may choose to make decisions around the pacing of units that address post-test concepts prior to the state examination in consideration of the state s testing program guidance (see ).NYC34 Planning GuideCritical Area 1: Fluency with Whole Numbers and Decimals Chapters 1 559 Days (Instructional Days: 49; Assessment Days: 10) Critical Area 2: Operations with Fractions Chapters 6 831 Days (Instructional Days: 25; Assessment Days: 6)Focus or Main CC Standards Write and interpret numerical Use parentheses, brackets, or braces in numerical expressions, and evalu-ate expressions with these Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

4 Understand the place value Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of Read, write, and compare decimals to Read and write decimals to thousandths using base-ten numer-als, number names, and expanded form, , = 3 100 + 4 10 + 7 1 + 3 (1/10) + 9 (1/100) + 2 (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of Use place value understanding to round decimals to any operations with multi-digit whole numbers and with deci-mals to Fluently multiply multi-digit whole numbers using the standard Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplica-tion and division.

5 Illustrate and explain the calculation by using equations, rectangular arrays, and/or area Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of op-erations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning and extend previous understandings of multiplication and divi-sion to multiply and divide Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, , by using visual fraction models or equations to represent the problem. Write and interpret numerical Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

6 Use equivalent fractions as a strategy to add and subtract Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Solve word problems involving addition and subtraction of fractions refer-ring to the same whole, including cases of unlike denominators, , by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers . Apply and extend previous understandings of multiplication and divi-sion to multiply and divide Interpret a fraction as division of the numerator by the denominator (a/b = a b).

7 Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, , by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to fi nd areas of rectangles, and represent fraction products as rectangular Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

8 Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recog-nizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by Solve real world problems involving multiplication of fractions and mixed numbers, , by using visual fraction models or equations to represent the Apply and extend previous understandings of division to divide unit frac-tions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole num-ber, and compute such quotients.

9 Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit frac-tions, , by using visual fraction models and equations to represent the problem. Highlighted Mathematical Practices Make sense of problems and persevere in solving Attend to Look for and express regularity in repeated Construct viable arguments and critique the reasoning of Attend to Look for and make use of Questions How can you use place value, multiplication, and expression to represent and solve problems? ( chapter 1) How can you divide whole numbers? ( chapter 2) How can you add and subtract decimals? ( chapter 3) How can you solve decimal multiplication problems?

10 ( chapter 4) How can you solve decimal division problems? ( chapter 5) How can you add and subtract fractions with unlike denominators? ( chapter 6) How do you multiply fractions? ( chapter 7) What strategies can you use to solve division problems involving fractions? ( chapter 8)Assessment OpportunitiesShow What You Know Mid- chapter checkpoint chapter Review/Test chapter Test chapter Performance TaskCritical Area Performance TaskShow What You Know Mid- chapter checkpoint chapter Review/Test chapter Test chapter Performance TaskCritical Area Performance TaskNYCDOE Fall Benchmark AssessmentDO NOT EDIT--Changes must be made through File info CorrectionKey=BDO NOT EDIT--Changes must be made through File info CorrectionKey= 3406/06/13 9:41 PMNYC Scope and SequenceNYC Scope and Sequence NYC35 Critical Area 1: Fluency with Whole Numbers and Decimals Chapters 1 559 Days (Instructional Days: 49; Assessment Days: 10) Critical Area 2: Operations with Fractions Chapters 6 831 Days (Instructional Days: 25.)