Go Math! Recommendations for Curriculum Adoption and Modification

Recommendations for Curriculum Adoption and Modification 2014-15 475 Riverside Drive Suite 1270 New York, NY 10115 212 870-3505 www.teachingmatters.org

This document provides a standards-based analysis of the curriculum program. Our intention was to clarify the degree to which grade-level standards are addressed within the materials and to recommend ways to supplement with readily available, Common Core aligned resources where necessary. This document covers grades kindergarten, 3 and 5, which may be used as models for analyzing other grades. The analysis aims to help school leaders, coaches and teacher teams make informed instructional decisions as they continue to adopt the New York City recommended programs. Summary of Key Findings While details can be found in the pages that follow, here are a few key highlights. Strengths of the Curriculum Provides students with a strong foundational background for grade-level concepts Gives students opportunities to practice basic skills and apply different strategies to strengthen fluency Provides teachers with a wide variety of resources to meet students needs and ability levels Gaps of the Curriculum Requires additional emphasis on conceptual understanding of grade-level concepts and standards of emphasis Lacking in variety of real-world applications Strategies are presented, but not developed, to provide students with a complete understanding, and application, of the strategies designed to reinforce conceptual understanding and fluency Copyright Teaching Matters

Kindergarten: Counting and Cardinality What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 5, Lesson 24 Culminating Task - Cooperative Group Task. K.CC.1 Count to 100 by ones and by tens. Know number names and the count sequence. (K.CC.1, K.CC.2, K.CC.3) Chapter 8, Lessons 8.5, 8.6, 8.7, 8.8 Additional modeling needed. EngageNY, Module 5: Topics A, D 5 (assesses Topic A) 8 5 End-of- Module (assesses Topic D) K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). Know number names and the count sequence. (K.CC.1, K.CC.2, K.CC.3) Chapter 4, Lesson 4.4 Chapter 8, Lesson 8.3 Extending and exploring numbers EngageNY, Module 5: Topic D 5, Lesson 24 Culminating Task - Cooperative Group Task. 5 End-of- Module (assesses Topic D) 4 8 K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Know number names and the count sequence. (K.CC.1, K.CC.2, K.CC.3) Chapter 1, Lessons 1.2, 1.3, 1.7, 1.9, 1.10 Chapter 3, Lesson 3.2, 3.4, 3.6, 3.8 Chapter 4, Lesson 4.2 Chapter 7, Lessons 7.2, 7.4, 7.6, 7.8, 7.10 Chapter 8, Lesson 8.2 Lacking in subsequent working with numbers in different configurations. EngageNY, Module 1: Topics D, E, F EngageNY, Module 5: Topic B 1, Lesson 37, Culminating Task - materials needed numeral/dot cards from 0-10). 1 (assesses Topic D) 1 End-of- Module (assesses Topics E & F) 5, Lesson 24, Culminating Task - Cooperative Group Task. 1 3. 4 7 5 (assesses Topic B) 8 Copyright Teaching Matters

Kindergarten: Counting and Cardinality What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality. Count to tell the number of objects. (K.CC.4, K.CC.4a, K.CC.4b, K.CC.4c, K.CC.5) Chapter 1, Lessons 1.1, 1.3, 1.5, 1.6, 1.8 Additional lessons needed to support Chapter 1 concepts. Lack of modeling with counting tool - Rekenrek (abacus). EngageNY, Module 1: Topics B, C, D, E, F, G, H 1: Lesson 37 - Culminating task - materials needed numeral/dot cards from 0-10) 1 (assesses Topics B, C & D) 1 End-of- Module (assesses Topics E, F, G & H) 1 K.CC.4a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Modeling with arrays - Rekenrek (abacus) Count to tell the number of objects. (K.CC.4, K.CC.4a, K.CC.4b, K.CC.4c, K.CC.5) Chapter 1, Lessons 1.1, 1.3, 1.5, 1.6, 1.8 Additional lessons to support Chapter 1 concepts. 1: Topics B,C, D, E, F, G, H 1: Lesson 37 - Culminating task - materials needed numeral/dot cards from 0-10) 1 (assesses Topics B, C & D) 1 End-of- Module (assesses Topics E, F, G & H) 1 K.CC.4b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Count to tell the number of objects. (K.CC.4, K.CC.4a, K.CC.4b, K.CC.4c, K.CC.5) Chapter 1, Lesson 1.6 Additional modeling needed. 1: Topics B, C, D, E, F, G, H 1: Lesson 37 - Culminating task - materials needed numeral/dot cards from 0-10) 1 (assesses Topics B, C & D) 1 End-of- Module (assesses Topics E, F, G & H) 1 Copyright Teaching Matters

Kindergarten: Counting and Cardinality What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 1: Lesson 37 - Culminating task - materials needed numeral/dot cards from 0-10). K.CC.4c Understand that each successive number name refers to a quantity that is one larger. Count to tell the number of objects. (K.CC.4, K.CC.4a, K.CC.4b, K.CC.4c, K.CC.5) Chapter 1, Lesson 1.8 Additional modeling needed. 1: Topics B,C, D, E, F, G, H 5: Topic C 6: Topic A 1 (assesses Topics B, C & D) 1 End-of- Module (assesses Topics E, F, G & H) 5: Last Instructional Day, Lesson 24 Culminating Task - Cooperative Group Task. 5 (assesses Topic C) 6 - Lesson 8, Culminating Task - collaborative project. 6 End-of- Module (assesses Topic A) 1, Lesson 37 - Culminating task - materials needed numeral/dot cards from 0-10). 1 K.CC.5 Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. Count to tell the number of objects. (K.CC.4, K.CC.4a, K.CC.4b, K.CC.4c, K.CC.5) Chapter 3, Lessons 3.1, 3.3, 3.3, 3.5, 3.7 Chapter 4, Lesson 4.1 Chapter 8, Lesson 8.1 Chapter 3 lesson structure is identical to Chapter 1. Requires additional time on working with numbers in different configurations; compose and decompose numbers; and modeling using a counting tool, i.e. Rekenrek (abacus). 1: Topic C, D, E, F 5: Topics C, E 1 (assesses Topics C & D) 1 End-of- Module (assesses Topics E & F) 5, Last Instructional Day, Lesson 24 Culminating Task - Cooperative Group Task. 3. 4 8 5 (assesses Topic C) 5 End-of- Copyright Teaching Matters

Kindergarten: Operations and Algebraic Thinking What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)) sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. (K.OA.1, K.OA.2, K.OA.3, K.OA.4, K.OA.5) Chapter 5, Lessons 5.1, 5.2, 5.3 Chapter 6, Lessons 6.1, 6.2, 6.3 Chapters 5 & 6: Story situations and patterns need additional emphasis. 4: Topics A, C, D, G, H 4 Lesson 41 Culminating Task 4 Mid- Module (assesses Topics A, C & D) 4 End-of- Module (assesses Topics G & H) Mid- Chapter 6 K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. (K.OA.1, K.OA.2, K.OA.3, K.OA.4, K.OA.5) Chapter 5, Lesson 5.7 Chapter 6, Lessons 6.6, 6.7 Chapter 5: Requires supplementing for scenarios involving: add to with result unknown; put together with total unknown; when both addends are unknown. Lacking in pictorials and patterns. Chapter 6: Requires supplementing for story situations and patterns. 4: Topics C, D, F, G, H 4 Lesson 41 Culminating Task 4 Mid - Module (assesses Topics C& D) 4 End-of- Module (assesses Topics F, G & H) 5 6 1: Lesson 37 - Culminating task - materials needed numeral/dot cards from 0-10) K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. (K.OA.1, K.OA.2, K.OA.3, K.OA.4, K.OA.5) Chapter 5, Lessons 5.8, 5.9, 5.10, 5.11, 5.12 Lacking in story situations and looking at patterns. 1: Topic C 4: Topics A, B, D, E, G 1 Mid- Module (assesses Topic C) 4 Lesson 41 Culminating Task 4 Mid- Module (assesses Topics A, B & D) 5 4 End-of- Module (assesses Topics E & G) Copyright Teaching Matters

Kindergarten: Measurement and Data What is the essence of this domain? Where does our current curriculum (Go Math!) address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can Impact on we use to fill the gap? s K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. Describe and compare measurable attributes. (K.MD.1, K.MD.2) Chapter 11, Lesson 11.5 Lacking in comparison of volume, and clarification of measurable attributes. 3: Topics A, B, C, D, H 3 Lesson 32 Culminating Task 3 (assesses Topics A, B, C & D) 3 (assesses Topic H) 11 K.MD.2 Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. Describe and compare measurable attributes. (K.MD.1, K.MD.2) Chapter 11, Lessons 11.1, 11.2, 11.3,11.4 Lacking in comparison of volume. Additional modeling needed. 3: Topics A, B, C, D, H 3 Lesson 32 Culminating Task 3 (assesses Topics A, B, C & D) 3 (assesses Topic H) 11 K.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.) Classify objects and count the number of objects in each category. (K.MD.3) Chapter 12, Lessons 12.1, 12.2, 12.3, 12.4, 12.5, 12.6 Analyze, classify, and sort related objects. 1: Topics A, B 1 Lesson 37, Culminating task - materials needed numeral/dot cards from 0-10) 1 (assesses Topics A & B) 12 Copyright Teaching Matters

Kindergarten: Numbers and Operations in Base Ten What is the essence of this domain? Where does our current curriculum (Go Math!) address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. Work with numbers 11-19 to gain foundations for place value (K.NBT.1) Chapter 7, Lessons 7.1, 7.3, 7.5, 7.7, 7.9 Requires additional modeling with arrays using a Rekenrek (abacus). 5: Topics A, B, C, E 5 Lesson 24, Culminating Task 5 Mid - Module (assesses Topics A, B &C) 5 Endof-Module (assesses Topic E) 7 Copyright Teaching Matters

Kindergarten: Geometry K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. What is the essence of this domain? Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). (K.G.1, K.G.2, K.G.3) Where does our current curriculum () address the standards? Chapter 10, Lessons 10.7, 10.8, 10.9 Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) Requires additional applications of two-dimensional flat shapes and three-dimensional solid shapes. What materials can we use to fill the gap? EngageNY Module 2: Topics A, B Impact on 2, Lesson 10 Culminating Task, collaborative project 2, End-of- Module (assesses Topics A & B) s 10 K.G.2 Correctly name shapes regardless of their orientations or overall size. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). (K.G.1, K.G.2, K.G.3) Chapter 9, Lessons 9.1, 9.3, 9.5, 9.7, 9.9 Chapter 10, Lessons 10.2, 10.3, 10.4, 10.5 Requires additional applications of two-dimensional flat shapes and three-dimensional solid shapes. EngageNY Module 2: Topics A, B 2, Lesson 10 - Culminating Task, collaborative project 2 End-of- Module (assesses Topics A & B) 9 10 K.G.3 Identify shapes as two-dimensional (lying in a plane, "flat") or threedimensional ("solid"). Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). (K.G.1, K.G.2, K.G.3) Chapter 10, Lesson 10.6 Requires supplementing to exploring two-dimensional and threedimensional shapes. EngageNY Module 2: Topic C 2, Lesson 10 Culminating Task, collaborative project 2 End -of- Module (assesses Topic C) 10 K.G.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length). Analyze, compare, create, and compose shapes. (K.G.4, K.G.5, K.G.6) Chapter 9, Lessons 9.2, 9.4, 9.6, 9.8, 9.10, 9.11 Requires additional applications of two-dimensional flat shapes and three-dimensional solid shapes. Requires supplementing to explore two-dimensional and threedimensional shapes. EngageNY Module 2: Topics A, B, C 2, Lesson 10 - Culminating Task, collaborative project 2 End-of- Module (assesses Topics A, B & C) 9.. K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. Analyze, compare, create, and compose shapes. (K.G.4, K.G.5, K.G.6) Not addressed in Build, describe, compose flat and solid shapes. Lacks lessons on building, describing, and composing flat and solid shapes. EngageNY Module 6: Topic A 6, Lesson 8 - Culminating Task, collaborative project 6 End-of- Module Task (assesses Topic A) None Copyright Teaching Matters

Kindergarten: Geometry K.G.6 Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?" What is the essence of this domain? Analyze, compare, create, and compose shapes. (K.G.4, K.G.5, K.G.6) Where does our current curriculum () address the standards? Not addressed in Compose and decompose shapes. Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) Lacks lessons on composing and decomposing shapes. What materials can we use to fill the gap? EngageNY Module 6: Topic B Impact on 6, Lesson 8 - Culminating Task, collaborative project 6 End-of- Module Task (assesses Topic B) s None Copyright Teaching Matters

Grade 1: Operations & Algebraic Thinking What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Represent and solve problems involving addition and subtraction. (1.OA.1, 1.OA.2) Chapter 1, Lessons: 1.1, 1.2, 1.3, 1.4, 1.7 Chapter 2, Lessons: 2.1, 2.2, 2.3, 2.4, 2.6, 2.8 Chapter 4, Lesson: 4.6 Chapter 5, Lessons: 5.1, 5.7 adequately addresses the standard; EngageNY materials are included for enrichment or for review to be used later in the year. 1: Topics A, B, C, G, H 2: Topics A, B, C, D 3: Topics C, D 4: Topic E 6: Topics A, F 1 (assesses Topics A, B, C) 1 (assesses Topics G, H) 1 Mid- Chapter 2 Mid- Chapter 4 5 Mid- Chapter 1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Represent and solve problems involving addition and subtraction. (1.OA.1, 1.OA.2) Chapter 3, Lesson: 3.12 Additional application of the standard needed. 2: Topic A 2 (assesses Topic A) 3 1.OA.3 Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) Understand and apply properties of operations and the relationship between addition and subtraction. (1.OA.3, 1.OA.4) Chapter 1, Lessons: 1.5, 1.6 Chapter 3, Lessons: 3.1, 3.10, 3.11 Additional application and practice of the standard needed. 1: Topics E, F 1 (assesses Topics E, F) 1 3 Mid- Chapter 1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10-8 by finding the number that makes 10 when added to 8. Add and subtract within 20. Understand and apply properties of operations and the relationship between addition and subtraction. (1.OA.3, 1.OA.4) Chapter 4, Lessons: 4.2, 4.3 Additional application and practice of the standard needed. 1: Topics G, H 1 (assesses Topics G, H) 4 Mid- Chapter

Grade 1: Operations & Algebraic Thinking What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). Add and subtract within 20. (1.OA.5, 1.OA.6) Chapter 3, Lesson: 3.2 Chapter 4, Lesson: 4.1 Additional application and practice of the standard needed. 1: Topics B, D, G, I 1 (assesses Topics B, D) 1 (assesses Topics G, I) 3 Mid- Chapter 4 Mid- Chapter 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13-4 = 13-3 - 1 = 10-1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12-8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Add and subtract within 20. (1.OA.5, 1.OA.6) Chapter 1, Lesson: 1.8 Chapter 2, Lesson: 2.9 Chapter 3, Lessons: 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9 Chapter 4, Lessons: 4.4, 4.5 Chapter 5, Lessons: 5.2, 5.3, 5.4, 5.8, 5.10 Chapter 8, Lesson: 8.1 adequately addresses the standard; EngageNY materials are included for enrichment or for review to be used later in the year. 1: Topics A, B, C, F, I, J 1 (assesses Topics A, B, C, F) 1 (assesses Topics I, J) 1 2 3 Mid- Chapter 4 5 Mid- Chapter 8 Mid- Chapter 1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8-1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. Work with addition and subtraction equations. (1.OA.7, 1.OA.8) Chapter 5, Lesson: 5.7 Additional application and practice of the standard needed. 1: Topic E 1 (assesses Topic E) 5

Grade 1: Numbers & Operations in Base Ten What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. Extend the counting sequence. (1.NBT.1) Chapter 6, Lessons: 6.1, 6.2, 6.9, 6.10 Additional fluency practice is needed. 4: Topics A, B 6: Topic B 4 (assesses Topics A & B) 6 (assesses Topic B) 6 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: Understand place value. (1.NBT.2, 1.NBT.3) Chapter 6, Lessons: 6.6, 6.7 Additional application and practice of the standard needed. 4: Topics A, B, C 4 (assesses Topics A, B & C) 6 1.NBT.2a 10 can be thought of as a bundle of ten ones - called a "ten." Understand place value. (1.NBT.2, 1.NBT.3) Chapter 6, Lessons: 6.5, 6.8 Additional application and practice of the standard needed. 2: Topic D 6: Topic B 2 (assesses Topic D) 6 (assesses Topic B) 6 1.NBT.2b The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Understand place value. (1.NBT.2, 1.NBT.3) Chapter 6, Lessons: 6.3, 6.4 Additional application and practice of the standard needed. 2: Topic D 2 (assesses Topic D) 6

Grade 1: Numbers & Operations in Base Ten What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 1.NBT.2c The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). 1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Understand place value. (1.NBT.2, 1.NBT.3) Understand place value. (1.NBT.2, 1.NBT.3) Chapter 6, Lesson: 6.5 Chapter 6, Lesson: 6.8 Chapter 7, Lessons: 7.1, 7.2, 7.3, 7.4 Additional application and practice of the standard needed. adequately addresses the standard; EngageNY materials are included for enrichment or for review to be used later in the year. 6: Topic B 4: Topic B 6 (assesses Topic B) 4 (assesses Topic B) 6 6 7 1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. Use place value understanding and properties of operations to add and subtract. (1.NBT.4, 1.NBT.5, 1.NBT.6) Chapter 8, Lessons: 8.2, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9 adequately addresses the standard; EngageNY materials are included for enrichment or for review to be used later in the year. 4: Topics C, D, F 6: Topics C, D 4 (assesses Topics C & D) 4 (assesses Topic F) 6 (assesses Topics C & D) 8

Grade 1: Numbers & Operations in Base Ten What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Use place value understanding and properties of operations to add and subtract. (1.NBT.4, 1.NBT.5, 1.NBT.6) Chapter 7, Lesson 7.5 Additional application and practice of the standard needed. 4: Topic A 6: Topic B 4 (assesses Topic A) 6 (assesses Topic B) 7 1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use place value understanding and properties of operations to add and subtract. (1.NBT.4, 1.NBT.5, 1.NBT.6) Chapter 8, Lessons: 8.3, 8.9 Additional application, conceptual understanding and practice of the standard needed. 4: Topic C 6: Topic C 4 (assesses Topic C) 6 (assesses Topic C) 8

Grade 1: Measurement & Data What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object. Measure lengths indirectly and by iterating length units. (1.MD.1, 1.MD.2) Chapter 9, Lessons: 9.1, 9.2 Additional application and conceptual understanding of the standard needed. 3: Topics A, B 3 (assesses Topics A & B) 9, 1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. Measure lengths indirectly and by iterating length units. (1.MD.1, 1.MD.2) Chapter 9, Lessons: 9.3, 9.4, 9.5 Additional hands-on application, and conceptual understanding of the standard needed. 3: Topics B, C, D 3 (assesses Topics B, C & D) 9, 1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks. Recognize and identify coins, their names, and their value. Tell and write time and money. (1.MD.3) Chapter 9, Lessons: 9.6, 9.7, 9.8, 9.9 Recognizing and identifying coins, their names, and their value is absent from. Supplemental materials from EngageNY are necessary. 5: Topic D 6: Topic E 5 (assesses Topic D) 6 (assesses Topic E) 9

Grade 1: Geometry What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 1.G.1 Distinguish between defining attributes (e.g., triangles are closed and threesided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes. Reason with shapes and their attributes. (1.G.1, 1.G.2, 1.G.3) Chapter 11, Lessons: 11.1, 11.5 Chapter 12, Lessons: 12.1, 12.2 adequately addresses the standard; EngageNY materials are included for enrichment or for review to be used later in the year. 5: Topic A 5 (assesses Topic A) 11 12 1.G.2 Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn the formal names of the shapes.) Reason with shapes and their attributes. (1.G.1, 1.G.2, 1.G.3) Chapter 11, Lessons: 11.2, 11.3, 11.4 Chapter 12, Lessons: 12.3, 12.4, 12.5, 12.6, 12.7 adequately addresses the standard; EngageNY materials are included for enrichment or for review to be used later in the year. 5: Topic B 5 (assesses Topic B) 11 12

Grade 2: Operations & Algebraic Thinking What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Represent and solve problems involving addition and subtraction. (2.OA.1) Chapter 3, Lessons: 3.8, 3.9 Chapter 4, Lessons 4.9, 4.10 Chapter 5, Lessons 5.9, 5.10, 5.11 addresses the standard adequately. EngageNY materials are included to supplement what GoMath! provides, and to provide teachers with additional opportunities to apply problemsolving skills. 1: Topics A, B, C 4: Topics A, C, F 1 4 and Endof-Module 3 4 5 2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Add and subtract within 20. (2.OA.2) Chapter 3, Lessons: 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7 provides a chapter focusing on building fluency. EngageNY materials are included to provide opportunities for students to build fluency using mental math strategies at other points throughout the year. 1: Topics A, B 1 2 & 2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. Work with equal groups of objects to gain foundations for multiplication. (2.OA.3, 2.OA.4) Chapter 1, Lessons: 1.1, 1.2 Additional practice and application of the standard is needed. 6: Topic D 6 1 2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Work with equal groups of objects to gain foundations for multiplication. (2.OA.3, 2.OA.4) Chapter 3, Lessons: 3.10, 3.11 Additional practice and application of the standard is needed. 6: Topics A, B, C 6 and Endof-Module 3

Grade 2: Numbers & Operations in Base Ten What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on Go Math! s 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 2.NBT.1A. 100 can be thought of as a bundle of ten tens - called a "hundred." 2.NBT.1B The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2.NBT.2 Count within 1000; skipcount by 5s, 10s, and 100s. 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. Understand place value. (2.NBT.1, 2.NBT.2, 2.NBT.3, 2.NBT.4) Understand place value. (2.NBT.1, 2.NBT.2, 2.NBT.3, 2.NBT.4) Understand place value. (2.NBT.1, 2.NBT.2, 2.NBT.3, 2.NBT.4) Understand place value. (2.NBT.1, 2.NBT.2, 2.NBT.3, 2.NBT.4) Understand place value. (2.NBT.1, 2.NBT.2, 2.NBT.3, 2.NBT.4) Chapter 2, Lesson 2.2, 2.3, 2.4, 2.5 Chapter 2, Lesson 2.1 Chapter 2, Lesson 2.1 Chapter 1, Lessons: 1.8, 1.9 Chapter 1, Lessons: 1.3, 1.4, 1.5, 1.6, 1.7 Chapter 2, Lessons: 2.6, 2.7, 2.8 adequately addresses the standard; EngageNY materials are included for enrichment. One lesson does not provide an adequate amount of practice, application nor fluency. One lesson does not provide an adequate amount of practice, application nor fluency. Additional practice and application of the standard is needed. adequately addresses the standard; EngageNY materials are included to provide enrichment. 3: Topic A 3: Topics A, E 3: Topics A, E 3: Topic B, D, G 3: Topic C 3 3 and 3 and 3 and 3 2 2 2 1 1 2 and

Grade 2: Numbers & Operations in Base Ten What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on Go Math! s 2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. 2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations. Understand place value. (2.NBT.1, 2.NBT.2, 2.NBT.3, 2.NBT.4) Use place value understanding and properties of operations to add and subtract. (2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.8, 2.NBT.9) Use place value understanding and properties of operations to add and subtract. (2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.8, 2.NBT.9) Chapter 2, Lessons: 2.11, 2.12 Chapter 4, Lessons: 4.6, 4.7, 4.8 Chapter 5, Lessons: 5.1, 5.2, 5.35.4, 5.5, 5.6, 5.7, 5.8 Chapter 4, Lessons: 4.1, 4.2, 4.3, 4.4, 4.5, 4.11, 4.12 Additional practice and application of the standard is needed. adequately addresses the standard; EngageNY materials are included to provide enrichment. adequately addresses the standard; EngageNY materials are included to provide enrichment, or to reinforce mastery of the standard at other times during the year. 3: Topic F 1: Topic C 4: Topic A 4: Topic D 3 1 4 4 2 4 5 4

Grade 2: Numbers & Operations in Base Ten What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on Go Math! s 2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.NBT.8 Mentally add 10 or 100 to a given number 100 900, and mentally subtract 10 or 100 from a given number 100 900. Use place value understanding and properties of operations to add and subtract. (2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.8, 2.NBT.9) Use place value understanding and properties of operations to add and subtract. (2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.8, 2.NBT.9) Chapter 6, Lessons: 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 6.10 Chapter 2, Lessons: 2.9, 2.10 adequately addresses the standard; EngageNY materials are included to provide enrichment, or to reinforce mastery of the standard at other times during the year. Additional practice and application of the standard is needed. 4: Topics B, C, D, E, F 5: Topics A, B, C, D 4: Topics A, D 5: Topics A, D 4 and 5 and 4 and 5 and 6 2

Grade 2: Measurement & Data What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Measure and estimate lengths in standard units. (2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4) Measure and estimate lengths in standard units. (2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4) Measure and estimate lengths in standard units. (2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4) Measure and estimate lengths in standard units. (2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4) Chapter 8, Lessons: 8.1, 8.2, 8.4, 8.8 Chapter 9, Lessons: 9.1, 9.3 Chapter 8, Lesson: 8.6 Chapter 9, Lesson: 9.5 Chapter 8, Lessons: 8.3, 8.7 Chapter 9, Lessons 9.2, 9.6 Chapter 9, Lesson 9.7 adequately addresses this standard. EngageNY materials are included for enrichment or additional practice. Additional practice and application of the standard is needed. adequately addresses this standard. EngageNY materials are included for enrichment or additional practice. Additional practice and application of the standard is needed. 2: Topics A, B, C 7: Topics C, D 2: Topic C 7: Topic D 2: Topic B 7: Topic D 2: Topic C 7: Topic D 2 7 2 7 2 7 2 7 8 9 8 8 9 9

Grade 2: Measurement & Data What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. Relate addition and subtraction to length. (2.MD.5, 2.MD.6) Chapter 8, Lesson 8.5 Chapter 9, Lesson 9.4 Additional practice and application of the standard is needed. 2: Topic D 7: Topic E 2 7 8 9 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram. Relate addition and subtraction to length. (2.MD.5, 2.MD.6) Chapter 8, Lesson 8.5 Chapter 9, Lesson 9.4 Additional practice and application of the standard is needed. 2: Topic D 7: E, F 2 7 8 9 2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? Work with time and money. (2.MD.7, 2.MD.8) Work with time and money. (2.MD.7, 2.MD.8) Chapter 7, Lessons: 7.8, 7.9, 7.10, 7.11 Chapter 7, Lessons: 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7 adequately addresses this standard. EngageNY materials are included for enrichment or additional practice. adequately addresses this standard. EngageNY materials are included for enrichment or additional practice. 8: Topic D 7: Topic B 8 7 7 7

Grade 2: Geometry What is the essence of this domain? Where does our current curriculum () address the standards? Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY) What materials can we use to fill the gap? Impact on s 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Reason with shapes and their attributes. (2.G.1, 2.G.2, 2.G.3) 11, Lessons: 11.1, 11.2, 11.3, 11.4, 11.5 adequately addresses this standard. EngageNY materials are included for enrichment or additional practice. 8: Topic A 8 11 2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Reason with shapes and their attributes. (2.G.1, 2.G.2, 2.G.3) 11, Lesson: 11.6 Additional practice and application of the standard is needed. 6: Topic C 6 11 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Reason with shapes and their attributes. (2.G.1, 2.G.2, 2.G.3) 11, Lessons: 11.7, 11.8, 11.9, 11.10 adequately addresses this standard. EngageNY materials are included for enrichment or additional practice. 8: Topics B, C, D 8 and Endof-Module 11