Go Math! Recommendations for Curriculum Adoption and Modification

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Go Math! 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 Go Math! 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 Go Math! Curriculum ▪

Provides students with a strong foundational background for grade-level concepts

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Gives students opportunities to practice basic skills and apply different strategies to strengthen fluency

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Provides teachers with a wide variety of resources to meet students’ needs and ability levels

➢ Gaps of the Go Math! Curriculum ▪

Requires additional emphasis on conceptual understanding of grade-level concepts and standards of emphasis

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Lacking in variety of real-world applications

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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

Content Standards

Standards: 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 Go Math! we use to fill the assessments gap?

Go Math! Assessments

EngageNY Module 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

EngageNY Module 5 Mid-Module Assessment (assesses Topic A)

Go Math! Chapter 8 Summative Assessment

EngageNY Module 5 End-ofModule Assessment (assesses Topic D)

K.CC.2 Count forward beginning from a given Know number names and number within the known the count sequence. sequence (instead of having to (K.CC.1, K.CC.2, K.CC.3) begin at 1).

Chapter 4, Lesson 4.4 Chapter 8, Lesson 8.3

Extending and exploring numbers

EngageNY, Module 5: Topic D

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 4, Lesson 4.2 Chapter 7, Lessons 7.2, 7.4, 7.6, 7.8, 7.10 Chapter 8, Lesson 8.2

Go Math! Chapter 4 Mid-Chapter Checkpoint

EngageNY Module 5 End-ofModule Assessment (assesses Topic D)

Go Math! Chapter 8 Mid-Chapter Checkpoint

EngageNY Module 1, Lesson 37, Go Math! Chapter 1 Culminating Task - materials Mid-Chapter Checkpoint and needed numeral/dot cards from 0 Summative Assessment 10).

Chapter 1, Lessons 1.2, 1.3, 1.7, 1.9, 1.10 Chapter 3, Lesson 3.2, 3.4, 3.6, 3.8

EngageNY Module 5, Lesson 24 Culminating Task - Cooperative Group Task.

Lacking in subsequent working with numbers in different configurations.

EngageNY, Module 1: Topics D, E, F EngageNY, Module 5: Topic B

EngageNY Module 1 Mid-Module Assessment (assesses Topic D)

Go Math! Chapter 3 Mid-Chapter Checkpoint and Summative Assessment.

EngageNY Module 1 End-ofModule Assessment (assesses Topics E & F)

Go Math! Chapter 4 Mid-Chapter Checkpoint

EngageNY Module 5, Lesson 24, Culminating Task - Cooperative Group Task. EngageNY Module 5 Mid-Module Assessment (assesses Topic B)

Go Math! Chapter 7 Mid-Chapter Checkpoint and Summative Assessment Go Math! Chapter 8 Mid-Chapter Checkpoint

Copyright Teaching Matters

Kindergarten: Counting and Cardinality

Content Standards

K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.

Standards: What is the essence of this domain?

Where does our current curriculum (Go Math!) address the standards?

Count to tell the number of objects. Chapter 1, Lessons 1.1, (K.CC.4, K.CC.4a, 1.3, 1.5, 1.6, 1.8 K.CC.4b, K.CC.4c, K.CC.5)

Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY)

Additional lessons needed to support Chapter 1 concepts. Lack of modeling with counting tool Rekenrek (abacus).

What materials can Impact on Go Math! we use to fill the assessments gap?

Go Math! Assessments

EngageNY Module 1: Lesson 37 Culminating task - materials needed numeral/dot cards from 0 10) EngageNY, Module EngageNY Module 1 Mid-Module 1: Topics B, C, D, E, Assessment (assesses Topics B, F, G, H C & D)

Go Math! Chapter 1 Mid-Chapter Checkpoint and Summative Assessment

EngageNY Module 1 End-ofModule Assessment (assesses Topics E, F, G & H)

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)

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. Chapter 1, Lessons 1.1, (K.CC.4, K.CC.4a, 1.3, 1.5, 1.6, 1.8 K.CC.4b, K.CC.4c, K.CC.5)

EngageNY Module 1: Lesson 37 Culminating task - materials needed numeral/dot cards from 0 10) Additional lessons to support Chapter 1 concepts.

EngageNY Module 1: EngageNY Module 1 Mid-Module Topics B,C, D, E, F, Assessment (assesses Topics B, G, H C & D)

Go Math! Chapter 1 Mid-Chapter Checkpoint and Summative Assessment

EngageNY Module 1 End-ofModule Assessment (assesses Topics E, F, G & H)

Count to tell the number of objects. Chapter 1, Lesson 1.6 (K.CC.4, K.CC.4a, K.CC.4b, K.CC.4c, K.CC.5)

EngageNY Module 1: Lesson 37 Culminating task - materials needed numeral/dot cards from 0 10) Additional modeling needed.

EngageNY Module 1: EngageNY Module 1 Mid-Module Topics B, C, D, E, F, Assessment (assesses Topics B, G, H C & D)

Go Math! Chapter 1 Summative Assessment

EngageNY Module 1 End-ofModule Assessment (assesses Topics E, F, G & H)

Copyright Teaching Matters

Kindergarten: Counting and Cardinality

Content Standards

Standards: 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 Go Math! we use to fill the assessments gap?

Go Math! Assessments

EngageNY Module 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. Chapter 1, Lesson 1.8 (K.CC.4, K.CC.4a, K.CC.4b, K.CC.4c, K.CC.5)

EngageNY Module 1 Mid-Module Assessment (assesses Topics B, C & D) EngageNY Module 1 End-ofEngageNY Module 1: Module Assessment (assesses Topics B,C, D, E, F, Topics E, F, G & H) G, H Additional modeling needed.

EngageNY Module 5: Last EngageNY Module 5: Instructional Day, Lesson 24 Topic C Culminating Task - Cooperative Group Task. EngageNY Module 6: Topic A EngageNY Module 5 Mid-Module Assessment (assesses Topic C)

Go Math! Chapter 1 Summative Assessment

EngageNY Module 6 - Lesson 8, Culminating Task - collaborative project. EngageNY Module 6 End-ofModule Assessment (assesses Topic A) EngageNY Module 1, Lesson 37 Culminating task - materials needed numeral/dot cards from 0 10).

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.

Chapter 3, Lessons 3.1, Count to tell the number of 3.3, 3.3, 3.5, 3.7 objects. (K.CC.4, K.CC.4a, Chapter 4, Lesson 4.1 K.CC.4b, K.CC.4c, K.CC.5) 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).

EngageNY Module 1 Mid-Module Assessment (assesses Topics C & D) EngageNY Module 1: EngageNY Module 1 End-ofTopic C, D, E, F Module Assessment (assesses Topics E & F) EngageNY Module 5: Topics C, E EngageNY Module 5, Last Instructional Day, Lesson 24 Culminating Task - Cooperative Group Task.

Go Math! Chapter 3 Mid-Chapter Checkpoint and Summative Assessment. Go Math! Chapter 4 Mid-Chapter Checkpoint Go Math! Chapter 8 Mid-Chapter Checkpoint

EngageNY Module 5 Mid-Module Assessment (assesses Topic C) EngageNY Module 5 End-of-

Copyright Teaching Matters

Kindergarten: Counting and Cardinality

Content Standards

Standards: What is the essence of this domain?

K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of Compare numbers. objects in another group, e.g., (K.CC.6, K.CC.7) by using matching and counting strategies.(Include groups with up to ten objects.)

K.CC.7 Compare two Compare numbers. numbers between 1 and 10 (K.CC.6, K.CC.7) presented as written numerals.

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)

Chapter 2, Lessons 2.1, 2.2, 2.3, 2.4, 2.5

Chapter 2 requires supplementing for topics around more than, same as, fewer than.

Chapter 3, Lesson 3.9 Chapter 4, Lessons 4.5, 4.6 Chapter 8, Lesson 8.4

Chapters 3 & 4 requires supplementing of comparison of sets within 10. Chapter 8 is lacking in comparison of numerals.

What materials can Impact on Go Math! we use to fill the assessments gap?

Go Math! Chapter 2 Mid-Chapter Checkpoint and Summative Assessment

EngageNY Module 3, Lesson 32 Culminating Task - Determining the Go Math! Chapter 3 Summative attribute to be measured. Assessment EngageNY Module 3: Topics E, F G EngageNY Module 3 End-ofGo Math! Chapter 4 Summative Module Assessment (assesses Assessment Topics E, F & G)

Go Math! Chapter 8 Mid- Chapter Checkpoint EngageNY Module 3 Lesson 32 Culminating Task

Chapter 4, Lesson 4.7

Additional modeling needed.

Go Math! Assessments

EngageNY Module 3: Topics F, G EngageNY Module 3 End-ofModule Assessment (assesses Topics F & G)

Go Math! Chapter 4 Summative Assessment

Copyright Teaching Matters

Kindergarten: Operations and Algebraic Thinking

Content Standards

Standards: What is the essence of this domain?

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)

Understand addition as putting together and adding K.OA.2 Solve addition and subtraction to, and understand word problems, and add and subtract subtraction as taking apart within 10, e.g., by using objects or and taking from. drawings to represent the problem. (K.OA.1, K.OA.2, K.OA.3, K.OA.4, K.OA.5)

Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address What materials this standard adequately, by addressing procedural, conceptual, and can we use to fill the gap? application skills equally? If not, what are the gaps? (*KEY)

Impact on Go Math! assessments

EngageNY Module 4 Lesson 41 Culminating Task Chapter 5, Lessons 5.1, 5.2, 5.3 Chapter 6, Lessons 6.1, 6.2, 6.3

Chapter 5, Lesson 5.7 Chapter 6, Lessons 6.6, 6.7

Chapters 5 & 6: Story situations and patterns need additional emphasis.

Go Math! MidChapter Checkpoint

EngageNY Module 4 MidEngageNY Module Module Assessment (assesses 4: Topics A, C, D, Topics A, C & D) G, H Go Math! Chapter 6 Mid-Chapter EngageNY Module 4 End-ofCheckpoint Module Assessment (assesses Topics G & H)

Chapter 5: Requires supplementing for scenarios involving: add to with result unknown; put together with total unknown; when both addends are unknown. Lacking EngageNY Module 4: Topics C, D, F, in pictorials and G, H patterns. Chapter 6: Requires supplementing for story situations and patterns.

Go Math! Assessments

EngageNY Module 4 Lesson 41 Culminating Task EngageNY Module 4 Mid Module Assessment (assesses Topics C& D) EngageNY Module 4 End-ofModule Assessment (assesses Topics F, G & H)

Go Math! Chapter 5 Summative Assessment Go Math! Chapter 6 Summative Assessment

EngageNY Module 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.

EngageNY Module 1 MidModule Assessment (assesses EngageNY Module Topic C) 1: Topic C

Go Math! Chapter EngageNY Module 4 Lesson 5 Summative EngageNY Module 41 Culminating Task Assessment 4: Topics A, B, D, E, G EngageNY Module 4 MidModule Assessment (assesses Topics A, B & D) EngageNY Module 4 End-ofModule Assessment (assesses Topics E & G)

Copyright Teaching Matters

Kindergarten: Operations and Algebraic Thinking

Content Standards

Standards: What is the essence of this domain?

K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

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)

K.OA.5 Fluently add and subtract within 5.

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)

Where does our current curriculum (Go Math!) address the standards?

Chapter 4, Lesson 4.3 Chapter 5, Lesson 5.5

Chapter 5, Lessons 5.4, 5.5 Chapter 6, Lessons 6.4, 6.5

Does our current curriculum address What materials this standard adequately, by addressing procedural, conceptual, and can we use to fill the gap? application skills equally? If not, what are the gaps? (*KEY)

Chapters 4 and 5 are lacking in patterns.

Chapters 5 and 6 are lacking in story situations.

Impact on Go Math! assessments

Go Math! Assessments

EngageNY Module 4 Lesson 41 Culminating Task

Go Math! Chapter 4 Mid-Chapter

EngageNY Module 4 Lesson 41 Culminating Task

Go Math! Chapter 5 Mid-Chapter Checkpoint and Summative Assessment

EngageNY Module 4: Topic H EngageNY Module 4 End-ofGo Math! Chapter Module Assessment (assesses 5 Summative Topic H) Assessment

EngageNY Module 4: Topic D EngageNY Module 4 MidModule Assessment (assesses Topic D)

Go Math! Chapter 6 Mid-Chapter Checkpoint and Summative Assessment

Copyright Teaching Matters

Kindergarten: Measurement and Data

Content Standards

K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

Standards: What is the essence of this domain?

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 Go Math! assessments we use to fill the gap?

Go Math! Assessments

EngageNY Module 3 Lesson 32 Culminating Task 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.

EngageNY Module 3: Topics A, B, C, D, H

EngageNY Module 3 Mid-Module Assessment (assesses Topics A, B, C & D)

Go Math! Chapter 11 Summative Assessment

EngageNY Module 3 End-of-Module Assessment (assesses Topic H)

K.MD.2 Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the Describe and compare measurable attributes. attribute, and describe the difference. For example, directly (K.MD.1, K.MD.2) compare the heights of two children and describe one child as taller/shorter. 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.)

Where does our current curriculum (Go Math!) address the standards?

EngageNY Module 3 Lesson 32 Culminating Task Chapter 11, Lessons 11.1, 11.2, 11.3,11.4

Classify objects and count the Chapter 12, Lessons number of objects in each 12.1, 12.2, 12.3, 12.4, category. 12.5, 12.6 (K.MD.3)

Lacking in comparison of volume. Additional modeling needed.

EngageNY Module 3: Topics A, B, C, D, H

EngageNY Module 3 Mid-Module Assessment (assesses Topics A, B, C & D) EngageNY Module 3 End-of-Module Assessment (assesses Topic H)

Analyze, classify, and sort related objects.

EngageNY Module 1: Topics A, B

EngageNY Module 1 Lesson 37, Culminating task - materials needed numeral/dot cards from 0 -10) EngageNY Module 1 Mid-Module Assessment (assesses Topics A & B)

Go Math! Chapter 11 Mid-Chapter Checkpoint and Summative Assessment

Go Math! Chapter 12 Mid-Chapter Checkpoint and Summative Assessment

Copyright Teaching Matters

Kindergarten: Numbers and Operations in Base Ten

Content Standards

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.

Standards: 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, What materials can by addressing procedural, we use to fill the conceptual, and application skills gap? equally? If not, what are the gaps? (*KEY)

Impact on Go Math! assessments

EngageNY Module 5 Lesson 24, Culminating Task Work with numbers 1119 to gain foundations for Chapter 7, Lessons 7.1, place value 7.3, 7.5, 7.7, 7.9 (K.NBT.1)

Requires additional modeling with arrays using a Rekenrek (abacus).

EngageNY Module 5: Topics A, B, C, E

EngageNY Module 5 Mid Module Assessment (assesses Topics A, B &C) EngageNY Module 5 Endof-Module Assessment (assesses Topic E)

Go Math! Assessments

Go Math! Chapter 7 Mid-Chapter Checkpoint and Summative Assessment

Copyright Teaching Matters

Kindergarten: Geometry

Content Standards

Standards: What is the essence of this domain?

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.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). (K.G.1, K.G.2, K.G.3)

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)

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)

Where does our current curriculum (Go Math!) address the standards?

Chapter 10, Lessons 10.7, 10.8, 10.9

Chapter 9, Lessons 9.1, 9.3, 9.5, 9.7, 9.9 Chapter 10, Lessons 10.2, 10.3, 10.4, 10.5

Chapter 10, Lesson 10.6

K.G.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language Analyze, compare, create, and Chapter 9, Lessons 9.2, to describe their similarities, differences, compose shapes. 9.4, 9.6, 9.8, 9.10, 9.11 parts (e.g., number of sides and (K.G.4, K.G.5, K.G.6) vertices/"corners") and other attributes (e.g., having sides of equal length).

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 Not addressed in Go Math! compose shapes. Build, describe, compose (K.G.4, K.G.5, K.G.6) flat and solid shapes.

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.

Requires additional applications of two-dimensional flat shapes and three-dimensional solid shapes.

What materials Impact on Go Math! can we use to fill assessments the gap?

Go Math! Assessments

EngageNY Module 2: Topics A, B

EngageNY Module 2, Lesson 10 Culminating Task, Go Math! Chapter 10 collaborative project Summative EngageNY Module 2, End-of- Assessment Module Assessment (assesses Topics A & B)

EngageNY Module 2: Topics A, B

Go Math! Chapter 9 EngageNY Module 2, Lesson Mid-Chapter 10 - Culminating Task, Checkpoint and collaborative project Summative Assessment EngageNY Module 2 End-ofModule Assessment Go Math! Chapter 10 (assesses Topics A & B) Mid-Chapter Checkpoint

EngageNY Module 2, Lesson 10 Culminating Task, Requires supplementing to exploring collaborative project Go Math! Chapter 10 EngageNY two-dimensional and threeSummative Module 2: Topic C dimensional shapes. EngageNY Module 2 End -of- Assessment Module Assessment (assesses Topic C) Requires additional applications of two-dimensional flat shapes and three-dimensional solid shapes. Requires supplementing to explore two-dimensional and threedimensional shapes.

Lacks lessons on building, describing, and composing flat and solid shapes.

EngageNY Module 2: Topics A, B, C

EngageNY Module 6: Topic A

EngageNY Module 2, Lesson Go Math! Chapter 9 10 - Culminating Task, Mid-Chapter collaborative project Checkpoint and Summative EngageNY Module 2 End-of- Assessment. Module Assessment (assesses Topics A, B & C) . EngageNY Module 6, Lesson 8 - Culminating Task, collaborative project EngageNY Module 6 End-ofModule Assessment Task (assesses Topic A)

None

Copyright Teaching Matters

Kindergarten: Geometry

Content Standards

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?"

Standards: What is the essence of this domain?

Where does our current curriculum (Go Math!) address the standards?

Analyze, compare, create, and Not addressed in Go Math! compose shapes. Compose and decompose (K.G.4, K.G.5, K.G.6) 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 Impact on Go Math! can we use to fill assessments the gap?

EngageNY Module 6: Topic B

EngageNY Module 6, Lesson 8 - Culminating Task, collaborative project EngageNY Module 6 End-ofModule Assessment Task (assesses Topic B)

Go Math! Assessments

None

Copyright Teaching Matters

Grade 1: Operations & Algebraic Thinking

Content Standards

Standards: What is the essence of this domain?

Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address this standard What materials can adequately, by addressing we use to fill the procedural, conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY) EngageNY Module 1: Topics A, B, C, G, H

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.

Chapter 1, Lessons: 1.1, 1.2, 1.3, 1.4, 1.7 Represent and solve problems involving addition and subtraction. (1.OA.1, 1.OA.2)

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

EngageNY Module 2: Topics A, B, C, D

Go Math! adequately addresses the standard; EngageNY EngageNY Module 3: materials are included for Topics C, D enrichment or for review to be used later in the year. EngageNY Module 4: Topic E EngageNY Module 6: Topics A, F

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)

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)

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 Chapter 4, Lessons: 4.2, relationship between 4.3 addition and subtraction. (1.OA.3, 1.OA.4)

Chapter 3, Lesson: 3.12

Chapter 1, Lessons: 1.5, 1.6 Chapter 3, Lessons: 3.1, 3.10, 3.11

Additional application of the standard needed.

EngageNY Module 2: Topic A

Impact on Go Math! assessments

Go Math! Assessments

Go Math! Chapter 1 MidChapter Checkpoint and Summative Assessment

EngageNY Module 1 Mid-Module Go Math! Chapter 2 MidAssessment (assesses Chapter Checkpoint and Topics A, B, C) Summative Assessment EngageNY Module 1 Go Math! Chapter 4 End-of-Module Summative Assessment Assessment (assesses Topics G, H) Go Math! Chapter 5 MidChapter Checkpoint and Summative Assessment

EngageNY Module 2 Mid-Module Go Math! Chapter 3 Assessment (assesses Summative Assessment Topic A)

Go Math! Chapter 1 Summative Assessment

Additional application and EngageNY Module 1: practice of the standard needed. Topics E, F

Additional application and EngageNY Module 1: practice of the standard needed. Topics G, H

EngageNY Module 1 Mid-Module Assessment (assesses Go Math! Chapter 3 MidTopics E, F) Chapter Checkpoint and Summative Assessment

EngageNY Module 1 End-of-Module Go Math! Chapter 4 MidAssessment (assesses Chapter Checkpoint Topics G, H)

Grade 1: Operations & Algebraic Thinking

Content Standards

1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Standards: What is the essence of this domain?

Add and subtract within 20. (1.OA.5, 1.OA.6)

Where does our current curriculum (Go Math!) address the standards?

Chapter 3, Lesson: 3.2 Chapter 4, Lesson: 4.1

Does our current curriculum address this standard What materials can adequately, by addressing we use to fill the procedural, conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY)

Additional application and EngageNY Module 1: practice of the standard needed. Topics B, D, G, I

Impact on Go Math! assessments

Go Math! Assessments

EngageNY Module 1 Mid-Module Assessment (assesses Go Math! Chapter 3 MidTopics B, D) Chapter Checkpoint EngageNY Module 1 Go Math! Chapter 4 MidEnd-of-Module Chapter Checkpoint Assessment (assesses Topics G, I)

Go Math! Chapter 1 Summative Assessment 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 - Add and subtract 1 = 10 - 1 = 9); using the relationship within 20. (1.OA.5, between addition and subtraction 1.OA.6) (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).

Chapter 1, Lesson: 1.8

Go Math! Chapter 2 Summative Assessment

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

Go Math! adequately addresses the standard; EngageNY EngageNY Module 1: materials are included for Topics A, B, C, F, I, J enrichment or for review to be used later in the year.

Chapter 5, Lessons: 5.2, 5.3, 5.4, 5.8, 5.10 Chapter 8, Lesson: 8.1

EngageNY Module 1 Mid-Module Go Math! Chapter 3 MidAssessment (assesses Chapter Checkpoint and Topics A, B, C, F) Summative Assessment EngageNY Module 1 Go Math! Chapter 4 End-of-Module Summative Assessment Assessment (assesses Topics I, J) Go Math! Chapter 5 MidChapter Checkpoint and Summative Assessment Go Math! Chapter 8 MidChapter Checkpoint

1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and Work with addition and subtraction are true or false. For subtraction equations. Chapter 5, Lesson: 5.7 example, which of the following (1.OA.7, 1.OA.8) equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Additional application and EngageNY Module 1: practice of the standard needed. Topic E

EngageNY Module 1 Mid-Module Go Math! Chapter 5 Assessment (assesses Summative Assessment Topic E)

Grade 1: Operations & Algebraic Thinking

Content Standards

Standards: What is the essence of this domain?

1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three Work with addition and whole numbers. For example, subtraction equations. determine the unknown number that (1.OA.7, 1.OA.8) makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.

Where does our current curriculum (Go Math!) address the standards?

Chapter 2, Lessons: 2.5, 2.7 Chapter 5, Lessons: 5.5, 5.6,

Does our current curriculum address this standard What materials can adequately, by addressing we use to fill the procedural, conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY)

Additional application and EngageNY Module 1: practice of the standard needed. Topic D

Impact on Go Math! assessments

Go Math! Assessments

"Go Math! Chapter 2 MidChapter Checkpoint and Summative Assessment

EngageNY Module 1 Mid-Module Assessment (assesses Go Math! Chapter 5 MidTopic D) Chapter Checkpoint and Summative Assessment"

Grade 1: Numbers & Operations in Base Ten

Content Standards

Where does our Standards: current curriculum What is the essence (Go Math!) address of this domain? the standards?

1.NBT.1 Count to 120, starting at any number less than 120. In this Extend the counting Chapter 6, Lessons: range, read and write numerals sequence. (1.NBT.1) 6.1, 6.2, 6.9, 6.10 and represent a number of objects with a written numeral.

1.NBT.2 Understand that the two digits of a two-digit number Understand place represent amounts of tens and value. (1.NBT.2, ones. Understand the following as 1.NBT.3) special cases:

1.NBT.2a 10 can be thought of as Understand place a bundle of ten ones - called a value. (1.NBT.2, "ten." 1.NBT.3)

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: 6.6, 6.7

Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY)

Additional fluency practice is needed.

Additional application and practice of the standard needed.

Chapter 6, Lessons: 6.5, 6.8

Additional application and practice of the standard needed.

Chapter 6, Lessons: 6.3, 6.4

Additional application and practice of the standard needed.

What materials can we use to fill the gap?

EngageNY Module 4: Topics A, B EngageNY Module 6: Topic B

EngageNY Module 4: Topics A, B, C

EngageNY Module 2: Topic D EngageNY Module 6: Topic B

EngageNY Module 2: Topic D

Impact on Go Math! Go Math! assessments Assessments

EngageNY Module 4 Mid-Module Assessment Go Math! Chapter 6 (assesses Topics A Mid-Chapter & B) Checkpoint and Summative EngageNY Module 6 Assessment Mid-Module Assessment (assesses Topic B) EngageNY Module 4 Mid-Module Go Math! Chapter 6 Assessment Summative (assesses Topics A, Assessment B & C) EngageNY Module 2 End-of-Module Assessment Go Math! Chapter 6 (assesses Topic D) Mid-Chapter Checkpoint and EngageNY Module 6 Summative Mid-Module Assessment Assessment (assesses Topic B) EngageNY Module 2 Go Math! Chapter 6 End-of-Module Mid-Chapter Assessment Checkpoint (assesses Topic D)

Grade 1: Numbers & Operations in Base Ten

Content Standards

Where does our Standards: current curriculum What is the essence (Go Math!) address of this domain? the standards?

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).

Understand place value. (1.NBT.2, 1.NBT.3)

1.NBT.3 Compare two two-digit numbers based on meanings of Understand place the tens and ones digits, recording value. (1.NBT.2, the results of comparisons with 1.NBT.3) the symbols >, =, and <.

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.

Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY)

Additional application and Chapter 6, Lesson: 6.5 practice of the standard needed.

Go Math! adequately Chapter 6, Lesson: 6.8 addresses the standard; EngageNY materials are Chapter 7, Lessons: included for enrichment or 7.1, 7.2, 7.3, 7.4 for review to be used later in the year.

What materials can we use to fill the gap?

Impact on Go Math! Go Math! assessments Assessments

EngageNY Module 6: Topic B

EngageNY Module 6 Go Math! Chapter 6 Mid-Module Mid-Chapter Assessment Checkpoint (assesses Topic B) Go Math! Chapter 6 Summative Assessment

EngageNY Module 4: Topic B

EngageNY Module 4 Mid-Module Go Math! Chapter 7 Assessment Mid-Chapter (assesses Topic B) Checkpoint and Summative Assessment EngageNY Module 4 Mid-Module Assessment (assesses Topics C & D)

Use place value understanding and Chapter 8, Lessons: properties of 8.2, 8.4, 8.5, 8.6, 8.7, operations to add and 8.8, 8.9 subtract. (1.NBT.4, 1.NBT.5, 1.NBT.6)

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment or for review to be used later in the year.

EngageNY Module 4: Topics C, D, F EngageNY Module 6: Topics C, D

Go Math! Chapter 8 EngageNY Module 4 Mid-Chapter End-of-Module Checkpoint and Assessment Summative (assesses Topic F) Assessment EngageNY Module 6 Mid-Module Assessment (assesses Topics C & D)

Grade 1: Numbers & Operations in Base Ten

Content Standards

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.

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.

Where does our Standards: current curriculum What is the essence (Go Math!) address of this domain? 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)

Use place value understanding and Additional application and properties of Chapter 7, Lesson 7.5 practice of the standard operations to add and needed. subtract. (1.NBT.4, 1.NBT.5, 1.NBT.6)

Use place value understanding and properties of Chapter 8, Lessons: operations to add and 8.3, 8.9 subtract. (1.NBT.4, 1.NBT.5, 1.NBT.6)

Additional application, conceptual understanding and practice of the standard needed.

What materials can we use to fill the gap?

EngageNY Module 4: Topic A EngageNY Module 6: Topic B

EngageNY Module 4: Topic C EngageNY Module 6: Topic C

Impact on Go Math! Go Math! assessments Assessments

EngageNY Module 4 Mid-Module Assessment (assesses Topic A) Go Math! Chapter 7 Summative EngageNY Module 6 Assessment Mid-Module Assessment (assesses Topic B)

EngageNY Module 4 Mid-Module Assessment Go Math! Chapter 8 (assesses Topic C) Mid-Chapter Checkpoint and EngageNY Module 6 Summative Mid-Module Assessment Assessment (assesses Topic C)

Grade 1: Measurement & Data

Content Standards

Standards: What is the essence of this domain?

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)

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)

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.

Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address this standard adequately, by What materials can Impact on Go Math! Go Math! addressing procedural, we use to fill the assessments Assessments conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY)

Chapter 9, Lessons: 9.1, 9.2

Additional application and conceptual understanding of the standard needed.

EngageNY Module 3 End-of-Module Go Math! Chapter 9, EngageNY Module 3: Assessment Mid-Chapter Topics A, B (assesses Topics A & Checkpoint B)

Chapter 9, Lessons: 9.3, 9.4, 9.5

Additional hands-on application, and conceptual understanding of the standard needed.

EngageNY Module 3 End-of-Module Go Math! Chapter 9, EngageNY Module 3: Assessment Mid-Chapter Topics B, C, D (assesses Topics B, Checkpoint C & D)

Tell and write time and Chapter 9, Lessons: money. (1.MD.3) 9.6, 9.7, 9.8, 9.9

EngageNY Module 5 Recognizing and End-of-Module identifying coins, their EngageNY Module 5: Assessment names, and their value Topic D (assesses Topic D) Go Math! Chapter 9 is absent from Go Math!. Summative Supplemental materials EngageNY Module 6: EngageNY Module 6 Assessment from EngageNY are Topic E End-of-Module necessary. Assessment (assesses Topic E)

Grade 1: Measurement & Data

Content Standards

Standards: What is the essence of this domain?

1.MD.4 Organize, represent, and interpret data with up to three categories; ask and Represent and answer questions about the interpret data. total number of data points, (1.MD.4) how many in each category, and how many more or less are in one category than in another.

Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address this standard adequately, by What materials can Impact on Go Math! Go Math! addressing procedural, we use to fill the assessments Assessments conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY)

Go Math! adequately addresses the standard; Chapter 10, Lessons: EngageNY materials are EngageNY Module 3: 10.1, 10.2, 10.3, 10.4, included for enrichment Topic D 10.5, 10.6, 10.7 or for review to be used later in the year.

Go Math! Chapter 10 EngageNY Module 3 Mid-Chapter End-of-Module Checkpoint and Assessment Summative (assesses Topic D) Assessment

Grade 1: Geometry

Content Standards

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.

Where does our Standards: current curriculum What is the essence of (Go Math!) address this domain? the standards?

Reason with shapes and their attributes. (1.G.1, 1.G.2, 1.G.3)

1.G.2 Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, Reason with shapes right circular cones, and right and their attributes. circular cylinders) to create a (1.G.1, 1.G.2, 1.G.3) composite shape, and compose new shapes from the composite shape. (Students do not need to learn the formal names of the shapes.)

Chapter 11, Lessons: 11.1, 11.5 Chapter 12, Lessons: 12.1, 12.2

Chapter 11, Lessons: 11.2, 11.3, 11.4 Chapter 12, Lessons: 12.3, 12.4, 12.5, 12.6, 12.7

Does our current curriculum address this standard adequately, by What materials can addressing procedural, we use to fill the conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY)

Go Math! adequately addresses the standard; EngageNY materials are EngageNY Module 5: included for enrichment or Topic A for review to be used later in the year.

Go Math! adequately addresses the standard; EngageNY materials are EngageNY Module 5: included for enrichment or Topic B for review to be used later in the year.

Impact on Go Math! Go Math! assessments Assessments

EngageNY Module 5 End-of-Module Assessment (assesses Topic A)

EngageNY Module 5 End-of-Module Assessment (assesses Topic B)

Go Math! Chapter 11 Mid-Chapter Checkpoint and Summative Assessment Go Math! Chapter 12 Mid-Chapter Checkpoint Go Math! Chapter 11 Mid-Chapter Checkpoint and Summative Assessment Go Math! Chapter 12 Mid-Chapter Checkpoint and Summative Assessment

Grade 1: Geometry

Content Standards

Where does our Standards: current curriculum What is the essence of (Go Math!) address this domain? the standards?

1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use Reason with shapes the phrases half of, fourth of, and their attributes. and quarter of. Describe the (1.G.1, 1.G.2, 1.G.3) whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Chapter 12, Lessons 12.8, 12.9, 12.10

Does our current curriculum address this standard adequately, by What materials can addressing procedural, we use to fill the conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY)

Impact on Go Math! Go Math! assessments Assessments

EngageNY Module 5 Additional application and End-of-Module Go Math! Chapter EngageNY Module 5: practice of the standard Assessment 12 Summative Topics C, D needed. (assesses Topics C & Assessment D)

Grade 2: Operations & Algebraic Thinking

Content Standards

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.

Standards: What is the essence of this domain?

Where does our current curriculum (Go Math!) address the standards?

Chapter 3, Lessons: 3.8, 3.9 Represent and solve problems involving addition and subtraction. (2.OA.1)

Chapter 4, Lessons 4.9, 4.10 Chapter 5, Lessons 5.9, 5.10, 5.11

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 Go Math! Go Math! we use to fill the assessments Assessments gap?

Go Math! Chapter 3 EngageNY Module 1 Summative Go Math! addresses the End-of-Module Assessment standard adequately. EngageNY Module 1: Assessment EngageNY materials are Topics A, B, C Go Math! Chapter 4 included to supplement what EngageNY Module 4 Summative GoMath! provides, and to EngageNY Module 4: Mid-Module Assessment provide teachers with additional Topics A, C, F Assessment and Endopportunities to apply problemof-Module Go Math! Chapter 5 solving skills. Assessment Summative Assessment

Go Math! provides a chapter focusing on building fluency. 2.OA.2 Fluently add and subtract EngageNY materials are Chapter 3, Lessons: EngageNY Module 1 within 20 using mental strategies. By Add and subtract within included to provide EngageNY Module 1: 3.1, 3.2, 3.3, 3.4, 3.5, End-of-Module end of Grade 2, know from memory all 20. (2.OA.2) opportunities for students to Topics A, B 3.6, 3.7 Assessment sums of two one-digit numbers. build fluency using mental math strategies at other points throughout the year. 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 Chapter 1, Lessons: gain foundations for 1.1, 1.2 multiplication. (2.OA.3, 2.OA.4)

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 Chapter 3, Lessons: gain foundations for 3.10, 3.11 multiplication. (2.OA.3, 2.OA.4)

Go Math! Chapter 2 Mid-Chapter Assessment & Summative Assessment

Additional practice and application of the standard is needed.

EngageNY Module 6 Go Math! Chapter 1 EngageNY Module 6: End-of-Module Mid-Chapter Topic D Assessment Checkpoint

Additional practice and application of the standard is needed.

EngageNY Module 6 Mid-Module Go Math! Chapter 3 EngageNY Module 6: Assessment and End- Summative Topics A, B, C of-Module Assessment Assessment

Grade 2: Numbers & Operations in Base Ten

Content Standards

Where does our Standards: current curriculum What is the essence of (Go Math!) address this domain? the standards?

2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, Understand place value. Chapter 2, Lesson 2.2, and ones; e.g., 706 equals 7 (2.NBT.1, 2.NBT.2, 2.3, 2.4, 2.5 hundreds, 0 tens, and 6 ones. 2.NBT.3, 2.NBT.4) Understand the following as special cases:

Does our current curriculum address this standard adequately, by What materials can addressing procedural, Impact on Go Go Math! we use to fill the conceptual, and Math! assessments Assessments gap? application skills equally? If not, what are the gaps? (*KEY)

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment.

EngageNY Module 3: Topic A

One lesson does not 2.NBT.1A. 100 can be thought of as Understand place value. provide an adequate a bundle of ten tens - called a (2.NBT.1, 2.NBT.2, Chapter 2, Lesson 2.1 amount of practice, "hundred." 2.NBT.3, 2.NBT.4) application nor fluency.

EngageNY Module 3: Topics A, E

2.NBT.1B The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 Understand place value. refer to one, two, three, four, five, six, (2.NBT.1, 2.NBT.2, Chapter 2, Lesson 2.1 seven, eight, or nine hundreds (and 0 2.NBT.3, 2.NBT.4) tens and 0 ones).

EngageNY Module 3: Topics A, E

2.NBT.2 Count within 1000; skipcount by 5s, 10s, and 100s.

Understand place value. Chapter 1, Lessons: (2.NBT.1, 2.NBT.2, 1.8, 1.9 2.NBT.3, 2.NBT.4)

Chapter 1, Lessons: 2.NBT.3 Read and write numbers to Understand place value. 1.3, 1.4, 1.5, 1.6, 1.7 1000 using base-ten numerals, (2.NBT.1, 2.NBT.2, number names, and expanded form. 2.NBT.3, 2.NBT.4) Chapter 2, Lessons: 2.6, 2.7, 2.8

One lesson does not provide an adequate amount of practice, application nor fluency.

Additional practice and EngageNY Module application of the standard 3: Topic B, D, G is needed.

Go Math! adequately addresses the standard; EngageNY materials are included to provide enrichment.

EngageNY Module 3: Topic C

EngageNY Module 3 Go Math! Chapter Mid-Module 2 Mid-Chapter Assessment Checkpoint

EngageNY Module 3 Mid-Module Assessment and End-of-Module Assessment EngageNY Module 3 Mid-Module Assessment and End-of-Module Assessment EngageNY Module 3 Mid-Module Assessment and End-of-Module Assessment

Go Math! Chapter 2 Mid-Chapter Checkpoint

Go Math! Chapter 2 Mid-Chapter Checkpoint

Go Math! Chapter 1 Summative Assessment

Go Math! Chapter 1 Mid-Chapter Checkpoint and Summative EngageNY Module 3 Assessment Mid-Module Assessment Go Math! Chapter 2 Mid-Chapter Assessment and Summative Assessment

Grade 2: Numbers & Operations in Base Ten

Content Standards

Where does our Standards: current curriculum What is the essence of (Go Math!) address this domain? the standards?

Does our current curriculum address this standard adequately, by What materials can addressing procedural, Impact on Go Go Math! we use to fill the conceptual, and Math! assessments Assessments gap? application skills equally? If not, what are the gaps? (*KEY)

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.

Understand place value. Chapter 2, Lessons: (2.NBT.1, 2.NBT.2, 2.11, 2.12 2.NBT.3, 2.NBT.4)

Additional practice and EngageNY Module application of the standard 3: Topic F is needed.

Use place value 2.NBT.5 Fluently add and subtract understanding and within 100 using strategies based on properties of operations place value, properties of operations, to add and subtract. and/or the relationship between (2.NBT.5, 2.NBT.6, addition and subtraction. 2.NBT.7, 2.NBT.8, 2.NBT.9)

2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

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

Use place value understanding and properties of operations Chapter 4, Lessons: to add and subtract. 4.1, 4.2, 4.3, 4.4, 4.5, (2.NBT.5, 2.NBT.6, 4.11, 4.12 2.NBT.7, 2.NBT.8, 2.NBT.9)

Go Math! adequately addresses the standard; EngageNY materials are included to provide enrichment.

EngageNY Module 1: Topic C EngageNY Module 4: Topic A

Go Math! adequately addresses the standard; EngageNY materials are included to provide EngageNY Module enrichment, or to reinforce 4: Topic D mastery of the standard at other times during the year.

EngageNY Module 3 Go Math! Chapter End-of-Module 2 Summative Assessment Assessment Go Math! Chapter 4 Mid-Chapter EngageNY Module 1 Checkpoint and End-of-Module Summative Assessment Assessment EngageNY Module 4 Go Math! Chapter Mid-Module 5 Mid-Chapter Assessment Checkpoint and Summative Assessment Go Math! Chapter EngageNY Module 4 4 Mid-Chapter End-of-Module Checkpoint and Assessment Summative Assessment

Grade 2: Numbers & Operations in Base Ten

Content Standards

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.

Where does our Standards: current curriculum What is the essence of (Go Math!) address this domain? the standards?

Does our current curriculum address this standard adequately, by What materials can addressing procedural, Impact on Go Go Math! we use to fill the conceptual, and Math! assessments Assessments gap? application skills equally? If not, what are the gaps? (*KEY)

Use place value understanding and properties of operations Chapter 6, Lessons: to add and subtract. 6.1, 6.2, 6.3, 6.4, 6.5, (2.NBT.5, 2.NBT.6, 6.6, 6.7, 6.8, 6.9, 6.10 2.NBT.7, 2.NBT.8, 2.NBT.9)

EngageNY Module 4 Mid-Module Go Math! adequately Assessment and addresses the standard; EngageNY Module End-of-Module Go Math! Chapter EngageNY materials are 4: Topics B, C, D, E, Assessment 6 Mid-Chapter included to provide F Checkpoint and enrichment, or to reinforce EngageNY Module 5 Summative mastery of the standard at EngageNY Module Mid-Module Assessment other times during the 5: Topics A, B, C, D Assessment and year. End-of-Module Assessment

Use place value understanding and 2.NBT.8 Mentally add 10 or 100 to a properties of operations given number 100– –900, and mentally Chapter 2, Lessons: to add and subtract. subtract 10 or 100 from a given 2.9, 2.10 (2.NBT.5, 2.NBT.6, number 100– – 900. 2.NBT.7, 2.NBT.8, 2.NBT.9)

EngageNY Module 4: Topics A, D

Additional practice and application of the standard is needed. EngageNY Module 5: Topics A, D

EngageNY Module 4 Mid-Module Assessment and End-of-Module Assessment Go Math! Chapter 2 Summative EngageNY Module 5 Assessment Mid-Module Assessment and End-of-Module Assessment

Grade 2: Numbers & Operations in Base Ten Does our current curriculum address this standard adequately, by What materials can addressing procedural, Impact on Go Go Math! we use to fill the conceptual, and Math! assessments Assessments gap? application skills equally? If not, what are the gaps? (*KEY)

Content Standards

Where does our Standards: current curriculum What is the essence of (Go Math!) address this domain? the standards?

2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

Two lessons do not provide students with enough time to master this standard, particularly due Use place value to the emphasis on being understanding and able to explain why properties of operations Chapter 4, Lesson 4.4 addition and subtraction to add and subtract. standards work. (2.NBT.5, 2.NBT.6, Chapter 9, Lesson 5.3 EngageNY materials 2.NBT.7, 2.NBT.8, provide depth in order for 2.NBT.9) students to gain additional practice and application of the strategies and an explanation of why those strategies are successful.

EngageNY Module 4 Mid-Module Assessment and Go Math! Chapter EngageNY Module End-of-Module 4 Mid-Chapter 4: Topics A, B, C, D, Assessment Checkpoint E, F EngageNY Module 5 Go Math! Chapter EngageNY Module Mid-Module 5 Mid-Chapter 5: Topics A, B, C, D Assessment and Checkpoint End-of-Module Assessment

Grade 2: Measurement & Data

Content Standards

Where does our Standards: current curriculum What is the essence (Go Math!) address of this domain? the standards?

2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Measure and estimate lengths in standard units. (2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4)

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.

Measure and estimate lengths in standard units. (2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4)

Measure and 2.MD.3 Estimate lengths using estimate lengths in units of inches, feet, centimeters, standard units. and meters. (2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4)

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)

Does our current curriculum address this standard adequately, by What materials can addressing procedural, Impact on Go Math! Go Math! we use to fill the conceptual, and assessments Assessments gap? application skills equally? If not, what are the gaps? (*KEY)

Go Math! Chapter 8 EngageNY Module 2 Mid-Chapter Chapter 8, Lessons: Go Math! adequately EngageNY Module 2: End-of-Module Checkpoint and 8.1, 8.2, 8.4, 8.8 addresses this standard. Topics A, B, C Assessment Summative EngageNY materials are Assessment Chapter 9, Lessons: included for enrichment or EngageNY Module 7: EngageNY Module 7 9.1, 9.3 additional practice. Topics C, D End-of-Module Go Math! Chapter 9 Assessment Mid-Chapter Checkpoint EngageNY Module 2 Go Math! Chapter 8 Chapter 8, Lesson: EngageNY Module 2: End-of-Module Summative 8.6 Additional practice and Topic C Assessment Assessment application of the Chapter 9, Lesson: standard is needed. EngageNY Module 7: EngageNY Module 7 Go Math! Chapter 9.5 Topic D End-of-Module Summative Assessment Assessment Go Math! Chapter 8 Mid-Chapter EngageNY Module 2 Checkpoint and Chapter 8, Lessons: Go Math! adequately EngageNY Module 2: End-of-Module Summative 8.3, 8.7 addresses this standard. Topic B Assessment Assessment EngageNY materials are Chapter 9, Lessons included for enrichment or EngageNY Module 7: EngageNY Module 7 Go Math! Chapter 9 9.2, 9.6 additional practice. Topic D End-of-Module Mid-Chapter Assessment Checkpoint and Summative Assessment EngageNY Module 2 EngageNY Module 2: End-of-Module Additional practice and Topic C Assessment Go Math! Chapter 9 Chapter 9, Lesson 9.7 application of the Summative standard is needed. EngageNY Module 7: EngageNY Module 7 Assessment Topic D End-of-Module Assessment

Grade 2: Measurement & Data

Content Standards

Where does our Standards: current curriculum What is the essence (Go Math!) address of this domain? the standards?

Does our current curriculum address this standard adequately, by What materials can addressing procedural, Impact on Go Math! Go Math! we use to fill the conceptual, and assessments Assessments gap? application skills equally? If not, what are the gaps? (*KEY)

2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths Relate addition and Chapter 8, Lesson 8.5 Additional practice and that are given in the same units, subtraction to length. application of the e.g., by using drawings (such as (2.MD.5, 2.MD.6) Chapter 9, Lesson 9.4 standard is needed. drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally Relate addition and Chapter 8, Lesson 8.5 Additional practice and spaced points corresponding to subtraction to length. application of the the numbers 0, 1, 2, ..., and (2.MD.5, 2.MD.6) Chapter 9, Lesson 9.4 standard is needed. represent whole-number sums and differences within 100 on a number line diagram. 2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Work with time and money. (2.MD.7, 2.MD.8)

2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, Work with time and using $ and ¢ symbols money. (2.MD.7, appropriately. Example: If you 2.MD.8) have 2 dimes and 3 pennies, how many cents do you have?

Chapter 7, Lessons: 7.8, 7.9, 7.10, 7.11

EngageNY Module 2 Go Math! Chapter 8 EngageNY Module 2: End-of-Module Mid-Chapter Topic D Assessment Checkpoint EngageNY Module 7: EngageNY Module 7 Go Math! Chapter 9 Topic E End-of-Module Mid-Chapter Assessment Checkpoint

EngageNY Module 2 Go Math! Chapter 8 EngageNY Module 2: End-of-Module Mid-Chapter Topic D Assessment Checkpoint EngageNY Module 7: EngageNY Module 7 Go Math! Chapter 9 E, F End-of-Module Mid-Chapter Assessment Checkpoint

Go Math! adequately addresses this standard. EngageNY Module 8 Go Math! Chapter 7 EngageNY Module 8: EngageNY materials are End-of-Module Summative Topic D included for enrichment or Assessment Assessment additional practice.

Go Math! adequately Chapter 7, Lessons: addresses this standard. EngageNY Module 7 EngageNY Module 7: 7.1, 7.2, 7.3, 7.4, 7.5, EngageNY materials are Mid-Module Topic B 7.6, 7.7 included for enrichment or Assessment additional practice.

Go Math! Chapter 7 Mid-Chapter Checkpoint and Summative Assessment

Grade 2: Measurement & Data

Content Standards

2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole number units. 2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

Where does our Standards: current curriculum What is the essence (Go Math!) address of this domain? the standards?

Does our current curriculum address this standard adequately, by What materials can addressing procedural, Impact on Go Math! Go Math! we use to fill the conceptual, and assessments Assessments gap? application skills equally? If not, what are the gaps? (*KEY)

Represent and interpret data. (2.MD.9, 2.MD.10)

Chapter 7, Lesson: 8.9

Additional practice and application of the standard is needed.

Represent and interpret data. (2.MD.9, 2.MD.10)

Go Math! adequately Chapter 10, Lessons: addresses this standard. EngageNY Module 7 EngageNY Module 7: 10.1, 10.2, 10.3, 10.4, EngageNY materials are Mid-Module Topic A 10.5, 10.6 included for enrichment or Assessment additional practice.

EngageNY Module 7 Go Math! Chapter 8 EngageNY Module 7: End-of-Module Summative Topic F Assessment Assessment

Go Math! Chapter 10 Mid-Chapter Checkpoint and Summative Assessment

Grade 2: Geometry

Content Standards

Where does our Standards: current curriculum What is the essence of (Go Math!) address this domain? the standards?

Does our current curriculum address this standard adequately, by What materials can addressing procedural, we use to fill the conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY)

Impact on Go Math! Go Math! assessments Assessments

2.G.1 Recognize and draw shapes having specified attributes, Reason with shapes such as a given number of angles and their attributes. or a given number of equal faces. (2.G.1, 2.G.2, 2.G.3) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Go Math! Chapter 11, Lessons: 11.1, 11.2, 11.3, 11.4, 11.5

Go Math! adequately addresses this standard. EngageNY materials are included for enrichment or additional practice.

EngageNY Module 8 EngageNY Module 8: Mid-Module Topic A Assessment

Go Math! Chapter 11 Mid-Chapter Checkpoint

2.G.2 Partition a rectangle into Reason with shapes rows and columns of same-size and their attributes. squares and count to find the total (2.G.1, 2.G.2, 2.G.3) number of them.

Go Math! Chapter 11, Lesson: 11.6

Additional practice and EngageNY Module 6 EngageNY Module 6: application of the standard is End-of-Module Topic C needed. Assessment

Go Math! Chapter 11 Mid-Chapter Checkpoint

Go Math! Chapter 11, Lessons: 11.7, 11.8, 11.9, 11.10

Go Math! adequately addresses this standard. EngageNY materials are included for enrichment or additional practice.

2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half Reason with shapes of, a third of, etc., and describe the and their attributes. whole as two halves, three thirds, (2.G.1, 2.G.2, 2.G.3) four fourths. Recognize that equal shares of identical wholes need not have the same shape.

EngageNY Module 8 Mid-Module Go Math! Chapter EngageNY Module 8: Assessment and End- 11 Summative Topics B, C, D of-Module Assessment Assessment

Grade 3: Operations & Algebraic Thinking

Content Standards

3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

Standards: What is the essence of this domain?

Represent and solve problems involving multiplication and division. (3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4)

Represent and solve problems involving multiplication and division. (3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4)

Where does our current curriculum (Go Math!) address the standards?

Chapter 3, Lessons: 3.1, 3.2,

Chapter 6, Lessons: 6.2, 6.3, 6.4

Does our current curriculum address this standard What materials can we Impact on Go Math! adequately, by addressing use to fill the gap? assessments procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY)

Lacks in hands-on applications of multiplication strategies.

Lacks in hands-on applications of division strategies.

EngageNY, Module 1: Topics A, C, D

EngageNY, Module 1: Topics A, D

Represent and solve problems involving multiplication and division. (3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4)

Chapter 4, Lessons: 4.1, 4.2, 4.3 Chapter 6, Lessons: 6.1, 6.5, 6.6, 6.7 Chapter 7, Lessons: 7.1, 7.3

EngageNY Module 1 End-of-Module Assessment (assesses Topic D)

Go Math! Chapter 3 MidChapter Checkpoint

EngageNY Module 1 Mid-Module Assessment (assesses Topics A, B & C) Go Math! Chapter 6 MidChapter Checkpoint and EngageNY Module 1 Summative Assessment End-of-Module Assessment (assesses Topics D through F)

Go Math! Chapter 3 MidChapter Checkpoint and Summative Assessment

Chapter 3, Lessons: 3.3, 3.5 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

EngageNY Module 1 Mid-Module Assessment (assesses Topics A & C)

Go Math! Assessments

Lacks in hands-on applications of multiplication and division strategies; additional application of concepts and strategies needed.

EngageNY, Module 1: Topic F EngageNY, Module 3: Topics B, C, D, E

EngageNY Module 3 MId-Module Assessment (assesses Go Math! Chapter 4 MidChapter Checkpoint Topics B and C) Go Math! Chapter 6 MidEngageNY Module 3 Chapter Checkpoint and End-of-Module Assessment (assesses Summative Assessment Topics D and E) Go Math! Chapter 7 MidChapter Checkpoint

Copyright Teaching Matters

Grade 3: Operations & Algebraic Thinking

Content Standards

Standards: What is the essence of this domain?

3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 =?

Represent and solve problems involving multiplication and division. (3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4)

3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6= 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Understand properties of multiplication and the relationship between multiplication and division. (3.OA.5, 3.OA.6)

Understand properties of 3.OA.6 Understand division as an unknown-factor multiplication and the problem. For example, find 32 ÷ 8 by finding the relationship between number that makes 32 when multiplied by 8. multiplication and division. (3.OA.5, 3.OA.6)

Where does our current curriculum (Go Math!) address the standards?

Chapter 5, Lesson: 5.2 Chapter 7, Lesson: 7.8

Chapter 3, Lessons: 3.6, 3.7 Chapter 4, Lessons: 4.4, 4.6 Chapter 6, Lesson: 6.9

Chapter 6, Lesson: 6.7

Does our current curriculum address this standard What materials can we Impact on Go Math! adequately, by addressing use to fill the gap? assessments procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY)

Additional conceptual modeling needed.

Lacks in hands-on applications of multiplication and division strategies; additional application of concepts and strategies needed.

Lacks in hands-on applications of division strategies. Requires additional practice with unknown factor problems.

EngageNY, Module 1: Topic D EngageNY, Module 3, Topics A, B, C, D

EngageNY, Module 1: Topics C, E, F EngageNY, Module 3: Topics A, B, C, D, F

EngageNY, Module 1: Topics B, D

Go Math! Assessments

Go Math! Chapter 5 MidEngageNY Module 3 Chapter Checkpoint Mid-Module Assessment (assesses Go Math! Chapter 7 Topics A, B & C) Chapter 7 Summative Assessment

Go Math! Chapter 3 Summative Assessment

EngageNY Module 1 End-of-Module Go Math! Chapter 4 MidAssessment (assesses Chapter Checkpoint Topics E & F) Go Math! Chapter 6 Summative Assessment

EngageNY Module 1 Mid-Module Assessment (assesses Topic B) EngageNY Module 1 End-of-Module Assessment (assesses Topic D)

Go Math! Chapter 6 Summative Assessment

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Grade 3: Operations & Algebraic Thinking

Content Standards

Standards: What is the essence of this domain?

3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 Multiply and divide within = 40, one knows 40 ÷ 5 = 8) or properties of 100. (3.OA.7) operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

3.OA.8 Solve two-step word problems using the four operations. 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.

3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Where does our current curriculum (Go Math!) address the standards?

Chapter 4, Lessons: 4.5, 4.8, 4.9 Chapter 6, Lesson: 6.8 Chapter 7, Lessons: 7.2, 7.4, 7.5, 7.6, 7.7, 7.9

Does our current curriculum address this standard What materials can we Impact on Go Math! adequately, by addressing use to fill the gap? assessments procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY)

EngageNY, Module 1: Lacks in hands-on applications of Topics D, E, F multiplication strategies; additional application of concepts and EngageNY, Module 3: strategies needed. Topics A, B, C, D, E

Chapter 1, Lesson: 1.12 Solve problems involving the Chapter 3, Lesson: 3.4 four operations and identify and explain patterns in Chapter 4, Lesson: 4.10 arithmetic. (3.OA.8, 3.OA.9) Chapter 7, Lessons: 7.10, 7.11

Solve problems involving the Chapter 1, Lesson: 1.1 four operations and identify and explain patterns in Chapter 4, Lesson: 4.7 arithmetic. (3.OA.8, 3.OA.9) Chapter 5, Lesson: 5.1

EngageNY, Module 1: Topic F Additional depth needed in the EngageNY, Module 3: application of the four operations. Topics E, F EngageNY, Module 7: Topic A

Requires additional depth, as opposed to one lesson in three different units.

EngageNY, Module 3: Topics A, B, D, E, F

Go Math! Assessments

EngageNY Module 1 End-of-Module Assessment (assesses Go Math! Chapter 4 Topics D, E & F) Summative Assessment EngageNY Module 3 Go Math! Chapter 6 Mid-Module Summative Assessment Assessment (assesses Topics A, B & C) Go Math! Chapter 7 MidChapter Checkpoint and EngageNY Module 3 Summative Assessment End-of-Module Assessment (assesses Topics D & E)

EngageNY Module 1 End-of-Module Go Math! Chapter 1 Assessment (assesses Summative Assessment Topic F) Go Math! Chapter 3 EngageNY Module 3 Summative Assessment End-of-Module Assessment (assesses Go Math! Chapter 4 Topics E & F) Summative Assessment EngageNY Module 7, Go Math! Chapter 7 Mid-Module Summative Assessment Assessment (assesses Topic A)

EngageNY Module 3 Go Math! Chapter 1 MidMid-Module Chapter Checkpoint Assessment (assesses Topics A & B) Go Math! Chapter 4 Summative Assessment EngageNY Module 3 End-of-Module Go Math! Chapter 5 MidAssessment (assesses Chapter Checkpoint Topics D, E & F)

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Grade 3: Numbers and Operations in Base Ten

Content Standards

Standards: What is the essence of this domain?

3.NBT.1. Use place value understanding to round whole numbers to the nearest 10 or 100.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (3.NBT.1, 3.NBT.2, 3.NBT.3)

3.NBT.2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (3.NBT.1, 3.NBT.2, 3.NBT.3)

3.NBT.3. Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (3.NBT.1, 3.NBT.2, 3.NBT.3)

Where does our current curriculum (Go Math!) address the standards?

Chapter 1, Lessons: 1.2, 1.3, 1.8

Chapter 1, Lessons: 1.4, 1.5, 1.6, 1.7, 1.9, 1.10, 1.11

Chapter 5, Lessons: 5.3, 5.4, 5.5

Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY)

Lacks adequate hands-on activities and modeling.

Lacks adequate hands-on activities and modeling of strategies to build fluency.

Additional application of strategies needed.

What materials can Impact on Go Math! Go Math! we use to fill the assessments Assessments gap?

EngageNY, Module 2: Topic C

EngageNY Module 2 Mid-Module Assessment (assesses Topic C)

Go Math! Chapter 1 Mid-Chapter Checkpoint and Summative Assessment

EngageNY, Module 2: Topics A, B, D, E

EngageNY Module 2 Mid-Module Assessment (assesses Topics A & B) EngageNY Module 2 End-of-Module Assessment (assesses Topics D & E)

Go Math! Chapter 1 Mid-Chapter Checkpoint and Summative Assessment

EngageNY, Module 3: Topic F

EngageNY Module 3 End-of-Module Assessment (asseses Topic F)

Go Math! Chapter 5 Mid-Chapter Checkpoint and Summative Assessment

Copyright Teaching Matters

Grade 3: Numbers and Operations - Fractions Content Standards Standards: Note: Grade 3 expectations in this domain What is the essence of this are limited to fractions with denominators domain? 2, 3, 4, 6, 8

Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address this standard adequately, What materials by addressing procedural, can we use to fill conceptual, and application skills the gap? equally? If not, what are the gaps? (*KEY)

3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Develop understanding of fractions Chapter 8, Lessons: 8.1, 8.2, Requires additional conceptual as numbers. (3.NF.1, 3.NF.2, 8.3, 8.4, 8.7, 8.8, 8.9 modeling and application. 3.NF.3)

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Develop understanding of fractions Go Math! addresses each of as numbers. (3.NF.1, 3.NF.2, the sub-standards associated 3.NF.3) with this standard.

Impact on Go Math! assessments

Go Math! Assessments

EngageNY, Module 5: Topic B

EngageNY Module 5 Mid-Module Assessment (assesses Topic B)

Go Math! Chapter 8 Mid-Chapter Checkpoint and Summative Assessment

3.NF.2a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into Develop understanding of fractions Chapter 8, Lesson: 8.5 b equal parts. Recognize that each part has as numbers. (3.NF.1, 3.NF.2, size 1/b and that the endpoint of the part 3.NF.3) based at 0 locates the number 1/b on the number line.

Lacking in application of fractions on the number line.

EngageNY, Module 5: Topic D

EngageNY Module 5 End-of-Module Assessment (assesses Topic D)

Go-Math! Chapter 8 Mid-Chapter Checkpoint

3.NF.2b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Develop understanding of fractions as numbers. (3.NF.1, 3.NF.2, 3.NF.3)

Requires supplementation; not addressed in a specific lesson.

EngageNY, Module 5: Topic D

EngageNY Module 5 End-of-Module Assessment (assesses Topic D)

No assessment.

3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Develop understanding of fractions Go Math! addresses each of as numbers. (3.NF.1, 3.NF.2, the sub-standards associated 3.NF.3) with this standard.

3.NF.3a. Understand two fractions as Develop understanding of fractions equivalent (equal) if they are the same size, or as numbers. (3.NF.1, 3.NF.2, Chapter 9, Lesson: 9.6 the same point on a number line. 3.NF.3)

Lacking in adequate practice and application of concepts.

EngageNY, Module 5: Topic D

EngageNY Module 5 End-of-Module Assessment (assesses Topic D)

Go Math! Chapter 9 Summative Assessment

3.NF.3b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Lacking in adequate practice and application of concepts.

Develop understanding of fractions as numbers. (3.NF.1, 3.NF.2, Chapter 9, Lesson: 9.7 3.NF.3)

Go Math! Chapter 9 Summative Assessment

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Grade 3: Numbers and Operations - Fractions Content Standards Standards: Note: Grade 3 expectations in this domain What is the essence of this are limited to fractions with denominators domain? 2, 3, 4, 6, 8

Where does our current curriculum (Go Math!) address the standards?

3.NF.3c. Express whole numbers as fractions, and recognize fractions that are equivalent to Develop understanding of fractions whole numbers. Examples: Express 3 in the as numbers. (3.NF.1, 3.NF.2, Chapter 8, Lesson: 8.6 form 3 = 3/1; recognize that 6/1 = 6; locate 3.NF.3) 4/4 and 1 at the same point of a number line diagram.

Does our current curriculum address this standard adequately, What materials by addressing procedural, can we use to fill conceptual, and application skills the gap? equally? If not, what are the gaps? (*KEY)

Impact on Go Math! assessments

Lacking in adequate practice and application of concepts.

EngageNY Module 5 End-of-Module Go Math! Chapter 8 Assessment Summative (assesses Topics D Assessment & E)

3.NF.3d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that Go Math! provides adequate Develop understanding of fractions comparisons are valid only when the two Chapter 9, Lessons: 9.1, 9.2, material; EngageNY materials are as numbers. (3.NF.1, 3.NF.2, fractions refer to the same whole. Record the 9.3, 9.4, 9.5 included for teachers looking for 3.NF.3) results of comparisons with the symbols >, =, enrichment or extensions. or <, and justify the conclusions, e.g., by using a visual fraction model.

EngageNY, Module 5: Topics D, E

EngageNY, Module 5: Topics C, D, F

EngageNY Module 5 Mid-Module Assessment (assesses Topic C) EngageNY Module 5 End-of-Module Assessment (assesses Topics D & F)

Go Math! Assessments

Go Math! Chapter 9 Mid-Chapter Checkpoint and Summative Assessment

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Grade 3: Measurement and Data

Content Standards

3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Where does our Standards: current curriculum What is the essence of this (Go Math!) address domain? the standards?

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. (3.MD.1, 3.MD.2)

Chapter 10, Lessons: 10.1, 10.2, 10.3, 10.4, 10.5

3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. (3.MD.1, 3.MD.2)

3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

Chapter 2, Lessons: Represent and interpret data. 2.1, 2.2, 2.3, 2.4, 2.5, (3.MD.3, 3.MD.4) 2.6

Chapter 10, Lessons: 10.7, 10.8, 10.9

Does our current curriculum address this standard What materials adequately, by addressing can we use to fill procedural, conceptual, and the gap? application skills equally? If not, what are the gaps? (*KEY)

Impact on Go Go Math! Math! assessments Assessments

Lacks in problems where time is presented on a number line; instead focuses on using a number line as a strategy.

EngageNY, Module 4: Topics A, C

EngageNY Module 4 Mid-Module Assessment Go Math! Chapter (assesses Topic A) 10 Mid-Chapter Checkpoint and EngageNY Module 4 Summative Assessment End-of-Module Assessment (assesses Topic C)

EngageNY, Module 4: Topics B, C

EngageNY Module 4 Mid-Module Assessment Go Math! Chapter (assesses Topic B) 10 Mid-Chapter Checkpoint and EngageNY Module 4 Summative End-of-Module Assessment Assessment (assesses Topic C)

EngageNY, Module 6: Topic A

Go Math! Chapter 2 EngageNY Module 6 Mid-Chapter Mid-Module Checkpoint and Assessment Summative (assesses Topic A) Assessment

Lacks adequate application of the strategies.

Requires additional practice in solving one- and two-step problems based on scaled bar graphs.

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Grade 3: Measurement and Data

Content Standards

Where does our Standards: current curriculum What is the essence of this (Go Math!) address domain? the standards?

Does our current curriculum address this standard What materials adequately, by addressing can we use to fill procedural, conceptual, and the gap? application skills equally? If not, what are the gaps? (*KEY)

3.MD.4 Generate measurement data by measuring lengths using rulers marked with Chapter 2, Lesson: 2.7 halves and fourths of an inch. Show the data Represent and interpret data. Requires additional exploration by making a line plot, where the horizontal (3.MD.3, 3.MD.4) other than two lessons. Chapter 10, Lesson: scale is marked off in appropriate units whole 10.6 numbers, halves, or quarters.

3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.

3.MD.5a. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (3.MD.5, 3.MD.6, 3.MD.7)

Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (3.MD.5, 3.MD.6, 3.MD.7)

Chapter 11, Lesson: 11.4

Chapter 11, Lesson: 11.4

EngageNY, Module 6: Topic B EngageNY, Module 7: Topic D

Impact on Go Go Math! Math! assessments Assessments

EngageNY Module 6 Mid-Module Go Math! Chapter 2 Assessment Summative (assesses Topic B) Assessment EngageNY Module 7 Go Math! Chapter End-of-Module 10 Summative Assessment Assessment (assesses Topic D)

Requires additional time to explore EngageNY, Module the application and conceptual 4: Topics A, B, C understanding.

EngageNY Module 4 Mid-Module Assessment (assesses Topics A Go Math! Chapter & B) 11 Mid-Chapter Checkpoint EngageNY Module 4 End-of-Module Assessment (assesses Topic C)

Requires additional time to explore EngageNY, Module the application and conceptual 4: Topics A, B & C understanding.

EngageNY Module 4 Mid-Module Assessment (assesses Topics A Go Math! Chapter & B) 11 Mid-Chapter Checkpoint EngageNY Module 4 End-of-Module Assessment (assesses Topic C)

Copyright Teaching Matters

Grade 3: Measurement and Data

Content Standards

3.MD.5b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Does our current curriculum address this standard What materials adequately, by addressing can we use to fill procedural, conceptual, and the gap? application skills equally? If not, what are the gaps? (*KEY)

Impact on Go Go Math! Math! assessments Assessments

Requires additional time to explore EngageNY, Module the application and conceptual 4: Topics A, B, C understanding.

EngageNY Module 4 Mid-Module Assessment (assesses Topics A Go Math! Chapter & B) 11 Mid-Chapter Checkpoint EngageNY Module 4 End-of-Module Assessment (assesses Topic C)

Chapter 11, Lesson: 11.6

Requires additional time to explore EngageNY, Module the application and conceptual 4: Topics B, C, D understanding.

EngageNY Module 4 Mid-Module Assessment (assesses Topics A Go Math! Chapter & B) 11 Summative EngageNY Module 4 Assessment End-of-Module Assessment (assesses Topic C)

Chapter 11, Lesson: 11.6

EngageNY Module 4, Topics B, C and Requires additional time to explore D address the subthe application and conceptual standards for this understanding. standard (see 3.MD.7a & 3.MD.7b)

Where does our Standards: current curriculum What is the essence of this (Go Math!) address domain? the standards?

Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (3.MD.5, 3.MD.6, 3.MD.7)

3.MD.6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (3.MD.5, 3.MD.6, 3.MD.7)

3.MD.7 Relate area to the operations of multiplication and addition.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (3.MD.5, 3.MD.6, 3.MD.7)

Chapter 11, Lesson: 11.5

Go Math! Chapter 11 Summative Assessment

Copyright Teaching Matters

Grade 3: Measurement and Data

Content Standards

3.MD.7a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

Where does our Standards: current curriculum What is the essence of this (Go Math!) address domain? the standards?

Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (3.MD.5, 3.MD.6, 3.MD.7)

Chapter 11, Lesson: 11.6

Does our current curriculum address this standard What materials adequately, by addressing can we use to fill procedural, conceptual, and the gap? application skills equally? If not, what are the gaps? (*KEY)

Impact on Go Go Math! Math! assessments Assessments

Requires additional time to explore EngageNY, Module the application and conceptual 4: Topics B, C, D understanding.

EngageNY Module 4 Mid-Module Assessment (assesses Topic B) Go Math! Chapter EngageNY Module 4 11 Summative End-of-Module Assessment Assessment (assesses Topics C & D)

3.MD.7b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (3.MD.5, 3.MD.6, 3.MD.7)

Chapter 11, Lesson: 11.7

Requires additional time to explore EngageNY, Module the application and conceptual 4: Topics B, C, D understanding.

3.MD.7c. Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (3.MD.5, 3.MD.6, 3.MD.7)

Chapter 11, Lesson: 11.8

Requires additional time to explore EngageNY, Module the application and conceptual 4: Topics C, D understanding.

EngageNY Module 4 Mid-Module Assessment (assesses Topic B)

Go Math! Chapter 11 Summative EngageNY Module 4 Assessment End-of-Module Assessment (assesses Topics C & D)

EngageNY Module 4 End-of-Module Go Math! Chapter 11 Summative Assessment (assesses Topics C Assessment & D)

Copyright Teaching Matters

Grade 3: Measurement and Data

Content Standards

3.MD.7d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Where does our Standards: current curriculum What is the essence of this (Go Math!) address domain? the standards?

Geometric measurement: understand concepts of area and relate area to multiplication and to addition. (3.MD.5, 3.MD.6, 3.MD.7)

Chapter 11, Lesson: 11.8

Geometric measurement: Chapter 11, Lessons: recognize perimeter as an attribute of plane figures and 11.1, 11.2, 11.3, 11.9, 11.10 distinguish between linear and area measures. (3.MD.8)

Does our current curriculum address this standard What materials adequately, by addressing can we use to fill procedural, conceptual, and the gap? application skills equally? If not, what are the gaps? (*KEY)

Requires additional time to explore EngageNY, Module the application and conceptual 4: Topics B, C, D understanding.

Go Math! adequately addresses this standard; EngageNY materials EngageNY, Module are included for enrichment or 7: Topics C, D, E extension.

Impact on Go Go Math! Math! assessments Assessments

EngageNY Module 4 Mid-Module Assessment (assesses Topic B)

Go Math! Chapter 11 Summative EngageNY Module 4 Assessment End-of-Module Assessment (assesses Topics C & D)

EngageNY Module 7 Mid-Module Assessment Go Math! Chapter (assesses Topic C) 11 Mid-Chapter Checkpoint and EngageNY Module 7 Summative End-of-Module Assessment Assessment (assesses Topics D & E)

Copyright Teaching Matters

Grade 3: Geometry

Content Standards

Standards: 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, What materials by addressing procedural, can we use to fill conceptual, and application skills the gap? equally? If not, what are the gaps? (*KEY)

Impact on Go Math! assessments

Go Math! adequately addresses this standard. EngageNY materials are included for enrichment and extension.

EngageNY, Module 7: Topics B, E

EngageNY MidModule Assessment Go Math! Chapter (assesses Topic B) 12 Mid-Chapter Checkpoint and EngageNY End-of- Summative Module Assessment Assessment (assesses Topic D)

EngageNY, Module 5: Topic A

EngageNY Module 5 Mid-Module Assessment (assesses Topic A)

3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define Reason with shapes and their attributes. (3.G.1, a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares 3.G.2) as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Chapter 12, Lessons: 12.1, 12.2, 12.3, 12.4, 12.5, 12.6, 12.7, 12.8

3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Requires additional time to explore Chapter 12, Lesson: 12.9 the application and conceptual understanding.

Reason with shapes and their attributes. (3.G.1, 3.G.2)

Go Math! Assessments

Go Math! Chapter 12 Summative Assessment

Copyright Teaching Matters

Grade 4: Operations & Algeraic Thinking

Content Standards

4.OA.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.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.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.

Standards: What is the essence of this domain?

Use the four operations with whole numbers to solve problems. (4.OA.1, 4.OA.2, 4.OA.3)

Use the four operations with whole numbers to solve problems. (4.OA.1, 4.OA.2, 4.OA.3)

Use the four operations with whole numbers to solve problems. (4.OA.1, 4.OA.2, 4.OA.3)

Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address this standard adequately, by What materials can Impact on Go Math! Go Math! addressing procedural, we use to fill the assessments Assessments conceptual, and application gap? skills equally? If not, what are the gaps? (*KEY)

Chapter 2, Lesson: 2.1

EngageNY Module 3 EngageNY Module 3: Mid-Module One lesson does not provide Topics: A, D Assessment Go Math! Chapter an adequate amount of 2 Mid-Chapter practice, application nor EngageNY Module 7: EngageNY Module 7 Checkpoint fluency. Topic A End-of-Module Assessment

Chapter 2, Lesson: 2.2

EngageNY Module 3 EngageNY Module 3: Mid-Module One lesson does not provide Topics: A, D Assessment Go Math! Chapter an adequate amount of 2 Mid-Chapter practice, application nor EngageNY Module 7: EngageNY Module 7 Checkpoint fluency. Topics A, B End-of-Module Assessment

Chapter 2, Lessons: 2.9, 2.12 Chapter 3, Lesson: 3.7 Chapter 4, Lessons: 4.3, 4.12

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment and additional practice.

EngageNY Module 1: Topics D, E, F

EngageNY Module 1 Go Math! Chapter End-of-Module 2 Summative Assessment Assessment

EngageNY Module 3 Go Math! Chapter Mid-Module 3 Summative EngageNY Module 3: Assessment and End- Assessment Topics D, G of-Module Assessment Go Math! Chapter EngageNY Module 7: 4 Mid-Chapter Topics B, C EngageNY Module 7 Checkpoint and End-of-Module Summative Assessment Assessment

Grade 4: Operations & Algeraic Thinking

Content Standards

Standards: What is the essence of this domain?

4.OA.4 Find all factor pairs for a whole number in the range 1– –100. Recognize that a whole number is a multiple of each of its factors. Gain familiarity with Determine whether a given whole factors and multiples. number in the range 1– –100 is a (4.OA.4) multiple of a given one-digit number. Determine whether a given whole number in the range 1– –100 is prime or composite. 4.OA.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 Generate and analyze number 1, generate terms in the patterns. (4.OA.5) 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.

Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address this standard adequately, by What materials can Impact on Go Math! Go Math! addressing procedural, we use to fill the assessments Assessments conceptual, and application gap? skills equally? If not, what are the gaps? (*KEY)

Go Math! adequately addresses the standard; Chapter 5, Lessons: EngageNY materials are 5.1, 5.2, 5.3, 5.4, 5.5 included for enrichment and additional practice.

Chapter 5, Lesson: 5.6 Chapter 10, Lesson: 10.7

Go Math! Chapter EngageNY Module 3 5 Mid-Chapter EngageNY Module 3: End-of-Module Checkpoint and Topic H Assessment Summative Assessment

Topic H in Module 5 is one lesson, and is Additional practice and EngageNY Module 5: considered to be application of the standard is Topic H optional. Therefore, needed. it is not assessed on the assessments.

Go Math! Chapter 5 Summative Assessment Go Math! Chapter 10 Summative Assessment

Grade 4: Numbers & Operations in Base Ten

Content Standards

Where does our Standards: current curriculum What is the essence of (Go Math!) address this domain? 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)

4.NBT.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 700 ÷ 70 = 10 by applying concepts of place value and division.

Generalize place value understanding for multiChapter 1, Lessons: digit whole numbers. 1.1, 1.5 (4.NBT.1, 4.NBT.2, 4.NBT.3)

Go Math! Chapter 1 Additional practice and EngageNY Module 1 Mid-Chapter EngageNY Module 1: application of the standard Mid-Module Checkpoint and Topic A is needed. Assessment Summative Assessment

4.NBT.2 Read and write multidigit whole numbers using baseten numerals, number names, Generalize place value and expanded form. Compare understanding for multiChapter 1, Lessons: two multi-digit numbers based digit whole numbers. 1.2, 1.3 on meanings of the digits in (4.NBT.1, 4.NBT.2, each place, using >, =, and < 4.NBT.3) symbols to record the results of comparisons.

Additional practice and EngageNY Module 1 Go Math! Chapter 1 EngageNY Module 1: application of the standard Mid-Module Mid-Chapter Topics A, B is needed. Assessment Checkpoint

What materials can Impact on Go Math! Go Math! we use to fill the assessments Assessments gap?

4.NBT.3 Use place value understanding to round multidigit whole numbers to any place.

Generalize place value understanding for multidigit whole numbers. Chapter 1, Lesson: 1.4 (4.NBT.1, 4.NBT.2, 4.NBT.3)

One lesson does not provide an adequate amount of practice, application nor fluency.

EngageNY Module 1 Go Math! Chapter 1 EngageNY Module 1: Mid-Module Mid-Chapter Topic C Assessment Checkpoint

4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Use place value understanding and properties of operations Chapter 1, Lessons: to perform multi-digit 1.6, 1.7, 18 arithmetic. (4.NBT.4, 4.NBT.5, 4.NBT.6)

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment and additional practice.

EngageNY Module 1 Go Math! Chapter 1 EngageNY Module 1: End-of-Module Summative Topics D, E Assessment Assessment

Grade 4: Numbers & Operations in Base Ten

Content Standards

Where does our Standards: current curriculum What is the essence of (Go Math!) address this domain? the standards?

4.NBT.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.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (4.NBT.4, 4.NBT.5, 4.NBT.6)

4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit 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.

Use place value understanding and Chapter 4, Lessons: properties of operations 4.1, 4.2, 4.4, 4.5, 4.6, to perform multi-digit 4.7, 4.8, 4.9, 4.10, 4.11 arithmetic. (4.NBT.4, 4.NBT.5, 4.NBT.6)

Chapter 2, Lessons: 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.10, 2.11 Chapter 3, Lessons: 3.1, 3.2, 3.3, 3.4, 3.5, 3.6

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 Go Math! Go Math! we use to fill the assessments Assessments gap?

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment and additional practice.

Go Math! Chapter 2 Mid-Chapter Checkpoint and EngageNY Module 3 Summative Mid-Module Assessment EngageNY Module 3: Assessment and EndTopics B, C, D, H of-Module Go Math! Chapter 3 Assessment Mid-Chapter Checkpoint and Summative Assessment

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment and additional practice.

Go Math! Chapter 4 EngageNY Module 3 Mid-Chapter EngageNY Module 3: End-of-Module Checkpoint and Topics E, G Assessment Summative Assessment

Grade 4: Numbers & Operations Fraction

Content Standards

Does our current curriculum address this standard Where does our Standards: adequately, by addressing Impact on Go current curriculum What materials can we What is the essence procedural, conceptual, and Math! (Go Math!) address the use to fill the gap? of this domain? application skills equally? If assessments standards? not, what are the gaps? (*KEY)

Go Math! Assessments

4.NF.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.

Extend understanding of fraction equivalence and ordering. (4.NF.1, 4.NF.2)

EngageNY Module 5: Topics B, E

EngageNY Module 5 Mid-Module Assessment and End-of-Module Assessment

Go Math! MidChapter Checkpoint

4.NF.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 >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Extend understanding of fraction equivalence and ordering. (4.NF.1, 4.NF.2)

EngageNY Module 5: Topics C, E

EngageNY Module 5 Mid-Module Assessment and End-of-Module Assessment

Go Math! Chapter 6 Summative Assessment

EngageNY Module 5: Topic E

EngageNY Module 5 End-of-Module Assessment

Build fractions from unit fractions by applying and 4.NF.3 Understand a fraction a/b extending previous with a > 1 as a sum of fractions 1/b. understandings of operations on whole numbers. (4.NF.3, 4.NF.4)

Chapter 6, Lessons: 6.1, 6.2, 6.3, 6.4, 6.5

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment and additional practice.

Chapter 6, Lessons: 6.6, 6.7 6.8

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment and additional practice.

Grade 4: Numbers & Operations Fraction

Content Standards

Does our current curriculum address this standard Where does our Standards: adequately, by addressing Impact on Go current curriculum What materials can we What is the essence procedural, conceptual, and Math! (Go Math!) address the use to fill the gap? of this domain? application skills equally? If assessments standards? not, what are the gaps? (*KEY)

Build fractions from unit fractions by 4.NF.3A Understand addition and applying and subtraction of fractions as joining extending previous and separating parts referring to the understandings of same whole. operations on whole numbers. (4.NF.3, 4.NF.4) 4.NF.3B 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. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (4.NF.3, 4.NF.4)

4.NF.3C Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.3D 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 and equations to represent the problem.

Chapter 7, Lesson: 7.1

One lesson does not provide an adequate amount of practice, application nor fluency.

EngageNY Module 5: Topic D

Go Math! Assessments

EngageNY Module 5 Mid-Module Assessment

Go Math! Chapter 7 Mid-Chapter Checkpoint

Chapter 7, Lessons: 7.2, 7.6

Additional practice and application of the standard is needed.

EngageNY Module 5: Topic A

EngageNY Module 5 Mid-Module Assessment

Go Math! Chapter 7 Mid-Chapter Checkpoint and Summative Assessment

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (4.NF.3, 4.NF.4)

Chapter 7, Lessons: 7.7, 7.8, 7.9

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment and additional practice.

EngageNY Module 5: Topic F

EngageNY Module 5 End-of-Module Assessment

Go Math! Chapter 7 Summative Assessment

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (4.NF.3, 4.NF.4)

Go Math! adequately addresses the standard; Chapter 7, Lessons 7.3, EngageNY materials are 7.4, 7.5, 7.10 included for enrichment and additional practice.

EngageNY Module 5: Topics D, F

EngageNY Module 5 Mid-Module Assessment and End-of-Module Assessment

Go Math! Chapter 7 Mid-Chapter Checkpoint and Summative Assessment

Grade 4: Numbers & Operations Fraction

Content Standards

Does our current curriculum address this standard Where does our Standards: adequately, by addressing Impact on Go current curriculum What materials can we What is the essence procedural, conceptual, and Math! (Go Math!) address the use to fill the gap? of this domain? application skills equally? If assessments standards? not, what are the gaps? (*KEY)

Build fractions from unit fractions by 4.NF.4 Apply and extend previous applying and understandings of multiplication to extending previous multiply a fraction by a whole understandings of number. operations on whole numbers. (4.NF.3, 4.NF.4) Build fractions from 4.NF.4A Understand a fraction a/b unit fractions by as a multiple of 1/b. For example, applying and use a visual fraction model to extending previous represent 5/4 as the product 5 × understandings of (1/4), recording the conclusion by operations on whole the equation 5/4 = 5 × (1/4). numbers. (4.NF.3, 4.NF.4) 4.NF.4B 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.)

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (4.NF.3, 4.NF.4)

Chapter 8, Lesson: 8.1

One lesson does not provide an adequate amount of practice, application nor fluency.

Additional practice and Chapter 8, Lessons 8.2, application of the standard is 8.3 needed.

Go Math! Assessments

EngageNY Module 5: Topic G

EngageNY Module 5 End-of-Module Assessment

EngageNY Module 5: Topic A

EngageNY Module 5 Mid-Module Assessment

Go Math! Chapter 8 Mid-Chapter Checkpoint

EngageNY Module 5 End-of-Module Assessment

Go Math! Chapter 8 Mid-Chapter Checkpoint and Summative Assessment

EngageNY Module 5: Topic G

Grade 4: Numbers & Operations Fraction

Content Standards

Does our current curriculum address this standard Where does our Standards: adequately, by addressing Impact on Go current curriculum What materials can we What is the essence procedural, conceptual, and Math! (Go Math!) address the use to fill the gap? of this domain? application skills equally? If assessments standards? not, what are the gaps? (*KEY)

Go Math! Assessments

4.NF.4C 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?

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (4.NF.3, 4.NF.4)

4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Understand decimal notation for fractions, Chapter 9, Lessons: and compare decimal 9.3, 9.6 fractions. (4.NF.5, 4.NF.6, 4.NF.7)

Additional practice and application of the standard is needed.

4.NF.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.

Understand decimal notation for fractions, Chapter 9, Lessons: and compare decimal 9.1, 9.2, 9.4 fractions. (4.NF.5, 4.NF.6, 4.NF.7)

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment and additional practice.

Chapter 8, Lessons: 8.4, 8.5

Additional practice and application of the standard is needed.

EngageNY Module 5: Topic G

EngageNY Module 5 End-of-Module Assessment

Go Math! Chapter 8 Summative Assessment

EngageNY Module 6: Topics B, D

EngageNY Module 6 Mid-Module Assessment and End-of-Module Assessment

Go Math! Chapter 9 Mid-Chapter Checkpoint and Summative Assessment

EngageNY Module 6: Topics A, B, D

EngageNY Module 6 Mid-Module Assessment and End-of-Module Assessment

Go Math! Chapter 9 Mid-Chapter Checkpoint

Grade 4: Numbers & Operations Fraction

Content Standards

Does our current curriculum address this standard Where does our Standards: adequately, by addressing Impact on Go current curriculum What materials can we What is the essence procedural, conceptual, and Math! (Go Math!) address the use to fill the gap? of this domain? application skills equally? If assessments standards? not, what are the gaps? (*KEY)

Go Math! Assessments

4.NF.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.

Understand decimal notation for fractions, and compare decimal Chapter 9, Lesson: 9.7 fractions. (4.NF.5, 4.NF.6, 4.NF.7)

Go Math! Chapter 9 Summative Assessment

One lesson does not provide an adequate amount of practice, application nor fluency.

EngageNY Module 6: Topic C

EngageNY Module 6 End-of-Module Assessment

Grade 4: Measurement & Data

Content Standards

Standards: What is the essence of this domain?

4.MD.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 twocolumn 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), ...

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. (4.MD.1, 4.MD.2, 4.MD.3)

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)

Go Math! adequately Chapter 12, Lessons: addresses the standard; 12.1, 12.2, 12.3, 12.4, EngageNY materials are 12.6, 12.7, 12.8, included for enrichment 12.11 and additional practice.

What materials can Impact on Go Math! Go Math! we use to fill the assessments Assessments gap?

EngageNY Module 2 EngageNY Module 2: End-of-Module Go Math! Chapter 12 Topics A, B Assessment Mid-Chapter Checkpoint and EngageNY Module 7: EngageNY Module 7 Summative Topics A, B, C End-of-Module Assessment Assessment

Grade 4: Measurement & Data

Content Standards

Standards: What is the essence of this domain?

Where does our current curriculum (Go Math!) address the standards?

4.MD.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.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. (4.MD.1, 4.MD.2, 4.MD.3)

4.MD.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 viewing the area formula as a multiplication equation with an unknown factor.

Solve problems involving measurement and conversion of Chapter 13, Lessons: measurements from a 13.1, 13.2, 13.3, 13.4, larger unit to a smaller 13.5 unit. (4.MD.1, 4.MD.2, 4.MD.3)

Does our current curriculum address this standard adequately, by addressing procedural, conceptual, and application skills equally? If not, what are the gaps? (*KEY)

Chapter 9, Lesson: 9.5

Go Math! adequately addresses the standard; EngageNY materials are Chapter 12, Lessons: included for enrichment 12.7, 12.9, 12.10 and additional practice.

Go Math! adequately addresses the standard; EngageNY materials are included for enrichment and additional practice.

What materials can Impact on Go Math! Go Math! we use to fill the assessments Assessments gap?

EngageNY Module 2 End-of-Module EngageNY Module 2: Assessment Go Math! Chapter 9 Topics A, B Summative EngageNY Module 6 Assessment EngageNY Module 6: End-of-Module Topic E Assessment Go Math! Chapter 12 Summative EngageNY Module 7: EngageNY Module 7 Assessment Topics B, C End-of-Module Assessment

Go Math! Chapter 13 EngageNY Module 3 Mid-Chapter EngageNY Module 3: Mid-Module Checkpoint and Topic A Assessment Summative Assessment

Grade 4: Measurement & Data

Content Standards

Standards: What is the essence of this domain?

4.MD.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 Represent and using information presented in line interpret data. plots. For example, from a line plot (4.MD.4) find and interpret the difference in length between the longest and shortest specimens in an insect collection. 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

Geometric measurement: understand concepts of angle and measure angles. (4.MD.5, 4.MD.6, 4.MD.7)

4.MD.5A 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 “ “one-degree angle,“ ” and can be used to measure angles.

Geometric measurement: understand concepts of angle and measure angles. (4.MD.5, 4.MD.6, 4.MD.7)

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 Go Math! Go Math! we use to fill the assessments Assessments gap?

Chapter 12, Lesson: 12.5

One lesson does not provide an adequate amount of practice, application nor fluency.

EngageNY Module 5 Go Math! Chapter 12 EngageNY Module 5: End-of-Module Mid-Chapter Topics F, G Assessment Checkpoint

EngageNY Module 4 EngageNY Module 4: Mid-Module Topic B Assessment

Additional practice and EngageNY Module 4 Go Math! Chapter 11 Chapter 11, Lessons: EngageNY Module 4: application of the standard Mid-Module Mid-Chapter 11.1, 11.2 Topic B is needed. Assessment Assessment

Grade 4: Measurement & Data

Content Standards

Standards: What is the essence of this domain?

Geometric 4.MD.5B An angle that turns measurement: through n one-degree angles is understand concepts said to have an angle measure of of angle and measure n degrees. angles. (4.MD.5, 4.MD.6, 4.MD.7) Geometric 4.MD.6 Measure angles in whole- measurement: number degrees using a understand concepts protractor. Sketch angles of of angle and measure specified measure. angles. (4.MD.5, 4.MD.6, 4.MD.7) 4.MD.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.

Geometric measurement: understand concepts of angle and measure angles. (4.MD.5, 4.MD.6, 4.MD.7)

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 Go Math! Go Math! we use to fill the assessments Assessments gap?

Chapter 11, Lesson: 11.2

One lesson does not provide an adequate amount of practice, application nor fluency.

EngageNY Module 4 Go Math! Chapter 11 EngageNY Module 4: Mid-Module Mid-Chapter Topic B Assessment Assessment

Chapter 11, Lesson: 11.3

One lesson does not provide an adequate amount of practice, application nor fluency.

EngageNY Module 4 Go Math! Chapter 11 EngageNY Module 4: Mid-Module Mid-Chapter Topic B Assessment Assessment

Additional practice and EngageNY Module 4 Go Math! Chapter 11 Chapter 11, Lessons: EngageNY Module 4: application of the standard End-of-Module Summative 11.4, 11.5 Topic C is needed. Assessment Assessment

Grade 4: Geometry 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?

Content Standards

Where does our Standards: current curriculum What is the essence of (Go Math!) address this domain? the standards?

4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.

Draw and identify lines and angles, and classify Chapter 10, Lessons: shapes by properties of 10.1, 10.3 their lines and angles. (4.G.1, 4.G.2, 4.G.3)

Additional practice and application of the standard is needed.

EngageNY Module 4 Mid-Module Go Math! Chapter EngageNY Module 4: Assessment and End- 10 Mid-Chapter Topics A, D of-Module Checkpoint Assessment

4.G.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.

Draw and identify lines and angles, and classify Chapter 10, Lessons: shapes by properties of 10.2, 10.4 their lines and angles. (4.G.1, 4.G.2, 4.G.3)

Additional practice and application of the standard is needed.

EngageNY Module 4 EngageNY Module 4: End-of-Module Topic D Assessment

Go Math! Chapter 10 Mid-Chapter Checkpoint

4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry.

Draw and identify lines and angles, and classify Chapter 10, Lessons: shapes by properties of 10.5, 10.6 their lines and angles. (4.G.1, 4.G.2, 4.G.3)

Additional practice and application of the standard is needed.

EngageNY Module 4 EngageNY Module 4: End-of-Module Topic D Assessment

Go Math! Chapter 10 Summative Assessment

Impact on Go Math! Go Math! assessments Assessments

Grade 5: Operations and Algebraic Thinking

Content Standards

Standards: What is the essence of this domain?

Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address this standard What materials can Impact on Go Math! Go Math! adequately, by addressing we use to fill the assessments Assessments procedural, conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY) EngageNY Module 2 Mid-Module Assessment (assesses Topics A, B, & C)

5.OA.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Write and interpret numerical expressions (5.OA.1, 5.OA.2).

5.OA.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation Write and interpret Q add 8 and 7, then multiply by 2R as 2 × (8 numerical expressions + 7). Recognize that 3 × (18932 + 921) is (5.OA.1, 5.OA.2). three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Chapter 1, Lessons: 1.11, 1.12

Lessons lack conceptual modeling of expressions and authentic application

EngageNY, Module 2: EngageNY Module 4 Topics A, B, C Mid-Module Assessment EngageNY Module 4: (assesses Topic D) Topics D, G, H

Go Math! Chapter 1 Summative Assessment

EngageNY Module 4 End-of-Module Assessment (assesses Topics G & H) EngageNY Module 2 Mid-Module Assessment (assesses Topics B EngageNY, Module 2: & C) Topics B, C Chapter 1, Lessons: 1.10

Lessons lack conceptual modeling of expressions and authentic application

EngageNY Module 4 EngageNY Module 4: Mid-Module Topics D, H Assessment (assesses Topic D) EngageNY Module 6: Topic B EngageNY Module 6 Mid-Module Assessment (assesses Topic B)

Go Math! Chapter 1 Summative Assessment

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Grade 5: Operations and Algebraic Thinking

Content Standards

Standards: What is the essence of this domain?

5.OA.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate Analyze patterns and plane. For example, given the rule "Add 3" relationships (5.OA.3). and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Where does our current curriculum (Go Math!) address the standards?

Chapter 9, Lessons: 9.5, 9.6, 9.7

Does our current curriculum address this standard What materials can Impact on Go Math! Go Math! adequately, by addressing we use to fill the assessments Assessments procedural, conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY)

Lessons lack conceptual modeling of expressions and authentic application

EngageNY, Module 6: Topics B, D

EngageNY Module 6 Mid-Module Assessment (assesses Topic B) EngageNY Module 6 End-of-Module Assessment (assesses Topic D)

Go Math! Chapter 9 Summative Assessment

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Grade 5: Numbers and Operations in Base Ten

Content Standards

5.NBT.1 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 left.

Standards: Where does our current What is the essence of this curriculum (Go Math!) domain? address the standards?

Understand the place value system (5.NBT.1, 5.NBT.2, 5.NBT.3a,b, 5.NBT.4).

5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain Understand the place value patterns in the placement of the decimal system (5.NBT.1, 5.NBT.2, point when a decimal is multiplied or 5.NBT.3a,b, 5.NBT.4). divided by a power of 10. Use wholenumber exponents to denote powers of 10.

5.NBT.3 Read, write, and compare decimals to thousandths.

Understand the place value system (5.NBT.1, 5.NBT.2, 5.NBT.3a,b, 5.NBT.4).

Chapter 1, Lessons: 1.1, 1.2; Chapter 3, Lessons: 3.1

Chapter 1, Lessons: 1.4 1.5

Does our current curriculum address this standard adequately, by addressing What materials can Impact on Go Math! procedural, conceptual, and we use to fill the gap? assessments application skills equally? If not, what are the gaps? (*KEY)

Needs more modeling with patterns

Needs more modeling with patterns

EngageNY, Module 1: Topic A EngageNY, Module 2: Topics A, D, E

EngageNY, Module 1: Topics A, D, E EngageNY, Module 2: Topics A, D, E, G

Chapter 3, Lessons: 3.2 & 3.3

Needs more modeling with manipulatives

EngageNY, Module 1: Topics B, D, E, F

5.NBT.3a. Read and write decimals to thousandths using base-ten numerals, Understand the place value number names, and expanded form, e.g., system (5.NBT.1, 5.NBT.2, 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × 5.NBT.3a,b, 5.NBT.4). (1/10) + 9 × (1/100) + 2 × (1/1000).

Chapter 3, Lessons: 3.2

Needs more modeling with manipulatives

EngageNY, Module 1: Topics B, D, E, F

5.NBT.3b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Chapter 3, Lessons: 3.3

Needs more modeling with manipulatives

EngageNY, Module 1: Topics B, D, E, F

Understand the place value system (5.NBT.1, 5.NBT.2, 5.NBT.3a,b, 5.NBT.4).

EngageNY Module 1 Mid-Module Assessment (assesses Topic A)

Go Math! Assessments

Go Math! Chapter 1 Mid-Chapter Checkpoint and Summative Assessment

EngageNY Module 2 Go Math! Chapter 3 Mid-Module Assessment (assesses Mid-Chapter Checkpoint and Topics A & D) Summative EngageNY Module 1 Mid-Module Assessment (assesses Topic A) Go Math! Chapter 1 EngageNY Module 1 Mid-Chapter End-of-Module Checkpoint and Assessment (assesses Summative Topics D & E) Assessment EngageNY Module 2 Mid-Module Assessment (assesses Topics A & D) EngageNY Module 1 Go Math! Chapter 3 Mid-Module Mid-Chapter Assessment (assesses Checkpoint and Topic B) Summative Assessment EngageNY Module 1 EngageNY Module 1 Go Math! Chapter 3 Mid-Module Mid-Chapter Assessment (assesses Checkpoint and Topic B) Summative Assessment EngageNY Module 1 EngageNY Module 1 Go Math! Chapter 3 Mid-Module Mid-Chapter Assessment (assesses Checkpoint and Topic B) Summative Assessment EngageNY Module 1

Copyright Teaching Matters

Grade 5: Numbers and Operations in Base Ten

Content Standards

Standards: Where does our current What is the essence of this curriculum (Go Math!) domain? address the standards?

Understand the place value Chapter 3, Lessons: 3.4 system (5.NBT.1, 5.NBT.2, 5.NBT.3a,b, 5.NBT.4). Perform operations with multi5.NBT.5 Fluently multiply multi-digit whole digit whole numbers and with Chapter 1, Lessons: 1.6, 1.7 numbers using the standard algorithm. decimals to hundredths (5.NBT.5, 5.NBT.6, 5.NBT.7). 5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using Chapter 1, Lessons: 1.3, Understand the place value strategies based on place value, the 1.8, 1.9; Chapter 2, system (5.NBT.1, 5.NBT.2, properties of operations, and/or the Lessons: 2.1, 2.2, 2.3, 2.4, 5.NBT.3a,b, 5.NBT.4). relationship between multiplication and 2.5, 2.6, 2.8, 2.9 division. Illustrate and explain the calculation by using equations, 5.NBT.4 Use place value understanding to round decimals to any place.

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and Understand the place value strategies based on place value, system (5.NBT.1, 5.NBT.2, properties of operations, and/or the 5.NBT.3a,b, 5.NBT.4). relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Does our current curriculum address this standard adequately, by addressing What materials can Impact on Go Math! procedural, conceptual, and we use to fill the gap? assessments application skills equally? If not, what are the gaps? (*KEY) Needs more modeling with manipulatives

EngageNY, Module 1: Topic C

Needs more modeling with manipulatives

EngageNY, Module 2: Topics B, D

Needs more modeling in 1.3 & 1.9 EngageNY, Module 2: Chapter 2 needs modeling and Topics E, F, H lacks authentic tasks for application

EngageNY, Module 1: Topics D, E, F Chapter 3, Lessons: 3.5, Needs authentic performance 3.6, 3.7, 3.8, 3.9, 3.10, 3.11, tasks for application 3.12

EngageNY, Module 2: Topics C, D, G, H EngageNY, Module 4: Topics E, G

EngageNY Module 1 Mid-Module Assessment (assesses EngageNY Module 2 Mid-Module Assessment (assesses Topic B & D)

Go Math! Assessments

Go Math! Chapter 3 Mid-Chapter Checkpoint and Go Math! Chapter 1 Mid-Chapter Checkpoint Go Math! Chapter 1 Summative Assessment

EngageNY Module 2 End-of-Module Assessment (assesses Go Math! Chapter 2 Mid-Chapter Topics E, F, H) Checkpoint and Summative EngageNY Module 1 End-of-Module Assessment (assesses Topics D, E & F) EngageNY Module 2 Go Math! Chapter 3 Mid-Module Assessment (assesses Summative Assessment Topics C & D) EngageNY Module 2 End-of-Module Assessment (assesses Topics G & H)

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Grade 5: Numbers and Operations - Fractions

Content Standards

5.NF.1 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. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Standards: What is the essence of this domain?

Use equivalent fractions as a strategy to add and subtract fractions (5.NF.1, 5.NF.2)

5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction Use equivalent fractions as a models or equations to represent the problem. strategy to add and subtract Use benchmark fractions and number sense of fractions (5.NF.1, 5.NF.2) fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Where does our current curriculum (Go Math!) address the standards?

Chapter 6, Lessons: 6.4, 6.5, 6.6, 6.7, 6.8, 6.10

Chapter 6, Lessons: 6.1, 6.2, 6.3, 6.9

Does our current curriculum address this standard What materials Impact on Go adequately, by addressing procedural, conceptual, and can we use to fill Math! assessments application skills equally? If the gap? not, what are the gaps? (*KEY)

Go Math! Assessments

Lacks authentic tasks for application.

EngageNY Module 3 Mid-Module Assessment (assesses Topics A & B) EngageNY, Go Math! Chapter Module 3: Topics 6 Summative EngageNY Module Assessment A, B, C, D 3 End-of-Module Assessment (assesses Topics C & D)

Lacks authentic tasks for application.

EngageNY Module 3 Mid-Module Assessment (assesses Topic Go Math! Chapter 6 Mid-Chapter EngageNY, B) Module 3: Topics Checkpoint and B, C EngageNY Module Summative Assessment 3 End-of-Module Assessment (assesses Topic C)

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Grade 5: Numbers and Operations - Fractions

Content Standards

Standards: What is the essence of this domain?

Where does our current curriculum (Go Math!) address the standards?

5.NF.3 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, e.g., by using visual Apply and extend previous fraction models or equations to represent the understandings of multiplication problem. For example, interpret 3/4 as the result and division to multiply and Chapter 8, Lesson: 8.3; of dividing 3 by 4, noting that 3/4 multiplied by 4 divide fractions (5.NF.3, Chapter 2, Lesson: 2.7 equals 3, and that when 3 wholes are shared 5.NF.4a,b, 5.NF.5, 5.NF.6, equally among 4 people each person has a 5.NF.7a,b,c). share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NF.4a. 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. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

Apply and extend previous understandings of multiplication and division to multiply and Chapter 7, Lessons: 7.1, 7.2, divide fractions (5.NF.3, 7.3, 7.4, 7.5, 7.6, 7.7 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

Apply and extend previous understandings of multiplication and division to multiply and Chapter 7, Lessons: 7.1, 7.2, divide fractions (5.NF.3, 7.3, 7.6 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

Does our current curriculum address this standard What materials Impact on Go adequately, by addressing procedural, conceptual, and can we use to fill Math! assessments application skills equally? If the gap? not, what are the gaps? (*KEY)

Lesson 2.7 needs more modeling

Needs more modeling

Lesson 7.1 & 7.6 needs more modeling

Go Math! Assessments

Go Math! Chapter 8 Mid-Chapter EngageNY Module Checkpoint and 4 Mid-Module Summative EngageNY, Assessment Assessment Module 4: Topic B (assesses Topic Go Math! Chapter B) 2 Summative Assessment

Go Math! Chapter 7 Mid-Chapter Checkpoint and Summative Assessment

EngageNY Module 4 Mid-Module Assessment (assesses Topics Go Math! Chapter C & D) EngageNY, 7 Mid-Chapter Module 4: Topics Checkpoint and C, D, E EngageNY Module Summative 4 End-of-Module Assessment Assessment (assesses Topic E)

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Grade 5: Numbers and Operations - Fractions

Content Standards

Standards: What is the essence of this domain?

Where does our current curriculum (Go Math!) address the standards?

5.NF.4b. 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 find areas of rectangles, and represent fraction products as rectangular areas.

Apply and extend previous understandings of multiplication and division to multiply and Chapter 7, Lessons: 7.4, 7.7 divide fractions (5.NF.3, 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

5.NF.5 Interpret multiplication as scaling (resizing), by:

Apply and extend previous understandings of multiplication and division to multiply and Chapter 7, Lessons: 7.5, 7.8, divide fractions (5.NF.3, 7.10 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

5.NF.5a. 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.

Apply and extend previous understandings of multiplication and division to multiply and Chapter 7, Lessons: 7.5, 7.8 divide fractions (5.NF.3, 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

5.NF.5b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing 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 1.

Apply and extend previous understandings of multiplication and division to multiply and Chapter 7, Lessons: 7.5, 7.8, divide fractions (5.NF.3, 7.10 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

Does our current curriculum address this standard What materials Impact on Go adequately, by addressing procedural, conceptual, and can we use to fill Math! assessments application skills equally? If the gap? not, what are the gaps? (*KEY)

Go Math! Assessments

Needs more modeling

EngageNY Module 5 End-of-Module EngageNY, Assessment Module 5: Topic C (assesses Topic C)

Go Math! Chapter 7 Mid-Chapter Checkpoint and Summative Assessment

Needs more modeling

EngageNY Module 4 End-of-Module EngageNY, Assessment Module 4: Topic F (assesses Topic F)

Go Math! Chapter 7 Mid-Chapter Checkpoint and Summative Assessment

Needs more modeling

EngageNY Module 4 End-of-Module EngageNY, Assessment Module 4: Topic F (assesses Topic F)

Go Math! Chapter 7 Mid-Chapter Checkpoint and Summative Assessment

Needs more modeling

EngageNY Module 4 End-of-Module EngageNY, Assessment Module 4: Topic F (assesses Topic F)

Go Math! Chapter 7 Mid-Chapter Checkpoint and Summative Assessment

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Grade 5: Numbers and Operations - Fractions

Content Standards

Standards: What is the essence of this domain?

Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address this standard What materials Impact on Go adequately, by addressing procedural, conceptual, and can we use to fill Math! assessments application skills equally? If the gap? not, what are the gaps? (*KEY)

Go Math! Assessments

EngageNY Module 4 Mid-Module Assessment (assesses Topic D) 5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 32

Apply and extend previous understandings of multiplication and division to multiply and Chapter 7, Lesson: 7.9 divide fractions (5.NF.3, 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

Needs more modeling

EngageNY, EngageNY Module Module 4: Topics Go Math! Chapter 4 End-of-Module D, E, F Assessment 7 Summative (assesses Topics Assessment EngageNY, E & F) Module 5: Topic C EngageNY Module 5 End-of-Module Assessment (assesses Topic C)

5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1

Apply and extend previous understandings of multiplication Chapter 8, Lessons: 8.1, 8.2, and division to multiply and divide fractions (5.NF.3, 8.4, 8.5 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

5.NF.7a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

Apply and extend previous understandings of multiplication and division to multiply and Chapter 8, Lessons: 8.1 divide fractions (5.NF.3, 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

Needs more modeling

EngageNY Module 4 End-of-Module EngageNY, Assessment Module 4: Topic G (assesses Topic G)

Go Math! Chapter 8 Mid-Chapter Checkpoint and Summative Assessment

Needs more modeling

EngageNY Module 4 End-of-Module Go Math! Chapter EngageNY Module Assessment 8 Mid-Chapter 4: Topic G (assesses Topic Checkpoint G)

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Grade 5: Numbers and Operations - Fractions

Content Standards

Standards: What is the essence of this domain?

Where does our current curriculum (Go Math!) address the standards?

5.NF.7b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

Apply and extend previous understandings of multiplication and division to multiply and Chapter 8, Lessons: 8.1, 8.2 divide fractions (5.NF.3, 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

5.NF.7c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Apply and extend previous understandings of multiplication and division to multiply and Chapter 8, Lessons: 8.4, 8.5 divide fractions (5.NF.3, 5.NF.4a,b, 5.NF.5, 5.NF.6, 5.NF.7a,b,c).

Does our current curriculum address this standard What materials Impact on Go adequately, by addressing procedural, conceptual, and can we use to fill Math! assessments application skills equally? If the gap? not, what are the gaps? (*KEY)

Go Math! Assessments

Needs more modeling

EngageNY Module 4 End-of-Module Go Math! Chapter EngageNY Module Assessment 8 Mid-Chapter 4: Topic G (assesses Topic Checkpoint G)

Needs more modeling

EngageNY Module 4 End-of-Module Go Math! Chapter EngageNY Module Assessment 8 Summative 4: Topic G (assesses Topic Assessment G)

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Grade 5: Measurement and Data

Content Standards

5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Standards: What is the essence of this domain?

Convert like measurement units within a given measurement system (5.MD.1).

5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line Represent and interpret plots. For example, given different data (5.MD.2). measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address this standard What materials can adequately, by addressing we use to fill the procedural, conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY)

Chapter 10, Lessons 10.1, Needs more manipulatives to 10.2, 10.3, 10.4, 10.5, 10.6, model relationships 10.7

Chapter 9, Lessons: 9.1

Impact on Go Math! assessments

EngageNY Module 1 Mid-Module EngageNY, Module 1: Assessment Topic A (assesses Topic A) EngageNY Module 4: Topic E

EngageNY Module 4 End-of-Module Assessment (assesses Topic E)

Go Math! Assessments

Go Math! Chapter 10 Mid-Chapter Checkpoint and Summative Assessment

Standard addressed adequately

EngageNY Module 4 EngageNY, Module 4: Mid-Module Topic A Assessment (assesses Topic A)

Go Math! Chapter 9 Mid-Chapter Checkpoint and Summative Assessment

Standard addressed adequately

EngageNY Module 5 Mid-Module EngageNY, Module 5: Assessment Topics A, B (assesses Topics A & B)

Go Math! Chapter 11 Mid-Chapter Checkpoint and Summative Assessment

5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

Geometric measurement: understand concepts of volume and relate volume to Chapter 11, Lessons: 11.5 multiplication and to addition (5.MD.3a,b, 5.MD.4, 5.MD.5a,b,c).

5.MD.3a. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

Geometric measurement: understand concepts of volume and relate volume to Chapter 11, Lessons: 11.6 Standard addressed adequately multiplication and to addition (5.MD.3a,b, 5.MD.4, 5.MD.5a,b,c).

EngageNY Module 5 Mid-Module Go Math! Chapter 11 EngageNY, Module 5: Assessment Summative Topics A, B (assesses Topics A & Assessment B)

5.MD.3b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Geometric measurement: understand concepts of volume and relate volume to Chapter 11, Lessons: 11.7 Standard addressed adequately multiplication and to addition (5.MD.3a,b, 5.MD.4, 5.MD.5a,b,c).

EngageNY Module 5 Mid-Module Go Math! Chapter 11 EngageNY, Module 5: Assessment Summative Topics A, B (assesses Topics A & Assessment B)

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Grade 5: Measurement and Data Where does our current curriculum (Go Math!) address the standards?

Does our current curriculum address this standard What materials can adequately, by addressing we use to fill the procedural, conceptual, and gap? application skills equally? If not, what are the gaps? (*KEY)

Content Standards

Standards: What is the essence of this domain?

5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Geometric measurement: understand concepts of Chapter 11, Lessons: 11.7, volume and relate volume to Standard addressed adequately 11.8 multiplication and to addition (5.MD.3a,b,

EngageNY Module 5 EngageNY, Module 5: Mid-Module Topic A Assessment (assesses Topic A)

Go Math! Chapter 11 Summative Assessment

5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Geometric measurement: understand concepts of volume and relate volume to Chapter 11, Lessons: 11.9, Standard addressed adequately 11.10, 11.11, 11.12 multiplication and to addition (5.MD.3a,b, 5.MD.4, 5.MD.5a,b,c).

EngageNY Module 5 EngageNY, Module 5: Mid-Module Assessment Topics B (assesses Topic B)

Go Math! Chapter 11 Summative Assessment

5.MD.5a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

Geometric measurement: understand concepts of volume and relate volume to Chapter 11, Lessons: 11.9 Standard addressed adequately multiplication and to addition (5.MD.3a,b, 5.MD.4, 5.MD.5a,b,c).

EngageNY Module 5 EngageNY, Module 5: Mid-Module Topic B Assessment (assesses Topic B)

Go Math! Chapter 11 Summative Assessment

5.MD.5b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

Geometric measurement: understand concepts of volume and relate volume to Chapter 11, Lessons: multiplication and to 11.10, 11.11 addition (5.MD.3a,b, 5.MD.4, 5.MD.5a,b,c).

Standard addressed adequately

EngageNY Module 5 EngageNY, Module 5: Mid-Module Topic B Assessment (assesses Topic B)

Go Math! Chapter 11 Summative Assessment

5.MD.5c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems.

Geometric measurement: understand concepts of volume and relate volume to Chapter 11, Lessons: multiplication and to 11.12 addition (5.MD.3a,b, 5.MD.4, 5.MD.5a,b,c).

Standard addressed adequately

EngageNY Module 5 EngageNY, Module 5: Mid-Module Topic B Assessment (assesses Topic B)

Go Math! Chapter 11 Summative Assessment

Impact on Go Math! assessments

Go Math! Assessments

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Grade 5: Geometry

Content Standards

Standards: What is the essence of this domain?

Does our current curriculum address this standard adequately, by Where does our current addressing procedural, What materials can Impact on Go Math! curriculum (Go Math!) conceptual, and we use to fill the gap? assessments address the standards? application skills equally? If not, what are the gaps? (*KEY)

5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, yaxis and y-coordinate).

Graph points on the coordinate plane to solve Chapter 9, Lessons: 9.2 real-world and mathematical problems (5.G.1, 5.G.2)

5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Graph points on the coordinate plane to solve Chapter 9, Lessons: 9.3, real-world and mathematical 9.4 problems (5.G.1, 5.G.2)

5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

Classify two-dimensional figures into categories based Chapter 11, Lessons: on their properties (5.G.3, 11.1, 11.2, 11.4 5.G.4)

5.G.4 Classify two-dimensional figures in a hierarchy based on properties.

Classify two-dimensional figures into categories based Chapter 11, Lessons: on their properties (5.G.3, 11.2, 11.3 5.G.4)

Standard addressed adequately

Needs composition and decomposition of shapes

Needs composition and decomposition of shapes

Go Math! Assessments

EngageNY, Module 6: Topics A, B, C

EngageNY Module 6 Mid-Module Assessment (assesses Go Math! Chapter 9 Topic A & B) Mid-Chapter Checkpoint and EngageNY Module 6 Summative End-of-Module Assessment Assessment (assesses Topic C)

EngageNY, Module 6: Topics C, D

Go Math! Chapter 9 EngageNY Module 6 Mid-Chapter End-of-Module Checkpoint and Assessment (assesses Summative Topic C & D) Assessment

EngageNY, Module 5: Topic D

Go Math! Chapter 11 EngageNY Module 5 Mid-Chapter End-of-Module Checkpoint and Assessment (assesses Summative Topic D) Assessment

EngageNY, Module 5: Topic D

Go Math! Chapter 11 EngageNY Module 5 Mid-Chapter End-of-Module Checkpoint and Assessment (assesses Summative Topic D) Assessment

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EngageNY – Math Key Modeling Strategies Kindergarten Module 1 (Counting and Cardinality) Five Dot Mat Five Frames Ten Frames Number Path Number Cards Dot Cards Rekenrek (abacus) Problem Sets Configurations: linear, array, circular, scattered Module 2 (Geometry) Two-dimensional shapes: circle, hexagon, rectangle, square, and triangle Three-dimensional shapes: cone, sphere, cylinder, and cube Module 3 (Measurement and Data) Listen, Draw Linking Cubes Centimeter Cubes Dot Cards Pattern Blocks Visualize the Number in Set A and Set B Balance Scales Module 4 (Operations and Algebraic Thinking) Dot Cards Linking Cubes Number Bonds Number Path Number Towers Sets of Objects

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Showing fingers the Math way Say Ten Way Rekenrek (abacus) Listen, Draw Story Situations Pictorials Module 5 (Counting and Cardinality) (Numbers & Operations in Base Ten) Number Cards Dot Cards Number Tower Number Bonds Ten Frames Rekenrek Hide Zero Cards Linking Cubes Patterns Configurations: linear, array, circular, scattered Say Ten Way Module 6 (Counting and Cardinality) (Geometry) Pattern Blocks Two – dimensional shapes: circle, hexagon, rectangle, square, and triangle Three – dimensional shapes: cone, sphere, cylinder, and cube

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EngageNY – Math Key Modeling Strategies Grade 1 Module 1 (Sums and Differences to 10) Number bonds Addition chart Rekenrek Counters Number path 5-Group cards Hide Zero cards Module 2 (Introduction to Place Value Through Addition and Subtraction Within 20) 5-Group formations (5-groups (and 5-group cards), 5-group rows, 5-group column) Hide Zero cards Number bonds Number path Rekenrek

Module 3 (Ordering and Comparing Length Measurements as Numbers) Centimeter cubes Centimeter rulers String lengths of about 25 centimeters Module 4 (Place Value, Comparison, Addition and Subtraction to 40) Arrow notation Comparison symbols: >, <, = Dime Hide Zero cards Hundred chart Number bond Penny Place Value Chart Quick Ten Rekenrek Tape Diagram

Module 5 (Identifying, Composing and Partitioning Shapes) Pattern blocks Square tiles Straws Student clocks Three-dimensional shape models including cube, cone, cylinder, rectangular prism, and sphere Module 6 (Place Value, Comparison, Addition and Subtraction to 100) 100-bead Rekenrek Tape diagram

EngageNY – Math Key Modeling Strategies Grade 2 Module 1 (Sums and Differences to 20) Dice Hide Zero cards Linking cubes Personal white boards Rekenrek Ten-frame Two-sided counters for each student Module 2 (Addition and Subtraction of Length Units) Manipulatives that are 1 centimeter long Centimeter ruler for each student Paper meter strips for each student Centimeter ruler Meter stick Module 3 (Place Value, Counting, and Comparison of Numbers to 1,000) “Clock” number line with corresponding analog template Dice Base Ten Blocks (Hundreds, Tens and Ones) Personal boards and markers Place Value Chart with Headings Place value charts black line master Place value charts and mats Place value cards showing numbers 1–5, 10–50, and 100—1,000 Place value disks Play money: $1, $5, $10, and $100 bills; Pennies and Dimes Rubber bands Module 4 (Addition and Subtraction Within 200 with Word Problems to 100) Chip model Hide Zero cards Place value charts and mats Place value disk sets

Module 5 (Addition and Subtraction Within 1,000 with Word Problems to 100) Number Cards Dot Cards Number Tower Number Bonds Ten Frames Rekenrek Hide Zero Cards Linking Cubes Patterns Configurations: linear, array, circular, scattered Say Ten Way Module 6 (Foundations of Multiplication and Division) Counters Number path Rectangular array Square tiles Module 7 (Problem Solving with Length, Money, and Data) Bar graph Centimeter Ruler Inch ruler Line plot Meter stick Money (i.e., dollars, coins) Number bond Number line Picture graph Table Tape diagram Yardstick Module 8 (Time, Shapes, and Fractions as Equal Parts of Shapes) Cubes Geoboards Large instructional-geared clock Pattern blocks Rulers

Square tiles Student clocks

EngageNY - Math Key Modeling Strategies Grade 3

Modules 1, 3 and 4: Multiplication and Division Strategies and Application Number bonds Tape Diagrams Arrays Area Models Module 2: Addition and Subtraction via Place Value Strategies and Measurement Application Place Value Charts Number Disks Hide Zero cards Module 5: Fractions as Numbers on the Number Line Tape Diagram with the Number Line; Number Bonds Fraction Strips Rectangular Fraction Models Module 6: Collecting and Displaying Data Relate tape diagrams to bar graphs Application of partitioning a whole into equal parts, leading to the creation of a ruler Module 7: Geometry and Measurement Word Problems Tape Diagrams Tangrams (used to explore composing and decomposing shapes) Tesselations (used to explore perimeter) Tetrominoes (used to explore composing and decomposing shapes) Line Plots

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EngageNY – Math Key Modeling Strategies Grade 4 Module 1 (Place Value, Rounding, and Algorithms for Addition and Subtraction) Number lines (vertical to represent rounding up and rounding down) Personal white boards Place value cards Place value chart Place value disks Tape diagrams Module 2 (Unit Conversions and Problem Solving with Metric Measurement) Beakers or liter container Number line Ruler Meter stick Measuring tape Scale Weights Tape diagrams Module 3 (Multi-Digit Multiplication and Division) Area model Place value disks Place value mats Module 4 (Place Value, Comparison, Addition and Subtraction to 40) Arrow notation Comparison symbols: >, <, = Dime Hide Zero cards Hundred chart Number bond Penny Place Value Chart Quick Ten

Rekenrek Tape Diagram

Module 5 (Identifying, Composing and Partitioning Shapes) Pattern blocks Square tiles Straws Student clocks Three-dimensional shape models including cube, cone, cylinder, rectangular prism, and sphere Module 6 (Place Value, Comparison, Addition and Subtraction to 100) 100-bead Rekenrek Tape diagram

EngageNY - Math Key Modeling Strategies Grade 5 Module 1 (Place value and decimal fractions) Place value charts Place Value disks Number lines and a large one for the back wall of the classroom Module 2 (Multi-digit whole number and decimal fraction operations) Area models (an array) Number bond Number disks Module 3 (Addition and subtraction of fractions) Paper strips (for modeling equivalence) Number line Rectangular fraction model Fraction strips Bar diagrams Module 4 (Multiplication and division of fractions and decimal fractions) Area models Number lines Tape diagrams Module 5 (Addition and multiplication with volume and area) Ruler Protractor Set square Module 6 (Problem solving with the coordinate plane) Ruler Protractor Set square Tape diagrams

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