Eureka Math Grades 6-12 for New York City (Duma)

TABLE OF CONTENTS PAGE

2 Introduction to Eureka Math 4 Educator & Family Support Resources 5 EngageNY Math vs. Eureka Math 6 Eureka Math Models 8 Frequently Asked Questions 10 Supporting Differentiated Instruction 12 Affirm: Digital Assessment & Practice Tool 13 Professional Development 15 Advice from Eureka Math Champions 17 New York State Standards Alignment Study 18 Lesson Structures 20 Curriculum Map 21 Curriculum Reviewer Guide

FOR NEW YORK CITY

A New Curriculum for a New Day

Eureka Math is Diffe ent Created by the nonprofit Great Minds®, Eureka Math® helps teachers deliver unparalleled math instruction that builds students deep understanding and fluency in math. Crafted by teachers and math scholars, the curriculum carefully sequences the mathematical progressions to maximize coherence from grade PK through 12 — a principle tested and proven to be essential in student mastery of math.

Teachers and students using Eureka Math find the trademark “Aha!” Eureka moments to be a source of joy and inspiration, lesson after lesson, year after year.

Eureka Math is EngageNY Math Eureka Math was awarded grant to develop EngageNY Math in 2012. The curriculum has since become a top-rated and widely used math curriculum nationally. The curriculum is available for free download on the Great Minds website, along with essential support resources suitable for parents and anyone teaching EngageNY Math or Eureka Math.

National Impact According to the RAND Corporation, over 50% of U.S. school teachers accessed Eureka Math or the version of the curriculum found on the EngageNY website. Additionally, Eureka Math is the only curriculum found by EdReports.org to align fully with the Common Core State Standards for Mathematics for all grades, K–8.

Schools and districts nationwide are seeing growth and impressive test scores after using Eureka Math. See their stories and data at greatminds.org/data.

Full Suite of Resources The teacher-writers who created the curriculum have developed a number of essential resources, available only from Great Minds, including the following: • Printed Material in English and Spanish • Digital Resources • Professional Development • Classroom Tools & Manipulatives • Teacher Support Materials • Parent Resources

The most widely used math curriculum in America.

Source: RAND Corporation

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844.853.1010 | greatminds.org/emnyc

The entire PK–12 Eureka Math curriculum is available as free PDF downloads at greatminds.org/math

Print Materials Student Materials

• Succeed Book (K–5)

Teacher Editions (PK–12)

(Available in English & Spanish)

Features additional problem sets ideal for

Full-color bound books with complete lesson

homework and Homework Helpers that

plans, all student-facing materials, and

A student’s in-class companion that

illustrate how similar problems are solved.

answer keys.

includes Application Problems, Problem

• Learn, Practice, Succeed Book (6–8)

Sets, Exit Tickets, and Templates.

All three books are combined into one

• Practice Book (K-5)

book per module for Grades 6-8. Currently

• Learn Book (K–5)

Features fluency activities, including

only available in English.

Sprints, that will build on newly acquired

• Student Editions (9–12)

skills and reinforce previous knowledge.

Student workbooks organized by module.

Available in Spanish Grades K-8.

Alternative material configurations available to meet your specific needs.

Tools & Training Eureka Digital Suite (PK–12)

Affirm®

Manipulatives (PK–12)

The suite combines two essential online

The Eureka Math digital assessment and

Eureka Math writers have curated a

resources:

practice tool that provides educators with

collection of classroom materials and tools

formative items and analytics to track

to develop student understanding, and

student progress and identify areas of need.

maximize coherence between grades. These

• The Navigator: A digital version of the complete PK-12 curriculum complete with embedded videos, organized by grade level.

materials can be purchased in grade-level Professional Development

kits or a la carte from Didax at

To support new and sustaining

eurekamath.didax.com.

• Teach Eureka Video Series: An

implementation of Eureka Math, Great Minds

on-demand video series, hosted by

offers regional PD Institutes. These Institutes

Webinar Library

the curriculum authors, featuring

bring educators together to strengthen their

A collection of free reoccurring and on-

explanations of concepts and

understanding of Eureka Math. To learn

demand webinars to assist teachers with

instructional strategies.

more, visit eurmath.link/PD.

pacing, RTI strategies, social-emotional learning, Guided Math, and more.

Support Homework Helpers (K–12) These grade-level books provide step-bystep explanations of how to work problems similar to those found in every homework assignment in the curriculum. Perfect for parents who want to support their child’s learning. Visit eurmath.link/helpers to purchase.

Overview Videos

Math Night Materials

These videos orient teachers and

These materials include a letter, video,

administrators to the structure and

and handouts for parents that explain how

components of each grade-band of the

Eureka Math is different and why it works.

curriculum.

Parent Tip Sheets (K–8) Teacher Resource Pack

These topic-level tip sheets for parents

Essential resources for educators including

explain math strategies and models, and

the following:

provide key vocabulary, sample problems,

Study Guides (PK–12)

• Pacing and Preparation Guides

These grade-level guides provide an

• Curriculum Overview

overview of the key components of the

• Curriculum Maps

curriculum. Available from Didax at

• Standards Checklists

and links to useful video. Also available in Spanish.

Available free at greatminds.org/math

eurekamath.didax.com.

EVERY CHILD IS CAPABLE OF GREATNESS greatminds.org

3 © Great Minds 2019

FOR NEW YORK CITY

Educator Resources & Support Teacher Resource Pack eurmath.link/resource-pack

Eureka Math Blog eurmath.link/blog

Includes: Pacing & Preparation Guide, Curriculum Maps, Curriculum

Implementation advice on a variety of topics directly from the writers of

Overview, Materials Lists, Standards Checklists.

Eureka Math.

Affirm® — The Eureka Math Digital Assessment & Practice Tool greatminds.org/digital-assessment

Case Studies And Q&As eurmath.link/champions

Digital assessment and practice tool that includes a database of

Hear from schools and districts across the nation about their

formative items and analytics tools designed to help teachers track

implementation of Eureka Math.

student progress and identify areas of need.

Data greatminds.org/data

Eureka Digital Suite eurmath.link/digital-suite

See test scores and stories of student achievement from various Eureka Math schools and districts.

An easy to navigate, digital version of the PreK-12 curriculum, coupled with our on-demand PD video series (18 one-hour sessions per grade) hosted by the curriculum

Webinar Library eurmath.link/webinars

Online Communities eurmath.link/social

A collection of free reoccurring and on-demand webinars to assist

Join our online communities on social media (Facebook, Twitter,

Math, and more.

with pacing, RTI strategies, social-emotional learning, Guided

Pinterest) to connect with other educators, exchange resources, discuss and best practices.

Parent Resources & Support Parent Tip Sheets eurmath.link/tip-sheets | eurmath.link/consejos

Grade Roadmaps eurmath.link/roadmaps | eurmath.link/span-roadmaps

Free, topic-level tip sheets, organized by grade (K-8). Tip Sheets are

A year-long roadmap of what your child will in the coming year.

arranged in the same sequence as the student homework. Also availble

Available for grades K-7, in English and Spanish.

in Spanish (Consejos para padres).

Math Night Resources eurmath.link/math-night

Homework Helpers eurmath.link/hwh

Handouts and videos that introduce parents to the curriculum and

A grade-level resource (K-12) that provides step-by-step explainations

provide them with an overview of parent resources available to

of how to work problems found in student homework. Available

support them.

in English digitally and in print (K-12). Digital Spanish versions available (K-8).

Professional Development Upcoming Events eurmath.link/upcoming-pd Eureka Math hosts PD institutes across the country throughout the school year designed to equip instructional leaders with the tools they need to support both new and continuing use of Eureka Math.

EVERY CHILD IS CAPABLE OF GREATNESS greatminds.org/connecticut

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© Great Minds 2019

Did You Know?

Eureka Math® is the updated, revised version of EngageNY Math with additional resources for teachers, students, and parents.

What’s the difference?

✓ ✓ ✓ ✓ ✓ ✓ ✓

Same PreK-12 Math Curriculum Print Materials (English & Spanish) In-Depth Professional Development Manipulatives Digital Assessments Parent Resources Pacing & Preparation Guides And more!

To learn more, scan QR code or go to: greatminds.org/engage-ny

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✕ ✕ ✕ ✕ ✕ ✕ ✕

Giving Students a Choice of Tools to Solve GivingProblems Students a Choice of Tools to Solve Math

MathGiving Problems Students a Choice of Tools to Solve Math Problems Giving New York City achildChoice At Great Minds , we receive many questions from Students parents asking why their needs to learn more ÂŽ

math and multiple strategies for solving problems. Some parents suggest that simply of conceptual Tools to Solve Math Problems learning the traditional method for solving a math problem (e.g., 2 + 2 = 4 or 6 Ă— 8 = 48) is enough.

At Great Minds , we receive many questions from parents asking why their child needs to learn more conceptual math and multiple strategies for solving problems. Some parents suggest that simply Great MindsŽmethod , we receive many questions from parents their needs to learn more learningAt the traditional for solving a math problem (e.g.,asking 2 + 2 =why 4 or 6 × child 8 = 48) is enough. conceptual math and multiple strategies for solving problems. Some parents suggest that simply We agreelearning that students need method to learnfor traditional methods for(e.g., computation. the best tool the traditional solving a math problem 2 + 2 = 4 orOften, 6 × 8 =they’re 48) is enough.

We agree that students need to learn traditional methods for computation. Often, they’re the best tool for the job. for the job.

At Great MindsŽ, we manystudents questionsneed from to parents why their child needs to learn more Often, conceptual math and multiple Wereceive agree that learn asking traditional methods for computation. they’re the best tool for the job. strategies for solving problems.

Some parents suggest that simply learning the traditional method for solving a math problem However, sometimesstudents students need more options—they tools their toolbox.

If students However, sometimes need more options—they needneed more more tools in theirintoolbox.

If students (e.g., 2 OHDUQ PXOWLSOH PDWK VWUDWHJLHV QRW RQO\ FDQ WKH\ VROYH PRUH NLQGV RI SUREOHPV PRUH ḢFLHQWO\ EXW + 2 = 4 or 6 × 8 = 48) is enough.

OHDUQ PXOWLSOH PDWK VWUDWHJLHV QRW RQO\ FDQ WKH\ VROYH PRUH NLQGV RI SUREOHPV PRUH ḢFLHQWO\ EXW However, sometimes students need more options—they need more tools in their toolbox. If students they gain aadeeper deeperunderstanding understanding of mathematics and to how usedaily it inlife. daily life. they also alsoOHDUQ PXOWLSOH PDWK VWUDWHJLHV QRW RQO\ FDQ WKH\ VROYH PRUH NLQGV RI SUREOHPV PRUH ḢFLHQWO\ EXW gain of mathematics and how useto it in Ž

We agree that students need to learn traditional methods for computation. Often, they’re the best tool for the job. However, sometimes

they also gain a need deeper understanding of mathematics how to use it instrategies, daily life.not only can they solve more students need more options—they more tools in their toolbox.

If studentsand learn multiple math

Consider the examples.

Consider the following followingthree three examples.

kinds of problems more efficiently, but they also gain a deeper understanding of mathematics and how to use it in daily life.

Consider the following three examples.

Consider the following three examples.

Number Bonds

NUMBER BONDS NUMBER BONDS NUMBER BONDS Add 998 and 337.

Add 998 Add 998and and337.

337.

Add 998 To andsolve 337.a problem such as 998 + 337 with a traditional method, students must learn a complex To solve asteps. problem suchnumber as 998 + 337 with athis traditional students must learn a complex solve a problem such as bonds 998 + 337 with a traditional method, students must learn a complex series ofTo But using makes problem method, simple.

To solve aseries problemof such as 998 + 337 with a traditional method, students must learn a complex series of steps.

But using number bonds series of But steps.

But using number bonds makes thisproblem problem simple. steps. using number bonds makes this simple. makes this problem simple.

First, students First, students learn students tolearn break First, students to First, learn to break numbers into breaklearn numbers small, tointo break numbers into small, manageable manageable units.into numbers small, manageable units. small, manageable units.

Then, cansee Then,students students can Then, students see that 7 + 8 is the can that 7 + 8 isstudents the same Then, can see that 7 + same as 10 + 5. 8 is the as see 10same + 5. that 7 + 8 is as 10 + 5. the

same as 10 + 5.

units.

Once students understand the concept of number bonds and how to use them in computation,

Once the students understand the concept ofuse number bonds and how tocan use them solve in computation, Once students understand concept number bonds and how to them computation, a more they can quickly solve aofmore complex problem, such asin998 + 337. Asthey above,quickly the first step is tocomplex problem, they can quickly solve a more complex problem, such as 998 + 337. As above, the first step is to make 998 a more manageable number. Notice that 998 is close to 1,000; we just need to add 2.

We can get the can 2can from 337 by using a number 337 number – 2 = 335.

We get the 2 from bybond: using bond: bond: 337 – 337 2as = 335. they quickly solve more complex such 998 337. As above, the first step is to We can get the 337 2 afrom 337 byausing aproblem, number – 2 = +335.

such as 998 + 337.students As above, the first step is to the make 998 a Notice more number.

Notice that to 998 is close to 1,000; we 2. just need to add 2.

Once understand concept ofmanageable number how them in add computation, make 998 a more manageable number. that 998 bonds is closeand to 1,000; weuse just need to

make 998 a more manageable number. Notice that 998 is close to 1,000; we just need to add 2.

We can get the 2 from 337 by using a number bond: 337 – 2 = 335.

The twoThe numbers are noware 1,000 335, even young students can quickly add to get two numbers nowand 1,000 andwhich 335, which even young students can quickly add to get 1,335, the same sum as 998 + 337.

This method is faster, and the student gains practice in The two numbers are1,335, now 1,000 and 335, which even+young students can quickly add and to get 1,335, the same sum as 998 +in 337. This method is the same sum as 998 337. This method is faster, the student gains practice math. conceptual math. faster, and conceptual the student gains practice in conceptual math.

The two numbers are now 1,000 and 335, which even young students can quickly add to get 1,335, the same sum as 998 + 337. This method is faster, and the student gainswww.Eureka.Support practice in 2017 Great Minds Š 2017 GreatŠMinds www.Eureka.Support conceptual math.

www.Eureka.Support

Š 2017 Great Minds

EVERY CHILD IS CAPABLE OF GREATNESS greatminds.org

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Š Great Minds 2019

Visualizing Fractions

Tape Diagrams

TAPE DIAGRAMS

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Learn More

www.Eureka.Support

FREQUENTLY ASKED QUESTIONS How do the materials support ELLs in mastering the content and rigor of the FREQUENTLY ASKED QUESTIONS

Supporting All New York City Students standards?

Eureka Math uses a deliberate progression from concrete to pictorial to abstract representations. The

Frequently Asked Questions How do the materials ELLs in mastering thelessons content rigorand of across the grade progression is noticeable support within a given lesson, across multiple andand modules, levels. Further, the use of concrete and pictorial representations are inextricably linked with abstract standards?

representations. For example, a student working on a problem involving several teddy bears may ma-

How do the materials support ELLs in“7mastering the and nipulate bear figures and then write bears 5 bears +to2content bears.” The sentence the student writes Eureka Math uses a deliberate progression from=concrete pictorial to abstract representations.

The is an abstract representation.

On the spectrum of abstraction, it is less abstract than the “7 = 5 + 2” that progression is noticeable within a given lesson, across multiple lessons and modules, and across grade rigor of the standards?

the students willuse progress toward over the course of the year. are It isinextricably also important to recognize that not levels.

Further, the of concrete and pictorial representations linked with abstract

Appropriate ELLrepresentations. instruction corresponds to strong math teaching; begins with every lesson moves students concrete toitpictorial tocomprehensible abstract.

The first lesson a sequence Fordirectly example, a from student working on a problem involving several teddy in bears may ma-may

nipulate bear figures and then write “7afew bears =5 bearsstudents + 2 bears.”

Thepictorial sentence the student writes input, often at the concrete/pictorial level.

Eureka Math uses deliberate progression fromtoward concrete to use concrete objects, then the next may move representations.

is an abstract representation.

On the spectrum of abstraction, is less abstract than the “7 = 5 + 2” that pictorial to abstract representations.

The progression is noticeable within a given lesson,itacross multiple theOnce students will progress toward over the course ofof the year.

It is also important to recognize that not students have had an appropriate amount time working in the lessons and modules, and across grade levels.

Further, the use of concrete and pictorial representations are every lesson moves students from concrete to pictorial to aFor abstract.

Thealgofirst lesson in a sequence may pictorial stage they are moved into the abstract work. example, inextricably linked with abstract representations.

For example, a student working on problem involving userithms, concrete the next may move= 5students pictorial byobjects, definition, are abstract procedures.

These are onlyrepresentations. several teddy bears may manipulate bearthen figures and thenfew write “7 bears bears +procedures 2 toward bears.” The sentence truly understood when students are provided the opportunity to work in the the student writes is an abstract representation. On the spectrum of abstraction, it is less abstract than the Once students have had an appropriate amount of time working in the concrete and pictorial stages first.

When students forget part of the proce“7 = 5 + 2” that the students will progress toward over the course of the year. It is also important to recognize pictorial they are moved intotake the abstract work. dure ofstage the algorithm, they can a step back intoFor theexample, pictorial algostage to rethat not every lesson moves students from concrete to pictorial to abstract. The first lesson in a sequence may rithms, by definition, are abstract procedures.

These procedures are algorithm. only call how they performed a computation, then relate it back to the use concrete objects, then the next few may move students toward pictorial representations. truly understood when students are provided the opportunity to work in the Noticeand thepictorial deliberate use of “bears” in students the previous example.

Theproceunit form gives all students, concrete stages When forget part ofare the Once students have had an appropriate amount offirst. time working in the pictorial stage they moved into the including ELLs, the opportunity to access new, more challenging concepts while using representations dure of thealgorithms, algorithm, can take a step procedures. back into the pictorial stage to reabstract work. For example, by they definition, are abstract These procedures are only truly that are familiar and comfortable.

For example, in Grade 3 a unit may have a value of 8, thus 7 such call how they performed a computation, then relate it back to the algorithm. understood when students are provided the opportunity to work in the concrete and pictorial stages first. When units is expressed as 7 eights. This system lends itself naturally to the distributive property. In terms students forget part the procedure of the algorithm, can take a step back the The pictorial stage to gives Notice the deliberate of “bears” in the previous example. unit form all students, ofofmultiplication atuse Grade 3: 7they eights multiplied by 3into eights is the unit form of 7(8)×3(8), which can be recall how they performed a computation, then relate it back to the algorithm. including ELLs, the opportunity to access new, more challenging concepts while using representations expressed as (7+3)8 or 10 eights. that are familiar and comfortable. For example, in Grade 3 a unit may have a value of 8, thus 7 such Notice the deliberate use of “bears” in the previous example. unit form gives all students, including ELLs, Consider the implications such aThe system; 7 eighths as the unit form of the property. In terms units is expressed as 7 eights.ofThis system lends itself naturally to the distributive the opportunity to access new,7/8 more challenging concepts while using representations that are familiar and same fraction can give rise to why adding numerators of fractions with the of multiplication at Grade 3: 7 eights multiplied by 3 eights is the unit form of 7(8)×3(8), which can be comfortable. Forexpressed example, Grade 3why a unit may have a value of 8,that thus do 7 such is expressed 7 eights. unit isinok and numerators notunits have the sameasunit is not ok. as (7+3)8 oradding 10 eights.

This system lends itself naturally to theitdistributive property.

In the terms of multiplication at Grade7x 3:is 7 eights Further, when is understood that unit in the expression x, it makes Consider the ofwhich suchcan a7x system; eighths as the formthe of the multiplied by 3 eights is thethat unit implications form of 7(8)×3(8), be expressed as (7+3)8 or 10unit eights. sense combining the terms and 3x7 is appropriate, because unit is the fraction 7/8 can give rise to why adding numerators of fractions with the same, as opposed to the common mistake of combining 7x and 3 or 7xsame and 3x^2.

Consider the implications of and such why a system; 7 eighths as the unitthat formdo of the 7/8same can give riseistonot whyok. unit is ok adding numerators notfraction have the unit adding numerators of fractions with theunderstood same unit is ok andthe whyunit adding numerators that do not have the Further, when itELL is that indirectly the expression 7x is x, it makes Appropriate instruction corresponds to strong math teaching; it same unit is not sense ok. begins Further, when it is understood that the unit in the expression 7x is x, it makes sense that thatwith combining the terms input, 7x andoften 3x is at appropriate, because thelevel. unit is the comprehensible the concrete/pictorial same, to the common mistake of combining 7x and 3 or 7x and 3x^2. combining the terms 7x as andopposed 3x is appropriate, because the unit is the same, as opposed to the common mistake of combining 7x and 3 or 7x and 3x^2.for opportunities to engage students in dynamic stanELL instruction calls Appropriate ELL instructionIn corresponds directly to strong math teaching; itinfordards-based instruction.

Eureka Math new terminology is introduced ELL instruction calls for opportunities to engagecontext, students inoften dynamic standards-based instruction.

In Eureka begins with input,within at the concrete/pictorial level. mally in acomprehensible meaningful powerful experiences, and then clarified Math new terminology is introduced informally meaningful context,lesson within powerful and thenon the within the same lessoninora in a subsequent or gradeexperiences, level, depending clarified within the same lesson or incalls a appropriateness subsequent lesson or level, depending onThis thedynamic developmental ELL instruction for opportunities engage students in standevelopmental ofgrade a to formal definition. consolidates instruction.

In Eureka newhave terminology is opportunities introduced appropriatenessdards-based of a formal definition.

Thislearning consolidates andMath formalizes the learning after students haveinforhad and formalizes the after students had many to, hear and use the new mally in a and meaningful context, powerful experiences, and then terminology, within thewithin lesson and inthe their practice.

This is inclarified complete many opportunities to, hear useboth the new terminology, both within lesson and in their practice.

This is in alignment with best within lesson or instruction. in a subsequent lesson or grade level, depending on the practices for ELL instruction. complete alignment withthe bestsame practices for ELL developmental appropriateness of a formal definition. This consolidates and formalizes the learning after students have had many opportunities to, hear and use the new . terminology, both within the lesson and in their practice. This is in complete alignment with best © Great Minds 2017 www.Eureka-Math.org practices for ELL instruction.

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© Great Minds 2017

8 © Great Minds 2019

www.Eureka-Math.org

Where can you find caffold ?

Where can you find scaffolds?>

The scaffolds integrated into A Story of Units (UDL Margin Boxes), A Story of Ratios (Scaffolding MarginA Boxes) and Story ofisFunctions (Scaffolding Also within Story ofAUnits, Universal Design

Margin Boxes) for giveLearning alternatives(UDL) for howboxes, studentsand access information well in A Story of as Ratios as express andand demonstrate learning. Strategically placed margin A Story their of Functions is “Scaffolding” boxes.

notes are provided within eachoffer lessonpowerful elaborating on the use of specific These boxes scaffolds for all learnscaffolds at applicable times. They address many needsof presented by ers (including ELLs) at the point instruction

English language learners, students with disabilities, performing rather than disconnected from students the lesson in a above grade level, and students performing separate teacher’s guide.below grade level.

This method of providing scaffolds discourages the too-easy mistake of

This method of providing scaffolds discourages the too-easy mistake of treating ELL students as unthe curriculum encourages teaching that is responsive and sensitive in the der-performers. Rather, the curriculum encouragmoment of instruction, whichthat promotes inclusion. The presence of ELLs es teaching is responsive and sensitive in the and diverse learners in classrooms improves math instruction because the moment of instruction, which promotes inclusion. teacher must rely less on talk, and more on clear examples, peer sharing, The presence of ELLs and diverse learners in and connections between numerical andmath concrete/pictorial work. classrooms improves instruction because the teacher must rely less on talk, and more on clear examples, peer sharing, and connections between numerical and concrete/pictorial work. That said, there are boxes called out specifically for ELL students. treating students with learning differences as under-performers. Rather,

What materials are available for intervention groups?

Unless specified in individualized plans, believe it is for important for students to work with grade-level content. Here are some What materials areweavailable intervention groups? considerations:

We currently do not provide separate materials for intervention. Unless specified in individualized plans, we believe it is important for students to work with grade-level content. Here are some and/or understandings that are needed in today’s lesson. considerations: • The simple complex structure is intended to help focusopportunity on the parts that are more appropriate foridentified different student • toCustomizing fluency activities isteachers a powerful to address weaknesses in the needs. For example, when assigning Problem Set youand/or might have one group of students solve problems while another previous lesson tothe reinforce skills understandings that are needed in1-2, today’s lesson.group of students •solveThe problems 3-4, your most advanced solve 5-6. simple toand complex structure isstudents intended toproblems help teachers focus on the parts that are more appropriate for different student needs.

For example, when assigning Problem Set you might • Teacher notes boxes are found on the right-hand margins of the lessons, providing suggestions forthe scaffolding student learning. have one of students solve problems while another(UDL) group of students problems 3-4, Many of the suggestions in group our curriculum are organized

by Universal1-2, Design for Learning principles and aresolve applicable to and your most advanced solve problems 5-6. more than one population.

They address manystudents needs presented

by English language learners, students with disabilities, students Wegrade-level, also provide tips for performing teachers in thegrade-level.

Notes Boxes downwill the right-hand of the lesson performing •above and students below Teachers note that many margin of the suggestions are plans. applicable to other students and overlapping populations.

• Customizing fluency activities is a powerful opportunity to address weaknesses identified in the previous lesson to reinforce skills

Are there enrichment and supplemental materials built into the program?

Are there enrichment and supplemental materials built into the program?

Enrichment experiences are crafted within the experience of Eureka Math. The lesson sequence, and even the components within

Eureka not often offerfind supplemental or enrichment is provided each lesson, move fromMath simple currently to complex.does Teachers that the complex problems nearmaterial the end ofbeyond teachingwhat sequences (e.g.,

in the curriculum itself.

However, the lesson sequence, and even the components within each lesson, move near the end of a Sprint, K-5 Homework or 6-12 Problem Set) are useful tools for providing enrichment experiences. from simple to complex. Teachers often find that the complex problems near the end of teaching seLikewise, simple problems that near may be useful can Homework be found at the of a teaching sequence. the case quences (e.g., the endfor ofremediation a Sprint, K-5 orbeginning 6-12 Problem Set) are usefulIntools for of crafting enrichment remediation, teachers mightexperiences. find it useful to trace a sequence back into the grade level before to find their students’ last point of success. They may refer to the Module Overviews for “Foundational Standards” to find the modules that support the work at hand.

Likewise, simple problems that may be useful fortaught remediation found at the beginning of A Story of Units teachers will see that Fluency activities revisit previously material,can and be may find these quick and easy to

a teachcase of remediation, teachers might find it useful to trace a sequence back into the grade level before to find their students’ last point of success. They may refer to the Module Overviews We offer two professional development sessions that need to differentiate material: Focus Fluency and Preparation for “Foundational Standards” to address find thethe modules that support the work atonhand.

A Story of Units teachand Customization of Eureka Math Lessons. ers will see that Fluency activities revisit previously taught material, and may find these quick and easy to implement activities helpful as well. ing sequence. the implement activities helpful asIn well.

The most widely used math We offer two professional development sessions that address the need to differentiate material: Focus curriculum in America. on Fluency and Preparation and Customization 9 of Eureka Math Lessons.

Source: RAND Corporation

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Learn, Practice, Succeed, A

m

FOR NEW YORK CITY

Supporting Differentiated Instruction Learn, Practice, Succeed, Affirm® from Eureka Math® offers teachers multiple ways to differentiate instruction, provide extra practice, and assess student learning. These versatile companions to A Story of Units® (Grades K–5) guide teachers in response to intervention (RTI), provide extra practice, and inform instruction.

Learn

Problem Sets: A carefully sequenced Problem

Eureka Math Learn serves as a student’s

differentiation.

Set provides an in-class opportunity for independent work, with multiple entry points for

in-class companion where they show their thinking, share what they know, and watch their

Exit Tickets: These exercises check student

knowledge build every day.

understanding, providing the teacher with

Build Knowledge Every Day Application Problems: Problem solving in a real-world context is a daily part of Eureka Math, building student confidence and perseverance as students apply their knowledge

immediate, valuable evidence of the efficacy of that day’s instruction and informing next steps.

Templates: Learn includes templates for the pictures, reusable models, and data sets that students need for Eureka Math activities.

in new and varied ways.

Practice

Eureka Math fluency activities provide

With Practice, students build competence in

manipulatives, others use a personal whiteboard,

newly acquired skills and reinforce previously

and still others use a handout and paper-and-

learned skills in preparation for tomorrow’s lesson.

pencil format. They provide each student with the

Together, Learn and Practice provide all the print

printed fluency exercises for his or her grade level.

differentiated practice through a variety of formats—some are conducted orally, some use

materials a student uses for their core instruction.

Build Fluency

Sprints Sprint fluency activities in Eureka Math Practice

Eureka Math contains multiple daily

build speed and accuracy with already acquired

opportunities to build fluency in mathematics.

skills. Used when students are nearing optimum

Each is designed with the same notion—growing

proficiency, Sprints leverage tempo to build a low-

every student’s ability to use mathematics with

stakes adrenaline boost that increases memory

ease. Fluency experiences are generally fast-

and recall. Their intentional design makes Sprints

paced and energetic, celebrating improvement

inherently differentiated – the problems build

and focusing on recognizing patterns and

from simple to complex, with the first quadrant

connections within the material.

of problems being the simplest, and each subsequent quadrant adding complexity.

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10

© Great Minds 2019

Succeed

from simple-to-complex to naturally scaffold

Eureka Math Succeed enables students to work

models and language, ensuring that students

individually toward mastery.

feel the connections and relevance to their

Demonstrate Understanding Teachers and tutors can use Succeed books

student practice. They align with Eureka Math and use the curriculum’s mathematical

daily instruction, whether they are working on foundational skills or getting extra practice on the current topic.

from prior grade levels as curriculum-consistent tools for filling gaps in foundational knowledge.

Homework Helpers: Each problem set is

Students will thrive and progress more quickly,

accompanied by a Homework Helper, a set of

as familiar models facilitate connections to their

worked examples that illustrate how similar

current, grade-level content.

problems are solved. The examples, viewed side by side with the homework, support students

Additional Problem Sets: Ideal for Homework

as they reinforce the day’s learning. Homework

or extra practice, these additional problem sets

Helpers are also a great way to keep parents

align lesson-by-lesson with what is happening

informed about math class.

in the classroom. These problems are sequenced

Affirm

Affirm ®, Eureka Math’s digital assessment and practice tool, provides educators with a database of technology-enhanced formative items that align with the curriculum.

Affirm helps educators to better meet the needs of their students with instant grading and a number of analytics and reporting tools to help track student progress overtime.

The tool also provides students with ample opportunities for extra practice and preparation for standardized assessments. ► New Questions, including new topic level quizzes and mid- and end-of module assessments that cover DOK levels 1-3.

► Integrates with Google Classroom, Clever, Canvas, and more. ► Build and share assessments schooland share-assessments district wide. ► Instant grading to support remediation. ► Comprehensive reporting to track student progress over time and standards mastery at the student, class, school, and district levels.

LEARN MORE

greatminds.org/em-student-materials or contact your account manager.

Introducing the New Eureka Math Affirm Introducing Affirm®, the Eureka Math® digital assessment and practice tool, powered by Great Minds®. Affirm allows educators to seamlessly incorporate digital assessments into Great Minds curricula.

Affirm helps Eureka Math educators better meet the needs of their students, with instant grading and reporting to help track student progress over time.

The tool also provides students with extra practice and preparation for standardized assessments.

Fully aligned with Eureka Math’s Scope and Sequence Affirm contains Eureka Math digital topic quizzes and Mid-Module and End-of-Module Assessments for Grade 1 through Precalculus. These assessments are unique to Affirm and are not available in print or through EngageNY Math. Assessments are organized and recommended according to the Eureka Math scope and sequence. Assessments and items are searchable by grade, module, and topic.

Targeted Reporting Affirm’s reporting suite helps teachers identify weak spots and plan ways to address them. Reports highlight students’ lowest performance and proficiency across standards, linking these areas directly to the curriculum and to future assessments. In addition, the reporting feature allows teachers to compare their students’ performance with that of others in their class, school, and district and to see overall student performance at those levels as well. Reports also track student mastery of standards and student performance over time, providing ideal data for parent–teacher conferences.

Supported by the Great Minds Team For the first time ever, the Great Minds team will provide direct support to teachers using Affirm. This means enhanced professional development, faster responses, and one point of contact for sales, rostering, and support.

E V E R Y C H I L D I S C A P A B L E O F G R E A T N E S S 12

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© Great Minds 2020

PROFESSIONAL DEVELOPMENT FOR NEW YORK EDUCATORS The Eureka Math® team has crafted a multiyear sequence of professional development to support educators.

LAUNCH EUREKA MATH

FOCUS ON FLUENCY

PREPARATION & CUSTOMIZATION

MAJOR WORK OF THE GRADE BAND

SOLVING WORD PROBLEMS

ON-SITE COACHING

FOUNDATIONAL LEAD EUREKA MATH

SUSTAINING

ADMINISTRATORS

F O U N DAT I O N A L

S U S TA I N I N G

Foundational sessions prepare educators who are still relatively new to Eureka Math to implement the curriculum and customize it to meet student needs. The foundational topics (Lead, Launch, Focus on Fluency, Preparation and Customization) are recommended coursework for anyone implementing Eureka Math for the first time.

In Sustaining sessions, educators work with Eureka Math trainers to build capacity and deepen educators’ understanding of the curriculum. More seasoned practitioners who have completed some of the foundational courses can register for this advanced coursework that will strengthen their implementation of the curriculum.

EVERY CHILD IS CAPABLE OF GREATNESS greatminds.org

© 2019 Great Minds®

SESSIO ON NSS A D M IIN NIISSTTRRAT ATO ORRSS TR T RAAC C KK Lead Eureka Math

study, This two-day two-day session sessionis isdesigned designedfor foradministrators. administrators.ItItisisa abalance balanceofof experiential learning, analysis, and practice that setsthat participants up for study, experiential learning, analysis, and practice sets participants success in leading a newera implementation of the Eureka Math curriculum up for success in leading newer implementation of the Eureka Math in their districts anddistricts schools. and schools. curriculum in their

ALL GRADES

FOUN ND DAT ON NAALL TR T RAAC AT IIO C KK Launch Eureka Math

This session session prepares preparesnew newusers usersto toimplement implementEureka EurekaMath Mathsuccessfully. successfully.

Educators explore design and Educators explorethe thecurriculum curriculumtotounderstand understandhow howthe thelearning learning design lessons buildbuild a comprehensive and coherent understanding of mathematics. and lessons a comprehensive and coherent understanding of mathematics.

Focus on Fluency

Educators investigate Sprints, Educators investigatethe therole roleofoffluency fluencypractices, practices,including including Sprints, skip-counting and Participants experience, analyze, skip-counting, andother othercounting countingexercises. exercises.

Participants experience, and practice learn how to leverage powerful to build analyze, and routines practice to routines to learn how tothese leverage thesetools powerful tools and maintain students’student fluency.fluency. to build and maintain

Preparation and Customization of Eureka Math Lessons

The purpose toto empower teachers to to discern purposeof ofthis thisfull-day full-daysession sessionisisthreefold: threefold: empower teachers the decisions inherentinherent in each Eureka lesson, tolesson, study the curriculum’s discern the decisions in eachMath Eureka Math to study the teaching sequences, andsequences, to prepareand teachers to customize lessons to meet the curriculum’s teaching to prepare teachers to customize needs ofto their students. lessons meet the needs of their students.

GRADES K–5 GRADES 6–8 GRADES 9–12

S U S TA TAIIN NIIN NG G TR T RAAC C KK Major Work of the Grade Band

Educators Educators experience experiencethe thetrajectory trajectoryofoflearning learninginina agrade gradeband, band,revealing which the coherence the curriculum equippingParticipants participantsdeepen to better understand reveals theof coherence of the and curriculum. their the role of each of grade and to meet understanding the within role of that eachspan grade in to theadjust gradeinstruction band and learn student needs. strategies for adjusting instruction to meet student needs.

GRADES K–2 GRADES 3–5

Solving Word Problems

Participants byby using Participants learn learnhow howto toeffectively effectivelymodel modeland andteach teachword wordproblems problems math The study practice of solving word problems further using drawings. math drawings.

Theand study and practice of solving word problems reveals coherence of the curriculum and how this mathematical model further the reveals the coherence of the curriculum and how this mathematical supports studentstudent learninglearning across the grades. model supports across the grades.

GRADES 6–8

VIR

AN NN NIIN NG G PPD D PPLLA

Great Minds® and the Eureka Math® PD team can work with your school or district to create a PD plan that supports successful Great Minds® andofthe Eureka Math PD teamhave can questions work with or your school to create a PD plan supports your successful implementation the curriculum.

If you would likeortodistrict learn more about how to that schedule PD for your school implementation ofcontact the curriculum. you havethe questions or would like to learn more about how to schedule PD for your school or or district, please our teamIfby using information below. district, please contact our team by using the information below.

GENERAL PD PD INQUIRIES INQUIRIES GENERAL

sales@greatminds.org | 202-223-1854 pd@greatminds.org | 202-223-1854 For more information on PD, visit: greatminds.org/math/pd

WEST

Colleen Burns Regional Sales Manager colleen.burns@greatminds.org

CENTRAL

Amy Allen Regional Sales Manager amy.allen@greatminds.org

EAST

Lori Chaney Regional Sales Manager lori.chaney@greatminds.org

For more information on PD, visit greatminds.org/math/pd.

55MMStreet StreetSE, SE,Suite Suite340 340| Washington | Washington 20003| 202-223-1854 | 202-223-1854 | greatminds.org GREAT MINDS || 55 DCDC 20003 | greatminds.org

Eureka Champions Offer Practical Advice One of the unique features of our approach at Eureka Math® is the extensive peer-to-peer support that educators receive from their colleagues. Through our Facebook and Pinterest pages, blog, website, Fellows Network, and professional development sessions, we are intentionally building a community of adult learners. Educators are regularly helping educators across the country solve common implementation challenges.

To that end, we asked our Champions to share practical advice for addressing the typical classroom issues that arise every day.

Our series is organized into six parts: • What Student Learning Looks Like

• Study the Lessons in Advance

• Focus and Customize

• Be Patient, Trust the Curriculum

• Pace Your Instruction, Mastery Takes Time

• Professional Support Is Key

What Student Learning Looks Like With Eureka Math® Teachers say the most rewarding aspect of teaching Eureka Math is being able to see their sufferance in their students. They are more knowledgeable, more confident, and more engaged. They can explain big ideas and make connections among them. They are more likely to challenge themselves and their peers. And they are more likely to enjoy math, sometimes for the first time ever.

A sampling of observations follows.

Using Diffe ent Strategies to Explain Concepts

Being Confident nough to Explain the Math

Starting the Year More Prepared

The students are thinking in ways that

The main difference is students’ confidence

My 5th graders came this year knowing

I have not seen before. They are using

with math. They can tell you what they’re

number bonds, area models, and place

strategies that are appropriate for each

doing and use the right vocabulary. They feel

value charts. It kind of blew my mind. Five

individual. It is amazing to see them read,

like math thinkers and they are. They feel a

years ago when I last taught, kids just didn’t

draw, write, and explain their thoughts,

little superior. They want to explain it. They’re

know these models and resisted focusing on

strategies, and mathematical reasoning.

going home and showing their older brothers

“strategies.” They’ve now had two years of

The majority of our students are showing

and sisters and parents and grandparents

Eureka Math (fourth year of implementation

mastery with the problem sets, exit slips,

how to do math. And they have an attitude

in middle schools) and Singapore Math

and mid- and end-module assessments.

that they want to learn more.

before that. You can see the difference.

Erika Wimmer, Teacher, Spanishburg

Sally Todorow, Math Instructional Coach,

Elementary School, Mercer County, WV

Kuumba Academy Charter School,

Beth Higgins, Grade 1 Teacher, R.V. Daniels Elementary School Duval County (FL) Public Schools

E V E R Y C H I L D I S C A P A B L E O F G R E A T N E S S 15

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Each year students are so much more ready.

Wilmington, DE

© Great Minds 2019

Better Prepared We’re seeing more students coming into middle school on grade level, with a better understanding of math.

Skip Counting Leads to Multiplication My ‘Eureka Moment’ came this year while teaching multiplication. Since I began teaching seven years ago, we have always

Dawn Henry, Secondary Curriculum

taught multiplication strategies for problem

Supervisor, West Baton Rouge (LA)

solving, but when it came to memorizing

Public Schools

facts, we used drill and practice. I had tried building ice cream cones, rockets, stickers—

Discussing the Meaning of Fractions

you name it—to help my kids learn their multiplication tables. With mixed results.

Personally, when Eureka came in, I was a

Weighing Diffe ent Strategies The hard work pays off. I recently observed in a 2nd grade classroom and witnessed a student explain why she chose one strategy over another to solve a problem. Seeing such conceptual understanding along with application was a memorable moment for me! Instead of producing robots, we’re producing thinkers.

Robin Nelson, Director of K-5 Math Caldwell (LA) Parish Public Schools

skeptic. But watching the content develop

But once my students had fluency practice

has been eye opening for me. As a math

and learned how to skip count by 2s, by

specialist, my second week in this job, I

5s, by 3s, by 6s, etc.—both forwards and

walked into a 4th grade classroom and

backwards — their multiplication fluency

Students are performing better and

listened to the kids talk about fractions

really took off. My kids could multiply

learning more. I recently saw two fifth

and what fractions meant. I walked out of

quickly because of skip counting. It

graders discussing different approaches

that classroom thinking if only my freshmen

changed their thinking about math.

for solving a math problem. One said,

students had that understanding of fractions when they started Algebra I, how

Kim Graham, Teacher, Guntersville (AL)

easy my life would have been.

City Schools

Jamie Hebert, Math Academic Specialist, Lafayette (LA) Parish Public Schools

referring to well-known strategy, “It would be easier this way.” The other said, “But the result would be clearer if we did it with this strategy.” Conversations like this would

Adding And Subtracting To 20 I could tell [they were over the hump]

Amazed at Her Own Children

Comparing Math Strategies

by probably the end of October or early November, once my kids really mastered

I can speak from my own experience

that first 2nd grade module—learning to

as a parent. My own kids are 23, 16, 14

add and subtract to 20. In the beginning,

and 7 (twins). I’m just amazed what my

kids were counting on their fingers. Once

1st graders can do and their conceptual

they were familiar with word problems and

understanding. They understand the

sprints and I could get them to feel more

concept of 10s and 1s, and can add two-

confident they could figure out the answer,

digit numbers in their heads. My older kids

they were more willing to take a chance.

could not do this at that age. And it’s not

As the year went on, wrong answers were

the kids who are different. It’s the work they

a personal challenge to find where they’d

are doing in math class.

made a mistake.

Nicki McCann, High School Director and

Brittany Taraba, Teacher, Cypress Point

Director of Accountability Caldwell (LA)

Elementary School, Monroe, LA

have been unheard of a few years ago.

Carey Laviollete, Assistant Superintendent, Iberia (LA) Parish Public Schools

Parish Public Schools

16

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ALIGNED TO NEW YORK STANDARDS Great Minds has created a free detailed analysis to demonstrate how each grade of Eureka Math aligns with New York's specific standards for math.

Visit greatminds.org/ny-alignment-math or scan the QR code to access the Eureka Math alignment study for New York.

Eureka Math Lesson Structures

BY CATRIONA ANDERSON & BEAU BAILEY

We are often asked for clarification about the differences between the elementary lesson structure and the secondary lesson structures. When preparing for instruction, it is certainly helpful to understand the differences in order to capitalize on the design.

A Story of Units (Grades PK-5) Each lesson in A Story of Units is comprised of four critical components: fluency practice, concept development (including the problem set), application problem, and student debrief (including the Exit Ticket). Each component described below serves a distinct purpose. Together they promote balanced and rigorous instruction.

Above is the suggested lesson structure for Grade 2 Module 1 Lesson 5.

Fluency Practice: Almost all lessons begin with this component to support development of fluency skills for maintenance (staying sharp on previously learned skills), preparation (targeted practice for the current lesson), and/or anticipation (skills that ensure that students will be ready for the in-depth work of upcoming lessons). This component provides daily opportunities for students to gain confidence and motivation for continued learning.

Concept Development: This component addresses the new content being studied. Therefore, it is often allotted the majority of the instructional period to give students time for discussion and reflection. The concept development is generally comprised of carefully sequenced problems centered within a specific topic to begin developing mastery via gradual increases in complexity. It is also accompanied by an additional set of carefully crafted problems called the “problem set.� Teachers are encouraged to make choices within this set of problems to provide their students with generally about 10 minutes of additional practice.

Application Problem: In most lessons, this component is included to provide students with an opportunity to apply their skills and understandings in new ways. Sometimes the application precedes the concept development, functioning as a springboard into the new learning of the day. Often the application follows the concept development as an extension of learning.

Student Debrief: Every lesson closes with this critical component in which the teacher engages students in a whole-group discussion, challenging them to share their thinking and draw conclusions. This allows the teacher to gauge student understanding of the concept of the lesson, offering another chance for students to gain understanding before attempting the exit ticket.

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Story of Ratios (6-8) & Story of Functions (9-12) >>>

A Story of Ratios (Grades 6-8) and A Story of Functions (Grades 9-12) Mathematical content naturally increases in its complexity with each grade level. In order to address the level of difficulty at the secondary level, the formats of the lessons take on different forms starting in Grade 6. Each lesson is formatted as one of four types, each driven by the specific content of the lesson, including: problem set lessons, Socratic lessons, exploration lessons, and modeling lessons. (Notice that the term “problem set” arises as an entire lesson format in grades 6–12, leading to the need for clarification.)

Each lesson of the teacher materials for grades 6-12 begins with one of four symbolic icons indicating the instructional format of the lesson. The icon shown above indicates that this lesson, Grade 7 Module 2 Lesson 1, is a Problem Set Lesson.

Problem Set Lesson: This lesson format is the closest comparison to the lessons within A Story of Units. This format consists of teacher-led examples that are generally followed by guided exercises in which students apply their understanding to related problems. There are often short discussions within these lessons helping students make critical connections to develop understanding of concepts.

Socratic Lesson: Some content within the grades is of greater difficulty and it is necessary to maintain a dialogue with students to develop their understanding of such concepts. The Socratic lessons are primarily student/teacher discussions centered on the difficult concepts.

Exploration Lesson: Students are presented exploratory challenge(s) in the form of activities and/or exercises in which partners or small groups work toward achieving a common goal.

Exploratory challenges comprise the majority of the lesson.

Modeling Lessons: A practice that intensifies with each grade in middle and high school mathematics is the ability to model mathematically. Many misinterpret modeling as the use of manipulatives to show how the mathematics works. However mathematical modelling actually refers to the use of mathematical models to solve problems that arise in the real world. The modeling lessons consist of well- or ill-defined application problems for students to complete.

These problems involve the real world application of the mathematics that is learned in the classroom. The lessons are primarily reserved for high school, but there are at least three modeling tasks throughout each middle school grade level curriculum.

Through the course of this description, we’ve used the term “problem set” in more than one way. At grades 6–12 there is, as described previously, the problem set lesson. However, regardless of format, each K-12 lesson has an associated problem set, a supplemental set of problems based on the content of the current lesson. The major difference in the meaning of the term problem set lies in how the problem set is used. The PK-5 problem set is expected to be used as part of the classwork whereas the 6–12 problem set is generally expected to be used as independent practice at home. Either way, teachers are encouraged to be flexible in their use of items from the problem set to best meet the specific needs of their students to support their conceptual understanding.

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Pre-Kindergarten

Kindergarten

Grade 1

Grade 2

1st TRIMESTER

M1: Counting to 5 (45 days)

M5: Addition and Subtraction Stories and Counting to 20 (35 days)

M4: Number Pairs, Addition and Subtraction to 10 (47 days)

M3: Ordering and Comparing Length Measurements as Numbers (15 days)

M4: Place Value, Comparison, Addition and Subtraction to 40 (35 days)

M4: Addition and Subtraction Within 200 with Word Problems to 100 (35 days)

M5: Addition and Subtraction Within 1,000 with Word Problems to 100 (24 days) M6: Foundations of Multiplication and Division (24 days)

M5: Identifying, Composing, and Partitioning Shapes (15 days) M5: Numbers 10-20 and Counting to 100 (30 days)

M6: Place Value, Comparison, Addition and Subtraction to 100 (35 days)

M6: Analyzing, Comparing, and Composing Shapes (10 days)

Number

M7: Problem Solving with Length, Money, and Data (30 days)

M1: Properties of Multiplication and Division and Solving Problems with Units of 2-5 and 10 (25 days)

M1: Place Value, Rounding, and Algorithms for Addition and Subtraction (25 days)

M1: Place Value and Decimal Fractions (20 days)

**M2: Unit Conversions (7 days) M2: Multi-Digit Whole Number and Decimal Fraction Operations (35 days) M3: Multi-Digit M3: Multiplication and Division Multiplication and Division (43 days) with Units of 0, 1, 6-9, M3: Addition and Subtraction and Multiples of 10 of Fractions (25 days) (22 days) M2: Place Value and Problem Solving with Units of Measure (25 days)

M4: Multiplication and Area (20 days)

M5: Fractions as Numbers on the Number Line (35 days)

M4: Angle Measure and Plane Figures (20 days)

M5: Fraction Equivalence, Ordering, and Operations (45 days)

M6: Collecting and Displaying Data (10 days)

M8: Time, Shapes, and Fractions as Equal Parts of Shapes (20 days)

Key: Number and Geometry Geometry, Measurement

M7: Geometry and Measurement Word Problems (40 days)

M6: Decimal Fractions (20 days)

M7: Exploring Measurement with Multiplication (20 days)

M4: Multiplication and Division of Fractions and Decimal Fractions (38 days)

M5: Addition and Multiplication with Volume and Area (25 days)

M6: Problem Solving with the Coordinate Plane (40 days)

2015-16*

4th QUARTER

3rd TRIMESTER

M4: Comparison of Length, Weight, Capacity, and Numbers to 5 (35 days)

M3: Comparison of Length, Weight, Capacity, and Numbers to 10 (38 days)

M2: Introduction to Place Value Through Addition and Subtraction Within 20 (35 days)

M3: Place Value, Counting, and Comparison of Numbers to 1,000 (25 days)

Grade 5

3rd QUARTER

2nd TRIMESTER

M3: Counting to 10 (50 days)

**M2: 2D and 3D Shapes (12 days)

M1: Sums and Differences to 10 (45 days)

Grade 4

2nd QUARTER

M2: Shapes (15 days)

M1: Numbers to 10 (43 days)

M2: Addition and Subtraction of Length Units (12 days)

Grade 3

1st QUARTER

M1: Sums and Differences to 100 (10 days)

Fractions

*The columns indicating trimesters and quarters are provided to give you a rough guideline. Please use this additional column for your own pacing considerations based on the specific dates of your academic calendar. **Please refer to the modules themselves to identify partially labeled titles as well as the standards corresponding to all modules.

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Approx. test Approx. date for test grades date for 3-5 grades 3-5

Eureka Math® Grades 6–12 Reviewer Guide

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Contents Eureka Math Grades 6–12: Alignment at a Glance………………………………………………………………………………………………………………………………… 1 Evidence from Eureka Math Standards Alignment & Integration …………………………………………………………………………………………………………………………………………….. 3 Focus………………………………………………………………………………………………………………………………………………………………………………………………. 4 Coherence………………………………………………………………………………………………………………………………………………………………………………………. 5 Rigor………………………………………………………………………………………………………………………………………………………………………………………………. 7 Flexible Thinking…………………………………………………………………………………………………………………………………………………………………………… 9 Access & Differentiation……………………………………………………………………………………………………………………………………………………………….. 9 Assessment…………………………………………………………………………………………………………………………………………………………………………………… 11 Professional Development………………………………………………………………………………………………………………………………………………………….. 12 Technology & Digital Resources………………………………………………………………………………………………………………………………………………….. 13 Organization & Usability……………………………………………………………………………………………………………………………………………………………… 14

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Criteria of Effective Math Programs Eureka Math® Grades 6–12: Alignment at a Glance

Meets Criteria Yes

1. Standards Alignment & Integration a. Curricular materials align with college- and career-readiness standards. b. Curricular materials integrate the Standards for Mathematical Practices.

P

2. Focus Curricular materials focus coherently on the major work of the grade.

P

3. Coherence a. Curricular materials use logical incremental steps to build on learning from prior grades. b. Curricular materials use consistent models across grade levels. c. Curricular materials provide a variety of classroom experiences. d. Curricular materials use terminology that is accurate in earlier grades but is defined more precisely as students progress through grade levels.

P

4. Rigor a. Curricular materials contain a balance of rigor. b. Curricular materials support the development of students’ conceptual understanding of key mathematical concepts. c. Curricular materials are designed so that students attain the fluency and procedural skills that college- and career-readiness standards require. d. Curricular materials are designed to include application to real-world contexts.

P

5. Flexible Thinking Curricular materials encourage multiple solution paths to problem solving.

P

6. Access & Differentiation a. Curricular materials provide scaffolds and instructional supports for all students, including English learners. b. Curricular materials provide opportunities for extension to meet the needs of all students, including above-grade-level advanced learners. c. Curricular materials include culturally relevant and culturally responsive instructional practices that are inclusive of a variety of cultures and ethnicities and are free from bias.

P

7. Assessment Curricular materials include frequent and varied assessments that provide information to guide teachers and students.

P

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No

8. Professional Development a. Curricular materials support teacher learning and understanding of mathematical concepts and standards. b. Curricular materials include multiple dimensions of professional development for teachers. c. Curricular materials provide parents and guardians with resources to support student academic progress at home.

P

9. Technology & Digital Resources a. Digital materials enhance and extend classroom instructional practices. b. Digital materials provide an opportunity for real-time feedback to aid in classroom instruction.

P

10. Organization & Usability Curricular content provides instruction for a full academic year.

P

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Criteria of Effective Math Programs 1. Standards Alignment & Integration a. Curricular materials align with college- and careerreadiness standards.

Meets Criteria

Yes

P

No

Evidence from Eureka Math

Eureka Math Alignment and Program Examples Eureka Math was designed to align fully with modern college- and career-readiness standards. Eureka Math teacher–writers developed the curriculum while closely consulting the seminal Progressions Documents, which lay out the structure of mathematics and research in cognitive development and serve as the basis for modern readiness standards.

For detailed analyses demonstrating how each grade of Eureka Math aligns with your specific state standards, visit https://greatminds.org/resources/products/group/state-alignment-studies, select your state, and click Add to Dashboard in your Great Minds account.

b. Curricular materials integrate the Standards for Mathematical Practices.

P

Eureka Math prioritizes attention to the Standards for Mathematical Practice (MPs) over the course of each year, addressing all eight MPs in each grade level. The MPs are the practices necessary for students to reason mathematically, communicate conceptual understanding, and represent and solve problems. Rich tasks, development of flexible thinking, and frequent opportunities for student discourse encourage students to engage with the MPs during all lesson components.

Because of the interconnected nature of the Mathematical Practices, engagement with one MP often leads to engagement with others. For example, students reasoning about the quantities in a problem (MP.2) need to understand the meaning of the problem and the relationship of those quantities (MP.1).

The Teacher Edition’s Module Overview, which appears at the beginning of every module, lists the Focus Standards for Mathematical Practice along with a description of how each MP is applied. The curriculum clearly labels the MPs as they are applied in individual lessons. Margin notes do not indicate every instance the practice standards are addressed in lessons, but rather highlight noteworthy cases.

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Example In Grade 7 Module 1 Lesson 1 (p. 15), students explore the relationship between quantities in a word problem, decontextualizing the problem to calculate ratios and then restoring context to arrive at a final answer. This process engages students with MP.2—reason abstractly and quantitatively—and exemplifies how Eureka Math engages students with real-world contexts.

2. Focus

Yes

Curricular materials focus coherently on the major work of the grade.

P

No

Eureka Math Alignment and Program Examples Eureka Math focuses primarily on the major work of the grade. Lessons target the major work of each grade with depth and visible connections. Our Curriculum Maps indicate with an arrow an approximate date for standardized testing. The modules preceding the arrow focus on the major work of each grade; the subsequent modules generally focus on supporting work, which enhances and builds on work with the major work of the grade.

To find the Curriculum Maps, go to the Resource section of www.greatminds.org, and add the Teacher Resource Pack to your account’s dashboard. The Teacher Resource Pack contains many helpful resources, including the Curriculum Maps.

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3. Coherence

Yes

a. Curricular materials use logical incremental steps to build on learning from prior grades.

P

No

Eureka Math Alignment and Program Examples The Eureka Math teacher–writers carefully constructed the curriculum as a logical progression. Rather than checking off the boxes of separate disjointed skills, Eureka Math connects the major work for each grade to the larger progression of mathematical concepts over time. Eureka Math’s layered approach directs teachers to strategically revisit skills so that students develop mastery gradually over time; pursuit of mastery is not forced into a single lesson or module.

Within each lesson, problems and exercises are intentionally sequenced from simple to complex, reducing supports incrementally to promote student discovery and productive struggle. Through this process, students apply previous knowledge to the new learning of the day.

Throughout the modules, teachers will find explicit references to learning from previous grades. Module Overviews contain a Foundational Standards section, which outlines the standards from previous grade levels that provide a conceptual base for the new learning of the module.

b. Curricular materials use consistent models across grade levels.

P

Eureka Math uses the same core set of models and representations coherently within and across grade levels.

Many models learned in Grades K–5 evolve along with the growing complexities of mathematics and are representative of similar models that appear in Grades 6–12. This emphasizes to older students that there isn’t “elementary school math,” “middle school math,” and “high school math,” or even “easy math” and “hard math”—it’s all a part of the same story.

Example In Eureka Math, students start to use tape diagrams as early as Grade 1. In Grade 6, students begin to apply tape diagrams as a useful problem-solving tool in algebraic concepts. Students continue to use tape diagrams in Grade 7, Grade 8, and Algebra.

Grade 6

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Algebra Module Overviews open with a narrative outlining the module’s progression of mathematical concepts and demonstrating how those concepts can be expressed pictorially. For example, the Module Overview of Grade 6 Module 1 (pp. 7-8) uses visuals of a tape diagram, a double number line diagram, a ratio table, and a coordinate plane to represent the same equivalent ratios. c. Curricular materials provide a variety of classroom experiences.

P

Eureka Math organizes Grades 6-12 into four lesson types: Modeling Cycle, Exploration, Problem Set, and Socratic.

In Modeling Cycle lessons, students use mathematics to model real-world situations, which often facilitates cross-curricular connections.

Exploration lessons present students with an exploratory challenge(s) in the form of activities and/or exercises in which partners or small groups work toward achieving a common goal.

Problem Set lessons feature teacher-led examples that are generally followed by guided exercises in which students apply their understanding working individually or in small groups. Lessons often include short discussions that help students make critical connections to develop their understanding of concepts.

Socratic lessons feature a whole-group discussion that facilitates a deep dive into complex concepts.

This diversity in lesson type allows students to actively engage with a diverse range of activities, while also ensuring a balance in the three components of rigor.

All lessons contain a Closing, which encourages students to reflect on the new learning of the day and promotes the development of precise mathematical discourse.

Example Grade 6 Module 1 Topic C (p. 132) contains all four lesson types.

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d. Curricular materials use terminology that is accurate in earlier grades but is defined more precisely as students progress through grade levels.

P

4. Rigor

Yes

a. Curricular materials contain a balance of rigor.

P

Eureka Math balances the three components of rigorous mathematics education: conceptual understanding, procedural skill and fluency, and application to real-world contexts. Lessons provide experiences to expand, develop, apply, and practice conceptual understanding, as well as hone procedural and problem-solving skills through engaging real-world applications. The curriculum sometimes presents the three components separately but also often combines them, reinforcing the development of students as flexible thinkers on the path to mastery. Eureka Math addresses these areas with equal intensity, recognizing that all are vital parts of a coherent, effective curriculum.

b. Curricular materials support the development of students’ conceptual understanding of key mathematical concepts.

P

Eureka Math develops students’ conceptual understanding in critical ways, emphasizing deep knowledge building and ensuring that students understand the “why” rather than just the “how” of math. Concepts progress coherently so students understand that they are building on what they already know rather than starting over with every new topic.

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Eureka Math outlines precise terms for both teachers and students to use consistently. Rather than using rhymes and catchphrases that oversimplify math and detract from the focus on conceptual understanding, Eureka Math uses accurate terminology that remains consistent across grade levels. This ensures that students are prepared for later grades and recognize the reappearance of concepts they have already learned. Students practice using key terms to craft precise mathematical arguments in Socratic lessons and the Closing section of all lesson types.

The Terminology section of each Module Overview provides a list of key terms and their definitions. For example, the Terminology section of Algebra Module 1 (pp. 9-10) distinguishes between New or Recently Introduced Terms and Familiar Terms and Symbols and connects those terms to key topics explored throughout the module.

No

Eureka Math Alignment and Program Examples

Conceptual Development progresses from the visual to the abstract. Students learn to draw visual models and representations, which provides multiple points of entry and expands students’ problem-solving toolbox. These visual models are accompanied by the corresponding abstract symbolic representations, highlighting connections between the two. At the end of the progression, students can drop the pictorial representation and keep only the abstract symbolic representation. This progression builds a strong foundation of conceptual understanding and highlights connections between concepts.

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c. Curricular materials are designed so that students attain the fluency and procedural skills that college- and careerreadiness standards require.

P

d. Curricular materials are designed to include application to realworld contexts.

P

In the lessons, problems and exercises progress from simple-to-complex. Simpler problems often develop procedural fluency, while more complex problems promote flexible thinking as students choose their own set of problem-solving strategies.

Grades 6-8 include Sprints, whole-group activities carefully designed to promote and celebrate individual growth while stimulating the joy in mathematics. Teachers are encouraged to incorporate quick fluency activities at the beginning of class where formative assessment indicates gaps in understanding.

Example Grade 6 Module 3 Lesson 10 (p. 97) contains a Sprint to promote fluency in writing inequality statements.

Exercises in Problem Set and Exploration lessons provide real-world context, building fluency with word problems while demonstrating to students how math is always around them in their daily lives; Socratic Lessons often foster a dialogue exploring a concept through the lens of a real-world situation.

Example For example, a Grade 6 Module 1 Socratic lesson (p. 109) explores the connection between ratio tales and representations on the coordinate plane through the lens of a girl traveling with her soccer team to a tournament.

Many Modeling Cycle lessons provide students with experiences that move math off the page and into the world around them. For example, in Algebra II Module 1 Lessons 20 and 21, students are assigned the role of EPA surveyors and model a riverbed to establish flood zones.

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5. Flexible Thinking Curricular materials encourage multiple solution paths to problem solving.

Yes

No

Eureka Math Alignment and Program Examples In Eureka Math, students often choose their own solution strategy—problems and activities may also ask students to provide responses in multiple forms. Students are prepared to make these decisions, as the coherent usage of pictorial models and representations leads students to develop many tools for their problem-solving toolbox. This provides multiple points of entry, creating access for all learning styles and encouraging flexible thinking. Additionally, students come to a deeper understanding of underlying concepts as they compare problem-solving strategies.

P

Example Grade 7 Module 1 Lesson 14 (p. 129) guides students through three methods of solving a problem. Students are not required to use all three methods but are prompted to compare their classmates’ problem-solving methods with their own, highlighting the connections between the pictorial and the abstract.

6. Access & Differentiation a. Curricular materials provide scaffolds and instructional supports for all students, including English learners.

Copyright © 2019 Great Minds®

Yes

P

No

Eureka Math Alignment and Program Examples Curriculum writers built Eureka Math on the researched-based Universal Design for Learning (UDL). The curriculum seamlessly embeds scaffolding through the simple-to-complex sequencing of exercises and Problem Set items. This logical sequence gradually reduces supports and builds in complexity, allowing teachers to identify students’ last point of understanding and to differentiate assignments for either individual or smallgroup work. For all students, the gradual reduction of supports builds independent thinking and encourages productive struggle.

The lesson plans provide strategically placed margin notes that elaborate on the use of specific scaffolds at applicable times. The notes suggest supports and extensions for English learners, students with disabilities, students performing above grade level, and students performing below grade level.

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Example The following scaffolding boxes from Grade 8 Module 1 Lesson 4 (p. 42) guide teachers in creating access for both struggling and advanced students.

b. Curricular materials provide opportunities for extension to meet the needs of all students, including above-grade-level advanced learners.

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P

Throughout the curriculum, Eureka Math encourages teachers to assign classwork by using a “time frame” rather than a “task frame.” Within a given time frame, students are expected to do their personal best, working at their maximum potential. Some students will complete more work than others, and personal growth is emphasized over the number of correct responses. As a built-in extension, the final items in Problem Sets are often designed as synthesis items, drawing connections between multiple standards and providing an additional level of complexity for students who would benefit from a challenge. Further guidance for providing extensions appears in the margin notes (as pictured above) and is also embedded within the lesson plan activities.

The Preparing to Teach a Lesson section in the Module Overview of each grade level’s Module 1 guides teachers in identifying examples and exercises as Must Do, Could Do, or Challenge! problems, according to the unique needs of their classrooms. Challenge! problems also make excellent extension work. In Grade 7 Module 1, this resource appears on pages 8 and 9.

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c. Curricular materials include culturally relevant and culturally responsive instructional practices that are inclusive of a variety of cultures and ethnicities and are free from bias.

P

7. Assessment

Yes

Curricular materials include frequent and varied assessments that provide information to guide teachers and students.

P

Teacher–writers from across the country wrote Eureka Math to reflect the diverse experiences and backgrounds of students in today’s classrooms. The curriculum offers opportunities for students to explore themselves and their families and see positive representations of themselves through the materials. Names and pictures of people represent diversity, and problems and exercises relate to real-life experiences, perspectives, and contributions of people from various cultures, ethnicities, and gender identities.

No

Eureka Math Alignment and Program Examples Eureka Math employs a systematic approach to assessment: Daily formative assessments come in the form of Exit Tickets. Designed to help teachers reflect on what their students know and can do, Exit Ticket results drive instruction for the following day.

Mid-Module and End-of-Module Assessments are designed to tie together knowledge and skills that have been addressed to that point in the module. Questions vary in complexity, spanning Depth of Knowledge (DOK) levels 2 and 3. Some assessment items test understanding of specific topics, while others are synthesis items that assess more complex concepts that span multiple standards. Teacher Edition Mid-Module and End-ofModule Assessments include sample student work and standards-tagged rubrics to help teachers evaluate students’ achievement on the progression toward mastery.

Eureka Math Affirm™, the curriculum’s digital assessment and practice platform, provides premade assessments as well as an item bank* of more than 4,000 standards-tagged items that teachers can use to create custom assessments and differentiated assignments. Affirm’s extensive reporting features allow teachers and administrators to track student progress on a range of metrics.

Note: Eureka Math does not provide diagnostic assessments; teachers wishing to administer diagnostic assessments in their classrooms can use the Foundational Standards section of each Module Overview as a guide to create this resource, as well as Affirm’s standards-tagged item bank. *The item bank is available only for Grades 1-9.

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8. Professional Development

Yes

No

Eureka Math Alignment and Program Examples

a. Curricular materials support teacher learning and understanding of mathematical concepts and standards.

P

One of the great strengths of Eureka Math is its usefulness as a professional development tool for teachers.

Extensive teacher notes throughout the curriculum, as well as Module and Topic Overviews, provide explanations of important mathematical concepts and discussions about pedagogy, language, notation, lesson planning, and common student misconceptions. Many Eureka Math teachers have reported that they have developed a deeper understanding of the mathematics they teach.

b. Curricular materials include multiple dimensions of professional development for teachers.

P

Professional development (PD) is available to Eureka Math implementers in many forms, including embedded supports in the Teacher Edition, digital resources such as the Eureka Digital Suite and the Teacher Resource Pack (described in further detail in response to Criteria 9), and a series of in-person professional development sessions. Great Minds also offers on-site coaching and virtual professional development sessions. Find more information on Eureka Math PD sessions by visiting https://gm.greatminds.org/math/pd.

c. Curricular materials provide parents and guardians with resources that support student academic progress at home.

P

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Eureka Math Professional Development Sessions

Great Minds recognizes that parents and family are students’ biggest advocates and therefore works to keep them engaged in the learning process.

Parent Tip Sheets, available free online in English and Spanish, include key concepts, terms, sample problems, and models. Tip Sheets are particularly helpful to the many parents who learned math differently when they were in school and may not be familiar with the visual models and representations Eureka Math uses. Great Minds also provides free presentation materials if a school wishes to host a Family Math Night.

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Homework Helpers are a useful resource that illustrate problems similar to those assigned in class and demonstrate an example of the thinking that supports each problem. Each Homework Helper sheet corresponds to a specific homework assignment, making it easy for parents to follow along with their children’s progress. Homework Helpers are included in students’ Succeed workbooks for Grades 6-8, and digital Homework Helpers are available for purchase in English and Spanish.

Parent Tip Sheets are available for Grades K-8 and Homework Helpers are available for Grades K-12.

Example This is an example of a worked problem in a Homework Helper.

9. Technology & Digital Resources a. Digital materials enhance and extend classroom instructional practices.

Yes

P

No

Eureka Math Alignment and Program Examples The Eureka Digital Suite is a digital teacher resource that includes the Eureka Navigator and the Teach Eureka video series.

The Eureka Navigator provides users with the complete PK–12 curriculum in a professional development platform, which makes it easy for teachers to prepare their instruction by studying embedded demonstration videos and daily lessons, linking from lessons to the standards, reviewing scaffolding hints for Response to Intervention (RTI) efforts, and following teaching sequences within a module and across modules and grade levels. A streamlined, interactive interface makes it simple to access and navigate the entire Eureka Math curriculum online and provides easily downloadable lesson files.

The Teach Eureka video series provides users with a deeper understanding of mathematics through a study of the Eureka Math curriculum. In these videos, the curriculum’s authors explain the mathematical concepts and instructional strategies found within the topics of the modules. Each grade of the video series contains 18 onehour sessions organized sequentially by module. The on-demand format, streamed online, allows for viewing whenever and wherever, individually or in teams.

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The Eureka Math Teacher Resource Pack provides a selection of free instructional materials and tools including Curriculum Maps, Curriculum Overviews, Pacing and Preparation Guides, Standards Checklists, and Materials Lists. This resource is available free at www.greatminds.org by accessing the Resources section and adding the Teacher Resource Pack to your dashboard. b. Digital materials provide an opportunity for realtime feedback to aid in classroom instruction.

Affirm, Eureka Math’s digital assessment and practice platform, contains premade forms of both formative and summative assessment as well as an item bank* of more than 4,000 standards-tagged items that teachers can use to create custom assessments and differentiated assignments. The question types cover Depth of Knowledge (DOK) levels 1–3, and most can be automatically scored. The platform includes extensive reporting features to help teachers and administrators track student progress on a range of metrics. Teachers can also create classes and add students as well as sync class rosters with Google Classroom or Clever. The flexibility of Affirm empowers teachers to differentiate for individual students or groups of students.

P

*The item bank is available only for Grades 1–9.

10. Organization & Usability Curricular content provides instruction for a full academic year.

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Yes

P

No

Eureka Math Alignment and Program Examples Eureka Math was designed for a 180-day school year, including time for remediation and testing. This provides flexibility for teachers to customize instruction as appropriate.

Pacing and Preparation Guides are available to assist teachers in customizing the pace of instruction to meet the unique needs of their classrooms and communities. This resource is available free at www.greatminds.org by accessing the Resources section and adding the Teacher Resource Pack to your dashboard.

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LEARN MORE

Visit greatminds.org/new-york to access additional materials to review and evaluate Eureka Math for your school.

Laurie Duma| NYC Representative laurie.duma@greatminds.org