Topics: Differentiation Featured Instructional Design Eureka Math Squared

Response to Intervention with Eureka Math²

Alyssa Buccella

by Alyssa Buccella

November 3, 2023
Response to Intervention with Eureka Math²

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Posted in: Aha! Blog > Eureka Math Blog > Differentiation Instructional Design Eureka Math Squared > Response to Intervention with Eureka Math²

Response to Intervention (RTI), also referred to as a Multi-Tiered System of Support (MTSS), is a framework that describes both core and additional instruction. Within this system, Tier 1 support must ensure that all students are provided with high-quality, differentiated core mathematics instruction by using a standards-based curriculum that uses research-based pedagogy. In Tiers 2 and 3, students are provided with targeted, intensive instruction or interventions that enable students to reach grade-level proficiency.

Now more than ever, it is essential that educators have the necessary tools to provide coherent, accessible, and engaging instruction across all three RTI tiers.

Best Practices with Response to Intervention in Mathematics

In March 2021, the Institute of Education Sciences (IES) released a practice guide, developed by the What Works Clearinghouse (WWC) in conjunction with an expert panel, containing six recommendations for effective mathematics interventions. These recommendations are based on a meta-analysis of high-quality, evidence-based studies focused on mathematics intervention. (Fuchs et al. 2021)

These recommendations align with intentional design features of Eureka Math2—outlined in the table below—that appear across all tiers of instruction along with other evidence-based practices. This alignment of language, models, and strategies across all tiers leverages more background knowledge for students, promoting student understanding, while the use of familiar content, pedagogy, and materials also eases instructional planning and delivery for teachers.


IES Recommendation

Aligned Components of Eureka Math²


Systematic Instruction

Provide systematic instruction during intervention to develop student
understanding of mathematical ideas.

  • Levels, modules, topics, and lessons are taught as a coherent, logical story.
  • The curriculum contains a balance of explicit, guided, and student-driven instruction.
  • Practice of previously learned concepts is interleaved and distributed.

Mathematical Language

Teach clear, concise mathematical language and support students’ use of the language to effectively communicate understanding.

  • Terminology is systematically introduced and developed.
  • Discourse is encouraged and supported with tools such as instructional routines, the Talking Tool, digital lessons, and interactives.


Use concrete and semi-concrete representations to support students’ learning of mathematical concepts and procedures.

  • High-leverage, coherent models, such as arrays, tape diagrams, and number bonds, develop within and across levels in a Concrete–Pictorial–Symbolic progression.

Number Lines

Use the number line to facilitate the learning of mathematical concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics.

  • Number paths in levels K and 1 and number lines in levels 2+ help develop strong number sense.

Word Problems

Provide deliberate instruction on word
problems to deepen students’ mathematical understanding and support their capacity to apply mathematical ideas.

  • All problem types are presented in an intentional and coherent sequence.
  • The Read–Draw–Write and Read–Represent–Solve–Summarize routines, modeling experiences, and the Thinking Tool cultivate mathematical thinking and support independent problem solving.

Timed Activities

Regularly include timed activities as one way to build fluency in mathematics.

  • Math fact strategy development, Fluency activities, and Sprints focusing on patterns develop student automaticity with counting and calculating.


Tier 1: Accessibility, Differentiation, and Acceleration

Eureka Math2 is research-based, accessible by design, and easily differentiated. Teachers can use this intentional design and the many core curriculum components to target core instruction and effectively bridge learning gaps so that all students can excel with rigorous, grade-level content.

Leverage Core Curriculum Components

  • Simple to Complex Sequences: Every lesson, Sprint, and Problem Set is structured as a ladder with content that increases in complexity at each rung. Students who need more support can access concepts by using the less complex rungs on the lower part of the ladder, which progress toward target content in the middle of the ladder. Students can also work their way beyond target content with extension opportunities at the top of the ladder.

  • Concrete–Pictorial–Symbolic (CPS) Approach: Eureka Math2 helps students understand how representations within the CPS Approach are connected and intentionally builds bridges between representations through modeling and guided practice. Representations overlap throughout the curriculum to help students build familiarity with the next stage in the CPS Approach, even when they are primarily focused on an earlier one. Eureka Math2 also offers explicit scaffolding opportunities, enabling teachers to effectively move students back to earlier stages as needed so that students can successfully access advanced learning. 

  • Multilingual Learner (MLL) Support: Students receive language support in every Eureka Math2 lesson, and teachers are provided with point-of-use margin notes to help students with receiving (reading and listening) and producing (speaking and writing) English in mathematical contexts. For example, suggestions may define content-specific terminology or academic language, or they may clarify multiple-meaning words. Eureka Math2 also contains a Talking Tool with four sets of general sentence frames and starters to support students when sharing their thinking and to promote discourse.

  • Universal Design for Learning (UDL): Eureka Math2 offers margin notes with strategies and scaffolds that address the predictable variability of all learners. These notes promote flexibility with engagement, representation, and action and expression—the three UDL principles described by CAST—and are additional suggestions to complement the curriculum’s overall alignment with the UDL Guidelines.

  • Differentiation by Design: Eureka Math2 provides targeted ways to help meet the needs of different learners based on teacher observations or assessments. There are two types of suggestions: support and challenge. Teachers can use these suggestions to support students in the moment or to advance learning for students who have mastered a concept and are ready for a challenge.

  • Distributed Practice: The research-based distributed and interleaved practice embedded in the Fluency and Practice sections of lessons ensures that students naturally revisit concepts over time to develop and maintain proficiency.

  • Problem-Solving Processes: Eureka Math2 gives all students the opportunity to independently engage in rigorous problems through the clear and replicable Read–Draw–Write (RDW) process. RDW helps students in levels K–5 leverage reading and drawing to understand a problem and figure out a solution path. The RDW process is then bridged to the Read–Represent–Solve–Summarize process to support more complex problem solving in levels 6–9. The curriculum also contains a Thinking Tool, which provides a set of questions students can ask themselves before, during, and after any task, helping students to develop and apply metacognitive skills.

Lesson Customization Process

How will I maintain fidelity to the author’s intentions while also meeting my students’ needs?

  1. Preview the Learning: Read the Lesson Overview, which sets the stage for what students are expected to understand by the end of the lesson.

  2. Investigate the Development of Learning: Read the lesson in its entirety. Consider the flow of lesson components and do the math to gain insight into the sequence of problems and complexities within the sequences. This enables better understanding of student thinking and familiarity with the tools students may use to engage in the lesson.

  3. Prepare for Differentiated Instruction: Study the margin notes, Problem Sets, Practice, and Fluency.

Responsive Teaching

Responsive teaching begins with assessment so that teachers can accelerate, revisit, and extend student learning as needed within Tier 1 instruction.

  • Assessment: The Eureka Math2 assessment program is comprehensive and research-based, and the curriculum provides tools that help monitor student learning before, during, and after instruction.

    • Before instruction, Eureka Math2 Equip™ enables diagnostic assessment with Pre-Module Assessments that evaluate foundational knowledge.

    • During instruction, Observational Assessments, Exit Tickets, Topic Tickets and Topic Quizzes, and standards-aligned Achievement Descriptors and Proficiency Indicators help teachers understand expectations for student learning and analyze how well students understand the content.

    • After instruction, summative Module Assessments measure student proficiency with the major concepts, skills, and applications of the module, and premium Benchmark Assessments monitor the development of learning throughout the year.

  • Accelerate: The Eureka Math2 Equip™ diagnostic assessment system works with the curriculum to accelerate students’ access to on-level content through three main components. Pre-Module Assessments of foundational knowledge help identify unfinished learning and pinpoint gaps in understanding. Assessment reporting at the whole-class and individual-student levels helps guide instructional planning. Targeted supporting activities accelerate learning with short bursts of instruction that fit seamlessly into regular class time.

  • Revisit: When data shows a minor learning gap, teachers must provide problems that help identify students’ last point of success. This enables teachers to determine how to best intervene and what content to focus on. Since the concepts, lessons, topics, and modules in Eureka Math2 were designed to connect and layer, there are built-in opportunities to revisit content and develop student understanding over time. Teachers may also need to integrate short sprinkles of additional instruction to bridge the learning gap, revisiting one complexity at a time until the gap is filled, or teachers may make use of the curriculum’s 40 responsive teaching days to address a gap among a larger group of students.

    • Tools such as the Achievement Descriptors and Content Standards at a Glance and Progression of Lessons charts make the curriculum’s layering visible so that teachers can revisit content strategically.

  • Extend: Eureka Math2 presents students ready for a challenge with ample extension opportunities that deepen their grade-level mathematical thinking and skills. The Highly Proficient Achievement Descriptors in each module outline the target skills that students in need of extension should work on. Some extension ideas include:

    1. revisiting Differentiation: Challenge notes;
    2. completing unfinished Problem Sets and Practice problems;
    3. exploring additional Math Past and art connection activities;
    4. replicating instructional routines with different content;
    5. revisiting context videos, open-middle tasks, and open-ended tasks;
    6. rewriting word problems with more complex numbers;
    7. providing counting collections to sort, write, and record in a different way; and
    8. writing about math in math journals using numbers, pictures, and words.

Tiers 2 & 3: Interventions Using Curriculum-Aligned Resources

When students have a more significant learning gap, educators can use off-level content and resources from Eureka Math2 for intervention. Tier 2 intervention strategies address student learning gaps one or two years below grade level, while Tier 3 interventions serve those students whose knowledge and skills are more than two years below grade level.

To provide targeted Tier 2 interventions using Eureka Math2, educators backmap standards and then assess student understanding, group students according to data, plan instruction, and teach intervention content to fill foundational holes. Tier 3 interventions follow this same process but with greater intensity, meaning more intervention time, increased frequency of intervention time, or a decrease in student group size.

Backmapping and Narrowing Content in Tier 3

The backmapping process is the same for Tier 3 interventions as it is for Tier 2 interventions. Tier 3 interventions will have a keen focus on supporting students in reaching grade-level instruction or meeting their Individualized Educational Plan (IEP) goal, which often requires steeper catch-up growth than the typical growth a student makes in one year. This means educators will need to bring in more off-level content to help students reach their goals.

Educators will likely also need to strategically narrow the content focus of Tier 3 interventions to have enough time for the level of intensity required for success. This could include narrowing module and topic content or even each lesson’s focus based on:

  • students’ individual IEP goals,
  • the number and operation strands on state assessments, or
  • district-specific goals set through vertical articulation work in kindergarten through high school.
  1. Backmapping: Backmapping is defined as “identifying gaps in a student's knowledge by tracing a standard back through its logical prerequisites.” (Achieve the Core) To aid in this process, educators can use the Achievement Network’s Important Prerequisite Math Standards charts that outline the standards in levels 1–9 requiring important prerequisites from the prior grade level that may interfere with a student’s ability to access grade-level content.

    • Educators should spend additional time reteaching only those standards that are the grade’s major focus. The Institute of Education Sciences specifically recommends that math interventions focus intensely on the treatment of whole numbers, especially in grades K–5, and rational numbers, especially in grades 4–8. (Gersten et al. 2009)

  2. Assess and Group: By using items from Module Assessments, Benchmark Assessments, and Topic Tickets and Topic Quizzes that are relevant to a standard or an Achievement Descriptor, teachers can create a custom print or digital screener to determine the right instructional starting point and sequence. Pairing a focused assessment with individual or small-group conversations can help reveal students’ mathematical thinking and strategies to accurately place students in the appropriate standard band with the correct target instruction.

    Groupings should be flexible, providing students with access to the support needed at the time, and educators should consistently monitor data to determine when students have reached mastery and are ready to move on to another standard.

  3. Plan: Educators can use the progressive nature of the modules, topics, and lessons within Eureka Math2 to determine their choice of intervention lesson materials. The Module Overview for each module, Scope and Sequence grade level maps, and Standards and Achievement Descriptors charts help identify all the lesson locations of standards and the Achievement Descriptors of every grade level so that educators can find specific lessons and sequence instruction for the grade-level learning goal.

    • The Apply book is another option for intervention that is lighter on planning and more supportive with instruction. In Apply (available for levels 1–5), practice problems for each lesson include a parallel Practice Partner with an avatar that provides a solution path and illustrates student thinking for a sample problem. This can serve as a useful guide with ample content for intervention lessons, offering coherent models and language to Tier 1 instruction.

    • The Eureka Math2 Equip™ diagnostic assessment system can also be used to plan intervention lessons. The system maps foundational knowledge across grade levels and offers supporting activities for each item or Achievement Descriptor. The supporting activities are brief and have varying levels of scaffolding, which makes them ideal for intervention lessons. Each Item Overview also indicates where in the curriculum the item is found so that educators can easily pull related practice problems.

  1. Teach: When teaching intervention content, it is important to incorporate all the elements of high-quality mathematics instruction. Just as students should in Tier 1 instruction, students should engage in all eight Standards for Mathematical Practice during intervention time, which appear in margin notes throughout each lesson of every Eureka Math2 module. Discourse and instructional routines are also essential as they allow students to process and discuss the content. The routines and opportunities for discourse embedded throughout Eureka Math2 lessons can easily be applied and adapted to meet the needs of intervention time.

    As indicated by IES, systematic instruction, visual representations, direct instruction on word problems, and fact fluency are especially critical in Tier 2 and 3 interventions. (Fuchs et al. 2021; Gersten et al. 2009) These practices are supported by Eureka Math2, as outlined in the table on page 1. IES also finds evidence supporting the infusion of motivational strategies and progress monitoring into intervention instruction. (Gersten et al. 2009)

    • Infusing motivational strategies: Honoring what students already know, praising and thanking students for their effort, normalizing mistakes, and making learning fun through games and routines can all help build student engagement over time. Educators should also make learning goals clear so that students can track and celebrate success along the way.

    • Monitoring progress: There are several ways to monitor progress using Eureka Math2, including through Exit Tickets, Whiteboard Exchanges, Topic Quizzes, Module Assessments, Observational Assessments, and Achievement Descriptor rubrics. These tools help teachers decide when they may need to reteach content or when to progress students.

To get a more in-depth view of this process, we invite you to watch our two-part RTI webinar series: Tier 1: Accessibility, Differentiation, and Acceleration and Tiers 2 and 3: Interventions Using Curriculum-Aligned Resources.\

Achieve The Core. “Coherence Map.” Accessed August 7, 2023.

The Achievement Network. “Important Prerequisite Math Standards.” Accessed July 19, 2023. Retrieved from:

Fuchs, Lynn S., Ph.D., Nicole Bucka, M.A., Ben Clarke, Ph.D., Barbara Dougherty, Ph.D., Nancy Jordan, Ph.D., Karen Karp, Ed.D., John Woodward, Ph.D., Madhavi Jayanthi, Ed.D., Russell Gersten, Ph.D., Rebecca Newman-Gonchar, Ph.D., Robin F. Schumacher, Ph.D., Julia Lyskawa, M.P.P., Betsy Keating, M.P.P., Seth Morgan, M.A., and Kelly Haymond, M.A. Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades. Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education, 2021.

Gersten, Russell, Sybilla Beckmann, Benjamin Clarke, Anne Foegen, Laurel Marsh, Jon R. Star, and Bradley Witzel. Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools. Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education, 2009.

Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education, 2021.

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Topics: Differentiation Featured Instructional Design Eureka Math Squared