Response to Intervention with Eureka Math² California

Equitable and engaging math instruction is at the heart of the California Mathematics Framework and Eureka Math² California. Response to Intervention (RTI) is an essential framework for promoting equity and engagement in math classrooms. RTI is a three-tiered framework for delivering core and additional instruction. Tier 1 support provides all students with high-quality, research-based, and differentiated core math instruction. Tiers 2 and 3 offer targeted interventions to help students reach grade-level proficiency.

Now more than ever, it is essential that California teachers have high-quality tools to provide coherent, accessible, and engaging instruction across all three RTI tiers.

Best Practices with Response to Intervention in Mathematics

The Institute of Education Sciences (IES) outlines six evidence-based recommendations for effective math intervention (Fuchs et al. 2021). These align with key design features of Eureka Math² California, summarized in the table below. Eureka Math² California integrates these features across all tiers of instruction, ensuring consistent use of language, models, and strategies that leverage background knowledge and deepen student understanding. This intentional coherence of content, pedagogy, and materials also eases planning and instruction for teachers.

Tier 1: Accessibility, Differentiation, and Acceleration

Eureka Math² California is research-based, accessible by design, and easily differentiated. Teachers can use 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, Fluency, 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 California helps students understand how representations within the CPS Approach are connected, intentionally building 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. Eureka Math² California also offers explicit scaffolding opportunities, supporting teachers in helping learners advance and succeed.

Multilingual Learner (MLL) Support: Every Eureka Math² California lesson is designed with language support for students. Point-of-use margin notes support teachers in helping students receive (reading and listening) and produce (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 California also provides a Talking Tool with sentence frames to support students as they share their thinking and engage in discourse.

Universal Design for Learning (UDL): Eureka Math² California 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 California provides targeted ways to help meet the needs of different learners based on teacher observations or assessments. There are two types of suggestions— Differentiation: Support and Differentiation: Challenge. Teachers can use these suggestions to support students and to advance learning for those 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 California gives all students the opportunity to independently engage in rigorous problems through the Read–Draw–Write (RDW) process. RDW helps K–5 students leverage reading and drawing to understand a problem and find a solution path. The RDW process is a bridge to the Read–Represent–Solve–Summarize process, which supports more complex problem solving in levels 6–9. The curriculum also contains a Thinking Tool, which provides self-reflection questions for before, during, and after any task, helping students develop and apply metacognitive skills.

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 California 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 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 California 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 California 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

• revisiting Differentiation: Challenge notes;
• completing unfinished Problem Sets and Practice problems;
• exploring additional Math Past and art connection activities;
• replicating instructional routines with different content;
• revisiting context videos, open-middle tasks, and open-ended tasks;
• rewriting word problems with more complex numbers;
• providing counting collections to sort, write, and record in a different way; and
• 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 California 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 California, educators backmap standards, 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 to a greater extent, increasing time and frequency for intervention or decreasing the size of the student group.

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 California 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.

4. 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 California 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 California 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 California, 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 California, 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.

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