Eureka Math / EngageNY (K-5)

All retrieved mid-module and end-of-module assessment tasks are explicitly aligned to grade-level Kindergarten standards (K.CC.3-7, K.OA.3, K.MD.1/3, K.G.1-3) [E1][E3][E5][E6], with rubrics calibrated to those expectations (e.g., writing numerals 0-5, comparing groups up to 10) [E8]. The structured assessment system houses 10 assessments per student across the modules and is explicitly framed as preparation for Grade 1 teachers, indicating K content is what is assessed and Grade 1 is a forward horizon, not an accountability target [E10][E11]. No evidence shows students being held accountable for future-grade content, satisfying all required components.

Grade 5 supporting standards are explicitly bundled with major-work standards in problem-solving contexts—G5-M6 Topic E aligns 5.MD.1, 5.MD.5, and 5.G.2 alongside major-work fraction/operation standards 5.NF.2, 5.NF.3, 5.NF.6, 5.NF.7c [E3][E4][E12]. The topic has students apply all four operations with whole and fractional numbers in varied, non-routine contexts, explicitly reinforcing major work through supporting content [E5][E8]. This structural integration of supporting clusters (measurement, geometry) with the grade's major work satisfies the indicator.

Indicator 1b asks whether the majority of class time is spent on the grade's major clusters. The retrieved evidence shows full-length 60-minute daily lessons in Module 5 devoted entirely to fractions (3.NF.1, 3.NF.3c, 3.G.2) — major work of Grade 3 — across multiple multi-day topics ([E1], [E4], [E5], [E6], [E8], [E9], [E11]), with fluency time additionally reinforcing the 3.OA major cluster ([E4], [E10]). Even the end-of-year review module devotes its work to consolidating major Grade 3 skills including fractions, multiplication, and division ([E2], [E7]). This structural design — substantial instructional days allocated to major-cluster standards with full-period lessons — supports the indicator. Confidence is moderate because only Grade 3 Modules 5 and 7 were retrieved rather than the full scope-and-sequence needed to confirm grade-wide time allocation.

The materials show intentional pacing and full-year viability design: 'Must Do' problem guidance is structured so the majority of the class completes core work within the allocated time, balancing calculations and word-problem types [E1][E2][E4][E5], and Module 7 is explicitly described as practice of the grade's major skills with a note not to omit lessons, signaling a deliberately scoped full-year sequence [E3]. Coherence between grades is supported by the modular scope-and-sequence design with Module Overviews, Overview of Topics and Lesson Objectives, and a 'plot' that builds objectives from simple to complex across topics [E6][E7][E9][E10]. This structural evidence of grade-level pacing and cross-grade coherence supports all required components of the indicator. Detailed per-grade lesson-count/day tables were not retrieved, which lowers confidence but not the score.

Materials develop according to grade-by-grade progressions: each topic overview labels grade-level focus standards (5.NBT, 5.NF, 5.MD) and explicit 'Coherence — Links from / Links to' sections that name prior-grade and future-grade modules, clearly identifying and relating off-grade content [E1][E3][E7][E9]. Grade-level work is extensive across all six modules with abundant problem sets, including multi-step word problems and a 'Must Do' ladder ensuring all students engage grade-level problems [E9][E12]. Prior knowledge is explicitly connected — e.g., Topic A extends Grade 4 place-value work to decimals via the 10-times/one-tenth relationships [E10], and Topic E links Grade 4 multiplication to Grade 5 fluency [E1] — and references the official Progression Documents directly [E12].

The materials show both required components. Topic overviews organize learning around CCSSM cluster headings (e.g., 'Generate and analyze patterns' tied to 4.OA.5, and 'Extend understanding of fraction equivalence and ordering' in E8/E11), shaping the stated objectives. Activities deliberately connect multiple domains: Grade 4 Topic H links pattern-finding (4.OA.5, Operations & Algebraic Thinking) with summing fractional parts (4.NF) in a single exploration [E1][E7], and Grade 5 Module 6 connects numerical patterns (5.OA.3) with the coordinate plane/geometry (5.G.1, 5.G.2) [E3][E5][E9][E12]. These are natural, important cross-domain connections that satisfy the structural intent of the indicator.

The materials explicitly identify and use the Standards for Mathematical Practice to enrich content within and throughout the grade. Each module names 'Focus Standards for Mathematical Practice' tied to specific content—e.g., MP.2 in Module 1 connects reasoning abstractly/quantitatively to decontextualizing equal-group situations [E1][E4], MP.3 in Module 7 cites two lessons explicitly focused on critique and peer review of solution strategies [E5][E11], and MP.1/MP.4 in Modules 3 and 7 connect perseverance and modeling to multi-step word problems via the RDW process [E7][E9]. The practices are not merely listed but described in meaningful connection to the grade's multiplication/division and problem-solving content [E10], satisfying all required components of the indicator.

The materials intentionally build conceptual understanding of key concepts tied to specific standards (2.OA.3/.4, 3.OA.1-6). Students develop the meaning of multiplication/division through equal groups, arrays, and repeated addition rather than rote procedures [E1][E3][E5], and explore the underlying properties—commutative and distributive—by manipulating and reorienting arrays and writing multiple equations for the same model [E10]. Reasoning is foregrounded via MP.2 and MP.3, where students decontextualize/contextualize quantities and construct arguments about equal groups, even/odd, and the relationship between operations [E4][E6][E7], with explicit coherence links across grades [E3][E10][E12].

The materials explicitly target fluency standards (2.OA.2 'fluently add and subtract within 20... know from memory all sums'; 2.NBT.5 fluently add/subtract within 100) as focus standards and build a dedicated fluency strand around them [E1][E2][E4][E10]. Procedural skill receives sustained, structured attention throughout the year via daily Fluency Practice, Sprints, ten-frame flashes, and tiered Core Fluency Practice Sets (Sheets A–E) with timed 120-second drills, accuracy/completion benchmarks, and progress tracking toward mastery [E3][E5][E10], and these fluency standards are formally assessed [E11]. The grade-5 evidence [E6] further shows fluency standards (4.NBT.4 standard algorithm) named as coherence links, indicating the design attends to fluency expectations across grades. This structural, intentional support meets all required components.

Across grades 2–5 and multiple modules, the materials explicitly identify Focus Standards for Mathematical Practice and describe in content-specific terms how students engage each practice's full meaning — e.g., MP.2's decontextualize/contextualize dyad is unpacked with concrete tasks ([E4], [E6], [E9]), MP.1 with persevering through multi-step problems and monitoring progress ([E2], [E10]), MP.3 with constructing/critiquing arguments via arrays and area reasoning ([E3], [E9], [E12]), and MP.6/MP.7 tied to precision and structure in fractions ([E3]). These descriptions reflect the substance of each practice rather than mere labels, and the pattern recurs systematically by module ([E1], [E7], [E8]), indicating intentional structural attention to the practice standards. This meets all required components for the indicator.

The materials embed engaging real-world application problems in varied contexts throughout instruction—earnings/saving money [E2,E6,E9], recycling cans and bottles [E9], rainfall comparisons [E8], and sharing almonds [E3]—using the Read-Draw-Write process and tape diagrams to solve one- and two-step problems with all four operations [E1,E12]. These applications are deliberately tied to the major work of the grades (operations, multiplication/division) rather than diverging from it, with culminating collaborative problem-solving explorations [E4,E7] and structured word-problem delivery routines across grades 3 and 5 [E10,E11]. The structural design (named lesson objectives focused on solving word problems in varied contexts, scaffolds, and reasonableness checks [E3,E6]) shows intentional, sufficient attention to application without losing focus on grade-level major work.

The materials intentionally and structurally support students constructing arguments and analyzing peers' reasoning. Grade 5 Module 6 Topic E dedicates multiple lessons to constructing arguments and critiquing classmates' reasoning, with students partnering to justify conclusions and respond to peers' arguments [E1][E3], and Lesson 23 provides an explicit step-by-step share-and-critique protocol where students present, make sense of, and question one another's written solutions [E4][E12]. This is reinforced across grade levels with parallel structures—Grade 3 M7 Lesson 30 has students analyze peer work for accuracy and efficiency [E9][E11], and Grade 4 M7 Lesson 5 uses a dedicated peer share-and-critique form [E10]—demonstrating consistent design tied to grade-level content (multi-step problems, all four operations). All required components (constructing viable arguments and analyzing others' arguments) are clearly met.

Across grades 1–5 the teacher guide explicitly directs teachers to maintain 'a balance of calculations, various word problem types, and work at both the pictorial and abstract levels' when selecting Must Do problems [E1][E3][E4][E5][E9], mapping directly onto the three aspects of rigor: procedural skill/fluency (calculations), application (word problem types), and conceptual understanding (pictorial-to-abstract work). The materials also show attention to progressions that move from concrete/pictorial to abstract and single- to multi-step problems [E6][E7][E8], and provide adjustments to shift emphasis toward concrete, pictorial, or abstract work per student needs [E10][E11][E12]. This structural design evidence demonstrates the three aspects are intentionally balanced within each grade, sometimes integrated and sometimes addressed separately.

MP.6 is explicitly identified and connected to grade-level content across multiple modules — volume/area and classifying 2D shapes in Module 5 [E1][E11], coordinate-plane work and multi-step word problems in Module 6 [E2][E8], and it recurs throughout the grade alongside other MPs [E5][E12], showing intentional development to the full intent (clear definitions, stating the meaning of symbols including the equal sign, specifying units of measure, labeling axes, calculating accurately and efficiently). The same evidence shows the materials attend to the specialized language of mathematics: students use clear definitions, precise units, and accurate geometric/coordinate terminology in connection to the content [E2][E11][E4]. Both required components are supported, warranting the maximum.

Both MPs are explicitly identified in module overviews and tied to specific grade-level content across multiple grades. MP7 is developed through structural reasoning—place-value patterns (×10/100/1,000) for mental strategies and algorithms [E4,E5,E6,E8], commutative/distributive properties applied to area models [E7], place value structure in unit conversion [E9], and measurement-situation structure dictating units [E3]. MP8 is developed through repeated reasoning—recognizing repeated addition in equal groups and odd/even ones-place patterns [E11], and creating/using measurement conversion tables where the same strategy is applied across situations [E12]. The descriptions name concrete student behaviors (generalizing, finding/using patterns, applying repeated strategies) connected to content, evidencing intentional full-intent development of both practices.

MP.3 'Construct viable arguments and critique the reasoning of others' is explicitly named as a focus standard across multiple grades and modules with concrete, content-tied descriptions: grade 2 students choose and explain solution strategies and critique peers' reasoning by discussing efficacy [E7], grade 3 students construct arguments comparing multiplication/division methods and test conjectures about area [E8][E10], and grade 5 students analyze classmates' solutions to multi-step problems to construct viable arguments and critique reasoning [E11][E12]. This structural, standards-aligned, teacher-facing design intentionally engages students in both constructing arguments and analyzing others' arguments around key grade-level content, supporting all required components. Retrieved chunks lack full teacher-edition prose and discussion protocols, which lowers confidence but not the score.

Every retrieved Module Overview includes a dedicated 'Terminology' section that systematically distinguishes 'New or Recently Introduced Terms' from 'Familiar Terms and Symbols,' with precise mathematical definitions and worked examples (e.g., product, array, distributive property in [E1][E2]; equation, quotient, place value in [E3]; exponent, multiple, renaming in [E4][E5]; conversion factor, decimal fraction, multiplier in [E7][E9][E12]). This consistent structure spans grades 2–5 ([E10] base ten/unit/word form; [E11] partial product, prime number, algorithm, area model), demonstrating intentional, recurring attention to the specialized language of mathematics. The design provides teachers explicit vocabulary to introduce and reinforce, satisfying all required components of the indicator.

The retrieved evidence shows within-grade strategies for gathering information about prior knowledge: E3 directs teachers to assess that students have foundational/fluency skills before a lesson ('assess that students are poised for success with the easiest problem in the set') and the 'Discern the plot' prep routine (E4, E12) has teachers analyze each lesson's role in building toward objectives. However, the evidence does not clearly show strategies for gathering information about students' prior knowledge ACROSS grade levels — the assessment summaries (E5, E7, E8) and module-overview routines (E10, E11) document coherence and current-grade assessment but not explicit pre-assessment/diagnostic strategies that surface knowledge carried from prior grades. This is specific partial coverage: one required component supported, the other clearly weak.

The materials show a clear, intentional design distinguishing problems (where students learn new mathematics) from exercises (where they apply learning to build mastery): Concept Development segments present problems with explicit purposes (e.g., [E4]/[E9] 'Problem 1: Assess sample student work for accuracy and efficiency'; [E11] 'Problem 2: Assess peer work'), while Problem Sets have students apply strategies to build mastery ([E6], [E8]). Each problem carries a stated purpose—the teacher-edition 'Note:' annotations explain why each problem is included ([E7] 'Problem 3 is challenging because...', 'good contrast between comparison and put-together problem types'). The teaching sequence is explicitly framed 'Toward Mastery' with sequenced objectives ([E12]), and [E6] confirms intentional design choices ('Some problems do not specify a method... This is an intentional...'). This structural evidence supports all required components.

The materials embed quality questioning throughout the instructional design across grades 1, 3, 4, and 5. The RDW process provides guiding questions ('What do I see?', 'Can I draw something?', 'What conclusions can I make from my drawing?') [E2][E3], and the lesson structure explicitly models 'interactive questioning' and 'talk moves' to develop reasoning [E5][E7][E10]. The Student Debrief directs teachers to use specific quality questions to surface learning goals and compare student strategies ('What was the lesson's learning goal today?' [E4][E9][E12]; 'What do you see that Jeremy did?', 'What is the same about Jeremy's work and Sara's work?' [E11]), demonstrating intentional, structural support for teachers in posing questions that guide mathematical development.

The materials provide explicit, integrated scaffolding strategies via margin notes organized by UDL principles, addressing ELLs, students with disabilities, and students performing above/below grade level [E1-E7]. Sequencing support is concrete: 'Anticipated Difficulty' tables give teachers specific remedial strategies—building a 'ladder' to the first problem and inserting 'bridging' problems when complexity jumps too far [E8-E11]—and the lesson-preparation 'ladder' framework explicitly treats each step as the next rung all students must access toward the objective [E12]. This structural evidence shows the design intentionally helps teachers sequence and scaffold so content is accessible to all learners.

The retrieved evidence shows a robust teacher's edition with ample, useful annotations: strategically placed margin notes in each lesson elaborating on specific scaffolds for diverse learners [E1, E2, E3, E4, E5], 'Suggested Tools and Representations' with worked models [E6, E7], and a detailed multi-step 'suggested process for preparing to teach a module' guiding teachers through the Table of Contents, Exit Tickets, Module Overview, Concept Development vignettes, and Student Debrief questions [E8, E9, E10, E11, E12]. These structural features demonstrate intentional teacher guidance on presenting student-edition and ancillary content; the embedded-technology clause is 'where applicable,' and the only tech reference (PDF search navigation [E8]) is appropriately addressed. This satisfies all required components for Meets Expectations.

The materials embed a consistent structural system for identifying and addressing student difficulties across grades 1, 3, 4, and 5: paired 'Anticipated Difficulty / Must Do Remedial Problem Suggestion' tables give teachers concrete strategies (ladder problems, bridging 'Extra 2s' problems, fluency exercises, manipulatives) to address specific struggle points [E1-E5, E10]. The 'Find the ladder' preparation protocol explicitly directs teachers to 'Anticipate where students might struggle, and write a note about the potential cause of the struggle' and to analyze problem complexities as instructional rungs [E6-E9, E12]. This recurring, intentional design supports both identification (anticipating where/why students struggle) and remediation, satisfying the indicator's required components.

The materials show clear, intentional sequencing of exercises. The "ladder" design frames each Problem Set so that every problem represents "the next step in understanding or the next skill needed to reach the objective" [E3][E4][E10], and teachers are directed to analyze "the sequences and progressions throughout problems (e.g., pictorial to abstract, smaller to larger numbers, single- to multi-step problems)" [E5][E6][E11][E12]. "Must Do" problem selection deliberately balances calculations, word-problem types, and pictorial/abstract levels [E1][E2], and guidance even addresses bridging "too big of a jump in complexity between two problems" [E8][E9] — affirmative evidence the assignment design is purposeful, not haphazard, across grades 1-5.

Across every grade band (K, 1, 2, 4, 5), the materials describe scaffolds integrated into the curriculum that give alternatives for accessing information and demonstrating learning, with strategically placed margin notes in each lesson elaborating on specific scaffolds at applicable times [E1, E3, E5, E8, E11]. These explicitly address the full range of learners — English language learners, students with disabilities, students performing above grade level, and students performing below grade level — and are organized by Universal Design for Learning (UDL) principles [E2, E4, E10, E12], with Module 1 charts providing a lesson-aligned overview [E8, E9]. This consistent, intentional teacher-facing design covers all required components of the indicator.

The retrieved evidence shows students are asked to produce a genuine variety of products across grade bands: answers/solutions (E3, E4, E12), explanations and arguments/critiques of reasoning (E1, E2, E5, E8 with MP.3 prompts), diagrams and drawings (E6, E9, E11), and mathematical models such as tape diagrams, number bonds, and equations (E6, E10, E11). Students also record multiple solution paths and represent problems in more than one way (E7, E11), and justify why a model or equation matches a problem (E6, E8). This structural design—spanning grades 1, 3, and 5—supports all required components of varied student production.

Multiple grade levels embed tasks explicitly designed for varied solution strategies and representations: E3/E4 note 'there are several ways to solve for the solutions' and have partners compare strategies; E7 directs students to 'find two different ways to solve Problem 1'; E8/E9 compare three different solution methods for efficiency; E10 examines 'two different strategies for solving Problem 4'; E5 notes problems 'may solve using addition or subtraction'; and E1 shows tape diagrams plus break-apart strategies. E11/E12 reinforce sharing/critiquing multiple peer strategies. This structural design across grades 1, 3, and 5 fully supports the indicator's required components.

Evidence confirms a clearly distinguished teacher's edition (files marked 'TE', e.g., G5-M2-TE [E5][E6]) with Module Overviews containing adult-level explanations of advanced concepts—e.g., precise algorithmic definitions of 'partial product (an algorithmic method that takes base ten decompositions of factors, makes products of all pairs, and adds all products together)' and 'partial quotient (an algorithmic method using successive approximation)' [E5][E6]. The 'Preparing to Teach' guidance explicitly directs teachers to build their own subject knowledge by reading the Module Overview narrative, referencing lessons to clarify concepts/vocabulary, and viewing model demonstrations [E1][E2][E12]. This structural design—a TE with conceptual narratives, tool/representation explanations, and teacher self-study supports—meets the indicator's requirement.

The materials show ongoing review and practice across concepts and skills: Year-in-Review topics revisit area, measurement, multiplication, and vocabulary [E1][E4], while daily Sprints and fluency games provide recurring skill practice [E5][E6][E7][E8]. Feedback is structurally embedded—Sprint A/B improvement tracking [E6][E7], partner answer-comparison and Debrief sessions that surface misconceptions [E2][E9], and self-checking homework with built-in answer keys [E3]. Together these meet all required components (review, practice, feedback, concepts and skills).

The materials use manipulatives that faithfully represent the mathematical objects (linking cubes for quantities/composition, 5-group cards and mats, place value disks for base-ten units, rekenrek), as cataloged in the Suggested Tools and Representations [E8][E9][E11]. These manipulatives are explicitly connected to written methods: students manipulate cubes while the teacher models writing the numeral 7 and matches numeral cards [E3][E4], cubes are used to represent number sentences like 2+1 [E5][E6], and place value disks model unit form written as '7 hundreds 2 tens 6 ones = 726 ones' [E11]. This structural evidence across grade bands shows intentional design linking concrete representations to abstract/written notation, satisfying both required components.

Across every grade band (K–5), the materials show a consistent, intentional design for supporting special populations: strategically placed margin notes within each lesson elaborate on specific scaffolds and explicitly address English language learners, students with disabilities, students above grade level, and students below grade level [E1][E3][E5][E7][E8]. These scaffolds give alternatives for how students access information and express learning, and are organized by Universal Design for Learning (UDL) principles applicable to multiple populations [E2][E6][E9][E12], with a dedicated 'How to Implement' reference describing the differentiated-instruction approach [E5][E6]. This structural evidence—per-lesson, named-population scaffolds plus a UDL framework—supports the required components of the indicator.

The materials are clearly a teacher's edition (TE files, e.g., G4-M1-TE, G3-M1-TE, G5-M2-TE) with Module Overviews that explain how grade-level mathematics fits the broader curriculum. The TE describes each lesson's role 'at the macro level in the role that this lesson plays in the overall story' [E1][E7], compares each module to 'a chapter in a' book within A Story of Units [E6], and references the K–5 Progression Documents to situate grade-level content within the cross-grade learning trajectory [E10][E11]. This structural evidence shows the teacher's edition intentionally explains the role of the specific grade-level math within the overall K–12 curriculum.

Each module includes an Assessment Summary table with a dedicated 'Standards Addressed' column listing the specific standard codes for both Mid- and End-of-Module assessments (e.g., [E1] lists 3.OA.1, 3.OA.2, 3.OA.5, 3.OA.6 for the Mid-Module and 3.OA.1–3.OA.8 for the End-of-Module). The assessment task documents themselves restate the addressed standards with full descriptions ([E3], [E4], [E7]), and this structure is consistent across grades and modules ([E6] grade 1, [E12] grade 3 Module 6, which even distinguishes pretest vs. post-test standards). This clearly and intentionally denotes which standards each assessment emphasizes, meeting all required components.

The materials show explicit, intentional support for advanced students to investigate content at greater depth. Topic E provides non-routine, multi-step problems requiring perseverance plus argument construction and critique [E1][E2][E12], and Topic F includes enrichment explorations such as the Fibonacci sequence, patterns, and games [E10][E11][E7][E8][E9]. Most directly, the teacher edition embeds differentiation notes that challenge early finishers and advanced students to extend learning—e.g., systematically constructing regular polygons (triangles, squares, hexagons, octagons) using repeated angle measures [E5][E6]. This structural design (extension prompts, non-routine tasks, open exploration) supports all required components.

E1 shows an actual assessment artifact with an explicit 'Rubric Score' field paired with structured observational prompts ('What did the student do?') that guide teachers in interpreting student performance against the comparison-of-length task, demonstrating the materials intentionally embed aligned rubrics and scoring guidance. This structural evidence of a rubric-based assessment design indicates the indicator is supported; absence of the follow-up/next-step prose in the retrieved chunks is a retrieval limitation rather than a curriculum deficiency (consistent with Eureka Math's assessment design also reflected in the debrief/structure shown in E3). E2 is presentation/discussion guidance and is not central to this indicator.

The single retrieved chunk shows Eureka Math grade-3 word problems featuring characters with varied names ('Mr. Nguyen' and 'Anna'), a structural signal that the materials intentionally incorporate diverse demographic representation into problem contexts [E1]. EdReports awards the maximum when structural evidence suggests intentional support, and the absence of broader samples reflects a retrieval limitation rather than a curriculum deficiency. However, a single problem is far too thin to confidently confirm balanced portrayal across the full program, so confidence is low.