Open Up Resources K-5 Math

Structural evidence shows the materials are intentionally designed around the major work of each grade. Across grades 2-5, units explicitly state goals tied to major clusters—fractions on the number line and single-digit multiplication/division fluency [E1, E11], fraction operations and multi-digit arithmetic [E2], multi-digit division/multiplication and volume [E3], and add/subtract within 20/1,000 plus story problems [E9]—and these units also embed connections between supporting work (measurement and data) and major work (e.g., 'Apply concepts of measurement and data to solve problems') [E1]. The teacher guide documents a coherent progression organized by the standards [E8], and the End-of-Course Assessment's longest portion assesses the major work of the grade [E7]. This intentional design across all grades supports the indicator's requirement that the majority of materials address the major clusters.

Structural evidence shows the materials intentionally provide extensive grade-level work organized around the major work of each grade, with unit and section goals explicitly tied to grade-level standards across multiple grades ([E3], [E5], [E7], [E9]). The practice system supports extensive engagement—lesson practice problems for each lesson, distributed practice revisiting content over time, and exploration problems ([E1], [E2])—while off-grade content is deliberately kept supplementary: 'Are You Ready for More?' is explicitly opt-in and not expected of all students, and pre-unit prior-grade problems are framed as review ([E2], [E6]), so off-grade material does not displace grade-level work. The three-tier alignment scheme (building on, addressing, building towards) further evidences intentional design to meet the full intent of grade-level standards ([E10]).

Structural evidence shows IM Math intentionally designs assessments around grade-level standards: end-of-unit and end-of-course summative assessments are aligned to standards and assess the major work of the grade [E8][E12], while above-grade/prior-grade content is confined to formative pre-unit problems and 'Check Your Readiness' diagnostics that are explicitly used for review and pacing rather than holding students accountable [E1][E2][E11]. Above-grade items in diagnostics are described as rare and used only to tune instruction [E11], so they could be removed without impacting the structure of the materials. No retrieved evidence indicates K-5 assessments explicitly test probability, statistical distributions, or transformations/congruence.

Structural evidence shows supporting work is intentionally connected to major work rather than treated separately. The teacher guide (E4) explicitly states the in-depth culminating problems are 'usually focused on supporting work of the grade that provides a context where students apply the key ideas they have learned over the year' — a deliberate design linking supporting content to major work. The 'Putting It All Together' units reinforce this: Grade 3 pairs measurement/data application (supporting) with fraction and multiplication work (major) [E1,E7], Grade 4 connects measurement comparison with fraction and place-value operations [E3,E9], and Grade 2 embeds measurement tasks ('Measure on a Map,' 'Measure and Plot') within fluency and place-value work [E11]. These cross-grade patterns demonstrate connections that enhance focus on major work.

The materials show intentional within-grade connections across clusters/domains. The end-of-year 'Putting It All Together' units explicitly consolidate major work spanning fractions, multi-digit base-ten operations, and measurement [E2][E3][E5], connecting multiple major clusters/domains. Grade 5 Unit 5.2 connects fractions-as-quotients (NF) with division/multiplication and area concepts [E6], and Grade 3 Lesson 7 connects multiplication and division within OA [E10]. The K-5 progressions mapping table further documents deliberate cross-cluster connections by unit [E11], evidencing major-to-major connections throughout the grade-level materials.

Both required components are supported with content-level explanation, not just standard codes. Prior knowledge is explicitly related to grade-level work in lesson narratives describing specific earlier-grade content: 'In grade 3, students were introduced to fractions as numbers...' [E5], 'In grade 4, students studied decimal fractions with denominators 10 and 100...' [E11], and 'In grade 3, students reasoned about equivalent fractions...' [E12], reinforced by pre-unit/prerequisite design [E7][E8] and 'building on' alignments [E9]. Future content is identified and related via narratives describing connections to upcoming grade-level work [E1], curated articles on where concepts lead beyond the grade [E2], progressions-document mappings [E3], 'Are You Ready for More?' connections to the K-12 curriculum [E4], and explicit 'building towards' alignments [E9].

Both MPs are intentionally identified and connected to grade-level content across the grade band. MP1 is developed through rich problem-solving lessons where students make sense of and persevere on problems—e.g., Grade 3 Lesson 19 (two-step word problems, 3.OA.D.8, deciding if answers make sense) [E8], Grade 1 Lesson 26 (story problems, 1.OA) [E4], plus teacher reflection prompts [E11]—and supported by the 3 Reads sense-making routine [E10][E12]. MP2 is developed via quantitative/abstract reasoning lessons tied to content—e.g., Grade 4 Lesson 6 fractions [E5] and Lesson 8 interpreting remainders/reasonableness [E6]—with Lesson 12 explicitly carrying both MP1 and MP2 [E2]. Student-facing 'I Can' learning targets for MP1 and MP2 [E1][E3] and the lesson-narrative design describing how practices 'come into play' [E7] confirm intentional, full-intent development of both.

The materials are explicitly designed to develop conceptual understanding: the teacher guide describes a 'Developing Conceptual Understanding and Procedural Fluency' design principle and a concrete-to-abstract progression where ideas are introduced concretely then extended to diagrams, tables, and symbols [E1][E10][E12]. Grade-level units explicitly target conceptual standards/clusters — e.g., Grade 3 fractions as numbers (3.NF) [E3], Grade 5 fractions as quotients/multiplication (5.NF) [E6], and Grade 2 building multiplication foundations via arrays [E4][E9]. The lesson structure also provides independent demonstration: launch, then independent work time to grapple individually before group work, plus a cool-down to apply learning [E2][E10], satisfying both the 'develop' and 'independently demonstrate' components throughout the grade level.

The teacher guide explicitly frames the design around 'Developing Conceptual Understanding and Procedural Fluency' [E1], and fluency goals appear as named unit/section goals across multiple grades (e.g., 'Fluently add and subtract within 20/100' [E3][E4][E6][E7], 'Fluently multiply multi-digit whole numbers using the standard algorithm' [E9][E10]), aligning directly to the fluency standards the Evidence Guide cites (1.OA.6, 2.NBT.5, 3.OA.7, 4.NBT.4/5.NBT.5). Materials develop these skills progressively—building toward the standard algorithm with support before independent use [E12], and developing strategy-based fluency [E11]—satisfying the 'develop' component. Students independently demonstrate fluency through dedicated structures: fluency reflection/practice lessons [E2], centers designed to practice skills across the year [E8], and end-of-course assessments [E5], satisfying the independent-demonstration component. Both required components are met with structural evidence across the grade band.

Both halves of MP3 are intentionally developed in connection to grade-level content. Construct viable arguments: student-facing 'I Can' statements for MP3 (E1), preparing visual displays and explaining why solutions make sense (E7, E8), and 'making arguments' framed as core to doing grade-level mathematics (E10), with output principles targeting explaining reasoning and making generalizations on unit concepts (E6, E9). Critique the reasoning of others: dedicated error-analysis routines (Critique/Correct/Clarify) where students analyze flawed statements, identify reasoning errors, and improve them (E2, E3, E11), plus Compare routines where students tour and critique each other's work with teacher-provided probing questions (E7, E8). Teacher guidance for discourse, clarifying/probing questions, and comparing methods is explicit (E5, E11), satisfying full intent.

The materials include multiple routine and non-routine applications across grade levels: routine problem-solving (E4, Grade 4 fraction problems) and non-routine modeling tasks where students make assumptions and choose strategies—designing a carnival game (E2/E5, Grade 3), planning a garden (E3, Grade 3), creating a sticky-note design (E8, Grade 4), and planning a book fair (E11, Grade 5), all explicitly tagged MP4. The teacher guide confirms intentional design: anchor contexts motivate concepts and most units end with a real-world application lesson (E1), and the lesson structure builds in independent work time before peer collaboration (E7, E9), giving students opportunities to independently demonstrate applications. Both required components are met with consistent structural support throughout the grades.

Both required components are supported. MP6 is intentionally developed and connected to grade-level content via explicit student-facing 'I Can Attend to Precision' statements (e.g., 'I can use units or labels appropriately') [E1] and through instructional routines deliberately mapped to MP6, such as Which One Doesn't Belong for attending to precision [E2], with lesson routines embedding 'precision with language' [E4]. The materials also clearly attend to the specialized language of mathematics through systematic Mathematical Language Routines that amplify disciplinary language, refine precision in communication [E6][E7][E11], and formalize accurate definitions of terms previously encountered informally [E9]. Together these satisfy both the MP6 intent and specialized-language criteria for a score of 2.

Materials structurally support both constructing viable arguments and critiquing others' reasoning across grade bands. Explicit MP3 'I Can' standards ('explain or show my reasoning... listen to and read the work of others and offer feedback') anchor the design [E1], reinforced by recurring instructional routines like 'Critique, Correct, Clarify' that engage students in analyzing others' mathematical writing [E2][E7][E12] and 'Compare and Connect' for examining peers' approaches [E4]. A concrete grade-4 lesson explicitly tags MP3, having students judge whether classmates' statements are true/false, justify decisions, and revise their own claims to be stronger [E9], with parallel middle-school support for analyzing and critiquing reasoning [E6]. This evidence meets all required components tied to key grade-level content.

The materials explicitly attend to balancing the three aspects of rigor, with a dedicated 'Balancing Rigor' framing [E1] and an account of activities designed variously for developing a concept, mastering a procedural skill, or applying mathematics to real-world problems—showing all three present independently [E3][E4][E5][E11]. They also engage multiple aspects simultaneously: the materials state the three aspects are 'interwoven'/'interconnected,' with procedural fluency supported by understanding and application requiring both understanding and skill [E3][E6], and anchor contexts used to motivate concepts [E11]. This structural evidence supports both required components (independent presence AND simultaneous engagement) throughout each grade level.

Both MPs are intentionally developed and connected to grade-level content. MP7 appears explicitly across multiple grade-4 lessons on pattern structure (E4, E6, E8 'look for and make use of structure (MP7)') and grade-1 base-ten representations (E1), with student-facing 'I Can' statements (E7). MP8 is developed through repeated-reasoning lessons (E2 'look for and make use of structure' plus reasoning about repetition mathematically in E4), MP8 'I Can' statements about using patterns to come up with a general rule (E7), and routines like Number Talks explicitly tagged MP7/MP8 (E3). The unit-level Mathematical Practice chart (E9, E10) shows intentional, designed placement of MP7 and MP8 across units, and lesson narratives describe how MPs come into play (E12).

Materials provide intentional, teacher-supported structures for constructing arguments and analyzing others' reasoning: a dedicated 'Correct' routine engages students in critiquing a written statement with conceptual errors, supported by teacher meta-think-alouds and guiding questions like 'Are there any reasoning errors?' [E1][E3][E9]. MP3 'I Can Construct Viable Arguments and Critique the Reasoning of Others' is explicitly named with student-facing descriptors [E2], and Compare/Display routines have students tour and investigate each other's work with teacher-provided questions [E6][E10]. Warm-ups and lesson syntheses systematically prompt students to share reasoning and respond to others, with teachers positioned as facilitators of student thinking [E11][E12], satisfying both components of the indicator.

The materials explicitly and systematically attend to the specialized language of mathematics through eight Mathematical Language Routines embedded in lessons and design principles focused on disciplinary language [E6][E9][E2]. Each instructional unit includes an overview of the progression of academic language, and there is a student glossary with illustrations/diagrams plus routines that formalize definitions of mathematical terms previously encountered informally [E8][E10]. The curriculum addresses reading, writing, speaking, listening, conversing, and representing in math, and routines like Collect and Display capture and reference mathematical/disciplinary language over time [E3][E5][E11]. This structural evidence (named routines, per-unit language progressions, glossary, teacher-guide design) supports all required components of the indicator.

The materials provide comprehensive supply lists at multiple levels. Each lesson includes a 'Required Materials' section subdivided into 'Materials to Gather,' 'Materials to Copy,' and 'Required Preparation' [E2, E4, E7, E11], specifying exact quantities (e.g., 'Each group of 4 needs at least 8 pencils' [E11]). The teacher guide describes the overall supply design, including blackline masters, photocopying/cutting needs, and storage recommendations [E3, E6], and provides a grade-by-grade index of where reusable blackline masters first appear [E10]. This structural evidence across course, unit, and lesson levels demonstrates a comprehensive materials list.

The materials provide comprehensive guidance through unit, lesson, and activity narratives that explain the mathematical content, its place in the learning sequence, and how mathematical practices come into play [E2][E5][E6], plus front-matter Design Principles and a problem-based instructional framework articulating the teacher's role as listener, facilitator, and questioner [E9][E10][E12]. They also include sufficient, context-specific annotations tied to learning objectives: 'advancing student thinking' questions for monitoring [E8], cool-down 'Response to Student Thinking' with next-day/prior-unit support [E8], embedded warm-up and lesson activity routines and MLRs [E11], and representation/task-complexity supports for engaging all students [E3][E4]. Both required components — comprehensive presentation guidance and useful annotations within specific learning objectives — are clearly supported.

The materials regularly provide specific, lesson-level strategies and supports for students in special populations: 'Access for Students with Disabilities' supports are 'included in each lesson' and each is aligned to one of the three UDL principles—engagement, representation, action and expression [E3], [E6], [E10]. Supports are tagged with the areas of cognitive functioning they address so teachers can select appropriate ones [E12], and concrete strategies are detailed (manipulatives, assistive technology, graphic organizers, sentence frames, multiple modalities, graduated scaffolding) to enable access to rigorous grade-level content rather than below-grade work [E1], [E7], [E8], [E9], [E11]. This goes well beyond a generic chapter-opening statement, satisfying all required components.

The materials provide multiple structural opportunities for advanced students to engage grade-level math at higher complexity: the MS 'Are You Ready for More?' problems 'go deeper into grade-level mathematics,' are 'not routine or procedural,' and explicitly 'not just the same thing again but with harder numbers' [E1][E2], and the K-5 Exploration problems are 'more open-ended and challenging' and likewise 'go deeper into grade-level mathematics' [E4]. Both are described as opt-in extensions of learning rather than additional/more problems—directly satisfying the 'no instances of advanced students doing more problems than classmates' requirement [E1][E4]. This meets both required components for full credit.

The materials clearly contain both required components. Adult-level explanations of complex grade-level concepts appear through unit/lesson/activity narratives and curated essays addressing challenging topics like fraction division (with justification for invert-and-multiply), order of operations, and equivalent fractions [E2][E3][E6][E9][E12]. Adult-level explanations of concepts beyond the current course are explicitly curated—IM states articles show 'where concepts lead beyond the indicated grade level' [E1], including the number line K-12, trigonometry as an example of angle concepts beyond elementary, and the Number System 6-8 progression for K-5 teachers [E7][E12]. This structural design (named scholarly articles by McCallum, Lahme et al., plus Progressions mappings) intentionally supports teacher content knowledge of both grade-level and beyond-grade-level mathematics [E11].

Both required components are evidenced. Correlation information is present: the materials describe a three-tier standards alignment system (building on, addressing, building towards) [E1] and provide a domain-to-unit mapping tied to the CCSSM progressions documents [E2]. Explanations of the role of grade-level mathematics in the context of the series are also present: grade, unit, lesson, and activity narratives describe connections to prior and upcoming grade-level work and whether scope/sequence decisions are required by the standards [E3][E7][E8], and curated articles explain where concepts lead across the K–12 series [E9]. This satisfies both the correlation-present AND role-in-context requirements for full marks.

The teacher guides explicitly state that 'All summative assessment problems include a complete solution and standard alignment' across both K-5 [E4] and 6-8 [E10] materials, indicating standards are identified at the item level for end-of-unit, mid-unit, and end-of-course assessments. The materials systematically describe a coherent assessment system of formal summative assessments [E1][E12][E7] with consistent standard alignment, satisfying the requirement that materials consistently identify standards assessed for formal assessments. This is structural evidence of intentional, consistent standards identification across the series.

The materials explicitly state that all summative assessment problems include standard alignment: 'All summative assessment problems include a complete solution and standard alignment' for both K-5 [E3] and middle school [E2]. The end-of-course/end-of-unit assessments are organized to assess major work of the grade and key unit concepts [E3][E11], and assessments are tied to specific units with named goals [E9], showing standards being emphasized are clearly denoted. This structural evidence supports all required components of the indicator.

The materials include aligned rubrics for restricted constructed response and extended response items with tiered scoring descriptions that define performance levels (e.g., Tier 1-4 conceptual understanding/mastery) [E1][E2], and all summative problems include complete solutions and standard alignment, with distractors tied to common errors as a diagnostic [E4][E10][E12]. Scoring guidance for interpreting performance is supported by commentary on expected responses and potential misconceptions [E3][E9], and follow-up is explicitly addressed through next-day/prior-unit support and item-by-item guidance on diagnostic results [E5][E11]. This structural evidence supports all required components — aligned rubrics, scoring guidelines for interpretation, and follow-up suggestions.