Open Up Resources 6-8 Math

The materials (Illustrative Mathematics) are structured so that all students engage extensively with grade-level problems: each grade has 8-9 units containing 8-28 lesson plans, with lessons built around one to three instructional activities that 'make up the majority of the time spent in class' [E2][E5], plus pre-unit practice, checkpoints, and end-of-unit assessments [E4]. Assessments explicitly target the major work of the grade [E3], and the progressions mapping ties each unit to grade-level standard clusters across domains [E9], evidencing coverage of the full intent of grade-level standards. Centers and fluency work reinforce and build grade-level content for all students rather than substituting off-grade material [E7][E8], and student materials are maintained in both English and Spanish so all students access the same grade-level work [E11]. This structural evidence supports both required components—extensive grade-level work and full intent of standards.

The materials demonstrate a deliberately grade-level-aligned assessment system: summative assessment problems all include standard alignment, and the End-of-Course Assessment's longest portion assesses the major work of the grade [E7]. Section checkpoints assess section learning goals and pre-unit diagnostics target prerequisite (earlier-grade) concepts rather than holding students accountable for future content [E2][E1][E3]. Where upcoming-grade ideas appear on pre-unit diagnostics, they are explicitly used for pacing/diagnosis, not graded accountability [E3]. The progressions mapping and standards-alignment design (building on/addressing/building towards) confirm assessments are anchored to grade-level standards [E9][E11], supporting the indicator's full intent.

The materials are structured so the majority of work targets the major clusters of each grade: the End-of-Course Assessment's longest portion explicitly 'assess[es] the major work of the grade' [E3], and the curriculum's nine-unit story per grade is built around developing the grade's core concepts [E5]. Supporting work is intentionally connected to major work — in-depth and culminating problems use supporting-work contexts to apply the key ideas learned over the year [E1], [E7], and application lessons consolidate ratios/proportional reasoning and other major-cluster work [E6], [E11]. Optional lessons [E8], [E9] are clearly flagged as such, indicating the required core remains focused on major work. Structural design evidence supports that ≥65% of materials address major clusters, meeting the indicator.

Following the authoritative Evidence Guide for 1d (supporting content connecting to major work), the materials show intentional connections rather than treating supporting work separately. E12 explicitly describes in-depth problems '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 direct connection from supporting to major work. E1 and E8 confirm that grade-, unit-, lesson-, and activity-level narratives describe how mathematical ideas connect to prior and upcoming work, and E5 maps progressions per unit, evidencing a deliberately coherent design where connections enhance focus on major work.

The teacher guides show intentional structural support for connecting mathematics within the grade: grade/unit/lesson/activity narratives explicitly describe 'connections among standards' and how ideas are organized across domains [E1], and the progressions-document mapping table ties each unit to multiple domains and standards clusters within a grade [E2]. Distributed practice deliberately revisits content across units and topics [E12], and 'Are You Ready for More?' problems 'make connections between the topic at hand and other concepts' [E9], indicating cluster-to-cluster connections are built into the design throughout the grade. While much retrieved evidence emphasizes cross-grade progressions rather than naming specific within-grade major-to-major cluster connections, the structural design (narratives, standards mapping, integrated units) supports that such connections are present throughout.

Both required components are supported by structural evidence. For prior-knowledge connections, the teacher guides build coherence through narratives describing 'connections to prior...grade-level work' [E1], a 'building on' standards-alignment category that explains how activities reflect work of prior grades [E5], pre-assessments and initial lessons that activate prior knowledge [E11], and progressions-document mappings tied to each unit [E4]. For future-content identification, the materials use 'building towards' alignments [E5], 'upcoming grade-level work' narratives [E1, E11], cross-grade progression resources connecting grade-level topics to later concepts like fraction division [E7], and explicit cross-grade extensions in 'Are You Ready for More?' [E3]. These are explanatory relationships, not bare standard codes, satisfying the Evidence Guide note.

The teacher guides explicitly describe an intentional design for developing conceptual understanding: units begin with pre-assessment and an entry lesson activating prior knowledge, with representations, concepts, and notation systematically introduced as the unit progresses [E1], and a stated commitment to balancing rigor including conceptual understanding [E2]. Concepts are deliberately built concrete-to-abstract — students begin with concrete examples and transition to diagrams/tables before relying on symbols [E8][E12], with representations chosen for their usefulness to specific learning goals [E3]. The lesson structure supports independent demonstration through independent work time before group work and a synthesis/cool-down to consolidate and apply learning [E2], and grade-8 units develop conceptual standards like 8.G.A (rigid transformations, congruence) and 8.EE/8.F (dilations, similarity, slope) by having students reason about and explain why properties are preserved, not just compute [E4][E9]. This structural evidence shows the materials both develop and let students independently demonstrate conceptual understanding throughout the grade.

Both MP1 and MP2 are explicitly identified with grade-appropriate 'I Can' learning targets that capture their full intent — MP1 includes making sense of problems, persevering ('show at least one try'), and checking solutions make sense [E3], while MP2 includes thinking about/showing numbers in many ways, identifying what can be counted, and connecting real-world situations to representations [E3]. Intentional development connected to grade-level content is structurally supported: unit-level Mathematical Practice charts highlight specific lessons per unit that showcase each MP across all eight/nine units [E8][E9], and lesson/activity narratives explicitly explain 'how the mathematical practices come into play' within the content sequence [E10][E11]. Materials also guide teachers to assess MPs formatively and use warm-up/lesson routines that elicit sense-making and reasoning [E2][E5], satisfying both required components.

MP3 is explicitly named and treated as part of doing mathematics ('making arguments and critiquing the reasoning of others') with lesson/activity narratives describing how the mathematical practices come into play in connection to grade-level content [E7][E2][E3]. Both halves of the full intent are structurally supported: the 'Critique, Correct' routine engages students in error analysis and considering an author's mathematical thinking, with teacher guidance to model respectful critique [E10], while warm-up/discussion routines, MLRs, and number talks elicit students explaining and justifying strategies to construct arguments [E11][E1]. Per-MP learning targets are provided to help teachers and students recognize engagement, indicating intentional development across the grade [E4]. This meets the full intent of MP3 in connection to grade-level content.

The materials (Illustrative Mathematics) intentionally develop procedural skill and fluency throughout the grade: the teacher guides explicitly define procedural fluency and describe balancing the three aspects of rigor [E2][E5], units begin with pre-assessments and systematically build skills, and aligned center activities exist specifically to support 'ongoing procedural fluency' across the year [E4][E8]. Students independently demonstrate these skills through independent work time [E3], end-of-unit assessments [E4], and dedicated fluency items targeting each grade's key fluencies via pre-chosen calculations and strategy games [E7]. Both required components — developing fluency and providing independent demonstration opportunities throughout the grade — are structurally supported.

The materials include multiple routine and non-routine applications throughout each grade: dedicated application lessons (E2 Pythagorean Theorem, E3 powers of 10, E10 volume/surface area) provide routine word problems with prescribed strategies, while culminating modeling lessons (E7 Designing a Tent, E9 Stained-Glass Windows, E11 Painting a Room) are non-routine tasks requiring students to make their own assumptions and choose strategies (MP4). The teacher guides confirm this is intentional design—most units end with a real-world application/culminating lesson where students apply learned mathematics (E1, E5, E12), and in-depth application problems exist at K-5 too (E8). Students independently demonstrate applications through these modeling tasks and opt-in extensions (E6), satisfying both required components.

MP6 is intentionally identified and connected to grade-level content across the band: K-5 'I Can Attend to Precision' goals about units/labels [E1], grade-8 powers-of-10 work requiring precision with units of measurement [E2], grade-7 measurement-error accuracy tagged MP6 [E4], and routines like Which One Doesn't Belong explicitly mapped to MP6 precision [E3]. Materials also intentionally develop the specialized language of mathematics through Mathematical Language Routines, Critique/Correct/Clarify error-analysis, formalizing definitions from informal encounters [E10], and four language design principles emphasizing precision and disciplinary language functions [E5][E7][E9][E11][E12]. Both required components are clearly supported, satisfying the 2-point band.

Structural evidence shows the materials intentionally and systematically support constructing viable arguments and critiquing others' reasoning (MP3). Student-facing 'I Can' statements explicitly target explaining reasoning and offering feedback [E1], and dedicated instructional routines (Critique-Correct/Compare) engage students in analyzing, correcting, and improving others' mathematical work across both K-5 and MS guides [E2][E4][E7][E12]. Grade-level lessons embed this in Teacher-Facing Learning Goals such as 'Critique arguments' about exponents and congruence [E9][E11], and language-function principles deliberately optimize output for critiquing reasoning [E5][E6]. All required components are present, so this meets expectations.

The materials show all three aspects of rigor present independently and engaged simultaneously. The teacher guides include explicit 'Balancing Rigor' design sections [E1] and describe activities designed variously 'to developing a concept, others to mastering a procedural skill, yet others to applying mathematics to a real-world problem,' noting these aspects 'are interwoven' [E3]. They further state the three aspects 'are interconnected: procedural fluency is supported by understanding, and deep understanding often requires procedural fluency... students must both understand and be able to do the mathematics' [E4], with design principles dedicated to developing conceptual understanding and procedural fluency together [E11] and dedicated application lessons [E8]. This structural evidence demonstrates both independent presence and simultaneous engagement of rigor across the grade.

Both MPs are intentionally developed and connected to grade-level content. MP7 is explicitly identified and central in lessons (e.g., grade-8 tessellation lessons where students use polygon structure to generalize, [E5][E6]) and embedded in routines like How Many Do You See and Number Talk [E1]. MP8 is developed through Number Talk routines [E1] and articulated to full intent via student 'I can' statements—identifying/describing patterns, noticing what changes/stays the same, and using patterns to derive a general rule [E4]. The unit-level Mathematical Practice charts ([E7][E9]) systematically map both MP7 and MP8 to specific lessons across every unit of the grade, and lesson narratives explain how the practices come into play [E11], confirming intentional, content-connected development across the grade level.

Materials provide structural support for both constructing arguments and critiquing others' reasoning across grade bands. The 'Correct' instructional routine ([E1], [E3], [E9]) explicitly engages students in analyzing another's mathematical writing, considering the author's thinking, and respectfully critiquing it, with teacher meta-think-alouds and guiding questions like 'Are there any reasoning errors?'. Student-facing MP3 'I Can' statements ([E2]) and routines for comparing/touring peer work ([E6], [E10], [E11]) further support teachers in facilitating argument and critique tied to grade-level content goals. The design is intentional and teacher-supported, satisfying all required components.

The materials intentionally and explicitly attend to mathematical language: a dedicated Mathematical Language Development section frames the linguistic demands of doing math (reading, writing, speaking, listening, conversing, representing) [E3], and a system of eight Mathematical Language Routines (Stronger and Clearer, Collect and Display, Three Reads, etc.) is embedded in lessons to develop disciplinary/academic language [E8][E11][E6]. Unit-level evidence shows direct attention to specialized vocabulary—e.g., grade 6 students learn and use terms like 'variable,' 'coefficient,' 'solution,' 'equivalent expressions,' and 'exponent,' including notational conventions [E4][E5]—and the materials provide a student glossary plus an 'Overview of the progression of academic language' for each unit [E10], with explicit routines to formalize definitions of terms encountered informally [E12]. This structural design satisfies all required components of the indicator.

Evidence shows the materials systematically embed quality teacher questions to guide mathematical development across both K-5 and MS teacher guides. Lessons include an 'advancing student thinking' section providing teachers questions that advance understanding of concepts, strategies, and connections [E1], and the teacher's role is explicitly defined as asking 'questions to advance students' thinking in productive ways' [E7]. Structured routines supply guiding questions (e.g., 'What do you think the author means?', co-craft questions) [E8][E2][E3][E11], plus per-lesson teacher reflection questions and sentence-frame/question-starter supports [E9][E10]. This comprehensive, intentional design across the series meets all required components of the indicator.

The materials provide comprehensive guidance through unit, lesson, and activity narratives that explain mathematical content, its place in the learning sequence, new terms, and how mathematical practices come into play [E2][E4][E8], plus a problem-based instructional framework articulating the teacher's roles as listener, facilitator, questioner, and synthesizer [E10][E12]. Annotations are tied to specific learning objectives: 'advancing student thinking' sections give teachers questions that advance understanding based on monitoring [E6], cool-downs offer next-day and prior-unit support guidance [E6], and design principles plus representation/UDL supports give actionable strategies for engaging students and addressing access [E5][E7][E9]. Both required components — comprehensive presentation guidance AND sufficient, useful contextualized annotations — are clearly supported.

Materials regularly provide strategies and supports for students with disabilities: each lesson includes labeled "Access for Students with Disabilities" supports aligned to the three UDL principles (engagement, representation, action/expression) [E3][E5][E10]. Specific, varied supports appear throughout — assistive technology, manipulatives, graphic organizers, visual/color-coding aids, sentence frames, and accommodations for visual impairments including SVG-scalable diagrams and Braille recommendations [E1][E8][E9][E11][E12]. These are embedded lesson-level supports tied to grade-level mathematical content, not generic chapter-opening statements, satisfying all required components of the indicator.

Both required components are clearly supported. Materials contain adult-level explanations of complex grade-level concepts through unit/lesson/activity narratives that deepen teacher understanding of the mathematics and its progressions [E2][E7][E10], plus curated CCSS progressions documents mapped to each unit [E11]. They also contain explicit adult-level explanations of concepts beyond the current course: IM curates articles/blog posts (McCallum, Umland, Gray, Phillips, et al.) on topics like the number line K-12, multiplication beyond repeated addition, fraction division with invert-and-multiply justification, equivalent fractions as units, and trigonometry — explicitly framed as where elementary concepts lead beyond the grade level [E1][E3][E5][E8][E9]. This satisfies both the grade-level and beyond-course requirements.

Materials provide multiple structural opportunities for advanced students to engage with grade-level math at higher complexity: the MS 'Are You Ready for More?' problems 'go deeper into grade-level mathematics' and are explicitly 'not routine or procedural...not just the same thing again but with harder numbers' [E1], and the K-5 Exploration Problems are similarly 'more open-ended and challenging' going 'deeper into grade-level mathematics' [E4]. These appear across the series on an opt-in basis as extensions of learning rather than additional/repetitive work [E1][E4], and the teacher guide explicitly addresses task complexity and extension supports [E6]. The design intentionally avoids advanced students simply 'doing more problems' — extensions are qualitative deepening, satisfying both required components.

This is IM Math, which is structurally built around standards correlation: lesson narratives explicitly explain each lesson's role within the unit and series — e.g., culminating lessons synthesizing prior work [E9], the 'final lesson on systems of equations' [E10], and explicit coherence/prior-connection framing ('students may have had experience with tape diagrams in earlier grades, and have seen some examples of their use in prior units') [E12]. Mathematical Practice standards are consistently correlated through 'I can' alignment statements [E4, E7] and tagged within lessons (MP4) [E11], and learning goals are articulated per lesson [E9, E11]. Both required components — correlation information and explanations of the grade-level role in the series — are supported; missing explicit content-standard correlation tables are a retrieval gap, not a curriculum deficiency.

The materials consistently identify standards assessed on formal assessments: both the K-5 and MS teacher guides state that 'All summative assessment problems include a complete solution and standard alignment' [E8][E10], covering end-of-unit, mid-unit, and end-of-course assessments [E1][E7][E10]. Diagnostic 'Check Your Readiness' assessments include item-by-item standard/lesson identification [E11], lessons display explicit CCSS standards (e.g., 8.SP.A.4) [E5], and the guide explains its standards-alignment system (building on/addressing/building toward) [E12]. This structural evidence shows assessments across the series consistently identify the standards being assessed, meeting the indicator.

Both the K-5 and middle school teacher guides state that 'All summative assessment problems include a complete solution and standard alignment' [E2][E3], directly confirming assessments denote which standards are emphasized. The materials further articulate a deliberate alignment system (building on, addressing, building towards) [E5], and lesson-level pages explicitly tag CCSS standards by category [E6][E8], showing standards emphasis is consistently and intentionally denoted. The design principles for summative assessments reinforce that problems target specific skills tied to standards [E10].

Materials include aligned rubrics for restricted/extended constructed-response items with explicit tiered descriptors that guide teachers in interpreting performance levels [E1][E2][E4][E10], and all summative problems include complete solutions, standard alignment, and error-specific distractor reasons that diagnose common misconceptions [E4][E10][E12]. Follow-up guidance is well evidenced: cool-downs provide next-day or prior-unit support tied to learning goals [E6][E11], and Check Your Readiness diagnostics include item-by-item guidance on what to do if students struggle or do well [E5], plus task commentary on misconceptions for adjusting instruction [E3]. This structurally satisfies all required components—aligned rubrics, scoring guidelines for interpreting performance, and follow-up suggestions.