Open Up Resources 6-8 Mathematics (3rd Edition)

Structural evidence shows IM Math is built so that instructional activities 'are the heart of the mathematical experience and make up the majority of the time spent in class' [E2][E5], with 8-9 units of 8-28 lessons each designed around grade-level content [E4]. Assessments are standards-aligned and explicitly target 'the major work of the grade' [E3], and centers/fluency work reinforce grade-level standards and fluencies rather than off-grade content [E1][E7][E8]. Progressions documents are mapped to each unit to ensure full coverage and intent of grade-level standards [E9][E12], supporting extensive work with grade-level problems for all students. Full per-standard coverage tables were not retrieved, which lowers confidence but not the structural conclusion.

The materials show an intentional assessment design that targets grade-level standards: summative and end-of-unit assessment problems all include complete solutions and standard alignment, and the End-of-Course Assessment's longest portion assesses the major work of the grade [E7]. Below-grade content appears only in pre-unit diagnostics ('Check Your Readiness') used formatively to identify prerequisite needs, not to hold students accountable [E1][E3][E6], and above-grade content is treated as 'building towards' rather than assessed expectations [E11][E12]. No retrieved evidence indicates that K-5 assessments explicitly assess probability, statistical distributions/association, or similarity/transformations/congruence, so the K-5 exclusions are not triggered. This structural evidence supports all required components of the indicator.

Structural evidence shows the materials are intentionally organized around the major work of each grade: the End-of-Course Assessment's longest portion assesses 'the major work of the grade' [E3], and supporting work is deliberately connected to major work through in-depth problems that 'apply the key ideas they have learned over the year' [E1]. Connections between supporting and major clusters are visible in lessons that combine geometry with proportional reasoning and prior ratio work [E10], and that link representations/equations across units [E8]. Optional culminating lessons [E7][E8] do not detract from the core sequence of nine units per grade [E5] designed around grade-level concepts and progressions [E12], supporting that the majority of materials address major clusters.

Per the Evidence Guide, the question is whether supporting work is connected to major work to enhance focus. The materials structurally support this: lesson, unit, and grade narratives explicitly describe connections to prior and upcoming grade-level work and the purpose of each activity [E1][E8], and a progressions mapping ties each unit to standards strands [E5]. Most directly, the end-of-year design includes 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,' explicitly using supporting work as a vehicle for major work [E12], with centers also reinforcing grade-level standards [E3][E7]. This intentional design supports connections rather than treating supporting work separately.

The materials are a coherent, standards-aligned program (IM Math) whose narratives at grade, unit, lesson, and activity levels explicitly describe how mathematical ideas connect, and a progressions-mapping table notes 'key connections among standards' across domains within and across grades [E1][E2]. Concrete within-grade cross-domain/cluster connections are evident, e.g., connecting whole-number division and fraction division [E8], extending base-ten representations across number domains [E4], and 'Are You Ready for More?' problems that 'make connections between the topic at hand and other concepts' [E9]. Distributed practice deliberately revisits and links content across units [E12], and the structural design intentionally weaves clusters/domains together throughout the grade. This structural evidence supports connections from major-to-major and supporting-to-supporting work throughout, meeting the indicator.

Structural evidence shows both required components. Grade/unit/lesson narratives explicitly describe 'connections to prior and upcoming grade-level work' and the progressions of mathematical ideas [E1], and a progressions-document mapping ties each unit to cross-grade topic progressions [E4]. The standards-alignment system labels work as 'building on, addressing, and building towards' — explicitly relating grade-level content to both prior-grade and future-grade learning [E5], and pre-assessments/initial lessons activate prerequisite knowledge while gauging upcoming concepts [E11], with supporting centers reviewing prior-grade work [E8]. These go beyond bare standard codes to explain the content relationship, satisfying both 'future content identified and related' and 'grade-level concepts related to prior knowledge.'

The materials intentionally develop conceptual understanding throughout the grade level: teacher guides describe a deliberate concrete-to-abstract progression where concepts are 'introduced simply, concretely, and repeatedly, with complexity and abstraction developing over time' [E8] and representations are sequenced by usefulness from concrete to abstract [E12], establishing 'a base of conceptual understanding' [E7]. Unit-level structural evidence shows concepts (not just procedures) developed—e.g., students learn to understand and use terms like reflection/rotation/translation and dilation, recognizing preserved lengths/angles [E4, E9]. Independent demonstration is built into the lesson structure via 'independent work time that allows them to grapple with problems individually before working in small groups,' plus cool-downs to apply learning [E2], satisfying both required components.

The materials intentionally identify and develop both MP1 and MP2 in connection to grade-level content. Unit-level Mathematical Practice charts explicitly tag MP1 and MP2 to specific lessons across each unit ([E8], [E9]), and lesson/unit narratives explain 'how the mathematical practices come into play, as appropriate' within the content story ([E10], [E11]). Full-intent development is supported by learning targets that capture the substance of each practice—MP1 (make a try, persevere, check the solution makes sense) and MP2 ('identify the things that can be counted,' 'think about what the numbers mean,' 'make connections between real-world situations and objects, diagrams, numbers, expressions, or equations') ([E3])—plus formative guidance for teachers to observe these practices in action ([E2]).

The materials show intentional development of both halves of MP3 in connection to grade-level content. The 'Critique, Correct, Clarify' routine [E10] explicitly engages students in analyzing others' mathematical writing, performing error analysis, and considering the author's thinking — directly meeting the 'critique the reasoning of others' intent, with teacher supports for modeling respectful critique. The 'construct viable arguments' half is supported by discourse-focused routines and discussions designed around each lesson's mathematical goal [E11], small-group grappling and synthesis [E6], and the Five Practices for facilitating argumentation [E5], with MP3 named as a core practice students 'do' [E7]. MPs are tied to grade-level content through lesson/activity narratives that explain how practices come into play [E2][E3] and via per-practice learning targets [E4].

IM Math is explicitly designed around the three aspects of rigor including procedural fluency, with a teacher guide section on 'Developing Conceptual Understanding and Procedural Fluency' [E1][E5] and centers/activities aligned to support 'ongoing procedural fluency' throughout the year [E4][E8]. The materials develop procedural skill via warm-ups, instructional routines (Number Talks), and targeted fluency items that 'target the key fluencies for each grade' in pre-chosen calculations and strategy games [E7][E11]. Students independently demonstrate fluency through independent work time, center activities, pre-unit practice, checkpoints/checklists, and end-of-unit assessments [E3][E4], satisfying both required components throughout the grade level.

Materials include multiple routine and non-routine applications throughout the grades: routine application lessons applying specific concepts in context (E2 Pythagorean Theorem, E3 powers of 10, E10 volume/surface area), and non-routine modeling tasks where students make their own assumptions and choose strategies (E7 designing a tent, E9 stained-glass windows, E11 painting a room). The teacher guides confirm intentional design—most units end with a real-world application/culminating lesson (E1, E5, E12), and K-5 includes in-depth contextual problems (E8). Culminating lessons (E7, E9, E11) provide opportunities for students to independently demonstrate application by modeling situations, making assumptions, and selecting tools (MP4, MP5), satisfying both required components.

MP6 is intentionally identified and connected to grade-level content across grades—e.g., attending to precision with units of measurement in Grade 8 powers-of-ten problems [E2], examining measurement accuracy in Grade 7 [E4], and precision-focused routines like Which One Doesn't Belong [E3], plus 'I Can Attend to Precision' (units/labels) student-facing goals [E1]. The materials also robustly attend to the specialized language of mathematics through embedded Mathematical Language Routines that develop precision in disciplinary language, critique/clarify ambiguous statements, and formalize definitions of terms previously encountered informally [E5][E6][E9][E10][E11][E12]. Both required components are supported, satisfying the 2-point criteria.

The materials explicitly embed MP3 'Construct Viable Arguments and Critique the Reasoning of Others' as a core practice with student-facing 'I can' statements for explaining reasoning and offering feedback ([E1], [E3]). Dedicated instructional routines—'Critique, Correct, Clarify' across K-5 and middle school—structurally engage students in analyzing others' mathematical writing, correcting errors, and discussing reasoning with partners using guiding questions ([E2], [E7], [E12]), plus 'Compare' routines where students investigate and critique each other's work ([E4], [E5], [E10]). Grade-level lessons name explicit 'Critique arguments' learning goals tied to key content, e.g., exponent expressions in Grade 6 and congruence in Grade 8 ([E9], [E11], [E6]), confirming arguments concern grade-level mathematics in the content standards.

The materials are explicitly designed to balance all three aspects of rigor both independently and simultaneously. The teacher guide contains a dedicated 'Balancing Rigor' section [E1] and states the three aspects of mathematical proficiency are 'interwoven'—some activities develop a concept, others master procedural skill, others apply mathematics to real-world problems [E3]. The design principle 'Developing Conceptual Understanding and Procedural Fluency' [E11] and the description that '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] show multiple aspects engaged simultaneously, while distributed practice [E7] and end-of-unit application lessons [E8] show independent treatment. This structural evidence supports both required components.

Both MP7 and MP8 are intentionally identified and connected to grade-level content. MP7 is developed through routines (How Many Do You See, Number Talk) and grade-8 geometry tasks where students use structure to build tessellations [E1][E5][E6], while MP8 has explicit student-facing 'I can' goals (identify/describe patterns, notice what changes/stays the same, use patterns to come up with a general rule) and is tagged alongside MP7 in Number Talks [E1][E4]. The unit-level Mathematical Practice chart deliberately maps specific lessons to MP7 and MP8 across every unit of the grade [E7][E9], and lesson narratives explain how the practices come into play [E11], evidencing intentional, full-intent development of both.

Materials provide explicit teacher-supported structures for constructing arguments and critiquing others' reasoning: a 'Correct/Clarify' routine where students analyze a non-original mathematical statement, identify errors, and improve it, with teachers modeling respectful critique via meta-think-alouds and guiding questions like 'Are there any reasoning errors?' [E1][E3][E9]. MP3 'I Can' statements operationalize the practice for students ('explain or show my reasoning so it makes sense to others,' 'listen to and read the work of others and offer feedback') [E2], and compare-tour routines have students investigate each other's displays with teacher-provided questions [E6][E10]. Warm-ups and lesson syntheses further structure students sharing ideas and responding to the reasoning of others, with teacher facilitation [E11][E12]. This structural evidence supports all required components.

The materials structurally and intentionally attend to the specialized language of mathematics through eight Mathematical Language Routines embedded and suggested in lessons [E2][E8][E11], a dedicated language development framework adapted from Stanford's Understanding Language project [E1][E3], and an overview of the progression of academic language provided for each instructional unit plus a student glossary with illustrations [E10]. Unit-level evidence shows explicit attention to precise mathematical vocabulary—e.g., students learn to understand and use terms like 'variable,' 'coefficient,' 'solution,' 'equivalent expressions,' and 'exponent' [E4][E5]—and routines like 'Three Reads' and 'Formalize a definition' build meta-awareness and formal definitions of mathematical terms [E6][E12]. This satisfies all required components of the indicator.

The materials provide robust, intentional support for quality questioning to guide students' mathematical development. The teacher guide describes an 'advancing student thinking' section that gives teachers questions to advance understanding of concepts, strategies, and connections [E1], and frames questioning as a core teacher role to 'ask questions to advance students' thinking in productive ways' [E5][E7]. Specific question supports are embedded throughout: guiding questions for partner discussion (e.g., 'What do you think the author means?,' 'Are there any reasoning errors?') [E8], per-lesson teacher reflection questions drawn from defined categories [E9], question starters/sentence frames tied to language functions [E10], and the Co-craft Questions routine for student-generated mathematical questions [E2][E3][E11]. This structural evidence across K-5 and MS teacher guides shows all required components are supported.

The materials provide comprehensive teacher guidance through unit, lesson, and activity narratives that explain the mathematical content, its place in the learning sequence, new terms, and how mathematical practices come into play [E2][E4][E8]. They also include sufficient, objective-specific annotations and suggestions: 'advancing student thinking' questions, monitoring guidance, cool-downs with next-day/prior-unit support tied to each lesson's learning goal [E6], representation and access supports [E5][E7], task-complexity preparation [E3], and explicit guidance on the teacher's facilitation role [E10][E12]. Both required components — comprehensive presentation guidance AND useful annotations within the context of specific learning objectives — are clearly met.

The IM K-12 Math materials embed lesson-level 'Access for Students with Disabilities' supports in each lesson, each aligned to a UDL principle (engagement, representation, action/expression) [E3][E5], rather than relying on generic chapter-opening statements. Concrete, varied strategies are specified throughout: assistive technology and manipulatives [E1], graphic organizers and visual anchor charts for working-memory needs [E8], multi-modal representation and background-knowledge activation [E6][E7], flexible expression with sentence frames and graduated scaffolds [E9][E11], and detailed accommodations for visual impairments including long image descriptions, SVG magnification, and Braille versions [E12]. This demonstrates regular, intentional strategies, supports, and resources for special populations to actively participate in grade-level mathematics, satisfying all required components.

The materials contain a curated set of adult-level articles and essays (by McCallum, Umland, Gray, Phillips, etc.) explicitly providing explanations of complex grade-level concepts—e.g., fraction division with justification for invert-and-multiply [E8], equivalent fractions as units [E9], order of operations [E3]—satisfying the grade-level component. They also include explanations of concepts beyond the current course, such as the number line's role from K–12 [E1], trigonometric ratios, and the path 'beyond to irrational units' [E8,E9], plus a mapping of CCSS Progressions documents per unit [E11], satisfying the beyond-course component. Unit, lesson, and activity narratives and grade-level overviews (e.g., [E2,E7,E12]) further deepen teacher understanding of the mathematics and its progression, meeting BOTH required components.

The materials embed intentional, recurring extension structures: "Are You Ready for More?" in MS (E1, E2) and "Exploration Problems" in K5 (E4), both explicitly designed to go deeper into grade-level mathematics, described as "not routine or procedural" and "not just 'the same thing again but with harder numbers'" (E1, E4). These are higher-complexity investigations rather than more of the same work, and the teacher guidance frames them as opt-in for students who want to do more mathematics, with no expectation that advanced students complete additional required problem sets — satisfying both required components (multiple complexity extensions AND no pattern of advanced students simply doing more problems). Task Complexity guidance (E6) and optional synthesizing units (E8) further support purposeful extension of grade-level content.

The materials show clear variety in what students produce. Beyond answers and solutions, students create visual displays and multiple representations of their reasoning [E1, E3], construct arguments and critique others' reasoning [E4, E10], build mathematical models [E7, E11], and produce diagrams, tables, graphs, and equations [E2, E9, E12]. Assessments deliberately offer multiple modes (arithmetic/algebra, representations, and explanation) for demonstrating understanding [E2, E8], and grade-band lessons across 6–8 require students to interpret, explain, and represent contexts in varied grade-appropriate ways [E9, E10, E11, E12].

The materials consistently identify standards for formal/summative 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 [E7][E10]. Lesson-level evidence confirms explicit CCSS labeling (e.g., '8.SP.A.4 Addressing') [E5], and the guide documents a deliberate alignment scheme of 'building on, addressing, and building towards' standards [E12]. Diagnostic 'Check Your Readiness' items are also tied to specific lessons/skills [E11], showing standard identification across assessment types.

Multiple sources affirm that assessments explicitly denote standards: both the K-5 and MS teacher guides state that 'all summative assessment problems include a complete solution and standard alignment' [E2][E3], and the materials define three categories of standards alignment—building on, addressing, and building towards [E5]. Lesson-level evidence confirms standards are clearly labeled by these categories (e.g., 'Building On 6.SP.A.1; Addressing 6.SP.A.2... Building Towards 6.SP.A.3') [E8][E6], and the end-of-course assessment is organized to emphasize the major work of the grade [E3]. This structural evidence supports all required components of the indicator.

The materials include aligned rubrics with tiered scoring descriptors for restricted constructed and extended response items, plus complete solutions and standard alignment for all summative problems [E1][E2][E4][E8][E10], satisfying the rubric/scoring-guideline component. Multiple-choice distractors are built from common errors and serve a diagnostic function so teachers can interpret which misconceptions students hold [E12], and tasks carry commentary on expected responses and misconceptions [E3]. For follow-up, the materials provide item-by-item guidance on diagnostic (Check Your Readiness) results and cool-down 'next-day support'/'prior-unit support' to adjust instruction [E5][E11][E6]. All required components—aligned rubrics, interpretive scoring guidance, and follow-up suggestions—are structurally supported.