Illustrative Mathematics (Kendall Hunt OER)

Structural evidence shows the materials intentionally center major clusters: multiple grade-level units are explicitly framed around 'major work of the grade' and key fluency goals [E1][E2][E3], and the End-of-Course/summative assessments lead with items that 'assess the major work of the grade' [E4][E8]. The teacher guide further documents coherent progression mapping and intentional connections between supporting work and major work [E11][E12], consistent with a design where the majority of instructional time focuses on major clusters (IM K-5 structure). This satisfies the indicator's structural requirements (≥65% for 3-5).

Structural evidence shows an intentional, grade-focused assessment system: each unit opens with a pre-unit/diagnostic ('Check Your Readiness') that targets prerequisite/prior-grade content used for review or placement, not accountability [E1][E2][E11], while summative assessments, section checkpoints, and the end-of-course assessment explicitly target the major work of the grade with standard alignments provided [E5][E8][E12]. Where above-grade ideas appear in diagnostics they are used only to pace instruction, not to hold students accountable [E11], and earlier-grade content assessed via pre-unit problems is permissible under this indicator [E2]. No evidence shows above-grade topics being explicitly assessed in a way that would impact the materials' structure, and standard alignments support mathematical reasonableness [E8][E10].

The materials structurally integrate supporting work with major work: grade-level 'Putting It All Together' units explicitly state students 'consolidate and solidify their understanding of various concepts and skills related to major work of the grade' while including supporting-cluster goals like 'Apply concepts of measurement and data to solve problems' (grade 3, [E1][E6][E8]) and 'Solve problems involving measurement comparison' (grade 4, [E3][E5][E9]) alongside major-work fraction and place-value goals. The teacher guide confirms an intentional coherent design in which 'each lesson and unit tells a story' situating content in a deliberate learning sequence ([E11][E12]), indicating supporting work is not treated separately but woven into the major work. This matches the structural evidence EdReports requires for the maximum score, even though full coherence-map detail was not in the retrieved chunks.

E6 explicitly states that 'All summative assessment problems include a complete solution and standard alignment,' directly meeting the indicator's requirement that materials consistently identify the standards assessed for formal assessments. This is reinforced by the structured formal assessment system described throughout—end-of-unit assessments, checkpoints, mid-unit and end-of-course assessments (E1, E6, E7, E9, E10, E11)—with E6 noting the end-of-course assessment targets the major work of the grade. The structural evidence shows intentional standard-level identification of assessed content for formal assessments.

The materials show intentional connections among clusters/domains within grades through dedicated 'Putting it All Together' units: Grade 6 connects measurement conversions with volume/surface area of prisms and ratio reasoning with percentages and number/geometry features (GCF) [E2][E11], and Grade 7 connects proportional relationships, scale drawings, and measurement conversions [E3][E6][E7]. Individual lessons also link domains, e.g., Grade 6 Lesson 18 connects equations, graphs, and tables for constant-area/volume and doubling (exponent) relationships [E9]. 'Are You Ready for More?' problems and distributed practice problem sets further weave together concepts across units [E1][E10], providing structural, purposeful major-to-major connections throughout the grade-level materials.

End-of-unit, end-of-course, and summative assessments use a full range of item types (multiple choice, multiple response, short answer, restricted/extended constructed response) that vary in difficulty and depth of knowledge, with every summative problem carrying a standard alignment [E4][E8][E12], and items are designed (avoiding the 'double whammy') to give students full opportunity to show proficiency on grade-level content [E6][E7]. The materials also explicitly support assessing the Mathematical Practices through MP charts, routine-to-MP mappings, and per-practice learning targets used formatively [E2][E10][E11], so both grade-level standards AND practices have opportunities to be demonstrated across the series. This structural design satisfies the full intent required for the top band.

Both required components are structurally supported. Future-grade content is identified and related to grade-level work via narratives describing 'connections to prior and upcoming grade-level work' [E1], 'Building Towards' standards alignments [E5, E9], 'Are You Ready for More?' extensions [E3], and curated articles on where concepts lead beyond the grade [E2]. Explicit prior-knowledge connections appear through 'Building On' alignments [E5, E9], progressions-document mappings per unit [E4], pre-unit/prerequisite assessments [E7, E8], and lesson narratives naming earlier-grade foundations (e.g., 'In grade 4, students studied decimal fractions...') [E11].

Structural evidence shows the materials intentionally provide all students extensive work with grade-level problems: each lesson carries a practice problem set with distributed practice revisiting prior lessons/units [E1][E2], pre-unit and exploration problems extend engagement [E2], and 'Are You Ready for More?' offers opt-in deepening that is non-routine [E6]. Grade-level unit goals across grades 1, 2, 4, and 5 are explicitly tied to the major work and full fluency intent of the standards [E3][E5][E8][E11], and detailed lesson sequences (e.g., multi-digit multiplication/division progressions) show coverage developing the full intent of grade-level standards [E12]. The teacher guide's 'building on/addressing/building towards' alignment design [E9] further indicates deliberate coverage of grade-level standards. This meets both required components: extensive grade-level work AND opportunity to meet the full intent of standards.

The materials intentionally develop MP1 across the full grade band in connection to grade-level content: lesson narratives explicitly tag MP1 where students make sense of unscaffolded problems and persevere (grade 1 story problems with 1.OA standards [E3], grade 3 two-step word problems with 3.OA.D.8 [E4], grade 6 division interpretation [E2], grade 7 equation/percent problems [E5][E8]). The teacher guides describe the design intent—lesson narratives explain 'how the mathematical practices come into play' [E7][E9]—and provide MP learning-target lists for recognizing engagement [E1] plus MP1-specific teacher reflection questions [E6]. This structural evidence shows MP1 is used to enrich content and reaches its full intent across the grade level.

The materials intentionally develop conceptual understanding through a concrete-to-abstract progression, introducing representations before abstract symbols (e.g., grade 3 uses scaled picture graphs and concrete equal groups before multiplication expressions [E12], and tape diagrams to connect situations to multiplication [E8]; kindergarten counts/moves objects before 5- and 10-frames [E4], [E7]). Unit and lesson narratives explicitly describe building a base of conceptual understanding and coherent progressions tied to standards [E1], [E5], [E6], and unit goals emphasize understanding relationships (e.g., grade 5 fractions as quotients connecting division and multiplication [E9]). Students independently demonstrate understanding via independent work time, lesson syntheses where they make connections, and cool-downs to apply learning [E2], [E10], [E11]. Structural evidence across the teacher guides and grade-level lessons supports both required components throughout the grade levels.

MP2 is intentionally developed and explicitly connected to grade-level content across multiple grades: students attend to the meaning of an equation's solution in context for px+q=r and p(x+q)=r situations in grade 7 [E5][E8], reason about negative quantities in rational-number contexts [E4], reason quantitatively/abstractly solving fraction multiplication problems in grade 4 [E6], make sense of equations and diagrams for multiplicative comparison [E10], and interpret tape diagrams for measurement in grade 3 [E11]. The K-5 teacher guide provides explicit MP2 'I Can' learning targets (think about/show numbers in many ways, identify what can be counted, connect real-world situations to representations) and formative-assessment guidance, evidencing intentional design [E2][E9]. The full intent of MP2—both the abstracting (decontextualizing) and the quantitative (contextualizing) moves—is reached as students move between contexts and symbolic representations and interpret solutions back in context.

The teacher guide explicitly describes a design for developing procedural fluency alongside conceptual understanding, with pre-assessments and systematic progression [E1, E9]. Fluency is developed throughout multiple grades with standards-aligned fluency goals — e.g., grade 1 add/subtract within 10 [E12], grade 2 within 20/100 [E7, E10], grade 3 multiplication within 100 [E3], grade 4 multi-digit multiplication [E6], grade 5 standard algorithm multiplication [E2, E4, E5, E11]. Students independently demonstrate fluency through practice lessons, center games (Greatest Product), fluency-flip activities, and 'Putting It All Together' consolidation units [E2, E3, E5, E7]. Both required components — development across the grade and independent demonstration — are clearly supported.

The materials include multiple routine and non-routine applications across the grade band: dedicated application lessons such as 'Applications of Arithmetic with Powers of 10' [E1], 'Applying Volume and Surface Area' [E5], and 'Adding and Subtracting to Solve Problems' [E8], plus non-routine modeling tasks like 'Stained-Glass Windows' [E7] and Fermi problems in the optional 'Putting it All Together' units [E9][E12] where students make their own assumptions and simplifications. The teacher guide describes an intentional design where carefully-chosen anchor contexts motivate concepts and most units end with a real-world application lesson [E2][E11]. Students independently demonstrate application through structured independent work time before group work [E4] and by selecting their own strategies in complex, multi-concept tasks [E5][E7], satisfying both required components.

The materials intentionally develop both aspects of MP3 across grade bands. Student-facing 'I Can' statements explicitly name MP3 with both 'explain or show my reasoning in a way that makes sense to others' (constructing arguments) and 'listen to and read the work of others and offer feedback' (critiquing) [E1]. Dedicated instructional routines like Critique-Correct-Clarify engage students in analyzing others' mathematical writing, correcting errors, and respectfully critiquing reasoning in both K-5 [E3] and middle school [E2], while Compare/Connect routines have students prepare visual displays and critique each other's approaches [E7][E8][E9]. The design connects MP3 to grade-level content as students 'make arguments and critiquing the reasoning of others' while doing mathematics [E10][E12], satisfying the full intent in connection to content.

Evidence shows all three aspects of rigor are present both independently and in combination. E3 and E4 describe distinct activity types devoted separately to developing a concept, mastering a procedural skill, or applying mathematics, while E6 explicitly states the three aspects are interconnected (procedural fluency supported by understanding, application requiring both) and E11 shows anchor contexts integrating concepts with application. The 'Putting It All Together' units (E10, E12) and end-of-grade in-depth application problems (E5) demonstrate the three aspects engaged simultaneously to consolidate understanding of a single topic across the grade, with E1 naming an intentional 'Balancing Rigor' design.

MP4 is intentionally developed to its full intent across every grade band and connected to grade-level content. Materials explicitly engage the full modeling process—making simplifying assumptions and estimating ([E1], [E2], [E8]), choosing representations like diagrams/expressions/bar graphs ([E2], [E3]), and interpreting/checking results against the real-world situation ([E1], [E9], [E12]). Culminating modeling tasks (tent design [E11], linear models [E5], modeling with inequalities [E9]) and teacher-facing 'I can' MP statements ([E7]) show structural, intentional design tied to named standards (e.g., 2.NBT/2.OA in [E6], 5.MD/5.NBT in [E8]).

The materials intentionally develop MP5 across the full grade band in connection to grade-level content. Students strategically choose tools/representations in genuine content contexts: number cubes/spinners/blocks for probability simulations in grade 7 [E1], double number lines/tables/tape diagrams weighed for usefulness in grade 6 ratio problems [E3], measuring tools for proportional reasoning [E4][E9], objects for indirect length comparison in grade 1 [E5], and counters/5-frames in kindergarten [E7][E8]. Teacher-facing structures reinforce full intent—'I can' learning targets that include choosing tools, explaining thinking, and knowing how to use a variety of tools [E2], teacher reflection questions prompting observation of MP5 engagement [E8], and explicit formative-assessment guidance to highlight differing tool choices [E10]—and the teacher guide describes a deliberate concrete-to-abstract progression of representations [E6][E12].

Evidence shows intentional MP6 development connected to grade-level content across the full K-8 span: precise measurement units in grade 2 [E1], accuracy/rounding of decimal quantities tied to 5.NBT in grade 5 [E2][E6], estimation in grade 6 [E3], specifying units in grade 8 powers-of-10 work [E4], and measurement-error analysis in grade 7 [E8][E9]. Specialized mathematical language is intentionally developed through 'I can attend to precision' student-facing statements [E7], routines like Which One Doesn't Belong [E5] and the Critique/Correct/Clarify MLR routines that have students fix ambiguous mathematical statements [E10][E11][E12]. Teacher guides explicitly map MP6 to routines and content, demonstrating the design intent expected by the indicator (precise vocabulary, clear explanations, accurate calculation, units of measure).

The materials show intentional, content-connected development of MP7 across the full grade band. MP7 is explicitly tagged and developed in named lessons spanning grades 1–8: students use structure of systems of equations to choose solution approaches (grade 8, [E1]), build/analyze tessellations (grade 8, [E4]), analyze repeating, growing, visual, and numerical patterns (grade 4, [E3][E5][E7][E8]), and interpret base-ten representations of multiples of 10 (grade 1, [E6]). A unit-level Mathematical Practice chart deliberately highlights lessons showcasing each MP including MP7 ([E10]), instructional routines are mapped to MP7 (How Many Do You See, Number Talk per [E2]), and lesson narratives are designed to explain how the practices come into play ([E12]), with tasks reaching MP7's full intent—looking for patterns/structure to generalize, decomposing complicated into simpler, and comparing multiple approaches ([E11]). This satisfies the indicator's requirement of intentional MP7 development connected to grade-level content.

The materials show intentional development of MP8 connected to grade-level content across the full K-8 span and reaching its full intent. Students notice repeated calculations to derive algorithms and generalizations (e.g., discovering the exponent rule 10^n·10^m=10^(n+m) [E1], formalizing a×1/b = a/b through repeated reasoning [E4], using long division repeatedly to understand repeating decimals [E6]), create general rules from patterns (kindergarten one-to-one correspondence [E5], numerical patterns to find a rule [E7], grade-4 'use patterns to come up with a general rule' [E2]), and use repeated experiments to approach probability [E3]. The K-5 teacher guide provides explicit MP8 'I Can' statements and identifies routines (Number Talks) where MP8 is observed [E2][E8], evidencing teacher-facing design support for engaging students in the practice.

The materials affirmatively support special populations to access grade-level content: every lesson includes labeled 'Access for Students with Disabilities' supports aligned to the three UDL principles—engagement, representation, action/expression [E6][E7][E9]. Specific scaffolding strategies are present (manipulatives, assistive technology, graphic organizers, visual aids, sentence frames, graduated/gradually-released scaffolds) [E5][E11][E2][E12], and supports are tagged to cognitive functions including memory, attention, and social-emotional functioning to foster a safe, participatory environment [E4][E10]. Culminating activities and flexible expression options ensure regular and active participation alongside peers in rigorous, grade-level work [E3][E8]. This satisfies all required components of the indicator.

The materials provide comprehensive, structured teacher guidance: unit/lesson/activity narratives explain the mathematical content, its place in the learning sequence, and how mathematical practices come into play [E2][E5][E11]. Annotations are directly tied to mathematical development through 'advancing student thinking' questions, cool-down response-to-thinking next-day/prior-unit supports [E7], the problem-based instructional framework defining the teacher's roles as facilitator/questioner/synthesizer [E6][E10], and seamless integration of ancillary supports like embedded MLRs, warm-up routines, and representation/differentiation suggestions [E3][E4][E9]. This satisfies both the comprehensive-guidance and useful-annotations components of the indicator.

The materials regularly provide multiple extensions: the 'Are You Ready for More?' problems go deeper into grade-level mathematics, make connections across concepts, and are explicitly 'not routine or procedural' and 'not just the same thing again but with harder numbers' — i.e., more complex rather than more of the same [E1][E2]. The K-5 program includes parallel Exploration Problems and in-depth/culminating problems serving the same enrichment purpose [E3][E4][E6]. Critically, these extensions are 'used on an opt-in basis by students if they finish the main class activity early or want to do more,' so advanced students are not assigned more required work than classmates [E1], satisfying both required components.

The materials contain adult-level explanations and examples of grade-level concepts through unit/lesson/activity narratives that explain mathematical content and new terms [E11][E12], plus curated articles giving deep treatments of topics like fraction division, order of operations, and negative numbers [E1][E4][E7][E10]. They also explicitly address how concepts align to other grade levels: a table mapping CCSS Progressions documents to each unit [E2], narratives describing connections to prior and upcoming grade-level work and the coherent progression [E3][E9], and the building on/addressing/building towards alignment framework [E5]. Both required components — grade-level explanations AND cross-grade alignment for teacher learning — are clearly supported.

The materials clearly include a year-long scope and sequence (each grade told in 8-9 units with lesson/unit narratives describing placement in the learning sequence, E4, E6, E7) plus explicit standards correlation. Standards alignment is documented via 'building on, addressing, and building towards' categories (E3), per-lesson CCSS citations (E9: 'Building On 7.G.A / Addressing 8.G.A'), and correlation tables mapping mathematical practice standards (MP1-MP8) to specific units and lessons (E5). A progressions-to-unit mapping table (E1) further documents standard alignment across the grade band. This satisfies the single requirement for the 1-point band.

Materials explain the program's instructional approaches via the Design Principles and problem-based instructional framework [E3][E4], with detailed lesson/unit/activity narratives describing implementation [E6][E12]. Research-based strategies are explicitly cited—Hiebert et al., 1996 [E3], the 5 Practices framework from Smith & Stein, 2011 [E7], and MLRs developed by the Stanford UL/SCALE team [E11]. The role of the standards is explained through the 'building on, addressing, building towards' alignment system [E10] and narratives noting when scope decisions are required by standards versus author choices [E1]. All three required components are clearly met.

Every lesson includes an explicit 'Required Materials' section broken into 'Materials to Gather' and 'Materials to Copy,' plus 'Required Preparation' notes specifying quantities per activity (e.g., [E2], [E4], [E11] 'Each group of 4 needs at least 8 pencils'). The K-5 teacher guide describes the material system, copying/blackline-master logistics, and provides a list showing where each blackline master first appears by grade/unit/lesson ([E3], [E10]), with parallel structures in the MS teacher guide ([E6], [E9]). This structural evidence demonstrates a comprehensive, lesson-level supply list supporting instructional activities.

The assessment system provides consistent year-long opportunities: pre-unit diagnostics (Check Your Readiness), mid-unit assessments for longer units, end-of-unit summative assessments, daily cool-downs, and section checkpoints [E4][E5][E7][E11]. Teacher guidance for evaluating performance is present through commentary on expected responses and misconceptions, suggested questions, and graded/formative options [E1][E2][E11]. Guidance for interpreting results and determining next steps is explicit—item-by-item guidance on what to do if students struggle or excel on diagnostics, plus next-day and prior-unit support categories triggered by cool-down evidence [E6][E8][E9]. All three required components are clearly met.

The materials use a wide range of accurate physical and virtual manipulatives that faithfully represent mathematical objects—connecting cubes, pattern blocks, two-color counters, 5- and 10-frames, base-ten blocks, geoblocks, and counting mats ([E5], [E11], [E12])—and the teacher guide explicitly sequences these from concrete to abstract to build the base-ten system ([E1], [E2]). Crucially, the manipulatives are connected to written methods: kindergarten students move objects then represent them in 5-/10-frames leading to place-value diagrams and equations ([E1]), and grade 4 students use connecting cubes and discrete diagrams alongside equations to represent multiplicative comparison ([E4], [E7]). Both required components—accurate representation AND connection to written methods—are supported.