Kendall Hunt's Illustrative Mathematics K-5

Structural evidence shows the materials are intentionally designed around the major work of each grade. Every retrieved unit goal explicitly states students 'consolidate and solidify their understanding of various concepts and skills related to major work of the grade' across grades 2-5 [E1][E2][E3][E9], with section goals targeting core major-cluster content (fractions on the number line, place-value operations, multi-digit multiplication/division, addition/subtraction within 100/1000) and connecting supporting clusters (measurement/data) to major work [E1][E2][E3]. The teacher guide confirms a coherent progression organized around standards and that the End-of-Course Assessment's longest portion assesses the major work of the grade [E7][E8]. This intentional design across grades supports that at least 65% of materials address major clusters.

Structural evidence shows the materials are designed to give all students extensive work with grade-level problems anchored to the major work of each grade: unit goals across grades 1, 2, 4, and 5 explicitly target major work and fluency goals [E3][E5][E7][E9][E11][E12], and each lesson carries practice problem sets with distributed practice plus per-lesson practice problems [E1][E2]. Off-grade-level content is intentionally non-displacing—pre-unit problems are prior-grade review/diagnostics [E2] and 'Are You Ready for More?' extensions are explicitly opt-in and not required [E6], so they do not detract from grade-level work. The teacher guide's three-tier alignment scheme (building on, addressing, building towards) shows deliberate sequencing toward the full intent of grade-level standards [E10].

Summative assessments explicitly assess grade-level standards, with every problem including a standard alignment and the end-of-course assessment focused on the major work of the grade [E8][E12]. Pre-unit/diagnostic items target prerequisite (below-grade) concepts for review and any upcoming-grade items in 'Check Your Readiness' are used only for pacing/instruction, not for holding students accountable [E1][E2][E11]. This structural design — grade-level summative assessment with prerequisite formative items — supports the indicator, and there is no evidence of above-grade topics being explicitly assessed in a way that would impact the materials' structure.

The teacher guide [E4] explicitly describes the design intent that in-depth 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 direct, intentional connection between supporting and major work. The 'Putting It All Together' units across grades integrate supporting clusters with major work: grade 3 applies measurement/data alongside fraction and multiplication work [E1, E7], grade 4 pairs measurement comparison with fraction and place-value work [E3, E6], and grade 2 blends measurement with within-20 fluency in a single section ('Fluency Within 20 and Measurement') [E11]. This structural evidence shows supporting work is used to enhance focus on major work rather than being treated separately, satisfying the indicator.

The materials show intentional within-grade connections across clusters and domains. The 'Putting It All Together' units in grades 3–5 explicitly consolidate work spanning multiple domains—e.g., grade 4 connects fraction operations (NF), multi-digit arithmetic via place value (NBT), and measurement (MD) [E2]; grade 5 links division/multiplication (NBT) with volume (MD) [E3]; grade 3 links fractions (NF) with measurement/data (MD) and multiplication fluency (OA) [E5]. Grade 5 Unit 2 ties fractions as quotients, multiplication, and area together (NF/OA/MD) [E6], and the progressions mapping documents cross-unit/standard connections [E11], demonstrating major-to-major connections throughout the grade-level materials.

Both required components are clearly supported. Future content is identified and related to grade-level work: grade-level/unit/lesson narratives explicitly describe connections to upcoming grade-level work [E1], curated articles explain 'where concepts lead beyond the indicated grade level' [E2], progressions documents map topics across grades per unit [E3], and 'Are You Ready for More?' tasks connect to the broader K–12 curriculum [E4][E6]. Materials also relate grade-level concepts explicitly to prior knowledge with content (not just standard codes): lesson narratives describe specific prior learning—e.g., grade 3 fraction work activating grade 4 unit fractions [E5][E12] and grade 4 decimal fractions feeding grade 5 thousandths [E11]—plus pre-unit/pre-assessment design targeting prerequisites [E7][E8] and 'building on' alignments tied to prior grades [E9].

Both MPs are intentionally identified and connected to grade-level content across the grade band. MP1 is developed through rich contextual problem-solving where students make sense of and persevere (grade 4 multi-digit multiplication [E2], grade 3 two-step word problems with deciding if answers make sense [E8], grade 1 story problems [E4], kindergarten teacher reflection on MP1 [E11]). MP2 is developed through reasoning abstractly/quantitatively with units and representations (grade 4 fraction multiplication [E5], interpreting remainders in context [E6], plus MP2 'I Can' learning targets [E3]). The teacher guide structurally supports this with lesson narratives explaining how MPs come into play, learning targets, and sense-making routines like Three Reads [E1][E7][E9][E10], confirming full-intent development for both.

The materials (IM Math) intentionally develop conceptual understanding through a documented design: concepts progress from concrete to abstract [E10][E12], with manipulatives connecting concrete to abstract representations [E11], and lessons structured to build conceptual foundations (e.g., arrays leading to multiplication properties [E4], tape diagrams connecting situations to multiplication [E9]). Unit goals across the grade band explicitly center conceptual understanding of key concepts—fractions as numbers and equivalence in Grade 3 [E3] (3.NF), fractions as quotients/multiplication in Grade 5 [E6] (5.NF). Independent demonstration is built into the lesson structure via independent work time before group/whole-class synthesis and cool-downs [E2], satisfying both required components throughout the grade level.

The materials develop procedural skill and fluency throughout each grade and tie it to the standards EdReports cites: grade 1 fluency within 10 [E11] (1.OA.6), grade 3 multiplication within 100 [E2] (3.OA.7), grade 4 multi-digit multiplication [E12] (4.NBT.4), grade 5 standard algorithm multiplication [E9][E10] (5.NBT.5), with the teacher guide describing an intentional design that interweaves conceptual understanding and procedural fluency across units [E1]. Students independently demonstrate these skills through dedicated fluency lessons/activities (Fluency Flip, multiplication center day) [E2][E4], year-long practice centers [E8], and end-of-course assessments and 'Putting It All Together' units that consolidate fluency goals [E3][E5][E6]. Both required components — development across the grade AND independent demonstration — are clearly supported.

Both halves of MP3 are intentionally developed. Constructing viable arguments appears via student 'I can explain or show my reasoning' statements [E1], 'Stronger and Clearer' output principles for explaining reasoning and making generalizations [E6], and 'Displays of Their Work/Compare' routines where students prepare visual displays of why their solution makes sense and investigate each other's work [E7][E8][E10]. Critiquing the reasoning of others is intentionally developed through the 'Critique, Correct' routine—analyzing curated statements with embedded conceptual errors and correcting them [E2][E3][E9]—with explicit teacher-provided guiding questions ('What do you think the author means?', 'Are there any reasoning errors?') and meta-think-alouds modeling respectful critique [E11]. These routines are embedded across K-5 and MS teacher guides in connection to grade-level content, meeting the full intent.

The teacher guides describe intentional design for application: anchor contexts motivate concepts and 'most units include a real-world application lesson at the end' [E1], with independent work time built into every activity's launch-work-synthesis structure [E7]. Multiple non-routine modeling applications appear across grades — design a carnival game (G3) [E2][E5], plan a garden (G3) [E3], make a sticky-note design (G4) [E8], plan a book fair (G5) [E11] — all open-in-the-middle MP4 tasks where students make assumptions and choose strategies, alongside routine word problems addressing application standards like 4.NF.B.3.d/4.NF.B.4 [E8]. This structural evidence satisfies both required components (multiple routine and non-routine applications throughout the grade, and independent demonstration opportunities).

MP6 is explicitly identified and connected to grade-level content via student 'I can attend to precision' statements (units/labels) [E1] and routines like Which One Doesn't Belong, which the teacher guide ties directly to attending to precision (MP6) [E2], with lesson activities embedding 'precision with language' [E4]. The specialized language of mathematics is intentionally and extensively developed through Mathematical Language Routines across both K-5 and MS materials—including formalizing definitions previously encountered informally [E9], structured drafting/revision for precision [E6][E7], critiquing and correcting ambiguous statements [E5][E8], and design principles cultivating disciplinary language [E10][E11][E12]. Both required components (full-intent MP6 development AND attention to specialized language) are structurally supported.

The materials systematically embed MP3 (construct viable arguments and critique the reasoning of others) with explicit student-facing 'I Can' statements [E1] and a stated design philosophy that students learn by making arguments and critiquing reasoning [E3]. Dedicated, recurring instructional routines structurally support both components: 'Critique, Correct, and Clarify' has students analyze others' written mathematical work, identify errors/ambiguities, and improve it [E2][E7][E12], while 'Compare and Connect' has students investigate and compare each other's strategies [E4]. Grade- and lesson-level evidence confirms enactment, e.g., Grade 4 Lesson 18 explicitly tags students sharing/justifying mathematical claims and evaluating whether classmates' statements are true/false (MP3) [E9], with synthesis and warm-up structures prompting students to respond to others' reasoning [E10][E6]. This reflects intentional, pervasive support for both constructing and analyzing arguments around grade-level content.

The teacher guide includes an explicit 'Balancing Rigor' section [E1] and names all three aspects present independently—activities devoted to 'developing a concept, others to mastering a procedural skill, yet others to applying mathematics to a real-world problem' [E3], with dedicated fluency items targeting key grade fluencies [E4], mastery work [E5], and end-of-unit real-world application lessons [E11]. The materials also engage multiple aspects simultaneously, stating the three aspects 'are interwoven' [E3] and 'interconnected: procedural fluency is supported by understanding, and deep understanding often requires procedural fluency' [E6], using anchor contexts to motivate new concepts [E11]. This structural evidence shows both independent presence and simultaneous engagement to develop understanding of single topics across the grade.

Both MPs are intentionally developed and connected to grade-level content. MP7 appears throughout Grade 4's pattern lessons where students 'look for structure and make use of it' in connection to place value and operations [E2, E4, E6, E8] and Grade 1 base-ten representation work [E1]. MP8 is explicitly developed via 'I can' student statements (identify/describe patterns, 'use patterns to come up with a general rule') [E7] and routines like Number Talks that target MP8 [E3], with Grade 4 Lesson 4 having students 'find a rule and explain features of the pattern' [E2]. The teacher guide's unit-level MP charts deliberately tag which lessons showcase MP7 and MP8 across every unit [E9, E10], and lesson narratives explain 'how the mathematical practices come into play' [E12], showing intentional, full-intent development.

The materials provide explicit, recurring structural support for MP3: a 'Critique, Correct, Clarify' routine that engages students in analyzing others' mathematical writing, correcting errors, and clarifying meaning, with teacher meta-think-alouds and guiding questions modeling respectful critique [E1][E3][E9][E10]. Student-facing 'I Can' statements operationalize constructing arguments and critiquing reasoning [E2], and routines like preparing visual displays and touring/comparing each other's work give students structured opportunities to construct and analyze arguments [E6]. Teacher guidance further supports facilitating constructive conversation and disciplinary language functions such as explaining reasoning and critiquing others [E7][E11][E12], showing intentional design across grade bands (K-5 and MS). This satisfies all required components.

The materials explicitly and systematically attend to the specialized language of mathematics. There are eight named Mathematical Language Routines embedded and suggested across lessons [E9], an overview of the progression of academic language provided for each instructional unit, plus a student glossary with illustrations and language goals [E8]. Specific structures formalize mathematical terms previously encountered informally [E10], collect and display disciplinary language [E11], and provide dedicated practice using mathematical language [E12], with a teacher-guide design principle framework driving continuous language development [E3][E5][E6]. This structural evidence supports all required components of the indicator.

Materials provide supply lists at the lesson level via consistent 'Required Materials' sections broken 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' in E11). The teacher guides further support implementation with guidance on preparing and organizing materials and a series-level index of where reusable blackline masters first appear by grade/unit/lesson (E3, E6, E10). This structural evidence shows a comprehensive, intentionally designed supply list at course, unit, and lesson levels.

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][E5][E6]. They also include sufficient, context-specific annotations and suggestions tied to learning objectives: advancing-student-thinking questions, cool-down 'Response to Student Thinking' guidance with next-day/prior-unit supports [E8], the problem-based framework defining teacher roles [E10][E12], warm-up and MLR lesson routines [E11], and guidance on purposeful representations and task complexity [E1][E3][E4]. This satisfies BOTH required components (comprehensive guidance AND useful annotations within specific learning objectives).

The materials regularly provide lesson-level supports for students with disabilities: 'Supplemental instructional strategies, labeled "Access for Students with Disabilities," are included in each lesson' and each is aligned to one of the three UDL principles—engagement, representation, action/expression [E3, E6, E10]. Specific, concrete strategies are detailed (assistive technology, manipulatives, graphic organizers, sentence frames, graduated scaffolds, brain breaks) and tagged by area of cognitive functioning so teachers can select appropriate supports for individual students [E1, E8, E9, E11, E12]. These are designed to facilitate access to Tier 1, grade-level instruction rather than removing students from grade-level work [E5, E12], satisfying the requirement for lesson-embedded (not merely generic chapter-opening) differentiation.

Both the MS and K5 materials provide structured, recurring extension opportunities: 'Are You Ready for More?' problems that 'go deeper into grade-level mathematics' and 'are not just the same thing again but with harder numbers' [E1], and K5 Exploration Problems that are 'open-ended and challenging' and 'go deeper into grade-level mathematics' [E4]. These are explicitly opt-in extensions of learning rather than additional repetitive work, and the teacher guides clarify it is not expected that students do more problems than classmates [E1][E4], satisfying the 'no instances of advanced students doing more problems' criterion. Task complexity guidance further supports purposeful, varied complexity for advanced learners [E6].

Materials explicitly provide adult-level explanations of complex grade-level concepts through unit/lesson/activity narratives and progressions documents that deepen teacher understanding [E2][E6][E11], plus specific worked discussions like the invert-and-multiply justification for fraction division [E9] and why a negative times a negative is positive grounded in the distributive property [E12]. Materials also clearly contain adult-level explanations of concepts beyond the current course via curated IM articles that 'contain adult-level explanations and examples of where concepts lead beyond the indicated grade level' [E1], including the K-12 number line article, trigonometry's role beyond elementary school [E7], and the 6-8 Number System progression [E12]. Both required components are structurally and substantively supported.

Both required components are present. Correlation information for the standards is documented through the three alignment types—building on, addressing, building towards—[E1] and a table mapping CCSSM progressions documents to specific units [E2]. Explanations of the role of grade-level mathematics in the series context appear in the coherent-progression design, where grade/unit/lesson/activity narratives describe connections to prior and upcoming grade-level work and the place of each lesson in the learning sequence [E3][E7][E8], with additional adult-level articles tracing where concepts lead across K–12 [E9].

The materials consistently identify standards for formal assessments: both K-5 and 6-8 teacher guides state that 'All summative assessment problems include a complete solution and standard alignment' [E4][E10], applying to the named formal assessments — end-of-unit, mid-unit, and end-of-course assessments [E1][E7][E10][E12]. Diagnostic 'Check Your Readiness' items are also tied to specific lessons/skills [E11], and the assessment structure is clearly documented across units [E8]. This structural evidence shows standards/practices are consistently identified for the formal assessments, satisfying the 2-point criterion.

Both the K-5 and MS teacher guides state that 'All summative assessment problems include a complete solution and standard alignment' [E2][E3], directly denoting which standards each assessment item targets. The end-of-course assessment explicitly prioritizes items that 'assess the major work of the grade' [E3], and the materials define three explicit kinds of standards alignment (building on, addressing, building towards) [E5], showing assessments intentionally identify the standards emphasized. This structural evidence supports all required components of the indicator.

Materials include explicit rubrics with defined tiers (Tier 1-4) for restricted constructed and extended response items, giving teachers clear criteria for interpreting student performance [E1][E2][E4]. Summative problems include complete solutions, standard alignments, and diagnostic distractors with reasons for each common error, supporting interpretation of student work [E4][E10][E12]. Follow-up guidance is robust: item-by-item guidance on diagnostic ('Check Your Readiness') assessments tells teachers what to do if students struggle or excel, and cool-down/response-to-student-thinking sections offer next-day or prior-unit support [E5][E11][E6][E3]. All required components—aligned rubrics, scoring guidelines, performance interpretation, and follow-up suggestions—are structurally present.