Kendall Hunt's Illustrative Mathematics Traditional

Structural evidence shows the materials intentionally attend to the full intent of HS mathematical content: the teacher guide's design principles balance conceptual understanding, procedural fluency, and real-world application/modeling prompts [E1][E6], and lessons carry explicit HS CCSS alignment (e.g., HSF-IF.C.7.a) [E5]. Named units and lessons across functions, linear, and quadratic content demonstrate coherent grade-band placement [E5][E7][E9][E11], and the materials provide supports ensuring all students access rigorous grade-level content [E4][E10]. This satisfies the indicator's required components for awarding the maximum; remaining uncertainty is a retrieval limitation across the full conceptual categories, which lowers confidence but not the score.

The teacher guide explicitly articulates the full modeling process per the NGA framework—'Pose a problem... Identify variables... Modeling requires genuine choices' [E2]—and distinguishes dedicated modeling prompts (full cycle) from regular lessons tagged with 'Aspects of modeling' for partial-cycle work [E11]. Lessons structurally engage the complete cycle: students decide what model to use with deliberately 'messy' data, then validate and adjust based on fit [E1, E6], and culminating lessons have students specify quantities, identify relevant info, set constraints, create, and interpret models [E7]. Other lessons intentionally focus on discrete modeling practices (MP2/MP4) as scaffolded components [E4, E10, E12], showing a deliberate design that attends to the full intent across the band.

The retrieved evidence shows a complete IM Math high school curriculum (Algebra 1, Geometry, with teacher guide design principles in [E1][E4][E5]) whose lessons concentrate on the CCSSM widely applicable prerequisites — functions (HSF-LE.A.1, HSF-LE.A.2 in [E9]), interpreting categorical/quantitative data and statistics (HSS-ID.B, HSS-ID.B.6.a, HSS-ID.C in [E9][E11][E12]), modeling with mathematics ([E1][E9]), and geometry applications ([E6]). Classroom activities 'make up the majority of the time spent in class' ([E5]) and are built around these WAP concepts, with the supports materials reinforcing the same prerequisite content ([E2][E3][E7][E8][E10][E11]). Structural evidence indicates the design intentionally devotes the majority of student time to widely applicable prerequisite content, meeting the indicator.

Structural evidence shows the materials are intentionally designed to let students fully learn each standard: lessons carry explicit CCSS alignments differentiated as 'building on,' 'addressing,' and 'building towards,' with the teacher guide noting standards 'require weeks, months, or years to achieve' and are developed across lessons [E12, E2, E6-E11]. Learning targets summarize each lesson's goals and aggregate into a self-assessment per unit [E5], while distributed/cumulative practice supports retention over time [E5]. The design moves systematically from activating prior knowledge through conceptual development, procedural fluency, and real-world application [E1, E4], demonstrating that standards are taught to full depth when used as designed.

Materials regularly use HS-appropriate real-world contexts—carefully chosen anchor contexts motivate new concepts [E1], with applications like radioactive decay [E5], bivariate data modeling [E2], and modeling real-world data sets via transformations [E7]. Key takeaways from grades 6-8 are applied at HS sophistication rather than re-taught: lessons explicitly build from grade 8 function understanding and 6.EE/7.NS arithmetic toward HSF standards [E4, E6, E9, E11]. Across the courses students work with a range of real numbers through quadratics, exponential/radioactive-decay (irrational growth/decay), and polynomial/rational functions with asymptotes [E5, E10], supporting all three required components.

The materials show strong structural evidence of intentional coherence. Support lessons explicitly connect prior learning (grade 8 and earlier units) to upcoming Algebra 1 content [E1, E3], and the teacher guide describes a design where each unit activates prior knowledge and systematically introduces concepts [E6]. Meaningful connections span multiple clusters and domains: linking representations of functions [E2, E4], connecting linear equations/graphs to systems [E3, E7], building correlation coefficients on prior linear-model work [E10], and relating exponential, linear, and quadratic growth across units [E12]. These align directly with the indicator's requirement for connections within a course and across the series.

The materials explicitly identify Grades 6-8 standards and connect them to high school content throughout. Lessons tag specific middle-grades standards as 'Building On'/'Addressing' alongside high school targets — e.g., 6.EE/8.F.A.2/8.F.B.4 building toward HSF-IF.B.4 and HSF-LE.A.1 [E2], 6.EE.A.2.c and 6.EE.A.1 building toward HSF-IF.A.2 and HSF-LE.A.3 [E4], and 6.EE/6.RP building toward HSA-CED [E6]. Lesson narratives articulate purposeful extension rather than re-teaching: reviewing exponents from grades 6 and 8 to prepare equivalent-expression work [E1], extending grade 8 function understanding [E3], building on grade 8 correlation/two-way-table work to interpret correlation coefficients [E8], and Geometry building on middle-school transformations to prove congruence and similarity theorems [E9]. This structural evidence shows connections that allow students to extend prior knowledge, satisfying both required components.

Multiple lessons across the series intentionally identify and develop MP1 in connection to course-level content: Algebra 2 Lesson 10 [E4] uses relatively unscaffolded problems so students 'persevere in problem solving (MP1)' by choosing their own solution pathway, and Algebra 1 supports lessons present problems 'without providing much scaffolding, offering an opportunity for students to make sense of the problem and persevere in solving (MP1)' [E8] and to 'make sense of what is being asked' [E7]. The teacher guide provides structural support, with Lesson and Activity Narratives that explain 'how the mathematical practices come into play' [E6] and a stated design that students should 'do mathematics' by 'making sense of problems' [E2]. MP1 is connected to genuine mathematical content (sequences, functions, systems) rather than practiced in isolation, meeting the full intent of the practice across the series.

The teacher guide articulates an intentional design for developing conceptual understanding—students 'understand the why behind the how,' access concepts from multiple perspectives [E3], and progress concretely-to-abstractly with representations introduced gradually [E1][E7]. Specific lessons demonstrate this in standards lending themselves to conceptual understanding: hanger diagrams build understanding of equivalent equations (A-REI.A) [E4], double number lines/proportional reasoning develop radian sense [E6], and multiple lessons have students make connections across representations of linear/exponential functions (F-IF, F-LE) [E11][E8][E10]. Students independently engage with these conceptual tasks throughout the series, and representations are explicitly used to develop understanding rather than as ends in themselves [E5][E10], satisfying both required components.

Multiple lessons explicitly and correctly identify MP2 in connection to course-level content: students reason abstractly and quantitatively to match situations to linear equations (E4, HSA-CED.A.2/A.4), interpret functions in context (E7), decontextualize when connecting symbolic representations (E3), and connect symbolic expressions to contextual situations to evaluate equivalence of manipulations (E8). These instances show MP2 being used to enrich the mathematics—attending to the meaning of quantities, connecting scenarios to representations, and determining whether results make sense—not as standalone practice (E2, E5, E12). The recurring, content-tied appearances across multiple units provide structural evidence of intentional MP2 development to its full intent.

The teacher guide explicitly designs for developing procedural fluency throughout the series, with a stated philosophy that some activities are devoted to mastering procedural skill and warm-ups dedicated to strengthening number sense and procedural fluency [E1][E4][E5][E11]. Procedural development is intentionally embedded across courses: Algebra 1 Supports include Extra Support lessons whose warm-ups focus on procedural fluency and whose goals are to 'work fluently with exponents' and practice rewriting expressions (aligned to HSF-IF.A.2, distributive/exponent properties) [E2][E3][E7][E10], and Geometry provides dedicated practice lessons for calculating unknown values [E12]. Students independently demonstrate skills through row games, practice activities, and cool-downs that ask them to evaluate and rewrite expressions fluently [E7][E10][E12].

MP4 (modeling) is intentionally and pervasively developed across the series with explicit tagging and full modeling-cycle engagement: students create, interpret, and revise models in culminating lessons [E5][E6][E12], a dedicated set of modeling prompts is provided [E1], and a scaffolded supports strand builds discrete modeling skills toward the core lessons [E2][E3][E4][E11], all tied to course-level HS standards (HSF-LE, HSS-ID, HSF-IF) [E3][E11]. MP5 (using tools strategically) is also supported in connection to content—graphing technology is a required material and students make deliberate tool choices, e.g., selecting graphing windows to serve a modeling purpose [E7], creating scatter plots and fitting models with technology [E3][E4], and adjusting modeling demand via data-collection devices [E6]. The structural evidence (named lessons, MP-to-standard alignment, teacher-guide design description, and a supports sequence) shows intentional development of both MP4 and MP5 reaching full intent across the series.

Structural evidence shows intentional, series-wide support for both routine and non-routine applications. The teacher guide describes anchor contexts motivating new concepts, end-of-unit real-world application lessons, and a dedicated set of mathematical modeling prompts [E1][E9]. Specific application lessons appear across all courses—e.g., modeling battery power with functions (Alg 1, L18) [E6], radioactive decay requiring sense-making with less scaffolding (Alg 2, L7) [E8], applications of logarithmic functions to pH/earthquakes (Alg 2, L18) [E3], trigonometry/right-triangle problems and indirect measurement (Geometry L10, L16) [E10][E4], and circle/sector problems (Geometry L14) [E7]. Non-routine tasks where students draw their own diagrams, choose tools (MP5), and make assumptions [E8][E10][E4] give students opportunities to independently demonstrate applications, satisfying both required components.

The materials explicitly name and define all three aspects of rigor—conceptual understanding, procedural fluency, and application—and describe them as interwoven, with dedicated activities for developing a concept, mastering a procedure, and applying mathematics to real-world problems [E1, E4, E9, E11]. Multiple aspects are engaged simultaneously within single units: Geo.3 Similarity explicitly balances a focus on proof (conceptual) with using similar triangles to find unknown lengths and angles (procedural) [E5, E6, E12], and units commonly end with application/modeling lessons after concept development [E3, E7]. This structural evidence shows all three aspects present independently while multiple aspects develop understanding of a single topic, satisfying the 2-point criteria.

The retrieved evidence shows intentional, named development of MP7 (look for and make use of structure) and MP8 (express regularity in repeated reasoning) embedded in course-level content across the series. [E1] explicitly identifies both: contrasting visual patterns prompts MP7 while generating tables and generalizing relationships prompts MP8; [E5] and [E12] show MP7 (rewriting 1,000+200·4) and MP8 (generalizing from tables) tied to Algebra 1 modeling content. Numerous algebra-1-supports lessons ([E2],[E4],[E6],[E8],[E9],[E10],[E11]) deliberately use structure to factor quadratics, relate expressions to graphs, and recognize equivalence, and [E7] extends structural reasoning into Geometry proofs—demonstrating the practices enrich content (not isolated) and span the series. This structural, teacher-narrative evidence meets all required components.

The retrieved teacher-guide evidence shows the materials intentionally embed quality questions to guide students' mathematical development: E4 states lessons include 'suggested questions to help teachers better understand students' thinking' alongside commentary on expected responses and misconceptions, and E1 reinforces using questions with expected responses/misconceptions to build understanding during the lesson. E6 provides specific, purpose-tagged guiding questions across the modeling cycle (formulate/compute/interpret/validate/report), and E3/E7/E8 establish that asking questions to advance and push student thinking is a designed-in teacher role. This structural evidence supports all required components of the indicator.

The materials provide comprehensive teacher guidance: unit, lesson, and activity narratives explain the mathematical content, its place in the learning sequence, and the purpose of each activity (E2), and detailed structural guidance describes the teacher's role and the launch/work-time/synthesis arc (E3, E9). Annotations are tied to specific learning objectives through commentary on anticipated student responses, misconceptions, and suggested questions for formative use (E10, E12), plus first-instance detailed routine guidance (E4) and design-principle/pre-assessment supports (E11). Ancillary materials are addressed with embedded representation/differentiation supports and dedicated resources like Algebra 1 Supports (E1, E6), satisfying both required components.

The assessment system provides consistent year-long opportunities: each unit opens with a Check Your Readiness diagnostic, longer units add a mid-unit assessment, every unit ends with an end-of-unit summative, and every lesson has a cool-down plus practice problems [E2][E3][E4][E5][E7][E10]. Teacher guidance for evaluating performance is present via rubrics for constructed/extended response items, complete solutions with standard alignment, and distractor analysis flagging common errors [E5][E8][E9][E10]. Guidance for interpreting results and determining next steps is explicit—e.g., cool-down feedback prompts specific re-teaching strategies, diagnostics inform pacing/below-grade needs, and lesson commentary on misconceptions guides instructional adjustment [E1][E3][E6][E7][E11]. All three required components are met with structural evidence.

Materials contain adult-level explanations of grade-level concepts via lesson narratives that articulate the mathematical purpose and how to teach it (e.g., correlation coefficients in [E4]/[E7], function representations in [E6], equivalent expressions in [E5]), satisfying the first required component. They also explicitly explain cross-grade alignment: the standards framework of 'Building On,' 'Addressing,' and 'Building Towards' is defined for teachers in the HS teacher guide [E1] and applied consistently in lessons connecting prior-grade work to current and future course content (e.g., 8.F.A.3 building toward HSF-IF in [E3], grade 8 correlations preceding Algebra 1 work in [E7], 8.G.A.2 building toward HSG-CO in [E11]), satisfying the second component. Both required components are clearly present.

The materials clearly ask students to produce answers/solutions (E5, E10's multiple-choice/short-answer items), arguments and explanations (E6 has students explain reasoning and critique others' reasoning per MP3; E10 asks students to 'show and explain their work'), diagrams and representations (E1 cites tables, graphs, diagrams, expressions, and equations; E2 provides multiple means of representation), and mathematical models (E3, E4, E7, E9, E11, E12 describe an embedded mathematical modeling strand with the full formulate-compute-interpret-validate-report cycle). E1 explicitly states extended-response problems 'provide multiple ways for students to demonstrate understanding... through some combination of arithmetic or algebra, use of representations... and explanation,' which structurally confirms intentional variety across all required presentation types.

E1 states directly that 'All summative assessment problems include a complete solution and standard alignment,' showing assessments explicitly denote the standards being emphasized. E4 reinforces this by describing how specific standards are assessed on particular assessments (e.g., calculator-allowed vs. prohibited based on the standard's demands), and E8 documents the deliberate 'building on/addressing/building towards' alignment system used throughout the materials. This structural evidence shows the materials intentionally and clearly denote assessed standards.

The materials include 'Are You Ready for More?' problems embedded in select classroom activities that 'go deeper into grade-level mathematics and often make connections between the topic at hand and other concepts,' are explicitly 'not routine or procedural' and not 'the same thing again but with harder numbers,' and are designed for students who finish early or want to do more mathematics [E1][E2]. The teacher guide describes these as an intentional, opt-in structure for extending and deepening student investigation [E1], directly satisfying the requirement to support advanced students in investigating content at greater depth. This is clear structural evidence of intentional design meeting all required components of the indicator.

The materials provide robust guidance for interpreting performance and following up: cool-downs include explicit strategies for when students haven't understood a concept [E3], pre-unit diagnostics tell teachers how to identify below-grade needs and adjust pacing [E2], and multiple-choice distractors function as diagnostics tied to common errors [E4]. Summative assessments include complete solutions, standard alignment, and tiered rubrics for evaluating student answers [E7][E8][E12], and worked examples show concrete follow-up moves like targeted feedback, revision, and assigning related practice problems in upcoming lessons [E6][E10][E11]. This structural evidence supports all required components of the indicator.