McGraw-Hill Illustrative Mathematics AGA

The materials show intentional, structural support for the full intent of HS mathematical content: the teacher guide articulates a design that develops conceptual understanding, procedural fluency, and application/modeling, with anchor contexts and culminating application lessons [E1][E4][E6]. Standards alignment to HS CCSS is explicit (e.g., HSF-IF.C.7.a) across units covering functions, linear equations, and quadratics [E5][E7][E9][E11], and the supports are explicitly designed to keep all students reasoning at the same rigor as the core course [E3][E10]. This evidence indicates the design attends to the full intent of the content for all students; gaps in retrieved coverage of every conceptual category are a retrieval limitation, not a deficiency.

The materials show intentional, structural attention to the full modeling process. The HS teacher guide explicitly articulates the modeling cycle and the disposition behind it — genuine choices, room to interpret, a range of acceptable assumptions, and the 'Things the Modeler Does' from NGA 2010 [E2] — and distinguishes full modeling prompts from scaled-back classroom activities tagged with 'Aspects of modeling' [E11]. Lessons span the full cycle (formulate, compute, interpret, validate, report): students decide what model to use with deliberately messy data [E1], create and interpret their own constraint models [E7], adjust models to fit data and critique others' reasoning [E3,E6], and practice discrete modeling subskills in scaffolded supports [E5,E10,E12]. This combination of an explicit modeling framework plus lessons engaging both whole-cycle and component aspects across the courses supports all required components of the indicator.

The retrieved evidence shows a comprehensive IM Math high school program (Algebra 1, Geometry, with extra support materials) whose lessons are explicitly aligned to core widely-applicable-prerequisite standards: functions and modeling (HSF-LE.A.1, HSF-LE.A.2 in [E9]), statistics and data interpretation (HSS-ID.B, HSS-ID.B.6.a, HSS-ID.C in [E9][E12]), and geometry/circle theorems ([E6]). The teacher guide and design principles ([E4][E5]) describe units built around systematic development of these concepts as the majority of class time ('the heart of the mathematical experience and make up the majority of the time'), and supporting lessons connect prior grade 8 work to Algebra 1 prerequisites ([E2][E3][E11]). This structural alignment to the WAP content (functions, algebra, statistics, geometry) supports awarding the maximum. Confidence is moderate because a full scope-and-sequence quantifying time-on-WAP was not retrieved.

The materials show intentional structural design to fully develop each standard over time: units begin with pre-assessments and an entry-point lesson, then systematically introduce representations, concepts, language, and notation as the unit progresses [E1]. Standards are explicitly mapped to lessons via a coherent three-tier alignment system (building on / addressing / building towards), acknowledging that standards develop over weeks/months and across grades [E2][E6][E12]. Distributed/cumulative practice revisits prior content for retention [E5], lessons carry standards-aligned learning targets that double as self-assessment [E5][E7][E11], and conceptual understanding, procedural fluency, and application are deliberately balanced [E1][E4]. This is sufficient structural evidence that the materials, when used as designed, allow students to fully learn each standard.

The materials regularly use high-school-appropriate contexts—radioactive decay and dating distant events [E4], real-world data modeling via transformations [E6], constraint situations [E7], and dedicated end-of-unit application lessons plus modeling prompts [E1]. They apply (not re-teach) grade 6-8 takeaways at a sophisticated level: building on 6.EE.A.2/7.NS.A.2.c [E3], extending grade 8 function concepts to new representations and modeling [E5, E8], and explicitly noting prior math is applied to less-scaffolded problems requiring sense-making [E4]. Various types of real numbers appear across courses—negative inputs to quadratics [E3], higher-degree polynomials and rational functions with asymptotes and series [E9], and exponential growth/decay [E4]—satisfying all three required components.

The materials demonstrate intentional coherence both within and across courses. Algebra 1 Supports lessons explicitly link new content to prior learning (e.g., grade 8 and earlier units [E1]) and prepare students for upcoming associated Algebra 1 lessons [E2, E3, E4, E7, E9, E11], building knowledge systematically. Meaningful cross-cluster/domain connections appear throughout — connecting verbal/tabular/graphical/equation representations [E1, E2, E4], linking statistics (correlation coefficients) to linear-relationship understanding [E10], and progressing linear→exponential→quadratic within and across units [E12]. The teacher guide confirms this is a deliberate design principle: each unit activates prior knowledge and systematically introduces representations and concepts as learning progresses [E5, E6].

The materials explicitly identify Grades 6-8 standards and build on them toward high school work. Lesson standards charts tag prior-grade standards as 'Building On' (e.g., 6.EE.A.2.c, 6.EE.A.2.a/6.EE.B.6) alongside 'Building Towards'/'Addressing' high school standards like HSA-SSE, HSA-CED, HSF-IF, HSF-LE [E2, E4, E5, E6], and lesson narratives name the specific prior knowledge being extended — grade 6 exponents and grade 8 equivalent-expression work [E1], grade 8 function concept extended to function notation [E3], grade 6 algebraic expressions from verbal descriptions [E7], and grade 8 correlations/two-way tables toward correlation coefficients [E8]. The Geometry narrative explicitly builds on 'middle school study of transformations' to rigorously prove congruence and similarity theorems [E9], matching the guide's G-SRT.A/8.G.A and F-IF.A/8.F.A coherence examples. These are purposeful extensions for new HS learning, not re-teaching, satisfying all components for full credit.

MP1 is intentionally and explicitly developed in connection to course-level content across the series. Multiple lessons identify MP1 in genuine problem-solving contexts that enrich the mathematics: Algebra 2 Lesson 10 deliberately presents 'relatively unscaffolded' problems so students persevere and choose their own solution pathways [E4], and Algebra 1 supports lessons require students to make sense of situations and quantities [E7] and 'make sense of the problem and persevere in solving' with little scaffolding [E8]. The HS teacher guide structurally supports this, with lesson and activity narratives explaining how the mathematical practices 'come into play' and emphasizing students should *do* mathematics, including making sense of problems [E2][E6]. This is intentional development meeting the full intent of MP1 tied to HS content, not isolated practice work.

The materials (IM Math HS) intentionally develop conceptual understanding throughout the series, with a teacher-guide design principle dedicated to it that emphasizes understanding the 'why behind the how' and a deliberate concrete-to-abstract progression [E1, E3, E5, E7]. Specific lessons show this in practice on conceptually-oriented standards: hanger diagrams for equivalent equations (A-REI.A) [E4], radian/degree relationships via double number lines [E6], multiple equivalent representations of a situation [E8, E11], and area models for the distributive property [E10], with explicit attention to connecting representations. Students independently demonstrate understanding through the individual-to-pair-to-group progression and practice where they choose and explain representations [E2, E7, E11], satisfying both required components.

Multiple lessons across units show intentional MP2 development tied to course-level content: students decontextualize by connecting symbolic representations to functions [E3], reason abstractly and quantitatively to match situations to linear equations (HSA-CED.A.2/A.4) [E4], interpret functions in context across equations and graphs [E7], and connect symbolic expressions to contextual situations to evaluate validity of manipulations [E8]. These instances span Algebra 1 Units 2–5 and consistently use MP2 to enrich—not replace—the mathematics content (attending to meaning of quantities, relating scenarios to representations), meeting the full intent of the practice. The recurring, standards-connected framing constitutes structural evidence of intentional development across the series.

The curriculum's design principles explicitly name developing procedural fluency alongside conceptual understanding, citing research like Adding It Up and committing to lessons dedicated to mastering procedural skill [E1][E4][E9][E11]. Procedural development is structurally embedded: warm-ups specifically strengthen number sense and procedural fluency [E5], Extra Support lessons include procedural-fluency warm-ups [E3], and lessons target standards-aligned skills (HSF-IF.A.2) with goals like 'Practice evaluating expressions involving exponents' and student-facing 'Let's work fluently with exponents' [E7][E2]. Independent demonstration is evidenced through dedicated practice lessons and exercises across courses (e.g., Geometry practice lesson, Algebra 1 supports) [E10][E12], and the design notes ongoing practice supports procedural proficiency [E8], satisfying both required components throughout the series.

The indicator targets MP4 (modeling) and MP5 (using tools). Evidence shows intentional, full-intent development of MP4 across the series: culminating modeling lessons engage the full modeling cycle—identifying quantities, building/interpreting models, and revising with new information ([E5], [E6], [E12])—plus a dedicated set of mathematical modeling prompts ([E1]) and a scaffolded supports strand ([E2], [E3], [E4], [E11]). MP5 is developed through repeated, purposeful use of graphing technology, including selecting graphing windows for a purpose and creating scatter plots/models with technology ([E4], [E7], [E3]), all tied to course-level standards (HSF-LE, HSS-ID, HSF-IF). This structural and lesson-level evidence spans Algebra 1, Algebra 2, and the supports materials, meeting all required components.

The teacher guide describes intentional application design—anchor contexts motivating concepts, end-of-unit real-world application lessons, and a dedicated set of mathematical modeling prompts [E1, E9]. Multiple routine and non-routine applications appear across the full series: linear modeling of battery power [E6], standard deviation in real-world route decisions [E2], logarithmic models of earthquakes/acidity [E3], less-scaffolded radioactive decay requiring sense-making (MP1) [E8], trigonometry with student-drawn diagrams and unit conversion [E10], and indirect-measurement/bank-shot tasks where students choose their own tools (MP5) [E4, E7]. Students independently demonstrate applications via the individual-think-first progression [E5] and tasks requiring them to make assumptions, draw diagrams, and select strategies [E4, E8, E10], satisfying both required components.

The teacher guide explicitly names and defines all three aspects of rigor—conceptual understanding, procedural fluency, and application—and states they are interconnected, with procedural fluency supported by understanding and application requiring both [E1, E4, E7]. The design intentionally treats aspects both separately and together: some activities develop a concept, others master a procedure, others apply mathematics, and these 'aspects of mathematical proficiency are interwoven' [E9, E11]. Unit-level structural evidence confirms simultaneous engagement, e.g., Geo.3 Similarity 'balances a focus on proof with a focus on using similar triangles to find unknown side lengths,' combining conceptual justification with procedural/applied work within a single topic [E5, E6, E12], with end-of-unit application lessons providing dedicated focus on application [E3, E7]. This supports all required components of the indicator.

The materials show intentional, repeated development of MP7 (seeing structure) and MP8 (generalizing) tied directly to course-level content. MP7 is explicitly identified and content-enriching across algebra-1, algebra-1-supports, and geometry—e.g., contrasting linear/exponential/quadratic patterns [E1], rewriting and identifying equivalent expressions [E2][E11], recognizing factoring patterns [E4][E8], and connecting expression structure to graph features [E6]. MP8 is developed where students generate tables and generalize relationships from repeated reasoning [E1][E12] and perform repeated calculations to derive function properties [E9]. This structural evidence demonstrates both MPs reaching full intent in connection to the high school content standards across the series.

The materials provide quality, embedded questions to guide mathematical development: each lesson includes 'suggested questions to help teachers better understand students' thinking' along with expected responses and misconceptions [E4][E1], and the teacher's role explicitly centers on asking questions to advance thinking and orchestrate discussion [E3][E8]. Structured guiding questions are provided for modeling work across the full cycle [E6] and for supporting stuck students [E7]. This structural evidence supports all required components of the indicator.

Materials provide comprehensive teacher guidance: unit/lesson/activity narratives explain the mathematical content and its place in the learning sequence [E2], the three-phase launch/work/synthesis structure clarifies the teacher's role in advancing thinking [E3][E9], and instructional routines include detailed first-instance guidance [E4]. Annotations are tied to specific learning objectives through commentary on expected student responses, misconceptions, and suggested questions to probe thinking [E10], plus pre-assessments and design principles for enacting lessons [E11]. Ancillary materials are addressed via the Algebra 1 Supports with their own high-leverage routines [E6] and UDL representation supports [E1], satisfying both required components.

The assessment system provides consistent year-long opportunities: pre-unit diagnostics ('Check Your Readiness') at the start of each unit [E3][E6], mid-unit assessments in longer units [E10], end-of-unit summative assessments [E5], daily cool-downs as formative checkpoints [E7], and practice problems plus year-long modeling prompts [E1][E4]. Teacher guidance for evaluating performance is present through rubrics for constructed/extended response items, complete solutions, standard alignments, and reasons for each potential error on multiple-choice items [E8][E10]. Guidance for interpreting results and determining next steps is also explicit—cool-down feedback offers concrete reteaching strategies [E7], diagnostics are used to pace/tune instruction and identify below-grade needs [E3][E6], and lesson commentary on misconceptions directs instructional adjustment [E1][E11]—so all three required components are met.

Both required components are supported. The materials contain adult-level explanations of grade-level concepts via Lesson Narratives describing mathematical purpose and practices (e.g., E4, E7, E8 explain correlation coefficients and lines of best fit; E12 describes design principles for conceptual understanding/fluency). They also explicitly explain alignment to other grade levels through the standards system of 'Building On / Addressing / Building Towards' (E1, E2, E3, E5, E11) and narrative prose tracing progression (E4 'Previously, students learned...'; E7 'Students learned about positive and negative correlations in grade 8'; E8, E10 connecting to prior grades and the broader K–12 curriculum).

The materials clearly ask students to present mathematics in varied forms. Students produce answers and solutions to problems [E5], construct arguments and explanations while critiquing the reasoning of others (MP3) [E6], create diagrams and multiple representations such as tables, graphs, and equations [E2][E3], and build mathematical models through dedicated modeling prompts and lessons [E3][E4][E7][E12]. Assessments deliberately offer multiple ways to demonstrate understanding via arithmetic/algebra, representations, and explanation, with varied item types [E1][E10]. This satisfies all components of the indicator.

E1 states explicitly that 'All summative assessment problems include a complete solution and standard alignment,' directly showing assessments clearly denote the standards being emphasized. The teacher guide further describes a deliberate standards-alignment design ('building on, addressing, and building towards') applied throughout the materials [E8], and specifies how particular standards are assessed [E4]. Lesson-level standard tagging (e.g., HSG-CO.B.8, HSA-SSE.A.1) [E2][E9] confirms standards are systematically denoted, supporting that summative assessments denote emphasized standards.

The materials include a dedicated 'Are You Ready for More?' feature in select classroom activities [E1][E2], explicitly designed for advanced students to investigate content at greater depth—problems that 'go deeper into grade-level mathematics,' make connections between topics and the broader K–12 curriculum, and are deliberately 'not routine or procedural' and 'not just the same thing again but with harder numbers.' These are intended on an opt-in basis for students who finish early or want to do more mathematics independently [E1], which is precisely the structural support this indicator requires. This is an intentional, named, teacher-guide-described design feature for deepening (not merely accelerating) advanced students' work.

The materials provide robust guidance for interpreting performance: multiple-choice distractors function as diagnostics tied to common errors [E4], summative items include complete solutions, standard alignments, error reasons, and tiered rubrics for constructed/extended responses [E7][E8][E12]. They also give concrete follow-up suggestions — cool-down feedback strategies, revisiting topics in upcoming lessons, and detailed worked examples of misconception remediation [E1][E3][E6][E10][E11]. Diagnostic 'Check Your Readiness' assessments explicitly tell teachers how to use results to identify below-grade needs and pace instruction [E2][E5], satisfying all required components.