Imagine Learning Illustrative Mathematics IM 9-12 Math

Structural evidence shows the materials intentionally develop the full intent of high school content: the teacher guide articulates design principles balancing conceptual understanding, procedural fluency, application, and modeling prompts [E1][E6], and lessons carry explicit HS standards alignment (e.g., HSF-IF.C.7.a) [E5]. Named anchor lessons across Algebra 1 units address core HS topics—functions and representations, quadratics, linear equations, interpreting graphs in context—with math-practice integration (MP2, MP3, MP4, MP6) [E2][E7][E8][E9][E11][E12]. The 'for all students' dimension is supported by dedicated supports materials and accessibility design that hold rigor at grade level [E3][E4][E10]. No evidence contradicts coverage of HS content intent.

The materials attend to the full intent of the modeling process. The teacher guide explicitly enumerates 'Things the Modeler Does When Modeling with Mathematics' (pose a problem, identify variables, make assumptions, analyze, interpret, validate, report) [E3], and distinguishes dedicated full-cycle 'mathematical modeling prompts' from regular lessons with scaled-back, 'Aspects of modeling'-tagged activities [E11]. Individual lessons demonstrate the complete cycle—identifying quantities, building representations, analyzing, reflecting, and revising upon new information [E1], working with deliberately 'messy' real data and choosing/adjusting models [E2][E6], and a culminating lesson where students specify quantities, set constraints, create, and interpret models [E7]. The intentional gradation between partial-aspect practice [E4][E5][E10][E12] and full-cycle tasks shows the design deliberately covers the modeling standards' full intent.

The retrieved evidence shows a comprehensive HS course (Algebra 1, Geometry) built around content that is widely applicable as prerequisites: functions and their representations (HSF-IF, HSF-LE.A.1/A.2 in [E3], [E9]), statistics and modeling (HSS-ID.B/C and correlation in [E7], [E8], [E11], [E12]), and geometry/trigonometry applications ([E6]). The teacher guide [E1], [E4], [E5] confirms that classroom activities making up the majority of class time develop these core concepts with real-world application and mathematical modeling. This structural standards alignment to the algebra, functions, statistics, and geometry strands that constitute the WAPs supports that students spend the majority of their time on widely applicable prerequisite content.

The materials show intentional structural design to allow students to fully learn each standard: every lesson explicitly tags addressed CCSS standards with learning targets [E2, E6, E7, E8, E11], and the curriculum distinguishes 'building on,' 'addressing,' and 'building towards' alignments, acknowledging that standards develop over time [E12]. The teacher guide documents a coherent progression from pre-assessment and prior-knowledge activation through systematic introduction of representations and concepts, balancing conceptual understanding, procedural fluency via distributed practice, and application [E1, E4, E5]. This is consistent design evidence that the materials, when used as designed, support full learning of each standard.

Materials regularly use HS-appropriate real-world contexts—carefully-chosen anchor contexts, end-of-unit application lessons, and modeling prompts [E1], including radioactive decay [E4] and modeling real-world data sets [E6]. They engage students at a sophisticated level across number types via quadratics with negative inputs [E3], exponential functions [E4], and polynomial/rational functions with asymptotes [E9]. Key takeaways from grades 6-8 are applied (not re-taught), e.g., grade 8 function understanding is explicitly extended to function notation and multiple representations rather than retaught [E5, E8, E10], satisfying all three required components.

The materials structurally foster coherence through explicit, meaningful connections to prior learning and across the series. The algebra-1-supports lessons repeatedly link grade 8 and earlier-unit work to upcoming Algebra 1 lessons and connect multiple representations (verbal, tabular, graphical, equations) of the same relationship [E1][E2][E3][E4][E9][E11]. Cross-domain connections appear where statistics/correlation builds on linear relationships [E10] and where linear, exponential, and quadratic functions are deliberately related across units [E12]. The teacher guide confirms an intentional design: units open by activating prior knowledge and systematically introduce representations, contexts, and concepts to build understanding [E5][E6].

The materials explicitly identify Grades 6-8 standards and connect them to high school content in both lesson narratives and standards labels. Lesson narratives name specific prior-grade knowledge ('connects to previous work done in grade 6 when students learned to interpret expressions that use exponents...grade 8 when students learned how to create equivalent expressions' [E1], grade 8 function understanding [E3], grade 8 positive/negative correlations and two-way tables [E8]) and describe how it extends to HS work. Standards lists formally tag 'Building On' 6.EE.A.2.c [E4], 6.EE.A.2.a/6.EE.B.6 [E6] and 'Addressing/Building Towards' HS standards (HSF-IF, HSA-SSE, HSF-LE) [E2][E4][E5][E6], showing purposeful extension rather than re-teaching. The Geometry narrative likewise builds on middle-school transformations toward formal congruence/similarity proofs [E9], matching the Evidence Guide's coherence examples.

The materials show intentional development of MP1 connected to course-level content across the series: Algebra 2 Lesson 10 deliberately uses unscaffolded problems so students 'persevere in problem solving (MP1)' by choosing their own solution pathways [E4], 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 make sense of what is being asked [E7]. The teacher guide structurally embeds the MPs via lesson/unit narratives that explain 'how the mathematical practices come into play' [E6], and explicitly frames doing mathematics as engaging in practices including 'making sense of problems' [E2], using MP1 to enrich content rather than in isolation. This meets the full intent of MP1 across courses.

The teacher guide articulates an intentional design where students 'understand the why behind the how,' accessing concepts from multiple perspectives, with ideas introduced concretely and progressing to abstract over time [E1][E3][E7]. Concrete-to-abstract and representation-connection work appears throughout the series and grade bands: hanger diagrams for equivalent equations [E4], double number lines and proportional reasoning for radian measure [E6], multiple equivalent equations from contexts [E8], geometric area models for the distributive property [E10], and connecting verbal/tabular/equation representations of linear and exponential functions [E11] — directly addressing conceptual standards like F-IF.A, F-LE.1, and A-REI.A. Students independently demonstrate understanding through unit pre-assessments, individual think time before sharing, and activities requiring them to choose and explain representations [E1][E7][E8], satisfying both required components.

Multiple lessons explicitly and intentionally develop MP2 in connection to course-level content: [E4] has students 'reason abstractly and quantitatively (MP2) to make sense of the situations and match them to equations' (HSA-CED.A.2/A.4), [E8] develops decontextualizing/contextualizing as students 'connect symbolic expressions to contextual situations and using their understanding of what makes sense in context to evaluate the validity of symbolic manipulations,' [E3] names students 'practicing decontextualizing (MP2)' when moving between situations and symbolic representations, and [E7] applies MP2 to interpreting functions in context. These instances show MP2 enriching the mathematics (attending to quantities, connecting representations to scenarios, determining whether answers make sense) rather than being treated in isolation, meeting the full intent of the practice in connection to high school standards.

The teacher guide explicitly names procedural fluency as a core design principle interwoven throughout the series, with activities dedicated to 'mastering a procedural skill' [E9, E11] and a research-grounded definition of procedural fluency [E4]. Structural development is evident: every lesson opens with a warm-up that can 'strengthen number sense or procedural fluency' [E5], Extra Support lessons embed procedural-fluency warm-ups [E3], and targeted lessons have students fluently evaluate quadratic/exponential expressions, apply exponent and distributive properties, and practice proportional relationships aligned to specific standards like HSF-IF.A.2 [E2, E7, E10, E12]. Students independently demonstrate these skills through practice activities, row games, and 'Let's work fluently with exponents' tasks where they evaluate expressions and rewrite using properties [E7, E10, E12], satisfying both required components.

The materials show intentional, series-wide development of modeling (MP4) connected to course-level content: full modeling-cycle engagement in Algebra 1 culminating lessons where students specify quantities, set constraints, build and revise models [E5][E6][E12], scaffolded modeling-skill supports building toward those lessons [E2][E3][E4][E11], and a teacher guide describing anchor contexts plus dedicated modeling prompts [E1], extending into Algebra 2 [E9]. Use of tools (MP5) is also developed in connection to content, with graphing technology required and purposefully leveraged (creating scatter plots, choosing graphing windows to model a situation) [E3][E4][E5][E7]. These MPs enrich genuine content standards (HSF-LE, HSF-IF, HSS-ID) rather than standing alone, satisfying all required components across the series.

The teacher guide describes intentional application design: anchor contexts motivate concepts, units end with real-world application lessons, and a dedicated set of mathematical modeling prompts is provided ([E1], [E9]). Routine and non-routine applications appear throughout the full series — Algebra 1 (battery-power modeling where students choose their own model, [E6]), Algebra 2 (less-scaffolded radioactive decay and log applications requiring MP1 sense-making, [E8], [E3]), and Geometry (bank shots, pizza-deal sector analysis, flight-path problems requiring students to draw their own diagrams and choose tools, [E4], [E7], [E10]). Students independently demonstrate applications by making their own assumptions, selecting strategies/tools (MP5), and tackling non-routine summative tasks, satisfying both required components.

The teacher guide explicitly defines all three aspects of rigor and describes them as interconnected/interwoven, with some activities devoted to developing a concept, others to mastering a procedural skill, and others to applying mathematics [E1, E4, E9], demonstrating intent to treat aspects both separately and together. Application lessons appear at the end of units while concepts are developed first [E7], and the Geo.3 Similarity unit concretely balances a focus on proof (conceptual) with using similar triangles to find unknown side lengths and angles (procedural/application) [E5, E12]. This structural evidence shows the materials engage multiple aspects of rigor simultaneously within a single unit while allowing dedicated focus on each, satisfying the indicator's requirements.

The retrieved evidence shows MP7 (seeing structure) and MP8 (generalizing/regularity in repeated reasoning) are intentionally and explicitly developed in connection to course-level content across the series. Lesson narratives repeatedly name these practices tied to specific content: [E1] contrasts patterns to 'look for and make use of structure (MP7)' and generates tables to 'express regularity in repeated reasoning (MP8)'; [E12] has students generalize relationships from tables (MP8); [E4], [E6], [E8], [E9], [E10], [E11] embed MP7 in factoring, equivalent expressions, and graph-feature connections. Coverage spans Algebra 1, Algebra 1 Supports, and Geometry [E7], with the teacher-facing narratives explaining how the structure/generalizing work enriches (not replaces) the mathematics, satisfying the full intent.

The teacher guide intentionally embeds quality questions to guide mathematical development: teachers are directed to 'ask questions to advance students' thinking' [E3], lessons provide 'suggested questions to help teachers better understand students' thinking' alongside anticipated misconceptions [E4], and modeling prompts include stage-specific guiding questions like 'Under what conditions does your model work?' [E6]. Further guidance covers questioning students who are stuck [E7] and pushing thinking during problem-based discussions [E8], showing comprehensive structural support across lesson and activity levels.

The materials provide comprehensive teacher guidance through unit, lesson, and activity narratives that explain the mathematical content, its place in the learning sequence, and the purpose of each activity [E2], plus explicit guidance on the teacher's role in mediating learning and orchestrating discussions [E3][E9]. Annotations are tied to specific learning objectives via commentary on expected student responses, potential misconceptions, and suggested questions [E10], and detailed first-instance guidance for high-leverage instructional routines [E4]. Ancillary materials are addressed (e.g., Algebra 1 Supports with aligned routines [E6]), along with UDL/representation supports [E1] and pre-assessments to guide adjustments [E11], satisfying both required components.

All three required components are structurally supported. The system provides consistent opportunities throughout the year: per-unit diagnostics ('Check Your Readiness') [E3, E4, E6], mid-unit assessments in longer units [E10], end-of-unit summative assessments [E5, E10], daily cool-downs [E1, E7], practice problems [E1], and year-long modeling prompts [E4]. Teacher guidance for evaluating performance is present via rubrics for constructed/extended response items [E8, E10] and complete solutions with standard alignment [E10]. Guidance for interpreting results and determining next steps is explicit: distractor-based diagnostics [E9], misconception commentary [E1, E11], and concrete strategies for re-teaching when cool-downs reveal gaps [E7, E11].

Both required components are supported. The teacher guide explains grade-level concepts and their rationale via lesson narratives describing the mathematical purpose (e.g., correlation coefficients in [E4], [E7], slope-intercept connections in [E8]) and design principles for building conceptual understanding ([E12]). The materials also explicitly explain cross-grade alignment through the documented 'building on, addressing, building towards' framework ([E1]), with each lesson tagging prior-grade and future standards ([E2], [E3], [E5], [E11]) and narratives that articulate how current work builds on prior grades and prepares students for later courses (e.g., 'Students learned about positive and negative correlations in grade 8' in [E7]).

The materials intentionally require students to present mathematics in varied forms. Extended-response items explicitly provide multiple ways to demonstrate understanding 'through some combination of arithmetic or algebra, use of representations (tables, graphs, diagrams, expressions, and equations) and explanation' [E1], and assessments span multiple-choice, short answer, constructed response, and extended response with students asked to 'show and explain their work' [E10]. Beyond answers/solutions, students construct arguments and explanations and critique reasoning (MP3) while representing functions in different ways [E6], and a dedicated set of mathematical modeling prompts asks students to build, interpret, validate, and report models [E3][E4][E7][E11][E12]. This structural design covers all required presentation modes—solutions, arguments/explanations, diagrams, and mathematical models—supporting the indicator.

The teacher guide explicitly states that 'All summative assessment problems include a complete solution and standard alignment' [E1], directly satisfying the indicator's requirement that assessments denote emphasized standards. The materials further describe a deliberate standards-alignment system ('building on, addressing, and building towards') applied throughout [E8], and discuss how specific standards are targeted on assessments [E4]. Lesson-level evidence shows consistent, explicit CCSS standard tagging [E2, E3, E6], reflecting the same intentional alignment structure carried into assessments.

The materials include a dedicated 'Are You Ready for More?' feature in select activities, explicitly designed to let advanced students investigate content at greater depth: the problems 'go deeper into grade-level mathematics and often make connections between the topic at hand and other concepts,' are 'not routine or procedural,' and are 'not just the same thing again but with harder numbers' [E1][E2]. They are intentionally offered on an opt-in basis for students who finish early or want to do more mathematics independently [E1]. This is clear structural evidence of intentional support for advanced learners across the high school courses, satisfying the indicator.

The materials provide robust guidance for interpreting performance: summative items include complete solutions, standard alignment, reasons for each potential error/distractor, and tiered rubrics for constructed/extended responses [E4][E7][E8][E12]. Follow-up suggestions are explicit and actionable—cool-downs and diagnostics come with concrete remediation strategies (revisiting topics in upcoming lessons, displaying student work, adding warm-up questions, assigning targeted practice) [E3][E6][E10][E11], and pre-unit diagnostics tell teachers how to use results to pace or address below-grade needs [E2][E5]. This satisfies both required components—interpreting performance and suggestions for follow-up.