Open Up High School Mathematics Traditional

The evidence shows a complete three-course high school series (Algebra 1, Geometry, Algebra 2, plus Algebra 1 supports) with lessons explicitly aligned to non-plus standards spanning all conceptual categories: Geometry (HSG-C.A.2, HSG-GPE.B.4/5/7, HSG-CO.A.1/B.6 in [E1][E2]), Functions (HSF-IF.B.4/5, HSF-BF.B.3, HSF-LE.A.1/2/3 in [E6][E7][E8]), Statistics (HSS-ID.B/B.6.a/C in [E7][E11]), and Algebra/modeling across multiple function families—linear, exponential, polynomial, geometric sequences ([E4][E10]). The teacher guide ([E5]) describes intentional design connecting concepts, procedural fluency, application, and modeling prompts, and lessons require student choice and multiple representations consistent with full intent. Structural evidence of standards-aligned, multi-domain, multi-function-family coverage across the full series supports awarding the maximum; the only limit is retrieval breadth, which affects confidence rather than score.

Structural evidence shows the series intentionally develops the full modeling process: the HS teacher guide describes a dedicated 'set of mathematical modeling prompts' plus real-world application lessons at the ends of units [E7], and Algebra 1 modeling work has students 'decide what type of model to use, create a model, and use the model to make predictions' rather than dictating the model [E10]. Modeling standards (e.g., HSF-LE.A.1/A.2, HSS-ID.B.6.a in [E10]; HSG-MG.A.3 in [E3]; modeling with sequences/functions in [E4][E9]) are addressed across courses with student-driven variable/model choice and interpretation in context. This matches the indicator's requirement that the full intent of the modeling process leads to culminating experiences across the series.

The retrieved evidence shows a coherent, intentionally designed high school series (IM Math: Algebra 1, Geometry, Algebra 2) with units aligned to core WAP standards such as statistics (HSS-ID.B.6, HSS-ID.C.7 in [E6]) and right-triangle/trigonometry geometry content [E4], plus a teacher guide describing a deliberate scope-and-sequence built around developing and applying CCSSM concepts [E2][E5][E12]. The prerequisite review content is isolated in separate 'Algebra 1 Supports' extra-time materials [E1][E3], not embedded as distracting chapters in the core courses, and distributed practice revisits prior CCSSM content to reinforce rather than distract [E7]. This structural evidence indicates the series spends the majority of instructional time on WAP content without distracting prerequisite or additional topics.

The materials show intentional structural design to enable students to fully learn standards: each unit opens with a diagnostic 'Check Your Readiness' pre-assessment and closes with end-of-unit (and sometimes mid-unit) assessments, supporting the formative-assessment cycle EdReports looks for [E10][E4]. Distributed practice problem sets revisit content over time, with mastery-focused activities for topics students need more time on [E7][E12], and concepts develop concretely to abstractly with extra-support materials for struggling students [E8][E1]. Course content spans the expected high school domains with strategic tool use (geometry toolkit, ruler, protractor) across geometry/trig units [E5][E6], and real-world modeling prompts run throughout [E2][E10]. This structural evidence demonstrates the series, as designed, enables students to fully learn the non-plus standards.

The materials structurally support all three required components. Carefully-chosen anchor contexts motivate new concepts with frequent real-world application lessons and modeling prompts appropriate for high school [E1, E3, E12]. Key takeaways from grades 6-8 are clearly applied at a higher level of sophistication rather than re-taught—functions and modeling [E6, E7], proportional/bivariate data modeling [E6], and middle-school standards explicitly 'building toward' HS standards (e.g., 6.EE.A.2 and 7.NS.A.2.c building toward HSF-IF.C.7.a in [E10]; HSS-ID.B.6.a in [E6]). Work with various real numbers is evident, e.g., quadratics evaluated for negative inputs and rational-number arithmetic in service of new HS concepts [E10, E11].

The materials consistently foster coherence through meaningful mathematical connections to prior learning and across concepts. Support lessons explicitly connect new content to earlier grades (grade 6 expressions in [E9], grades 7-8 linear relationships in [E4], grade 8 functions in [E1]) and to upcoming Algebra 1 work, while connecting multiple representations—verbal, tabular, graphical, and symbolic ([E2], [E3], [E7], [E10]). The teacher guide describes intentional design where each unit activates prior knowledge and systematically builds concepts ([E6]) and makes connections to real-world contexts and modeling ([E5]). Lessons also link clusters/domains, e.g., connecting equation-solving moves with geometric formulas ([E12]) and slope/intercept reasoning across graphs, equations, and contexts ([E8], [E11]).

Materials explicitly name Grades 6-8 standards and use them to extend learning into high school content across multiple courses. Examples include reviewing grade 6/8 exponent work before Algebra 1 [E1], building on grade 8 scatter plots and two-way tables for two-variable statistics [E3], extending grade 8 transformations into rigorous congruence/similarity proofs [E6][E11][E12], grounding trigonometric ratios in the grade 8 Pythagorean Theorem and similar right triangles [E10], and building grade 7/8 volume work into high school volume derivations [E8]. These connections are purposeful extensions rather than re-teaching, clearly articulated for teachers in unit narratives, satisfying the 2-point band.

The teacher guide describes multiple formal assessment types—diagnostic 'Check Your Readiness,' mid-unit, and end-of-unit assessments [E2][E5][E7][E10]—and critically states that 'All summative assessment problems include a complete solution and standard alignment' [E10], with extended/constructed-response items including rubrics. This is direct structural evidence that the materials consistently identify the standards assessed for formal assessments at the item level. This satisfies the indicator's requirement for consistent standard identification on formal assessments.

Assessments span a full variety of types—diagnostic 'Check Your Readiness,' cool-downs, practice problems, mid-unit, and end-of-unit/summative assessments [E2][E4][E5][E6]—with multiple item types (multiple-choice, multiple response, short answer, restricted constructed response, extended response) that vary in difficulty and depth of knowledge [E2][E6]. Extended response items intentionally offer multiple modalities (arithmetic/algebra, representations, explanation) and avoid compounding errors so students can fully demonstrate proficiency, with rubrics provided [E1][E6]. Mathematical practices are explicitly assessed, including modeling (MP4) via projects and feedback-focused tasks, and technology-allowed/prohibited assessments mirroring standards' intent [E7][E8][E9]. This structural evidence shows the assessments are designed to allow students to demonstrate the full intent of both grade-level standards and practices across the series.

The teacher guide explicitly describes intentional conceptual development: units begin with pre-assessments and entry-point lessons that activate prior knowledge, with representations, concepts, and notation systematically introduced over time [E1], and ideas built deliberately from concrete to abstract before relying on symbols [E6], [E2]. The materials connect new representations to familiar ones and have students choose representations for given problems [E5], and they explicitly aim for students to 'independently solve problems they've never seen before' through flexible, connection-based understanding [E3]. Lesson-level evidence confirms this is enacted, not just stated: hanger/equality diagrams build understanding of equivalent equations as a concrete metaphor [E9] and students explore that one relationship can be expressed in multiple equivalent equations through contexts while critiquing others' reasoning [E12], [E11] — demonstrating both development and independent demonstration of conceptual understanding throughout the series.

Structural evidence shows MP1 is intentionally developed in connection to course-level content. The teacher guide states each lesson narrative explains 'how the mathematical practices come into play, as appropriate' [E3], and design principles emphasize students independently solving novel problems, flexible thinking, and perseverance [E2], plus real-world application lessons [E10]. Multiple lessons explicitly center making sense of problems and reasonable solution pathways in connection to Algebra 1 content—interpreting inequalities, situations with constraints, and error analysis to revise strategies [E1, E8, E9, E12], demonstrating MP1 enriches the mathematics rather than standing alone.

The teacher guide explicitly frames a design principle for 'Developing Conceptual Understanding and Procedural Fluency' across units [E1], and notes activities where students 'work toward mastery of a concept or procedure' for topics needing additional practice [E8]. Independent demonstration is supported through lesson-associated practice problem sets and distributed practice assigned for homework/self-assessment [E7][E10], plus in-context skill development (e.g., solving equations in one variable) [E6]. This structural evidence shows the materials both develop procedural skill/fluency throughout the series and give students opportunities to independently demonstrate it.

MP2 is explicitly named and intentionally developed in connection with course-level content across the series. Multiple lessons require students to represent situations symbolically, attend to the meaning of quantities, and connect scenarios to graphs/equations — e.g., reasoning abstractly and quantitatively while moving from specific calculations to general expressions [E8], connecting written descriptions, equations, and graphs [E1], making sense of solutions in context [E2], interpreting functions and points in situations [E4][E11], and judging whether values are reasonable in context [E5]. The full intent is met (representing symbolically, attending to units/quantities, interpreting meaning, checking reasonableness) and it spans courses including Geometry [E6], showing series-wide coverage rather than isolated MP-only work.

MP3 is intentionally developed in connection to course-level content across the series. Evidence shows the full intent of the practice: students construct conjectures and prove them ([E3] angle relationships, [E10] angle bisector/isosceles proofs, [E11] equilateral triangle distance claims), perform error analysis on provided work ([E1] quadratic-formula steps, [E4] inequality strategies, [E12] data interpretation errors), critique and read/comment on others' proofs ([E10]), and explain/justify reasoning ([E5], [E7], [E9]). Coverage spans Algebra 1, Algebra 1 supports, Algebra 2 ([E6] using simulation to support/oppose claims), and Geometry, and MP3 is consistently tied to specific content standards rather than treated in isolation.

Structural evidence shows intentional development of applications throughout the series: carefully-chosen anchor contexts motivate new concepts, students make connections between contexts and concepts, many units include a real-world application lesson at the end, and a dedicated set of mathematical modeling prompts provides additional application opportunities [E2]. Non-routine applications and independent demonstration are supported by modeling work (MP4) and contextualizing (MP2), with students answering questions with progressively less scaffolding and exercising student choice in problem-solving approach [E9][E11]. Distributed practice problem sets give students opportunities to independently apply the mathematics across lessons and units [E10]. This satisfies both required components—multiple routine and non-routine applications AND opportunities to independently demonstrate them.

The materials explicitly establish all three aspects of rigor independently and engage them simultaneously: E6 names conceptual understanding, procedural fluency, and application as 'interconnected' where 'procedural fluency is supported by understanding' and students 'must both understand and be able to do.' E9 directly describes the design intent—some activities 'developing a concept, others to mastering a procedural skill, yet others to applying mathematics to a real-world problem' that 'are interwoven.' Application/modeling is structurally supported (E3, E4, E7, E10) alongside dedicated procedural mastery and distributed practice (E5, E11), demonstrating both independent treatment and simultaneous engagement across units and the series.

The materials show intentional, series-wide development of MP4 in connection to course-level content. Full modeling-cycle engagement is present (Algebra 1 Lesson 1 'Planning a Pizza Party' where students identify quantities, make assumptions, create and evaluate a model [E3][E11]; Lesson 18 where students engage in 'many aspects of the modeling cycle' and revise models with new information [E10]; Lesson 26 culminating modeling with systems of inequalities [E6]), and MP4 spans courses into Algebra 2 [E9]. A dedicated supports strand scaffolds modeling skills (E1, E2, E4, E8) and the HS teacher guide explicitly articulates the modeling process and the 'Things the Modeler Does' cycle [E12], confirming MP4 is used to enrich content rather than taught in isolation.

Evidence shows intentional, series-wide development of MP5 connected to course-level content. Multiple lessons explicitly require genuine tool selection: choosing protractors vs. string/ruler or spreadsheets/calculators for sector problems [E2], deciding whether to make a table, graph, or other method on unscaffolded pattern tasks [E3], manipulating physical items to model weights [E4], and choosing their own tools for indirect measurement [E8]. The teacher guide describes a deliberate design where students are taught a suite of tools (graphing, geometry, spreadsheets) but make their own choices about when to use them, with digital tools included only when they enable better learning and lessons coded as require/suggest/allow [E7, E11], plus dedicated technology-skill lessons [E1, E12] — confirming tools enrich content rather than being practiced in isolation.

MP6 is intentionally developed across the full high school series in genuine connection to course-level content: Geometry uses precision in constructions and congruence proofs (using accurate terms, labeled points, and clear definitions) [E1][E4][E11][E12], Algebra 1 has students analyze errors and attend to each step when applying the quadratic formula [E10], Algebra 2 attends to precise language describing graph transformations [E6], and Algebra 1 supports lessons reinforce precise connection of representations [E2][E9]. These instances reflect substantive, non-trivial use of MP6 (precise vocabulary/conventions, accurate calculation, clear explanations, appropriate use of labels/graphs) that enriches rather than supplants the mathematics, and the spread across Geometry, Algebra 1, and Algebra 2 demonstrates development across the series. The evidence affirmatively supports intentional development to the full intent of MP6.

MP7 is intentionally and explicitly developed in connection with genuine course-level content across multiple courses in the series. In Algebra 1 students look for and make use of structure when factoring quadratics and noticing how sign/operation changes in factors affect standard form [E1, E4, E6, E11], using area/diagram models to expand and factor [E2], decomposing repeated addition into multiplication and recognizing linear vs. exponential growth [E8], and seeing one linear relationship across tables, situations, and equations [E10]; in Geometry students use structure to determine which triangle congruence theorems apply and to move from conjecture to proof about quadrilaterals [E3, E12]. These examples enrich the mathematics (decomposing 'complicated' into 'simpler,' generalizing patterns, analyzing structure) rather than treating MP7 in isolation, demonstrating full intent across the series.

MP8 is explicitly and intentionally identified across the series in connection to course-level content: students perform repeated numerical calculations and then generalize by writing expressions in terms of a variable (E8, E9, E11), generate tables of values and generalize relationships for quadratic/linear/exponential functions (E10, E7), and the supports lessons deliberately scaffold this reasoning toward associated Algebra 1 lessons (E1, E2, E3). The practice spans Algebra 1 and Algebra 2 (E12) and is tied to HS content standards (e.g., HSA-SSE, HSF-LE in E9), showing MP8 enriches the mathematics rather than standing alone. This structural evidence meets the full intent of intentional MP8 development across the series.

Materials provide comprehensive guidance for presenting both student and ancillary materials: unit/lesson/activity narratives explain mathematical content and its place in the learning sequence [E4], routines include detailed first-instance guidance [E2], and ancillary support materials are systematically cross-referenced to specific core lessons (e.g., the Algebra 1 supports lesson explicitly tied to Unit 6 Lesson 7) with their own learning goals and resource tables [E5, E6, E8-E12]. Annotations are tied to specific learning objectives—commentary on expected responses, misconceptions, and suggested questions to probe student thinking [E1], concrete instructional strategies for addressing skill gaps in context [E7], and UDL representation supports [E10]. Both required components are clearly met.

The materials provide systematic, lesson-embedded strategies for special populations: 'Access for Students with Disabilities' supports appear in each lesson aligned to the three UDL principles of engagement, representation, and action/expression [E2][E3][E6][E9]. Scaffolding is evident through concrete-to-abstract concept development, manipulatives, visual aids, and graphic organizers [E1][E7][E10], with assistive technology and visual-impairment accommodations explicitly addressed [E1][E5][E8]. Social-emotional support (brain breaks) and cooperative learning structures (individual-to-pair-to-group progression) foster active participation [E2][E10], and dedicated Algebra 1 Extra Support Materials plus teacher guidance on leveraging student strengths address diverse needs [E11][E12]. This structural evidence shows consistent strategies, supports, and resources enabling regular and active participation in grade-level work.

Both required components are supported. Lesson and unit narratives provide adult-level explanations of course-level concepts and the meaning of new terms, situating each in the learning sequence so teachers deepen their own understanding [E2][E8]. Alignment to other grade levels is explicit: support lessons name prior-grade standards 'Addressing' (e.g., 6.EE.A.1, 7.EE.B.3, 8.EE.A.1) and the HS standards they are 'Building Towards' (HSA-SSE, HSF-LE), with narratives describing how prior knowledge prepares students for the associated Algebra 1 lesson [E3][E4][E6][E10][E11], and 'Are You Ready for More?' connects topics to the broader K–12 progression [E5].

The materials include the structural 'Are You Ready for More?' feature in select activities throughout the course, which the teacher guide states 'go deeper into grade-level mathematics and often make connections between the topic at hand and other concepts,' are 'not routine or procedural,' and explicitly 'not just "the same thing again but with harder numbers"' [E1][E2]. These are designated for opt-in use when students finish early or want to do more mathematics on their own, providing meaningful depth and autonomy rather than added volume [E2]. This satisfies both required components: multiple extensions engaging advanced students at greater depth, with no evidence of advanced students simply doing more assignments than classmates.

The materials (IM K-12 Math) provide explicit standards correlation at the lesson level, with each lesson tagging CCSS content standards under 'Building On,' 'Addressing,' and 'Building Towards' categories [E4, E7, E9, E12]. The teacher guide documents the unit structure and the deliberate standards-alignment design system [E1, E2], and units are presented in a sequenced organization [E8]. This structural evidence—per-lesson standard references mapped to specific content within a unit-by-unit scope across courses—satisfies the requirement for a year-long scope and sequence with standards correlation information.

Materials clearly explain the program's instructional approaches—a problem-based curriculum with concrete-to-abstract progression, individual-to-group structures, and design principles for conceptual understanding and procedural fluency [E1][E2][E3][E4]. Research-based strategies are referenced explicitly: 'Current research says...' on flexible thinking [E8], the Five Practices framework [E6], and Mathematical Language Routines developed by the Stanford University UL/SCALE team [E12]. The role of standards is referenced through the Standards for Mathematical Practice that 'come into play' in lessons [E2] and standards-based grading via learning targets [E11], satisfying all three required components.

Each lesson includes an explicit 'Required Materials' section listing the physical supplies needed (e.g., geometry toolkits, internet-enabled device, mirrors, protractors, rulers, straws, string in [E1]; 1-inch strips and metal fasteners in [E8]/[E9]; pre-printed slips/blackline masters in [E10]), accompanied by 'Required Preparation' notes detailing how to assemble or photocopy items. The teacher guide reinforces this by describing manipulatives, digital device/projector requirements, and card-sort/cut-up paper needs across the program [E3][E11], and [E1] even offers substitutions (shallow bowls of water if mirrors are unavailable). This consistent, lesson-by-lesson supply listing constitutes the comprehensive, organized list of supplies the indicator requires.

The IM K-12 Math assessment system provides consistent, structured opportunities across the year: each unit opens with a diagnostic ('Check Your Readiness'), each lesson includes a formative cool-down and distributed practice problems, and units close with mid-unit and end-of-unit summative assessments [E1, E3, E5, E7, E11, E12]. A variety of item types (multiple-choice, multiple response, short answer, restricted/extended constructed response) capture different aspects of learning, with rubrics, complete solutions, and standard alignments supporting fair evaluation [E2, E4, E6, E11]. Teacher guidance for interpretation and next steps is explicit: distractors function diagnostically, task commentary flags misconceptions so teachers can adjust, and cool-down guidance offers concrete remediation strategies when students struggle [E3, E6, E7, E8]. All three required components are clearly met.

Indicator 3q concerns providing opportunities for teachers to use a variety of grouping strategies. The retrieved evidence consistently shows structured grouping designed into lessons across courses: partner 'take turns'/'trade roles' activities where students explain and critique reasoning [E4][E9][E12], and pair-based work with materials prepared per pair of students [E11]. This is intentional, embedded grouping guidance in the lesson design, supporting all required components.