The Utah Middle School Math Project

The materials present extensive grade-level work with both class activities and homework for each section, aligned to named grade-6 standards (6.NS.2, 6.NS.3, 6.NS.4 in [E12], and 6.RP percent work in [E11][E3]). Each section lists explicit 'Concepts and Skills to Master' addressing the full intent of standards—e.g., fluently performing all four operations with multi-digit decimals via the standard algorithm [E10], finding GCF/LCM and applying the distributive property [E6][E12], and the full range of percent reasoning including part/whole and real-world problems [E11]. The repeated paired Class Activity + Homework structure across sections [E8][E9] is structural evidence of extensive student work, and the teacher narrative shows intentional sequencing toward grade-level mastery [E5][E7]. This satisfies both required components: extensive grade-level work and full intent of grade-level standards.

The grade-6 materials are explicitly organized around grade-level standards with clear standard citations (6.RP.1, 6.RP.2, 6.RP.3 in [E7], [E9]; 6.NS fluency objectives in [E6], [E8]), and chapters open with named Utah Core Standards and embedded self-assessments tied to those standards ([E12], [E1], [E5]). Earlier-grade content is invoked only as foundational background (K-5 number-line work in [E3]), and concepts like similarity/transformations are deliberately deferred to Grades 7-8 rather than assessed in grade 6 ([E4] notes 'similar' is not defined until Grade 7; [E11] places transformations/congruence/similarity in Grade 8). This structural alignment to grade-level standards, with no evidence of above-grade items being assessed within the grade-6 assessments, supports all required components.

The retrieved evidence shows the Grade 7 materials are organized around the grade's major clusters: Chapter 1 covers probability, percent, and rational number equivalence (7.NS/7.RP) [E1], and proportional relationships are developed broadly via bar models, tables, graphs, and equations to solve real-life problems (7.RP) [E4]. Even the geometry chapters connect to major work through scale drawings and proportional reasoning ("same shape but different size" with proportional side lengths) [E9, E2, E10], representing supporting-to-major connections. This structural evidence indicates the majority of instructional time addresses major clusters and their connections, consistent with the 65% threshold.

The materials consistently weave connections that engage students in the major work of the grade, with chapter overviews explicitly linking content to the grade's major clusters. For example, measurement conversion (supporting-type content) is tied to ratios and proportional reasoning—major work of Grade 6 (6.RP)—rather than treated in isolation [E3], and ratio reasoning is connected to whole-number multiplication/division and graphing [E6][E10][E12]. The statistics/probability unit reinforces and builds on measures of center and spread rather than standing alone [E9], showing supporting work is intentionally connected to major work. This structural design demonstrates supporting content enhancing focus on the major work, satisfying the indicator.

The materials embed explicit 'Connections to Content' sections in each chapter that link clusters and domains within the grade, supporting connections among major work throughout. In Grade 6, ratio reasoning (6.RP) is carried into percent and measurement conversion within the grade (E12), and ratio work links to fraction operations and coordinate graphing (E5, E6). In Grade 7, geometry work is explicitly connected to rational numbers and proportional relationships (E4), and proportional-relationship work threads across chapters (E10), reflecting intentional major-to-major connections. The structural design showing connections made throughout the grade-level materials satisfies the indicator.

Both required components are present with content-level explanation, not mere standard codes. Prior knowledge is explicitly tied to grade-level work: E4 states inequality work 'builds on Grade 6 understandings where students were introduced to inequalities represented on a number line,' E7 notes 'In elementary school students have found the area of rectangles and triangles... but have not learned rigorous definitions of Circumference and Area,' and E1/E12 extend previously learned drawing of geometric figures and number-line/coordinate work. Future content is identified and related: E7 explains 'similarity is defined in Grade 8 using dilation... in Grade 8 students will justify [the triangle-angle sum] and extend that knowledge,' and E6 frames Grade 8 linear relations as a turn from the Grade 7 study of proportional relationships. Together these satisfy both the future-to-grade-level and prior-to-grade-level requirements for a 2.

The materials are explicitly designed to develop conceptual understanding over procedures—Chapter 2's stated goal is for students to 'gain an intuitive sense of comparison...using models and partial tables' and develop algorithmic approaches only after solid understanding [E7], and division of fractions is built with 'a variety of models (tape, double line, partial tables) to build conceptual understanding' rather than memorized algorithms [E3][E2]. This spans key conceptual clusters across the grade band: ratios progressing concrete→pictorial→abstract (6.RP.A) [E4][E5], fraction division reasoning that dividing equals multiplying by the reciprocal (6.NS.1) [E10], area-model reasoning for expressions (7.EE/G) [E11][E6], and exploratory transformational geometry (8.G.A) [E12]. Independent demonstration is supported through expectations that students create contexts for division, choose appropriate representations, and discover ideas through their own explorations [E2][E4][E12], satisfying both required components.

The materials show intentional, systematic development of the Standards for Mathematical Practice connected to grade-6 content: Chapter 0's teacher guide walks through individual MPs one by one and ties each to specific 6.NS standards (e.g., MP7 [E1], MP6 [E4]), demonstrating the design intentionally embeds practices in content. MP1 (make sense and persevere) is evident in directives to estimate and 'double check the output,' build a problem-solving 'tool box' of strategies [E3], and analyze base-ten models to make sense of algorithms [E9, E12]. MP2 (reason abstractly/quantitatively) appears in attending to units/meaning of quantities through estimation [E1], connecting models to symbolic representations [E9], and using the distributive property to write/examine equivalent expressions [E10]. Retrieval surfaced MP6/MP7 prose most explicitly, but the consistent structural pattern of MP-to-content development supports full intent for both MP1 and MP2.

MP3 is explicitly identified and tied to grade-level content: E9 (grade-7, Ch.5) names 'Construct viable arguments and critique the reasoning of others' and describes students constructing viable arguments for why objects are scale versions of each other and justifying with pictures, words, and abstract representations—directly connected to 7.RP proportional reasoning. The structural per-chapter MP tagging (E1, E8, E9) shows intentional development, and E3 (grade-8) and E11 (grade-8) extend argument/conjecture work (analyzing outliers' effect on lines of best fit, deriving their own definitions of functions) across the grade band. Direct evidence of the critique component (error analysis of others' work) was not heavily retrieved, which lowers confidence but is a retrieval limitation rather than affirmative absence, so the intentional development of MP3 in connection to grade-level content supports the full-intent band.

The materials include a dedicated fluency chapter (Chapter 0) targeting the grade-6 fluency standards 6.NS.2, 6.NS.3, and 6.NS.4 [E1][E3][E12], and explicitly develop procedural skill by connecting place-value models to standard algorithms for division and decimal operations [E4][E8]. Development is intentionally distributed across the year rather than isolated, as the text directs teachers to insert fluency work 'into the natural flow of the course' and 'maintained as a subtext throughout the whole grade' [E1][E6]. Students independently demonstrate fluency through dedicated Class Activity and Homework sets for adding, subtracting, multiplying, and dividing multi-digit numbers and decimals [E9][E11], satisfying both required components.

Materials include multiple routine applications in real-world contexts—tip and tax problems [E9], multi-step discount-plus-tax problems [E11], and a triangular yard perimeter/area/cost problem [E7]—plus non-routine, open-middle tasks such as 'write as many different numeric expressions as you can to represent each context' [E6] and Illustrative Mathematics tasks [E10]. There is a dedicated application section (3.3: Solve Multi-Step Real-World Problems) with both Class Activity and Homework versions [E8], and the chapter design explicitly has students 'take real world situations, model them with algebraic equations, and use properties of arithmetic to solve them' [E4]. The paired homework sets [E8] provide independent opportunities for students to demonstrate both routine and non-routine applications throughout the grade.

MP6 is explicitly identified and intentionally developed in connection to grade-level content: the program's design philosophy describes precision in both communication and computation [E1], and it is applied to concrete grade-6 work such as evaluating expressions under order of operations [E2], distinguishing precise fractions from decimal approximations [E4], and reasoning about percents/ratios with precision [E8]. The specialized language of mathematics is intentionally developed through explicit Academic Vocabulary lists using precise terminology (Commutative Property, coefficient, constant, fraction bar as division, grouping symbols) [E11] and lesson objectives requiring students to 'use and understand academic vocabulary' [E12]. Both required components are met to full intent.

Structural evidence across grades 6–8 shows materials intentionally prompt students to construct viable arguments and analyze others' reasoning. [E1] states that throughout the chapter problems require students to justify answers and explain strategies in multiple forms (words, models, equations). [E3] explicitly presents competing student statements (Mariah's, Tom's, Will's) for students to evaluate—directly analyzing the arguments of others. [E2] and [E8] have students explain a proof of the Pythagorean Theorem (8.G.6), [E7] asks students to compare and justify algebraic vs. arithmetic solutions, and [E9] prompts discussion and 'Why can you do this?' justification of structural reasoning.

All three aspects of rigor appear independently across the grades: procedural skill/fluency is deliberately structured (the grade-6 fluency chapter tied to 6NS.2,3,4 and inserted throughout the course [E2], and proficiency in simplifying expressions/solving equations [E7]); conceptual understanding is foregrounded (developing the structure of arithmetic operations as 'the most significant' standard [E6], concrete-to-abstract tool progression [E3]); and application is rich (probability simulations [E10], inferential statistics with real populations [E9]). Multiple aspects are also engaged simultaneously to build understanding of single topics—students use manipulatives, tape diagrams, tables, graphs, and equations together to solve real-world ratio problems [E3], move from concrete models to abstract equation-solving [E7], and justify application work through multiple representations and written/oral explanations [E11]. This structural evidence shows intentional balance both independently and in combination throughout each grade.

MP7 is intentionally developed and connected to grade-level content across multiple chapters: integer operations algorithms ([E1]), scientific notation regrouping powers of 10 ([E2]), structure of rational numbers on the number line ([E5]), and algebraic equation structure like 3x+4=5 reduced to x=1/3 ([E8], [E9]). MP8 is also intentionally developed to its full intent: students notice repeated calculations to understand why rational decimal expansions terminate or repeat ([E3]) and study patterns to express them in general forms (the 'Decorating a Patio' anchor problem moving from steps 1-3 to step 'x', [E7]). Teacher-facing prose explicitly names both practices and ties them to specific content, with prompts to generalize and create shortcuts, satisfying both required components.

The materials structurally support both constructing viable arguments and analyzing others' reasoning for key grade-8 content (angles, triangles, Pythagorean Theorem). E1, E3, and E4 describe students constructing mathematical arguments to explain why theorems are true, with emphasis on 'creating good' arguments. E2 explicitly guides teachers to develop students' sense of 'what makes a good argument,' asking 'Can they critique the reasoning of others?' and prompting claim-evidence-warrant structure, and MP3 ('construct viable arguments and critique the reasoning of others') is named as an emphasized practice (E3, E8). E5 provides a concrete analyze-and-support task (Pedro's quadrilateral claim), demonstrating teacher-facing prompts for argument analysis.

Materials explicitly attend to specialized mathematical language: E4 states students 'learn and use academic vocabulary (terms, like terms, constants, coefficients)' while manipulating expressions, and E10/E11 formally define and have students identify parts of expressions using terms (sum, term, product, factor, quotient, coefficient, constant, variable). E1 notes 'naming and formally defining properties appears at the beginning of the section so that students can attend to precision,' and E2/E7/E8 introduce precise terminology (variable, exponential notation/form, expanded form). E9 explicitly directs students to 'demonstrate precision by using correct terminology and symbols when working with expressions and equations,' showing intentional, structural attention to the language of mathematics.

The official Evidence Guide for 3f assesses whether materials provide a comprehensive list of supplies needed for instructional activities. The retrieved evidence consists of student problem pages, chapter overviews, and Mathematical Practice descriptions — it shows activities that clearly require physical materials (rulers, protractors, coordinate grids, technology in [E8] and [E12]; chips/tiles models in [E5] and [E10]), but no front-matter or lesson-level compilation that lists those supplies comprehensively was retrieved. There is scattered evidence that supplies are referenced within lessons, but no structural evidence of a course-, unit-, or lesson-level materials list, so partial coverage is the most defensible read.

The materials include dedicated 'mathematical-foundations' overview sections per chapter that give comprehensive pedagogical rationale and explain the instructional design (E1, E8), satisfying the comprehensive-guidance component. They also embed useful annotations and suggestions tied to specific learning objectives—e.g., guidance on progressing students from concrete to abstract representational tools (E2, E12), a concrete scaffolding suggestion for helping students arrive at an equation by first writing numerical expressions (E9), and emphasized mathematical practice standards mapped to specific activities (E6). These are presented within the context of the section goals and learning progressions (E4, E5, E7, E11), meeting both required components.

The retrieved teacher guidance consistently emphasizes general mathematical practice strategies and multiple representations (bar models, number lines, visuals, tables, graphs) intended for all students [E1][E2][E3][E5][E11], but none of it provides strategies, supports, or resources targeted to students in special populations, nor any grouping guidance or differentiation accommodations for them. The mathematical-foundations and practice-standards sections—precisely where such supports would appear—contain only generic content design [E6][E8][E10], showing the materials do not regularly provide special-population-specific supports while still offering some broadly accessible representational tools (so not a complete absence). This matches the 1-point band: materials do not regularly provide strategies, supports, and resources for special populations.

The teacher edition contains genuine adult-level explanations of complex grade-level concepts—e.g., a rigorous proof of why fractions with denominators of products of 2's and 5's terminate [E2], and an 'explanation of a proof' of the Pythagorean theorem with multiple approaches [E8, E12]. It also explicitly develops concepts beyond the current course: extension into the complex number system and integer-exponent properties in later courses [E3], inverse operations becoming inverse functions in later grades [E4/E5], and coordinate geometry where the Pythagorean theorem becomes the definition of distance, 'developed in a systematic way in secondary mathematics' [E11]. Both required components—complex grade-level concepts AND concepts beyond the course—are clearly present.

There is clear evidence of at least one genuine, purposeful extension that pushes advanced students into higher-complexity investigation of grade-level content rather than just more problems — the labeled 'Extension' in [E4] poses the higher-order question of whether decimal approximation gives every point on the plane for 'the persistent 7th grader.' However, the retrieved materials show mostly grade-level progression narratives and standard-to-standard connections ([E2], [E3], [E8]) rather than a systematic, recurring structure of advanced extensions, so 'multiple opportunities' across the series is only partially demonstrated. This matches the 1-point band: some opportunities for higher-complexity engagement are present, but robust, repeated extension supports are not clearly evidenced.

Per the authoritative Evidence Guide, both required components are present. Correlation information for specific CCSSM content (and practice) standards appears throughout: explicit codes like 7.EE.3, 7.EE.4/4a [E2], 7.EE.2 [E12], plus SMP correlations such as 'construct a viable argument' and 'Model with mathematics' [E1]. Explanations of the role of grade-level math within the K-12 progression are also present in chapter overviews — e.g., inequalities work that 'builds on Grade 6 understandings... The goal in Grade 7 is to move to solving simple one-step inequalities' [E6], and connections forward to 'functions in Grade 8' [E11], with [E5] building on prior equation understanding. Standards correlation plus series-context explanations satisfy both prongs for full marks.

The retrieved evidence shows instructional sections labeled with grade-level standards (e.g., Section 8.3 Volume tagged to 8.G.9 [E1]) and historical/conceptual content [E2], demonstrating the materials do associate content with standards. However, no formal assessments (formative, summative, quizzes, unit tests) were retrieved, so there is no direct evidence showing whether assessment items or assessment guidance identify which standards are assessed. This is a genuine retrieval gap for the assessment-specific requirement of this indicator.

The retrieved evidence shows the materials explicitly denote standards within instructional content (e.g., Section 8.3 Volume tagged with standard 8.G.9 in [E1]), indicating an intentional structural practice of labeling which standards are emphasized. However, no assessment artifacts (quizzes, chapter tests, end-of-unit assessments) were retrieved, so I cannot directly confirm that the assessments themselves carry this standards denotation. The consistent section-level standard tagging is structural evidence that the design denotes emphasized standards, but the absence of any assessment chunk makes this a genuine retrieval gap for the indicator's specific focus.

No curriculum evidence was retrieved for this indicator — the evidence section is empty, so I cannot point to any aligned rubrics, scoring guidelines, or follow-up suggestions to assess. Per scoring discipline, absence of retrieved evidence is a retrieval limitation and not proof the indicator is unsupported, so a 0 is not warranted; this is a genuine evidence gap rather than evidence of weak support. The best-guess value reflects that comprehensive K-12 programs typically include scoring rubrics with assessments, but this is a guess, not an assessment.