STEMscopes Texas Grade 6 Advanced Math

Evaluation for 1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.

The Grade 6 Advanced Scope and Sequence clearly outlines the progression of concepts across the course, beginning with fractions, decimals, and percents and ending with personal financial literacy. The document includes the Texas Essential Knowledge and Skills (TEKS) and the English Language Proficiency Standards (ELPS) alignment for each scope, the instructional components, and a pacing guide listing total instructional days.

The Grade 6 Advanced Course Rationale includes an explanation for the rationale of unit order and an outline of the TEKS and concepts covered in each scope. For example, educators see that the “Equivalent Numerical Expressions” scope covers the standard 6AM.3.G, connects with 6AM.3.F, and covers one major mathematical topic: numeracy.

The Texas Math ELPS Alignment—Grade 6 in the Teacher Toolbox outlines each scope and explores activities for both the 2007 and 2025 ELPS. For example, in the “Equivalent Numerical Expressions” scope, educators see that explore 1 aligns with the 2025 ELPS 1.BD and 2.BCEF.

Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).

The Implementation Guide states, “The provided Scope and Sequence documents are based on a typical 180-day instructional calendar. To modify for varying numbers of instructional days, activities can be added or removed.” The document then provides additional guidance on how to adjust for calendars with 165 days and those with more than 180 days. The document states, “The calendars are based on a 90-minute math block but can be adjusted by choosing elements completed and time spent on activities.”

Each unit includes a Suggested Scope Calendar in the “Home” section of each scope. This resource includes a suggested pacing guide in the scope, outlines which activities to complete each day, and describes numerous resources for effective implementation, including objectives, language objectives, and lesson focus outlines.

In the Teacher Toolbox, Lesson Planning Resources include planning guides to assist educators in outlining the daily and weekly agendas based on a five-day week for 50-minute and 90-minute block classes. Each document includes templates for both whole-group and small-group instruction that outline scopes with one to three Explore activities or three to six Explore activities.

Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.

Each unit includes a Content Support document in the “Home” section at the beginning of each scope. This resource includes “Background Knowledge” and “Current Scope” sections that describe how the new unit connects to prior learning and future units. For example, in the “Fractions, Decimals, and Percents” scope, educators read about previous grade 5 student work on fractions and decimals and how this scope will expand on that knowledge and introduce percents for the first time.

The Grade 6 Advanced Course Rationale provides a written explanation of unit
order, how recurring topics appear throughout the units, and a description of the vertical
alignment of standards throughout the course. The document states, “Each scope in Grade 6 Advanced STEMscopes Math is intentionally sequenced to build on prior knowledge while deepening students’ conceptual understanding and procedural fluency with increasingly sophisticated mathematical ideas. The progression of the Grade 6 Advanced Math scopes reflects a coherent development of number sense, algebraic reasoning, proportional thinking, and data analysis, ensuring students are equipped to make connections across domains and apply their learning in meaningful, real-world contexts.”

Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.

Each unit includes a Suggested Scope Calendar in the “Home” section of each scope that provides protocols and guidance to support effective internalization of the unit and lesson. This resource includes additional content support, a ”Content Unwrapped” section, a “Scope Overview” section, content and language objectives, and an outline of each lesson to be taught in the unit.

Each unit begins with a “Scope Overview” section that includes scope resources and a Teacher Guide. This guide includes a template and guidance for lesson internalization and a step-by-step breakdown of each lesson in the unit, including areas intended for educator annotation throughout the internalization process.

Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.

The Implementation Guide explains how the instructional materials implement the 5E learning model with an intervention and acceleration component for each unit. The guide also contains an “Administration and Instructional Coaches’ Support” section that includes scope and sequences, Suggested Scope Calendars, planning guides, educator preparation, and guidance to support educators in implementing the materials as designed. The document also provides guidance for administrators and instructional coaches when observing students and educators in the classroom. The guide outlines what observers should look for in both students and educators as they work through a scope. The guide describes foundational educator actions that “have the greatest influence” on learning outcomes and provides administrators an observation tool that explains educator, student, and observer actions based on the “Guiding Principles of Best Practice.”

Each unit includes a Suggested Scope Calendar in the “Home” section of each scope that allows instructional leaders to support educators in the effective implementation of the materials. This resource includes additional content support, a “Content Unwrapped” section, a “Scope Overview” section, content and language objectives, and an outline of each lesson to be taught in the unit.

Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.

The materials include a Content Support document for each scope that provides a comprehensive unit overview, including background knowledge, prior learning connections, and common misconceptions to support educators’ understanding of the content. The document also clearly defines key academic vocabulary and concepts that students will encounter, which ensures that educators are prepared to effectively introduce and develop the language and ideas in the unit. For example, in the “Fractions, Decimals, and Percents” scope, educators read about previous grade 5 student work on fractions and decimals and how this scope will expand on that knowledge and introduce percents for the first time.

The materials include a “Content Unwrapped” section for each scope that provides a detailed breakdown of theTEKS into clear, teachable components, including the specific skills, verbs, and academic vocabulary students must master. The section also supports instructional planning by providing guidance on misconceptions, prior knowledge, and vertical alignment, which ensures that educators have the content knowledge and context needed to teach the unit effectively.

Evaluation for 1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.

The materials include a take-home letter for each scope that provides family-facing supports in both English and Spanish and clearly explains unit concepts, key vocabulary, and examples to build understanding at home. For example, in the “Rational Numbers” scope, the take-home letter states, “In math class, your student is about to explore rational numbers. To master this skill, they will build on their knowledge of whole numbers, fractions, and decimals.” The letter is then followed by several examples of what the rational number system looks like, how to estimate rational numbers on a number line, how to use comparison symbols, practice problems that ask students to order rational numbers, and a vocabulary section with definitions of new academic terms being used during this scope.

For each scope, the take-home letter, which is available in both English and Spanish, offers practical suggestions and real-world discussion prompts to help families actively support their students’ learning and progress outside the classroom. For example, in the “Rational Numbers” scope’s take-home letter, the “Math Outside the Classroom!” section begins by stating, “We use rational numbers throughout our everyday lives. Chat about where you use rational numbers in your everyday life, and include experiences where we can compare and order these numbers. A few examples are listed here.” The letter then gives multiple examples of how rational numbers are used in the real world and ideas of where to look for more rational numbers.

Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).

The Suggested Scope Calendar provided for each scope includes comprehensive, structured daily lesson plans written in the 5E model that have clearly defined content and language objectives aligned with the TEKS and ELPS and have detailed instructional components, such as warm-ups, focus lessons, and guided practice. The calendar also incorporates embedded questions, tasks, materials, and a range of formative and summative assessments (e.g., exit tickets, Skills Quizzes, Mathematical Modeling Tasks) to support and measure student learning throughout the unit.

Each scope begins with a Homescreen that provides TEKS-aligned student expectations and corresponding key concepts written in student-friendly language, which ensures alignment between standards and instruction. The Homescreen also includes guiding (fundamental) questions that support lesson planning and deepen understanding, which provides educators a coherent framework for delivering content and assessing student learning. Other items available on the Homescreen include the “Scope Overview” section, the Suggested Scope Calendar, content support, the ”Content Unwrapped” section, a family take-home letter, and a Scaffolded Instruction Guide.

Evaluation for 1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.

The Suggested Scope Calendar provided for each scope includes a detailed lesson overview for each day that clearly outlines instructional components, required materials (e.g., Anchor Charts, Guided Notes, Interactive Vocabulary), and embedded resources for both educators and students. The calendar also includes suggested timing for each lesson segment—such as warm-ups (5–10 minutes), focus lessons (20–30 minutes), and assessments (10 minutes)—which ensures that educators can effectively plan and implement each component of instruction.

Each Explore activity includes Teacher Directions that provide a list of all printable and reusable materials, organized by group and individual use. The directions also include a list of preparation tasks that should be completed prior to teaching the lesson and the procedure and facilitation points to keep the lesson on track. This structured list supports effective lesson preparation and delivery.

Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).

The Suggested Scope Calendar provided for each scope includes clear guidance on extended practice through structured independent work and homework options embedded in each lesson, such as Spiraled Review, Choice Boards, and Interactive Vocabulary activities. The calendar also includes differentiated extension and enrichment opportunities and intervention supports, which ensures that educators can effectively assign and appropriately implement practice.

The Scaffolded Instruction Guide for each scope provides educators guidance on using various lesson materials to meet diverse student needs based on students’ performance on the scope’s assessments or other diagnostic tools. The guide is separated by the standards covered in each scope. For example, in the “Proportional Relationships” scope, if a student is scoring in the 80–100 percentile mastery range for the standard 6.AM.4.B, the guide recommends that the student work on the Would You Rather activity and the Choice Board in the “Acceleration” section of the scope.

Evaluation for 2.1a
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in types of tasks and questions.

Each scope provides a Suggested Scope Calendar that includes a comprehensive range of instructional assessments at both the lesson and unit levels, such as diagnostic tools (e.g., Accessing Prior Knowledge), ongoing formative checks (e.g., exit tickets, Observation Checklists, Show What You Know activities), and summative measures (e.g., Skills Quizzes, standards-based assessments, Mathematical Modeling Tasks). These assessments vary in format and task type, which provides multiple opportunities for students to demonstrate understanding through different question types and levels of rigor.

The Implementation Guide discusses a wide range of instructional assessments that appear throughout the instructional materials—diagnostic (e.g., Accessing Prior Knowledge, benchmark assessments), formative (e.g., exit tickets, Show What You Know activities, Observation Checklists), and summative (e.g., standards-based assessments, technology-enhanced questions)—at both the lesson and unit levels. These assessments vary in format and task type, including open-ended reasoning, real-world modeling tasks, and multiple-choice items, which provides students multiple ways to demonstrate understanding.

Technology-enhanced questions in each scope allow students to answer questions that are not possible in a pencil-and-paper format. For example, in the scope “Area and Volume,” the “Technology-Enhanced Questions” section includes multiple answer, sequence, griddable, fill-in-the-blank, sorting, and bar graph question types in the summative assessment.

Evaluation for 2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.

Each scope provides a Suggested Scope Calendar that defines the types of instructional assessment (diagnostic, formative, and summative) and explicitly describes their intended purposes in instruction. For example, the calendar explains how tools such as Accessing Prior Knowledge gauge readiness, how exit tickets measure immediate understanding, and how standards-based assessments evaluate mastery, which ensures that educators understand when and why to use each assessment type.

The Implementation Guide discusses each type of instructional assessment and explains each type’s intended purpose in instruction. For example, the guide specifies how diagnostic tools (e.g., Accessing Prior Knowledge) gauge readiness, how formative assessments (e.g., exit tickets, Show What You Know activities) monitor ongoing understanding, and how summative assessments (e.g., standards-based assessments, benchmarks) evaluate mastery and inform instructional decisions.

Evaluation for 2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.

Both the Standards-Based Assessment Teacher Directions and Skills Quiz Teacher Directions provide educator guidance for the consistent and accurate administration of the assessment, including preparation steps, distribution procedures, and implementation guidance. The documents also include directions for student responses, guidance on allowable supports, and recommendations for using results (e.g., Heat Map, Scaffolded Instruction Guide), which ensures consistent and accurate administration and use of assessment data across classrooms.

The Mathematical Modeling Task for the “Floor Plans” scope includes educator directions to support consistent and accurate assessment administration, including required materials, preparation guidance, reminders to provide supplemental aids as needed, and opportunities for students to use manipulatives upon request. The instructions also include a “Procedure and Facilitation Points” section that encourages students to refer to their Explore notes to review skills as needed. Additional educator supports include guiding questions to help students think through problems independently when they are stuck, opportunities for students to share and discuss solutions with the class, and tips, such as reviewing the rubric with students before beginning the assessment.

Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.

Each scope includes a Heat Map that aligns all assessment items with the TEKS, and each question is mapped to specific student expectations. This alignment ensures that diagnostic, formative, and summative assessments directly measure the objectives of the unit and course while also supporting targeted analysis of student performance by standard. The Heat Map also includes a student reflection section in which students can answer questions, such as “Which skill did you feel most confident with? Why?”

The “Skill Review and Practice Review” section in each scope aligns assessment components (Quick Check, Review, and Checkup) directly with the scope’s key concepts and standards, which ensures that the assessment components measure the intended TEKS-based learning objectives. The structured progression—from a formative quick check to review to independent assessment—supports monitoring students’ understanding of specific standards and informs targeted intervention and mastery of course objectives.

Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.

The Depth of Knowledge Level - Secondary document in the Teacher Toolbox provides an outline of how students engage with TEKS-aligned assessment items ranging from recall to extended thinking tasks, which ensures a progression in rigor. The document states, “Norman Webb’s Depth of Knowledge (DoK) Levels is a useful tool for understanding the rigor of the content and tasks we present to students. DoK labels academic work according to the complexity of thinking required to successfully complete it. STEMscopes math fully integrates with DoK to help you naturally transition students from Level 1 to Level 4, expanding their thinking and deepening their knowledge and skills.” The document classifies the different lesson elements in the instructional materials into DOK Levels 1–4. For example, the Skills Quiz in each scope is classified as DOK Level 1, and the Choice Board in each scope is classified as DOK Level 4.

The Standards-Based Assessment Answer Key includes TEKS-aligned assessment items that are labeled with Webb’s DOK levels, which demonstrates intentional variation in cognitive complexity. The tasks require students to apply reasoning, interpret models, and solve real-world problems, which ensures that assessments measure understanding across multiple levels of rigor aligned with TEKS expectations. Each standards-based assessment contains a range of questions from DOK Level1 to DOK Level 4.

Evaluation for 2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.

Each scope provides a Scaffolded Instruction Guide that includes explicit guidance for interpreting student performance through structured analysis of assessment data, including percentile ranges and standard-level breakdowns. The guide supports educators in making instructional decisions by linking student results to targeted resources and next steps for remediation, on-level support, and extension, which ensures that data is used meaningfully to guide instruction. For example, in the “Coordinate Planes” scope, if a student is scoring in the 0–25 percentile (previous grade-level remediation) range, recommendations include the student working on the Small Group Intervention activity, the Fluency Builder activity, the Interactive Practice activity, and specific Skills Quiz questions. Additionally, each performance assessment, such as the Mathematical Modeling Tasks, includes a rubric to determine mastery of mathematical concepts that is intended to be used alongside the Scaffolded Instruction Guide to differentiate instruction for students following the assessment.

Each scope includes a Heat Map that provides scoring guidance through a standards-aligned heat map that connects each assessment item to specific TEKS and categorizes student errors (e.g., miscalculation, explanation, misconception). The Heat Map also includes reflection questions that guide students and educators in analyzing performance, supporting meaningful interpretation of results, and informing next instructional steps.

Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.

The Scaffolded Instruction Guide provided in each scope gives explicit guidance on how to use assessment data to inform instruction, including steps for analyzing student performance by standard and percentile range. The guide then connects those performance trends to specific recommended activities and resources—such as intervention, on-level practice, and extension tasks—which enables educators to respond strategically to student needs.

The “Instructional Supports” and “Language Supports” sections in the Teacher Directions provide actionable guidance for how educators can use targeted instructional supports and language scaffolds to respond to student needs identified through assessment. The materials include differentiated strategies for addressing misconceptions, extending learning, and supporting discourse, which ensures that educators can adjust instruction based on student performance trends. For example, in the “Rates and Ratios” scope, an instructional support states, “If students need additional support with writing equivalent ratios so they can make comparisons more easily, provide students with rods or other modeling tools or representations, like tables, to help structure their thinking.”

Evaluation for 2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.

The Heat Map provided in each scope is a tool that allows both educators and students to track progress by standard by visually identifying strengths and areas for growth through color-coded performance indicators (e.g., correct responses, error types). The Heat Map also includes reflection questions that support student self-monitoring and goal-setting, which promotes ownership of learning and ongoing progress tracking.

The Observation Checklists included in each scope are tools for both educator and student progress monitoring. The student’s Observation Checklist allows students to self-assess mastery of TEKS-aligned skills using rating scales and reflection questions, such as “How would you rate yourself? I’ve Got It, Almost There, or Not Yet,” and the educator’s Observation Checklist includes structured observation categories, notes, and feedback sections to track performance across multiple modalities (e.g., modeling, discussion, written explanation). Together, these tools support ongoing tracking of growth and informed instructional decision-making.

Evaluation for 3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.

The Scaffolded Instruction Guide enables educators to differentiate instruction using assessment data. The guide includes specific recommendations for remediation, intervention, on-level support, and extension activities—such as small-group intervention, skill review, and guided practice—which ensures structured, scaffolded pathways for students who have not yet reached proficiency. For example, in the “Data” scope, if a student is scoring in the 0–25 percentile mastery range for that unit, the guide suggests that students work on three different small-group intervention activities, the unit’s Skill Quiz, and the unit’s standards-based assessment and includes links to each of these resources.

The “Instructional Supports” section in the Teacher Directions for each Explore lesson provides educators guidance on meeting the needs of a diverse classroom. For example, in the “Fractions, Decimals, and Percents” scope, the “Instructional Supports” section states, “If students need additional support with place value when converting among percentages, fractions, and decimals, provide a place value chart as a reference. At the top will be a fraction, an equivalent percentage, and an equivalent decimal; the decimal will also be written in columns labeled Ones, Tenths, and Hundredths.”

The materials include educator guidance on differentiated instruction, intervention, and scaffolding in the “Intervention” section of each scope to support students who have not yet reached proficiency on grade-level content and skills. For example, the materials direct educators to use Quick Checks and skill rubrics to identify learning gaps; provide targeted small-group reteaching using the Review activity; and use supplemental aids, Anchor Charts, and Interactive Notebooks to support student understanding.

Evaluation for 3.1b
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).

The “Language Supports” section in the Teacher Directions for each Explore lesson provides educators guidance on how to assist students with unfamiliar vocabulary and references. For example, in the “Ratios and Rates” scope, the “Language Supports” section states, “Bring real-world context to the term unit rate by having students count a specific motion (i.e., steps, jumping jacks, climbing stairs) for 1 minute. Then create an anchor chart for the class to help them visualize the concept of unit rate by showing them how much of the same motion they would be able to complete in 5 minutes, 20 minutes, 1 hour, etc.”

In the Teacher Directions of Explore lessons, the materials provide questions that allow students to access the task by discussing the scenario’s context. These directions allow educators to pre-teach necessary vocabulary and concepts. For example, in the “Rational Numbers” scope, task access questions include “Have you ever been to a carnival?” and “What games did you play?”

The materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text. For example, each scope includes Guided Notes that provide opportunities for students to understand unfamiliar vocabulary and connect the words to models and representations to support understanding, Anchor Charts that identify and display key components of the scope, and a Picture Vocabulary, which is a slide presentation that can be downloaded and printed for students and provides important vocabulary terms with a picture and definition.

Evaluation for 3.1c
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.

The Scaffolded Instruction Guide provides guidance for enrichment and extension through differentiated activities aligned with higher-performing students. For each TEKS, the guide recommends advanced tasks that promote deeper application, critical thinking, and flexible problem-solving beyond grade-level expectations. For example, in the “Two-Variable Relationships” scope, the materials recommend that students who score in the 50–80 percentile mastery range work on the Picture Vocabulary, the Interactive Vocabulary, the Anchor Chart, the Interactive Notebook, and the Language Connections.

The Suggested Scope Calendar provides guidance on enrichment and extension through structured opportunities in the “Practice” section. The calendar also differentiates for advanced students by including acceleration tasks and deeper application opportunities, which ensures that students who demonstrate proficiency engage in higher-level thinking and extended learning. For example, each scope suggests that students who demonstrate master-level proficiency complete the activities in the “Acceleration” section, which typically includes a Choice Board and a Would You Rather activity.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.

The Teacher Directions for Explore lessons give educators specific prompts and questions to activate prior knowledge, model and explain concepts, correct misconceptions, and reinforce concepts while remaining student-focused. For example, in the “Rational Number Operations” scope, the “Instructional Supports” section includes several guiding points for lesson instruction, such as “You can scaffold for students on their Student Journals by drawing the area model with the correct number of squares to match the factors. To help students make the connection between the number of place values in each factor and the number of squares, ask them why the area models have more or fewer squares compared to each other.”

The materials include explicit educator guidance that models and explains mathematical concepts through scripted facilitation prompts, sample explanations, and structured questioning in the “Procedure and Facilitation Points” section of each Explore activity. For example, during the Explore activity of the “Equivalent Numerical Expressions” scope, the materials direct educators to project the Cupcake Order Form and model how to rewrite prime factorizations as exponential expressions. The lesson prompts educators to ask targeted questions, such as “What is the prime factorization of 8?” and “How many twos are in the prime factorization expression?” before guiding students to identify patterns and connect repeated multiplication to exponents. The materials instruct educators to explain key concepts by stating, “Mathematicians call the number that we are repeatedly multiplying together the base” and “Mathematicians call this smaller number on the top right the exponent or power.” The lesson then directs educators to model writing the base and exponent in exponential expressions and to guide students in determining the correct base and exponent for additional examples. Throughout the activity, the materials provide sample responses, guiding questions, and Math Chat discussion prompts that help educators explain concepts, check for understanding, and reinforce vocabulary, such as base, exponent, power, prime factorization, and expanded form.

Evaluation for 3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.

The Teacher Directions for the Explore lessons guide effective lesson delivery using a variety of instructional approaches. The “Instructional Supports” section in the Teacher Directions offers additional options for educators to effectively meet the needs of their diverse classrooms. For example, in the “Instructional Supports” section of the “Triangle Properties” scope, the materials state, “Consider providing additional hands-on tools for students to further strengthen their conceptual understanding of the triangle sum theorem. For example, provide students with the vertices (labeled with angle measurements) cut off from various triangles along with chenille stems or straws to represent the sides of triangles. Students would then select three random angles from the set provided and attempt to build triangles with the angle pieces and chenille stems. Guide students to find the sum of the angles they selected and notice that they can only form a triangle when the sum is exactly 180 degrees.”

The “Procedure and Facilitation Points” section in the Teacher Directions for each Explore activity provides clear educator guidance for delivering instruction through multiple instructional approaches, including real-world contexts, partner collaboration, hands-on manipulatives, questioning strategies, structured conversations, and whole-class discussions. For example, in the “Rational Numbers” scope, the lesson directs educators to introduce concepts through a football-field context that connects number opposites and absolute value to students’ prior experiences. Educators facilitate learning by asking guiding questions, modeling concepts on horizontal number lines, and prompting students to explain their reasoning throughout the activity. For example, the materials instruct educators to have students use football scenario cards, number lines, and dry-erase markers to represent rational numbers, identify opposites, and determine absolute values. Educators monitor student thinking using embedded DOK-aligned questions, such as “How can you use that location to determine the opposite location?” and “How can a number line help you determine the absolute value of a number?” The materials also recommend collaborative learning structures by directing students to work with partners, participate in Math Chats, share strategies, ask questions, provide feedback, and engage in structured conversation routines.

Evaluation for 3.2c
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.

The “Skill Review and Practice Review” section in each scope supports multiple types of practice by incorporating independent work (Quick Check, Checkup), guided and intervention practice (Review), and optional collaborative small-group structures for reteaching. The Teacher Directions clearly outline when to use whole-group, small-group, and individual formats and include facilitation steps and differentiation strategies to support effective implementation. For example, in the “Algebraic Expressions” scope, the “Procedure and Facilitation Points” section states that each student should complete the Quick Check independently, the Review as either a small-group intervention or an independent activity, and the Checkup independently.

The Teacher Directions for the Explore lessons facilitate multiple types of practice by engaging students in collaborative, station-based problem-solving during the Explore activity and incorporate independent reflection and an exit ticket assessment. The educator guidance includes clear structures for whole-group facilitation, small-group collaboration, and individual work and provides embedded supports and questioning strategies to ensure effective implementation. For example, in the “Proportional Relationships” scope, the Teacher Directions state that students should be divided into small groups and to have “students work collaboratively to read each scenario on the Petting Zoo Cards at their stations. Instruct them to use this information to create unit rates and proportions in their Student Journals and solve for the equivalent measurement.”

The Suggested Scope Calendar provided for each scope supports multiple practice types: whole group, intervention, and collaborative. For example, in the Suggested Scope Calendar for the “Integer Operations” scope, the “Day 5” section lists materials for the lesson focus (whole group), recommendations for stations (collaborative), and independent work options. The Suggested Scope Calendar also provides suggestions for additional materials to use as independent practice and guided practice.

Evaluation for 3.3a
Materials include teacher guidance on providing linguistic accommodations for various levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

The “Language Supports” section in the Teacher Directions for each scope provides explicit educator guidance on supporting language development through vocabulary clarification, modeling pronunciation, and using visuals and gestures to reinforce meaning. The section also includes structured opportunities for student discourse by using sentence frames and questions, supporting varying levels of language proficiency, and promoting increasingly precise academic language aligned with the ELPS. For example, in the “Coordinate Plane” scope, the “Language Supports” section states that educators should provide “students with illustrations or examples of words and phrases used in this Explore: ordered pair. Model correct pronunciation of each phrase, and have students repeat as needed. Review the directions of north, south, east, and west. Use body motions, such as holding your arm vertically and pointing up, to indicate north. Use similar body motions for other directions. Read the location description for each building. As the description is read, have students trace with their fingers from the origin to the location of the specified building.”

The “Linguistic Diversity” section in the Teacher Toolbox provides information on language acquisition progression in the classroom and is followed by a list of resources and tools in each scope that support educators and students at varying levels of language proficiency. The materials state, “In an effort to promote equity in the classroom, STEMscopes Math has integrated research-based strategies and tools to support linguistically diverse learners at various proficiency levels. In the curriculum, we have created opportunities for linguistically diverse students to engage in authentic learning through multimodal communication.” Some of the resources and tools mentioned include Working on Words, sentence stems and frames, integrated accessibility features, Language Connections, and vocabulary strategies.

Evaluation for 3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.

The Implementation Guide guides educators on effectively using materials to support emergent bilingual (EB) students and on other linguistic accommodations to support their use in a bilingual or English as a second language (ESL) program. The guide states, “In the curriculum, we have integrated resources to support teachers and families. Descriptions of a few features and elements that can be used to support students at their level and provide an opportunity for families and caregivers to engage in student learning are outlined below.” This text is followed by a list of resources and tools found throughout the materials that support EB students. The Implementation Guide also states, “STEMscopes Math also includes a variety of Spanish translations and multilingual resources to support the diverse learners in your classroom.”

The “Linguistic Diversity” section provides comprehensive implementation guidance and embedded tools to support educators in effectively serving students in bilingual/ESL programs. The section outlines research-based strategies, proficiency-level supports, and specific resources—such as sentence stems, Language Connections, and tiered supports—that help educators differentiate instruction and scaffold language development across all domains.

Evaluation for 3.3c
Materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.

In each scope in the Teacher Directions, the “Language Supports” section promotes comprehension and academic language development by encouraging discussion, student explanation, and multiple representations and builds background knowledge through collaborative activities and discourse. For example, in the “Two Variables Relationships” scope, the “Language Supports” section states, “For Spanish-speaking students, relate the word independent to independiente. Discuss the similarities between other math terms in English and Spanish as related to this Explore, such as dependent for dependiente. Include speakers of all languages and ask whether they notice any similarities to their home languages in the math vocabulary. Collaborate to create a student-made anchor chart highlighting key words and elements for creating multiple representations for a given rate, such as independent variables, dependent variables, x-axis, y-axis, rate of change, graph, table, and equation. Consider adding the words in students’ home languages alongside the English words. Invite students to present one of their models from Part II to the class and explain the steps they took to solve.”

In each scope, the “Language Connections” section supports student learning by providing differentiated guidance across proficiency levels to build academic vocabulary and comprehension through structured listening, speaking, reading, and writing tasks. The section supports cross-linguistic connections and the development of background knowledge through visuals, sentence frames, partner discussions, and real-world connections, which ensures that students engage in meaningful oral and written discourse at increasing levels of complexity. Additionally, the materials include printable files for students of varying proficiency levels, although the levels have not been updated to match the 2025 ELPS proficiency levels.

Evaluation for 3.3d
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

Evaluation for 4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The “Scope Overview” section for each scope provides a progression of practice opportunities across the unit—including Explore activities, exit tickets, Show What You Know activities, and a Skills Quiz—that require students to apply, explain, and extend their understanding of TEKS-aligned concepts. Additionally, supplemental activities, such as Interactive Practice, Fluency Builders, and Mathematical Modeling Tasks, engage students in deeper reasoning, real-world application, and multiple representations, which ensures depth of understanding beyond procedural skills.

The Hook” in the “Engage” section of each scope engages students in meaningful, real-world problem-solving that requires them to apply and explain their thinking using TEKS-aligned concepts. The Hook incorporates questioning, discussion, and multiple representations to move students beyond procedural practice and into deeper reasoning, analysis, and justification. Additionally, the materials introduce students to the activity at the beginning of the unit and revisit the activity after students complete hands-on Explore lessons, which allows students to refine their understanding and demonstrate growth over time. For example, in the “Fractions, Decimals, and Percents” scope’s Hook, students compare two sale advertisements for a game system and determine which advertisement offers the better discount. The activity introduces and reinforces percent discounts through a real-world purchasing scenario that is revisited after students complete the Explore activities.

In “Explore 1: Represent Percents Using a Hundreds Grid” in the “Fractions, Decimals, and Percents” scope, students model percents using hundreds grids, represent percents as fractions and decimals, and solve real-world percent scenarios. Students collaborate to create models, simplify equivalent fractions, and make connections among multiple representations of rational numbers. Educators support deeper thinking through DOK-aligned facilitation questions, such as the DOK Level 2 prompt “How can we represent the lawn care company’s amount of lawns mowed as a part-to-whole ratio in fraction form?” which requires students to use evidence from their hundreds-grid model to justify their response. Students also engage in DOK Level 3 reasoning through questions, such as “How can we determine the missing percentage of the week for the remaining neighborhood?” that require them to analyze relationships among percentages, use the model strategically, and justify their conclusions. These opportunities require students to communicate mathematical reasoning; support conclusions with evidence; and connect fractions, decimals, percents, ratios, and visual models, which demonstrates depth of understanding aligned with the TEKS and mathematical process standards.

Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.

The progression of the Explore lessons in each unit increases in rigor and complexity, leading to grade-level proficiency in the mathematics standards. For example, in the “Equations and Inequalities” scope, students begin the unit in explore 1 by writing and modeling basic equations. These skills are developed throughout the unit and culminate in explore 4, in which students write, solve, and model equations and inequalities.

The Show What You Know activity in the “Explain” section of each scope provides a progression of questions and tasks that increase in rigor and complexity and supports mastery of grade-level coordinate plane concepts. For example, in the “Coordinate Planes” scope’s Show What You Know activity, students first demonstrate a foundational understanding by identifying, plotting, and labeling points on a coordinate plane; determining quadrants; interpreting ordered pairs; and connecting graphical representations to coordinate notation. The tasks require students to move among multiple representations as they analyze landmark locations and quadrant placement. Students then extend their understanding by graphing and interpreting points in all four quadrants, including positive and negative rational coordinates; identifying missing coordinates from graphical representations; and connecting symbolic labels to plotted locations. Students must analyze existing points and generate missing information, which increases the cognitive demand beyond simple plotting procedures. Throughout the sequence, the tasks progress from identifying and locating points to interpreting, analyzing, and creating coordinate representations, which builds toward grade-level proficiency with coordinate planes and graphing rational numbers.

Evaluation for 4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.

The Grade 6 Advanced Course Rationale in the Teacher Toolbox explicitly connects major mathematical concepts across the course and highlights how key ideas are developed and revisited throughout the year. The Course Rationale emphasizes a coherent progression of learning in which each scope builds on prior knowledge and reinforces connections between concepts, which ensures that students understand patterns and relationships across units. The document states, “Each scope in Grade 6 Advanced STEMscopes Math is intentionally sequenced to build on prior knowledge while deepening students’ conceptual understanding and procedural fluency with increasingly sophisticated mathematical ideas. The progression of the Grade 6 Advanced Math scopes reflects a coherent development of number sense, algebraic reasoning, proportional thinking, and data analysis, ensuring students are equipped to make connections across domains and apply their learning in meaningful, real-world contexts.”

The Grade 6 Advanced Scope and Sequence demonstrates a coherent progression of mathematical concepts across the units and course through TEKS-aligned scopes that build on prior knowledge and connect related ideas. The Scope and Sequence explicitly shows how concepts are revisited and extended across units by reinforcing patterns, big ideas, and relationships to support deeper understanding over time. The document states, “Each grade level contains a few areas of focus to provide insight on the major mathematical topics that will be covered within the instructional year. These areas of focus support the progression within and across the mathematical strands and emphasize the connections between major mathematical topics, which provides an integrated approach to math instruction.”

Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.

Accessing Prior Knowledge in the “Engage” section of each scope is a brief, educator-led activity to gauge students’ prior knowledge before they engage in the inquiry process. The activity is aligned with the previous grade level or previously taught content standards. For example, in the “Fractions, Decimals, and Percents” scope, the Accessing Prior Knowledge activity has students independently evaluate and justify their responses to decimals and fractions, then discuss their reasoning with multiple partners and as a class. The activity assesses prior knowledge and identifies misconceptions about tenths, hundredths, and decimal place value.

The “Content Unwrapped” section in the “Home” section of each scope explicitly shows vertical alignment across grade levels and connects prior learning. The “Content Unwrapped” section also unpacks academic vocabulary and skills in the standard and ensures continuity of both content and language development as students progress across courses. The section also includes a table of vertical-alignment TEKS that shows the connections between standards and skills across grade levels, both prior to and after grade 6.

The materials demonstrate coherence across grade levels through an explicit vertical alignment section in the “Scope Overview” section of each scope, which connects current learning to both prior and future mathematics content. For example, in the “Area and Volume” scope, students revisit grade 5 understandings of area and volume, including developing volume formulas for rectangular prisms, using unit cubes to measure volume, and solving perimeter, area, and volume problems. The materials then connect grade 6 learning to future grade 7 expectations involving composite figures, volume relationships between prisms and pyramids, and geometric problem-solving. These explicit connections help students understand how current learning builds on previous concepts and prepares students for future mathematical learning.

Evaluation for 4.2c
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..

The Scaffolded Instruction Guide in the “Home” section of each scope connects students’ prior knowledge to new learning through structured supports, such as Accessing Prior Knowledge, skill-review activities, and targeted remediation aligned with previous grade-level standards. The Scaffolded Instruction Guide organizes instruction by performance levels on assessments and diagnostic tools and links earlier concepts to current grade-level content, which ensures that students build on their existing understanding as they develop new mathematical knowledge and skills.

The Teacher Directions include a “Procedure and Facilitation Points” section that has questions to help connect big ideas, patterns, and relationships among mathematical concepts. For example, in the “Fractions, Decimals, and Percents” scope, the materials demonstrate lesson-level coherence that intentionally connects students’ prior knowledge of fractions, decimals, ratios, equivalent fractions, and place value to new learning about percents. The lesson activates previously learned concepts; uses familiar mathematical models, such as the hundreds grid, to bridge existing understanding to new content; and provides instructional supports that encourage students to apply prior procedures as they develop new mathematical knowledge. Reflection questions and discussions further reinforce these connections and help students recognize the relationships among fractions, decimals, and percents.

The “Instructional Supports” section for each Explore activity offers guidance to help educators activate and build on previously learned concepts before students engage with new content. For example, in the “Integer Operations” scope, the materials direct educators to review vocabulary, such as deposit, withdraw, rise, drop, and depth, from real-world integer contexts and explicitly connect those terms to positive and negative numbers. The materials also prompt educators to revisit students’ understanding of number lines by drawing number lines that include positive and negative values and labeling benchmark values in both fraction and decimal forms. Additionally, the lesson builds on students’ prior experiences with concrete representations by having students use counters and sign models to represent integer operations before transitioning to more-abstract drawings and equations. The materials further reinforce prior learning by encouraging educators to review the structure and features of number lines, including repeating intervals, directional arrows, and multiple orientations. These supports intentionally connect previously learned concepts and procedures to new mathematical understanding, which helps students build coherent and connected knowledge in the lesson.

Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.

The Spiraled Review in the “Elaborate” section of each scope embeds opportunities to revisit previously learned concepts and skills in new learning experiences. These ongoing practice tasks reinforce prior knowledge across lessons and units, support spaced retrieval, and help students build long-term understanding. Each Spiraled Review activity includes questions from previously covered scopes or activities in the materials and is most often given in an open-answer format, in which students must show their work and/or explain their reasoning for each question.

The Teacher Directions for every Explore activity in each scope provide discussion prompts that activate students’ prior knowledge of preceding concepts as an access point for building new mathematical understanding. For example, in the “Fractions, Decimals, and Percents” scope, the materials provide opportunities for students to retrieve and apply previously learned skills throughout the lesson. Students repeatedly recall prior knowledge of fractions, decimals, equivalent fractions, ratios, and place value as students represent, compare, and convert among percents, fractions, and decimals using multiple tasks and representations. The lesson reinforces these concepts through guided questioning, collaborative activities, reflection prompts, and an exit ticket, which allows students to revisit and strengthen previously learned mathematical skills while integrating new learning about percents.

The materials provide spaced retrieval opportunities for previously learned skills and concepts by incorporating Foundation Builder activities that require students to revisit and apply their understanding of numerical patterns, operations, ratios, and function rules before engaging in more-advanced work on two-variable relationships in the “Two Variable Relationships” scope. Throughout the activity, students analyze input-output tables and determine rules, such as “multiply by 5,” “add 6,” and “multiply by 3,” which requires the retrieval of multiplication, addition, and proportional reasoning skills developed in previous lessons and units. Students repeatedly examine relationships between paired values across multiple examples, which reinforces concepts of pattern recognition, numerical relationships, and functional thinking. The progression of tables includes both additive and multiplicative relationships and prompts students to compare different types of patterns and recall prior experiences with operations and proportional relationships. By revisiting these foundational concepts across several examples before extending learning to two-variable relationships, the materials intentionally support spaced retrieval of previously learned mathematical knowledge and skills across lessons and units.

Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.

The Spiraled Review in the “Elaborate” section of each scope provides interleaved practice through tasks that intentionally combine multiple previously learned skills in a single problem set. These mixed-concept problems require students to select and apply appropriate strategies across topics, which reinforces connections between skills and supports flexible, integrated understanding over time.

The Daily Numeracy activity in the “Scopes” section provides opportunities for students to revisit previously learned concepts and select and use diverse strategies, which promotes using of the most efficient strategy rather than relying on a single strategy for every problem. The materials describe the Daily Numeracy activity as “Students reason with numbers in an accurate, efficient, and flexible way through purposeful activities designed to help students build their thinking and reasoning around relationships and connections.” The activities are designed to be given to students daily, in weekly sets.

The materials provide interleaved practice opportunities in the “Skill Review and Practice Review” section in the “Intervention” section of each scope. For example, in the “Represent and Interpret Data” scope, students intentionally integrate multiple data representations and data analysis skills in the same lesson sequence and review resource. Rather than practicing a single representation in isolation, students engage with dot plots, histograms, stem-and-leaf plots, and box plots and repeatedly apply previously learned concepts, such as frequency, distribution, percentages, measures of center, quartiles, and data interpretation. Students must determine which mathematical tools and representations are appropriate for analyzing different datasets, which strengthens their ability to connect and apply related statistical concepts across lessons and units.

Evaluation for 5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.

The Explore activities in each scope offer a variety of tasks that require students to interpret, analyze, and evaluate models and mathematical representations. For example, explore 2 in the “Area and Surface Area” scope engages students in tasks that require them to interpret and analyze multiple data representations—including dot plots and stem-and-leaf plots—and to evaluate how well the representations align with given statistical questions and explanations. Students must justify their reasoning; describe patterns, such as shape and spread; and make predictions based on the data, which demonstrates deep analysis and evaluation of mathematical models and representations.

The “Skill Review and Practice Review” section in the “Intervention” section of each scope provides opportunities for students to work with different models and representations and allow students to use problem-solving methods, such as interpreting, analyzing, and evaluating solutions. For example, in the “Equations and Inequalities” scope, the “Skill Review and Practice Review” section allows students to interpret and analyze multiple representations of equations and inequalities, including algebra tiles, tape diagrams, symbolic equations, and number line graphs. Students evaluate relationships between these representations, justify solutions through substitution and modeling, and apply their understanding to real-world scenarios, which demonstrates higher-level reasoning about mathematical concepts.

The materials include questions and tasks in the Show What You Know activity of each scope that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. For example, in “Show What You Know – Part 2: Solving Percent Problems Using Benchmark Fractions and Percents,” students individually apply their learning from the Explore lesson by solving real-world percent problems using multiple representations. In the printable files, students analyze written scenarios and complete missing mathematical information by interpreting bar models and double number lines, selecting an appropriate solution strategy, and writing a solution statement. In the final scenario, students independently determine both the strategy and the solution statement, which requires them to evaluate the representations and apply them to solve the problem. Educator directions emphasize that this task is completed independently, builds directly on the corresponding Explore lesson, allows students to use manipulatives as needed, and serves as a formative assessment to determine whether additional intervention is needed. These opportunities require students to interpret visual models, analyze relationships among percents, benchmark fractions, and quantities, and evaluate how the representations support the mathematical solution.

Evaluation for 5.1b
Questions and tasks require students to create models to represent mathematical situations.

The Mathematical Modeling Task in the “Evaluate” section of each scope provides students an opportunity to create mathematical models that represent real-world situations. Students construct and use representations and then refine their models by analyzing relationships, interpreting results in context, and making decisions based on their representations. For example, in the “Two Variable Relationships” scope’s Mathematical Modeling Task, students model the costs of different Moon settlement items by constructing tables, graphs, numerical expressions, and equations that represent the relationship between the number of items and the total cost. Students then use these representations to explain and justify their reasoning and demonstrate how the mathematical models accurately describe the context of planning a Moon colony. By selecting their own items and creating multiple representations, students actively develop and apply mathematical models to analyze a realistic scenario.

The Choice Boards in the “Acceleration” section of each scope engage students in creating mathematical models through a variety of tasks and real-world situations. Across activities, students actively develop and apply models to make sense of problems and communicate their reasoning. For example, in the “Rational Number Operations” scope, the Choice Board provides students opportunities to create mathematical models that represent situations involving rational number operations. Students develop equations and answer keys for an original game board, apply rational number operations to model financial and budgeting scenarios, determine measurements for a real-world recipe, and create mathematical representations to support artistic designs. These tasks require students to construct and apply mathematical models to solve authentic problems and communicate their mathematical thinking in meaningful contexts.

Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.

The Mathematical Modeling Task in the “Evaluate” section of each scope helps students apply conceptual understanding to a new, real-world context through a multipart activity. Students transfer their knowledge to model a scenario, interpret results in context, and extend their thinking. For example, in the “Two Variable Relationships” scope, the Mathematical Modeling Task provides students opportunities to apply their conceptual understanding of mathematical relationships in a new, authentic context. Students transfer their knowledge of equations, tables, graphs, and numerical expressions to design a Moon settlement by modeling the costs of homes, transportation, and facilities. Students synthesize multiple mathematical representations, justify their reasoning, and explain how their representations describe the situation, which demonstrates an ability to apply conceptual understanding to solve a meaningful real-world problem.

The Choice Boards in the “Acceleration” section of each scope provide tasks that require students to apply their conceptual understanding in new and varied contexts, including real-world scenarios, cross-disciplinary connections, and open-ended problem situations. The activities, such as career research, real-life applications (e.g., art, science, everyday situations), and problem-solving tasks encourage students to transfer their knowledge and make connections beyond the initial learning context. For example, in the “Angle Relationship” scope, the Choice Board provides students opportunities to apply their conceptual understanding of angle relationships in new, meaningful contexts. Students use their knowledge of vertical, adjacent, complementary, and supplementary angles to solve problems involving real-world scenarios, such as pie diagrams, color wheels, and light reflection, while also making connections to engineering, art, and science. These activities require students to transfer and apply their understanding of angle relationships beyond routine exercises to authentic situations.

Evaluation for 5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.

The Daily Numeracy activity in the “Scopes” section provides consistent, structured daily practice opportunities that build student automaticity and fluency with key mathematical skills. The activities, such as Solve It, number line tasks, and reasoning routines, require students to regularly engage in mental math, number sense, and pattern recognition, thereby reinforcing efficient and flexible problem-solving strategies over time. The materials break down these activities, which are designed to be given individually or in small groups, into weekly tasks.

The Mathematical Fluency component in the “Scopes” section outlines a structured mathematical fluency program that intentionally builds automaticity through a progression of operations and repeated practice with rational numbers. The two-part approach—reinforcing strategies through discussion and visual models and applying them through practice and real-world contexts—supports students in developing the efficient, accurate, and flexible fluency needed for grade-level tasks. The materials state, “According to standards, students should be fluent in all operations with rational numbers. By using these standards as the foundation of the program, we ensure automaticity. Students progress naturally toward having a deep and intrinsic understanding of how to apply the fact strategies.”

The materials provide tasks to build the automaticity and fluency necessary to complete grade-level tasks by engaging students in repeated practice identifying, interpreting, and verifying ordered pairs on a coordinate plane. The Four Corners activity in the “Engage” section of the “Coordinate Planes” scope requires students to analyze multiple coordinate representations, identify errors in reasoning, and determine which set of coordinates correctly matches the plotted locations. As students compare the coordinate descriptions with the graph, students repeatedly apply the conventions of ordered pairs and coordinate plane navigation, which strengthens fluency with locating points and distinguishing between x- and y-coordinates. For example, students evaluate several possible coordinate descriptions of a bank, library, and post office and determine that slide 3 is correct because the coordinates accurately correspond to the plotted locations, while other slides reveal common misconceptions, such as reversing x- and y-coordinates and using the same coordinate value twice. This repeated analysis of correct and incorrect representations helps students develop automaticity in the coordinate plane concepts essential for future graphing and algebraic reasoning.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.

The Daily Numeracy activity in the “Scopes” section provides frequent opportunities for students to apply efficient, flexible, and accurate mathematical procedures through a variety of daily tasks and routines. The activities, such as mental math prompts, number line reasoning, and problem-solving discussions encourage students to use multiple strategies, justify their thinking, and refine their approaches across lessons, thereby supporting procedural fluency in meaningful contexts.

The Data Science activity in the “Elaborate” section of each scope is a structured opportunity for students to practice applying efficient, flexible, and accurate mathematical procedures through data-driven problem-solving and discussion-based tasks. Students apply procedures while also explaining and refining their approaches through guided questioning and multiple solution strategies. For example, in the “Data” scope, the Data Science activity provides students multiple opportunities to practice applying efficient, flexible, and accurate mathematical procedures as they analyze and interpret real-world data. Students use proportional reasoning, percent calculations, scaling, rounding, and data analysis to solve contextual problems, compare quantities, make inferences, and justify their reasoning. The discussion-based format encourages students to evaluate multiple solution strategies, refine their mathematical thinking, and apply appropriate procedures accurately across a variety of related tasks in the lesson.

The materials provide opportunities for students to practice applying efficient, flexible, and accurate mathematical procedures in each Explore activity of every scope. For example, in explore 4 of the “Fractions, Decimals, and Percents” scope, students use various strategies to find the whole, percent, and part when solving real-world percent problems. Students calculate final prices, sale prices, and discounts using concrete modeling tools, such as double number lines, fraction tiles, and tape diagrams. Students answer reflection questions, including “How are models useful when solving percent problems?” and “Why is it important to know multiple strategies to solve various percent problems?” The materials then prompt students to transition to more abstract numerical processes, such as proportions or equations, and prompt educators to ask, “How can you represent the percent as a fraction to solve the problem?” Later in the lesson, students apply this flexible thinking to a set of multistep problems by selecting and executing their preferred methods to solve the problems accurately.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.

The Daily Numeracy activity in the “Scopes” section engages students in evaluating multiple solution strategies and reasoning processes through discussion-based routines and reflective questioning. The activities prompt students to compare approaches, justify their thinking, and determine the efficiency and accuracy of different methods, which supports a deeper understanding of mathematical procedures over time.

The Would You Rather activity in the “Acceleration” section of each scope engages students in evaluating multiple solution methods and justifications by providing open-ended, discussion-based tasks. Students compare strategies, analyze outcomes, and justify which approach is most effective, which supports the evaluation of efficiency, flexibility, and accuracy. For example, in the “Measures of Data” scope, the Would You Rather activity provides students opportunities to evaluate mathematical procedures and solutions for efficiency, flexibility, and accuracy. Students analyze multiple numerical summaries—including the mean, median, range, and interquartile range—to compare two data distributions and determine which measures best support a conclusion. Students evaluate the effectiveness of different statistical measures, justify their reasoning with evidence from the data, and defend their chosen solution, which promotes the flexible and accurate use of statistical procedures rather than relying on a single measure.

The materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy in the lessons and throughout the unit. For example, the “Elaborate Fluency Builder – Two-Step Equations and Inequalities” activity engages students in a partner-based Fix the Mistake activity in which students analyze worked solutions to determine whether equations or inequalities have been solved correctly. Students examine both symbolic problems and contextual scenarios in which a named student has solved an equation or inequality, and students evaluate the accuracy of the solution and the procedure used to obtain it. When errors are identified, students determine where the mistake occurred in the process and correct the solution accordingly. Students record their reasoning on a student recording sheet and verify their responses using an answer key after all cards have been analyzed. This structure provides opportunities for students to evaluate and correct mathematical procedures and solutions with a focus on accuracy in the lesson.

Evaluation for 5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.

The Content Support document for each scope includes embedded supports—such as educator guidance, modeled strategies, and scaffolded representations—that help educators direct students toward more-efficient and more-effective problem-solving approaches. The resource provides clear pathways from conceptual understanding to more-streamlined procedures, which supports educators in refining student thinking and promoting increasingly efficient methods over time.

The Teacher Directions for each Explore activity embed supports that guide students toward increasingly efficient approaches, including intentional questions that prompt deeper thinking and the refinement of strategies. The “Procedure and Facilitation Points” section explains why specific tools and methods are appropriate and efficient, and the “Instructional and Language Supports” section helps educators understand the progression from less-efficient to more-efficient strategies, which enables targeted guidance throughout the lesson. For example, in the “Fractions, Decimals, and Percents” scope’s explore 1 activity, the lesson includes scaffolded facilitation questions, concrete and visual models using hundreds grids and two-color counters, structured progression from manipulatives to abstract representations, opportunities for collaborative strategy sharing, and targeted instructional supports for common misconceptions. The Teacher Directions provide educators guiding questions, differentiation strategies, language supports, and prompts that encourage students to refine their methods, compare solution strategies, and develop increasingly efficient and accurate procedures for representing and converting among percents, fractions, and decimals.

Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.

The Content Support document for each scope explicitly addresses both the conceptual and procedural emphases of the TEKS by clearly outlining how students develop their understanding and apply their skills. For example, in the “Integer Operations” scope, the instruction begins with a strong conceptual focus, using concrete and pictorial models (e.g., algebra tiles, number lines, real-world contexts) to build meaning and connections. This understanding is then intentionally linked to procedural fluency as students transition to standard algorithms and symbolic methods for solving integer operations. The materials make this progression explicit by describing how models connect to abstract representations and how repeated practice leads to fluency, which ensures alignment with both the conceptual and procedural expectations of the TEKS.

The Suggested Scope Calendar provided for each scope explicitly addresses both the conceptual and procedural emphasis of the TEKS through a clear progression of instruction. The lessons begin with conceptual understanding using models, representations, and real-world contexts, then transition to guided and independent practice to build procedural fluency. The daily Content Objectives further emphasizes this progression of learning by clearly outlining what students will understand and be able to do at each stage.

The materials explicitly state how both the conceptual and procedural emphasis of the TEKS are addressed through the “Content Unwrapped,” “Dissecting the Standard,” “Implications for Instruction,” and “Vertical Alignment” sections in the Teacher Toolbox. For example, in the “Triangle Properties” scope, the “Dissecting the Standard” section identifies the procedural expectations by breaking the TEKS into discrete skills, such as extending prior knowledge to determine triangle angle sums, analyzing the relationship between side lengths and angle measures, and determining whether three lengths form a triangle, while also defining the underlying concepts students must understand, including the triangle angle sum property and triangle inequality theorem. The “Implications for Instruction” section then explains the conceptual progression by emphasizing that students build on prior geometric knowledge, use models to understand the relationships among triangle properties, and apply those understandings to solve equations involving unknown angles. For example, the materials explicitly state that students should model the sum of angles in a triangle, the relationship between side lengths and angle measures, and the sum of the triangle’s side lengths before applying these concepts to solve equations and determine whether given side lengths form a triangle, which demonstrates how conceptual understanding supports procedural fluency. The “Vertical Alignment” section further reinforces the intended progression by showing how prior learning about classifying shapes builds toward grade-level reasoning about triangle properties and prepares students for future work on triangle similarity, congruence, and formal geometric proofs.

Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.

The materials incorporate concrete models, pictorial representations, and abstract representations throughout the Explore tasks in each scope. For example, in the “Fractions, Decimals, and Percents” scope’s explore 1 activity, students use manipulatives, such as two-color counters and hundreds grids (concrete), shade and interpret visual models of percents (pictorial), and translate those representations into fractions, decimals, and percent notation (abstract), which ensures alignment with the TEKS and supports conceptual understanding across multiple representations.

The “Skill Review and Practice Review” section in the “Intervention” section of each scope incorporates concrete and abstract models and pictorial representations into the tasks to support conceptual understanding. For example, in the “Equations and Inequalities” scope’s “Skill Review and Practice Review” section, students use manipulatives, such as algebra tiles, and visual models, such as balance scales and number lines (concrete and pictorial), and connect these manipulatives and models to symbolic equations and inequalities, including solving, graphing, and writing real-world problems (abstract). This intentional integration of representations supports understanding of mathematical relationships and aligns with the TEKS.

The materials incorporate concrete models, pictorial representations, and abstract representations throughout each scope’s Checkup to reinforce students’ understanding of the concepts in the unit and the alignment with the TEKS. For example, in the “Equations and Inequalities” scope’s Checkup, students transition between writing symbolic equations and inequalities by creating algebra tile models on a balance scale, interpreting and graphing solutions on number lines, and connecting mathematical representations to real-world contexts. For example, students are asked to draw an algebra tile model on a balance scale to represent the equation 4x = 12, graph the solution of an inequality on a number line after solving it, and interpret a number line graph to write both a real-world scenario and a corresponding inequality. These questions intentionally require students to connect concrete manipulatives, pictorial representations, and abstract mathematical notation to demonstrate conceptual understanding and procedural fluency.

Evaluation for 5.3c
Materials include supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS.

The Explore activities in each scope support students in connecting, creating, defining, and explaining concrete and representational models for abstract concepts. For example, in the “Fractions, Decimals, and Percents” scope, the explore 1 activity provides opportunities for students to use hands-on tools, such as two-color counters and hundreds grids, to build visual models; translate those models into symbolic forms (fractions, decimals, and percents); and justify their reasoning through guided questioning and reflection. The progression from modeling with manipulatives to completing tables and explaining relationships supports a clear connection from concrete representations to abstract mathematical concepts aligned with the TEKS.

The Explain activities provide a range of supports that help students connect concrete and visual representations to abstract mathematical concepts. The activities, such as Anchor Charts, Interactive Notebooks, Guided Notes, and Picture Vocabulary support students in creating, defining, and explaining models, and the “Language Connections” and “Interactive Vocabulary” sections deepen understanding by linking representations to symbolic and numeric reasoning aligned with the TEKS.

The materials include specific supports in the “Skill Review and Practice Review” section in the “Intervention” section of each scope, which help students connect, create, define, and explain representational models before transitioning to abstract mathematical concepts. For example, in the “Two Variable Relationships” scope, the Review begins by defining the relationship between independent and dependent variables using visual diagrams, input-output tables, and real-world scenarios before connecting these ideas to coordinate graphs and symbolic equations. Students are explicitly guided in translating among tables, graphs, equations, verbal descriptions, and real-world contexts, and there are explanations of how each representation corresponds to the others. The tasks require students to create graphs from tables, determine equations from graphs, distinguish additive and multiplicative relationships by interpreting graphical features, write verbal descriptions from equations and tables, and identify constants of proportionality across multiple representations. Throughout the Review, instructional prompts ask students to explain why relationships are additive or multiplicative and justify how representations are connected, which reinforces conceptual understanding before applying symbolic procedures.

Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.

The Content Support document for each scope provides structured opportunities for students to develop academic mathematical language through visuals, manipulatives, and multiple representations. Using the resources, students engage with concrete models (e.g., counters, algebra tiles), pictorial representations (e.g., number lines, graphs), and symbolic notation to build meaning for key concepts and vocabulary. These varied approaches help students make connections between mathematical ideas and the language used to describe them. For example, in the “Integer Operations” scope, the Content Support document prompts students to use two-color counters, number lines, and algebra tiles for modeling integer operations.

The Explore activities for each scope provide multiple opportunities for students to develop academic mathematical language through visuals, manipulatives, and structured activities. Students reinforce vocabulary and conceptual understanding through hands-on activities and visual supports. Additionally, structured discussions and reflection questions encourage students to articulate their thinking using precise mathematical language. For example, in the “Fractions, Decimals, and Percents” scope, the explore 1 activity asks students to use hundreds grids and two-color counters to define and understand percents as expressions of rate per 100.

The materials provide opportunities for students to develop academic mathematical language using visuals and language development strategies. Each scope has a Picture Vocabulary that introduces and reinforces key academic vocabulary. The materials provide definitions and visuals for each vocabulary word. For example, in the “Ratios and Rates” scope, a key vocabulary term is ratio. The materials provide the definition, “A comparison of two quantities that shows their sizes in relation to one another.” The materials pair this definition with a visual showing five girls and 10 boys, which illustrates different ways to represent the ratio of boys to girls. The Picture Vocabulary is intended for use during the Explore part of a lesson, and students can later use these materials as flashcards to practice and build automaticity with academic mathematical language.

Evaluation for 5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.

The Content Support document for each scope includes embedded educator guidance to support the development and use of academic mathematical vocabulary in meaningful contexts. Each resource provides clear explanations, key terms, and instructional notes that help educators introduce and reinforce vocabulary as students engage in conceptual learning and problem-solving. This intentional integration ensures that vocabulary is not taught in isolation but is consistently applied using representations, models, and real-world problem situations.

The Teacher Directions for each Explore activity in each scope embed educator guidance that scaffolds students’ development and use of academic mathematical vocabulary in context. The Teacher Directions provide guiding questions, modeling strategies, and prompts that help students define terms. This support ensures that vocabulary is introduced meaningfully and reinforced as students engage in problem-solving tasks. For example, in the “Fractions, Decimals, and Percents” scope, the Teacher Directions for explore 1 include Math Chat questions, such as “How do you represent a fractional percent between 0% and 1%?” “How do models help in understanding percents?” and “How are percents, fractions, and decimals related to one another?”

The materials include embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context. For example, each scope contains a Picture Vocabulary for use during the Explore phase. The Teacher Guide provides clear discussion prompts to introduce key unit terms, including “How can you connect this work to your work in the Explore?” “How would you rephrase the definition in your own words?” and “What do you picture in your mind when you hear this word?” Additionally, the materials direct educators to use the provided vocabulary games to reinforce students’ contextual mastery of academic vocabulary. This strategic guidance ensures that educators actively scaffold mathematical language acquisition during instruction.

Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.

The Teacher Directions for each Explore activity in each scope embed educator guidance to support students’ use of appropriate mathematical language through vocabulary, syntax, and discourse during instruction. The Teacher Directions include structured conversation routines, think-aloud strategies, and sentence stems to guide mathematical discussions and help students explain, justify, and refine their thinking with peers. Opportunities for collaboration and reflection exemplar responses, and guided questioning support the development of students’ mathematical language over time. For example, in the “Fractions, Decimals, and Percents” scope’s Teacher Directions for explore 1, educators introduce and reinforce key vocabulary by defining percent as “a special ratio that means out of 100,” explaining that a percent “can be represented as a fraction, decimal, or ratio” as a part-to-whole relationship, and discussing the meaning of the word percent by examining the roots per and cent. Students work collaboratively to read Mowing Cards, create hundreds-grid models, and discuss and justify their reasoning in their groups before educators facilitate opportunities for students to share their strategies, ask each other questions, and make connections. Throughout the lesson, the materials provide educators numerous discussion questions paired with exemplar student responses that model precise mathematical language, including such terms as hundredths, numerator, denominator, equivalent fraction, decimal, and part-to-whole ratio. The lesson concludes with a Math Chat and a structured conversation routine that provides additional opportunities for students to hear, refine, and use mathematical language with peers. At the same time, educators reinforce accurate mathematical discourse.

The materials include embedded educator guidance to support students’ development and use of academic mathematical language through vocabulary, syntax, and discourse across listening, speaking, reading, and writing domains in the “Language Connections” section for each scope. For example, in the “Fractions, Decimals, and Percents” scope’s “Language Connections” section, students use concrete and representational models, such as 10-by-10 grids, base 10 blocks, fraction strips, and strip diagrams, to connect visual representations to mathematical language as they discuss fractions, decimals, and percents. Structured sentence frames such as “We see two parts out of five of them are blue, so our fraction could be” and “____ is the same thing, or equivalent, to 0.4” support students and scaffold mathematical syntax and conceptual explanation. Educator prompts guide structured discourse through echo reading, choral reading, and guided questioning sequences, such as “What do you notice about the decimal chart and the percent chart?” and “What can we multiply this fraction by to get a denominator of 100?” Students engage in collaborative discussions in beginner, intermediate, and advanced language groups, in which they explain reasoning, justify representations, and respond to educator-led prompts using mathematical vocabulary, including fraction, decimal, percent, numerator, denominator, and equivalent fraction. Language supports further reinforce discourse development by prompting students to discuss the meaning of vocabulary, paraphrase peer responses, and construct written explanations using academic mathematical language.

Evaluation for 5.5a
TEKS process standards are integrated appropriately into the materials.

The Grade 6 Advanced Scope and Sequence shows that the materials intentionally integrate the TEKS process standards throughout the materials, as evidenced by the consistent inclusion of mathematical process standards in each scope. Additionally, the Scope and Sequence demonstrates that process standards are not taught in isolation but are systematically incorporated across all topics and learning experiences.

The materials integrate the TEKS process standards by explicitly outlining and embedding each practice in dedicated “Process Standards” resources in the Teacher Toolbox. Each file defines a specific process standard (e.g., analyzing relationships, creating representations, justifying reasoning) and guides students’ engagement in these practices through problem-solving, discussion, and real-world application. This structure ensures that process standards are not separate from instruction but that the materials intentionally weave the process standards into how students learn and demonstrate mathematical understanding.

The materials integrate the TEKS process standards throughout the “Proportional Relationships” scope’s Mathematical Modeling Task in the “Evaluate” section by embedding an authentic, multistep real-world problem rather than isolated procedural practice. Students apply mathematics to solve everyday problems as they plan a camping trip by selecting a destination, converting measurements, determining water needs, and calculating the weight of camping gear. Students use a problem-solving model to analyze information, select solution strategies, perform calculations, and justify how quantity affects the results. Students select and use mathematical tools and representations to organize information in tables, perform measurement conversions, and model proportional relationships. The task requires students to communicate mathematical ideas and create representations to organize and communicate thinking through written explanations, tables, and mathematical justifications. Students analyze mathematical relationships by connecting proportional reasoning across multiple measurement contexts, and students display, explain, and justify mathematical ideas using precise mathematical language when explaining the conversion process and defending how changes in quantity affect total amounts. Educator guidance reinforces these process standards by prompting educators to use guiding questions instead of procedural directions, to facilitate discussions of multiple solution methods, to encourage students to draw representations and write complete justifications, and to use structured mathematical conversations to deepen reasoning and communication.

Evaluation for 5.5b
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.

The Grade 6 Advanced Scope and Sequence clearly describes how the materials incorporate and connect the TEKS process standards across the course through both structural organization and instructional design. The Scope and Sequence outlines the alignment of process standards in each scope and provides a coherent progression that ensures that students repeatedly engage with and build proficiency in the TEKS process standards over time.

The “Process Standards” resources in the Teacher Toolbox include clear descriptions of how the materials incorporate and connect the TEKS process standards across instruction. Each resource explains the purpose of the standard, what it looks like in practice across grade levels, and how the standard supports student learning through reasoning, communication, and representation. By outlining educator actions, student expectations, and examples of implementation, the materials provide a cohesive explanation of how process standards are developed and reinforced over time. The “Process Standards” resources include specific guidance on how to analyze relationships to communicate ideas; how to communicate mathematical ideas and their implications; how to create and use mathematical representations; how to display, explain, and justify mathematical ideas; how to select tools and techniques to solve problems intentionally; and how to use a problem-solving model—all of which are written to integrate the TEKS process standards into the materials.

The materials include a comprehensive description of how the program incorporates and connects the TEKS process standards. The Implementation Guide explains that the materials intentionally weave the process standards throughout the curriculum to develop foundational mathematical thinking and serve as the bridge between knowing mathematical content and knowing how and when to apply it. The guide describes how lessons are designed around the “habits of effective thinkers,” emphasizing problem-solving, collaboration, reasoning, communication, and higher-order thinking across all grade levels rather than teaching the process standards in isolation. Additionally, the curriculum progression intentionally revisits mathematical concepts in multiple contexts, which allows students to apply the process standards repeatedly as they build conceptual understanding, connect prior learning, and solve increasingly complex problems throughout the course.

Evaluation for 5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.

The Content Support document for each scope includes a clear description of how the materials embed and connect the TEKS process standards throughout instruction in each unit. Each unit explicitly outlines the application of process standards (e.g., problem solving, use of tools, communication, justification) in the “Applying Mathematical Process Standards” section and demonstrates how these practices are integrated into concept development and student tasks. This consistent structure ensures that the unit intentionally reinforces the process standards as students engage with content through real-world applications, multiple representations, and mathematical reasoning.

The Teacher Directions for each Explore activity in every scope explicitly list the TEKS mathematical process standards at the beginning of each lesson to ensure that educators are aware of the specific practices students are expected to engage in. The materials reinforce the process standards through guiding questions, facilitation moves, and structured discussions that are embedded throughout the lesson, which supports consistent implementation across the course. This intentional integration helps ensure that the process standards are not taught in isolation but are continuously developed in daily instruction and student tasks.

The materials include a description for each unit of how the materials incorporate and connect the TEKS process standards throughout the unit. For example, the “Scope Overview” section for the “Fractions, Decimals, and Percents” scope explains that the “Progression of Learning” provides the suggested sequence of the core content and a pathway to mastering the standards in the scope. The “Supplemental Activities” provide educators options to assess, intervene, and enrich student learning throughout the unit. The “Scope Overview” organizes instruction through engage, explore, explain, elaborate, evaluate, intervention, and acceleration, and its “Fundamental Questions” require students to generate equivalent fractions, decimals, and percents using real-world problems; solve percent problems using concrete and pictorial models; represent benchmark fractions and percents using 10-by-10 grids, strip diagrams, number lines, and numbers; and use equivalent forms to represent the same whole. The “Assessment Planner” further connects these mathematical processes throughout the unit by identifying standards-based assessments, Skills Quizzes, Mathematical Modeling Tasks, technology-enhanced questions, and Heat Maps, and the ”Intervention section” extends these opportunities through Quick Checks, Reviews, Checkups, educator-guided small-group instruction, and acceleration activities.

Evaluation for 5.5d
Materials include an overview of the TEKS process standards incorporated into each lesson.

The Grade 6 Advanced Scope and Sequence provides a clear overview of the TEKS process standards in each lesson by consistently including mathematical process standards in every Explore activity and scope. The Scope and Sequence explicitly lists the aligned process standards for each instructional component, which ensures that educators can easily identify how the materials embed these practices in daily instruction. This structure supports planning and reinforces the integration of the TEKS process standards across all lessons.

The Teacher Directions include an overview of the TEKS process standards for each lesson and explicitly list the mathematical process standards at the beginning. This section identifies the specific standards (e.g., problem-solving, use of tools, communication, justification) that will be emphasized during the lesson, which provides educators a clear instructional focus. By consistently presenting this overview in each Explore lesson, the materials ensure that the process standards are intentionally incorporated into daily instruction. For example, the “Fractions, Decimals, and Percents” scope’s explore 2 lesson explicitly identifies mathematical process standards (A, B, D, F, and G) at the lesson level and integrates them throughout instruction as students use benchmark fractions and percents to solve percent problems with strip diagrams and double number lines. The lesson overview describes how students apply 6AM.1B through a structured problem-solving model in which they analyze contextual situations, determine appropriate benchmark percents, represent relationships using models, and justify solutions using reasoning and mathematical discussion. Students engage in 6AM.1D, 6AM.1F, and 6AM.1G when they create and interpret strip diagrams and double number lines to represent part-to-whole relationships, analyze how 10 percent and other benchmark percents scale in a whole, and communicate reasoning using precise mathematical language during guided questioning and Math Chats. The lesson further incorporates 6AM.1A through real-world contexts, such as the “Mowing Mansions Lawn-Care Company” scenario. The lesson supports 6AM.1E through required use of multiple representations, including strip diagrams.

Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.

The materials provide opportunities for students to think mathematically and persevere through problem-solving by engaging them in open-ended Daily Numeracy tasks that require reasoning, mental math, and flexible thinking. The tasks give students time to analyze prompts independently and encourage students to explore multiple approaches before sharing solutions, which supports persistence and sense-making. The materials state, “The goal of Daily Numeracy is to empower students to reason with numbers in an accurate, efficient, and flexible way. We have included carefully crafted, purposeful activities that are designed to help students build their thinking and reasoning around relationships and connections.”

The Data Science activities in the “Elaborate” section of each scope provide opportunities for students to think mathematically and persevere in problem-solving by engaging them in open-ended tasks that require interpreting data, making inferences, and applying concepts in real-world contexts. Students analyze datasets, consider multiple questions, and justify their conclusions, which supports sense-making and sustained problem-solving. For example, in the “Fractions, Decimals, and Percents” scope’s Data Science activity, students analyze a real-world health dataset by interpreting pie and bar graphs, answering open-ended questions about patterns in the data, calculating percentages and approximate values (e.g., determining the number of underweight females and obese males), and explaining how adding new participants changes the graph. This activity requires students to make sense of authentic data, reason through contextual problems, justify their mathematical thinking, and persevere as they analyze, interpret, and communicate their conclusions.

The materials provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics through the Mathematical Modeling Tasks in the “Evaluate” section of each scope, which are situated in meaningful real-world contexts. For example, the “Fractions, Decimals, and Percents” scope’s “Mathematical Modeling Task: Savvy Shopping” presents students with a back-to-school shopping scenario in which they determine whether a student has enough money to purchase discounted items, calculate the amount saved by purchasing items on sale, and evaluate whether the remaining savings can be used to purchase additional clothing items while meeting specified constraints. Rather than following a prescribed procedure, students analyze discount information presented in multiple formats, justify their solutions using mathematical reasoning, and apply their understanding of fractions, decimals, and percents to make financial decisions. The accompanying educator guidance encourages productive struggle by directing educators to use guiding questions rather than telling students what steps to take, to facilitate discussions of multiple solution strategies, and to provide opportunities for students to share and justify their reasoning. The Mathematical Modeling Task rubric further reinforces mathematical thinking by evaluating students’ understanding, strategy selection, reasoning, and use of mathematical language, emphasizing that students fully address all parts of the problem, employ appropriate strategies, support their reasoning with evidence, and communicate mathematical ideas clearly.

Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.

The materials support students in understanding that there are multiple ways to represent and solve problems by intentionally prompting them to compare strategies and discuss different solution paths in the Daily Numeracy activities. Guiding questions, such as “Is there a different strategy we could use?” and structured discussions help students explain and justify their reasoning while recognizing the validity of multiple approaches. For example, in “Daily Numeracy: Week 1,” students solve problems using mental math and different number-sense strategies, place numbers on blank number lines or coordinate planes, compare and classify mathematical objects in Not Like the Others and Same and Different activities, and explain their reasoning using prompts, such as “Is there a different strategy we could use?” and “How are these strategies similar? How are they different?” Students also evaluate classmates’ reasoning by agreeing, disagreeing, and justifying their responses, which reinforces that multiple valid solution methods and representations can be used to solve mathematical problems.

The Mathematical Modeling Task in the “Evaluate” section of each scope supports students in understanding, explaining, and justifying multiple ways to represent and solve problems through open-ended tasks. The task asks students to represent scenarios, justify relationships, and explain their reasoning in context, which allows for multiple valid approaches and solutions. This structure encourages students to compare strategies, defend their thinking, and recognize that different representations and methods can lead to meaningful and correct conclusions. For example, in the “Two Variable Relationships” scope, the Mathematical Modeling Task requires students to represent the same mathematical relationship in multiple ways and justify their choices. Students select two variables from the Moon settlement scenario, organize the data in a table, write a numerical expression and equation, create a graph, and explain how they represented their items and justify their answer. Because the task is open-ended and accepts multiple valid solutions, students must explain and defend their chosen representations and solution methods, which demonstrates that mathematical problems can be represented and solved in more than one way.

The materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks through the Show What You Know activities in the “Explain” section of each scope. For example, in the “Measures of Data” scope’s “Show What You Know: Comparing Different Representations of the Same Data” activity, students are required to analyze the same data using multiple representations, including a dot plot, a box plot, a stem-and-leaf plot, and a histogram. Students answer questions about measures of center, spread, distribution, and variability and justify each response by referencing and explaining a specific data representation. The task further requires students to compare representations to determine which one best communicates the data distribution, which encourages them to evaluate the strengths of different mathematical representations for a given purpose. These opportunities support students in explaining their reasoning, justifying conclusions with mathematical evidence, and recognizing that the same mathematical information can be represented and interpreted in multiple valid ways.

Evaluation for 6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and teachers.

The materials are designed to require students to make sense of mathematics through consistent opportunities to do, write about, and discuss mathematics with peers and educators in the Daily Numeracy tasks. Students engage in collaborative discussions, respond using sentence stems, and justify thinking during activities such as Solve It! and Not Like the Others, which promotes mathematical discourse and deeper understanding. The materials state, “The goal of Daily Numeracy is to empower students to reason with numbers in an accurate, efficient, and flexible way. We have included carefully crafted, purposeful activities that are designed to help students build their thinking and reasoning around relationships and connections.”

The Data Science activities in the “Elaborate” section of each scope allow students to make sense of mathematics through opportunities to do, write about, and discuss mathematics with peers and educators. Students engage in structured discussions, respond to open-ended questions, and explain their reasoning orally and in writing as they analyze datasets and solve contextual problems. These collaborative and reflective opportunities promote mathematical discourse and deeper understanding. For example, in the “Fractions, Decimals, and Percents” scope’s Data Science activity, students analyze and interpret a real-world dataset, solve percent problems (e.g., determining the number of underweight females and estimating the percentage of participants in the normal weight category), and write explanations to describe how adding new participants changes the pie graph. They also discuss open-ended questions about patterns in the data and compare how pie graphs and bar graphs represent the same information, which requires students to communicate and justify their mathematical thinking with peers and the educator.

The materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss mathematics with peers and educators in each of the Explore activities for every scope. For example, in “Fractions, Decimals, and Percents” scope’s “Explore 4: Finding the Price and Discount” activity, students work collaboratively as they rotate through six sale card stations to solve real-world percent problems involving finding the original price, sale price, or discount percentage. At each station, students use the percent model work mat and select representations, such as double number lines, fraction tiles, and tape diagrams, to model their thinking and determine solutions, then record their models, mathematical reasoning, and solution statements in Student Journals. Students write about their mathematical thinking through reflection questions, including “How are models useful when solving percent problems?” and “Why is it important to know multiple strategies to solve various percent problems?” Students discuss their strategies and make connections with peers as they compare approaches during the post-Explore Math Chat, including explaining how models represent the relationship between a percent, part, and whole and why different strategies may be more efficient for solving percent problems.

Evaluation for 6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.

The Teacher Directions for each Explore activity support educators in guiding students to share and reflect on their problem-solving approaches through structured tasks and reflection opportunities. The materials ask students to model, explain, and justify their thinking, as well as compare strategies and evaluate efficiency, which promotes discussion of reasoning and multiple approaches. Educator guidance further encourages facilitating Math Chats and reflection questions that prompt students to articulate explanations, arguments, and justifications.

The student’s Observation Checklist supports educators in guiding students to share and reflect on their problem-solving approaches through structured opportunities for reflection and discussion. The Observation Checklist prompts students to reflect on their thinking, explain their understanding of key concepts, and identify areas of growth, which encourages students to articulate and justify their reasoning. The materials guide educators to facilitate these reflections during and after activities to support meaningful mathematical discourse and self-assessment. For each learning target, students identify how they can demonstrate understanding (e.g., model it, draw it, apply it, talk about it, write about it) and rate their proficiency as “I’ve got it,” “Almost there,” or “Not yet.” The final page includes reflection questions and a self-rating of the mathematical process standards to encourage students to evaluate their learning, identify areas of growth, and set goals for future improvement.

The materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications. For example, the Teacher Toolbox includes a supporting “Structured Conversations” section that provides educators routines and facilitation guidance to promote meaningful mathematical discourse. Routines, such as Back and Forth, require students to explain their understanding of a concept, problem, or process and clarify misunderstandings with a partner. Pair, Square, Share guides students to collaborate, compare responses, analyze tasks, and revise thinking after peer discussions. Gallery Walk and Walk, Talk, Decide provide opportunities for students to analyze classmates’ ideas, discuss problem-solving approaches, defend responses, and address misconceptions. These routines support educators in intentionally facilitating conversations in which students communicate mathematical reasoning, evaluate strategies, and justify their solutions.

Evaluation for 6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.

The Teacher Directions for each Explore activity include intentional prompts and embedded educator guidance that support the delivery of explanatory feedback based on student thinking and potential misconceptions. The Teacher Directions provide guiding questions, sample responses, and monitoring strategies to help identify misunderstandings and respond with targeted feedback during instruction. This structure enables educators to use student responses to drive discussion, clarify misconceptions, and support deeper understanding of mathematical concepts.

The educator’s Observation Checklist includes prompts and guidance that support educators in providing explanatory feedback based on student responses and observed understanding. The Observation Checklist encourages educators to collect anecdotal notes during instruction and use reflection questions to assess student progress. This structure supports targeted, responsive feedback that helps students refine their understanding and improve their problem-solving approaches. For each standard, educators record how students demonstrated understanding (e.g., physical modeling, pictorial modeling, problem-solving, discussion, written explanation) and provide notes and feedback. The final page includes space to document evidence of the mathematical process standards and to reflect on prompts that guide educators in evaluating student proficiency, identifying next instructional steps, and considering which instructional strategies were most effective.

The materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions in the Teacher Guide for each scope. For example, in the “Algebraic Expressions” scope, the Teacher Guide provides in-depth guidance for educator facilitation throughout each lesson. The guide includes an “Identifying Misconceptions” section that outlines common student errors, which allows educators to anticipate and address them proactively. Additionally, facilitation tips embedded throughout the lesson outline key components, activity strategies, and potential misconceptions. Specifically, a facilitation tip during explore 1 states, “If students have the misconception that 3x can also be written as x3, then explain that in a multiplication expression, the coefficient always precedes the variable.” This targeted guidance provides educators the exact phrasing needed to deliver immediate, explanatory feedback in the moment based on potential student misconceptions.