STEMscopes Texas Grade 7 Advanced Math

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

The Grade 7 Advanced Scope and Sequence clearly outlines the progression of concepts across the course, beginning with real numbers 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 7 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 “Similar Figures” scope covers the standards 7AM.5.B and 7.AM.5.C and covers one major mathematical topic: proportionality.

The Texas Math ELPS Alignment—Grade 7 in the “Essentials, Additional Texas Alignment” section outlines the alignment of each scope and Explore activity with both the 2007 and 2025 ELPS. For example, in the “Similar Figures” scope, educators see that explore 2 aligns with the 2025 ELPS 1.BCDE and 2.BEF.

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 and 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 “Real Numbers” scope, educators read about previous grade 6 student work on rational numbers and how this scope will expand on that knowledge and introduce irrational numbers for the first time.

The Grade 7 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 7 Advanced STEMscopes Math is intentionally sequenced to build on students’ prior knowledge while extending their understanding of mathematical relationships, representations, and real-world applications. The progression emphasizes connections across number systems, algebraic reasoning, proportional thinking, geometry, and statistics to support a cohesive and rigorous mathematical experience that prepares students for increasingly abstract concepts in future mathematics courses.”

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, which 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 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 “Real Numbers” scope, educators read about previous grade-level student work on rational numbers and how this scope will expand on that knowledge and introduce irrational numbers for the first time.

The materials include a “Content Unwrapped” section for each scope that provides a detailed breakdown of the TEKS into clear, teachable components, including 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 “Real Numbers” scope, the take-home letter states, “In math class, your student is about to explore representation of real numbers and scientific notation. To master these skills, they will build on their knowledge of classifying rational numbers, describing the relationships between sets and subsets of rational numbers using visual representations such as Venn diagrams, and applying their knowledge of working with decimal place value.” The letter is then followed by several examples of what the real number system looks like, how to approximate irrational numbers on a number line, practice problems for students to compare and order real numbers, how to convert between scientific and standard notation, and a vocabulary section with definitions for many new academic terms being introduced in 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 “Real Numbers” scope’s take-home letter, the “Math Outside the Classroom!” section begins by stating, “Real numbers are used all around our everyday lives. Chat about where you use real numbers in your everyday life. Here are a few examples.” The letter then gives multiple examples of where real numbers are used in the real world and ideas of where to look for more real 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 printed 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 “Similar Figures” scope, if a student is scoring in the 80–100 percentile mastery range for the standard 7.AM.5.B, the guide recommends that the student work on the Would You Rather activity and the Choice Board in the “Acceleration” section and the “Mathematical Modeling Task in the “Evaluate” 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, and 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 “Similar Figures” scope, 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 “3-Strand Pearl Necklace” 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 prior to 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 Level 1 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 “Similar Figures” scope, if a student is scoring in the 0–25 percentile (previous grade-level remediation) range, recommendations include the student working on the skill reviews and practice, the Guided Notes, 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 “Circles” scope, an instructional support states, “If students need additional support with differentiating between diameter and radius, give them a vocabulary sheet with a labeled diagram of a circle that they can use as a reference sheet throughout the lesson.”

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 “Similar Figures” 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 skill review and practice activities, the unit’s Skill Quiz, and the unit’s Guided Notes 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 “Circles” scope, the “Instructional Supports” section states, “If students need additional support with rounding to the nearest inch, give them a ruler, and project the image of a ruler on the board. Circle a number on the projected ruler, such as 4.5, and discuss with the class what the nearest inch would be. Review the rules for rounding.”

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 “Personal Financial Literacy” scope, the “Language Supports” section states, “Introduce the terms necessity and cost of living. Provide students with items that might be included in a family budget in groups of 3 (for example, Food, Entertainment, and Housing). Students should discuss with a shoulder partner which of these items are considered necessities.”

In the Teacher Directions of Explore lessons, the materials provide questions that allow students to access the task by discussing the scenario’s context. This allows educators to pre-teach necessary vocabulary and concepts. For example, in the “Circles” scope, task access questions include “Why would Diego need to know the circumference of a pizza before ordering a pan?” and “Are there other reasons you might need to know an object’s circumference?”

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 “Similar Figures” scope, the materials recommend that students who score in the 50–80 percentile mastery range work on the Picture Vocabulary, the Interactive Vocabulary, the Interactive Notebook, one of the Fluency Builder activities, 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 the 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 “Circles” scope, the “Instructional Supports” section includes several guiding points for lesson instruction, such as “When working on Part II, some students may struggle with applying the formulas for circumference to solve problems. Break down the formula with students who are struggling by reviewing what each part of the formula means (r, d, pi) and why we multiply pi times the diameter or 2 times pi times the radius. You could offer students a model for the formula like C = _ · _ .”

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 “Determine Probability” scope, the materials provide explicit educator guidance that models and explains theoretical probability, experimental probability, compound events, dependent events, and complements. The lesson directs educators to introduce probability concepts through a carnival-game scenario involving dice and cards and guide students in determining probabilities without conducting simulations. The materials instruct educators to ask targeted questions, such as “What is the sample space of Roll a Die?” and “How can you use the information provided about each game to determine the expected probability of winning?” to help students connect favorable outcomes to total outcomes. During Math Chat discussions, the materials provide sample responses and explanations that distinguish theoretical probability from experimental probability and explain how to determine the probability of a complement by subtracting the probability of an event from 1. In Part II, the materials direct educators to model compound probability by introducing a card-selection scenario without replacement and prompting students to analyze how removing a card affects subsequent outcomes.

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 offer additional options for educators to effectively meet the needs of their diverse classrooms. For example, in the “Instructional Supports” section of the “Circles” scope, the materials state, “When working on Part II, some students may struggle with applying the formulas for circumference to solve problems. Break down the formula with students who are struggling by reviewing what each part of the formula means (r, d, pi) and why we multiply pi times the diameter or 2 times pi times the radius. You could offer students a model for the formula like C = _ · _ .”

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 “Volume” scope, the lesson begins with a real-world canning scenario that helps educators connect the concept of cylinder volume to an authentic context before introducing formal mathematical procedures. Educators activate prior knowledge by prompting students to discuss their previous experiences with volume and by guiding them to connect the volume formula for a rectangular prism to that for a cylinder. The materials then direct educators to facilitate hands-on learning by having students construct cylinder nets, fill cylinders with centimeter cubes, calculate base area, and discover the volume formula through exploration rather than memorization. Educators monitor understanding throughout the lesson using embedded DOK-aligned questions that prompt students to compare cylinders and rectangular prisms, explain how to determine volume, justify the use of formulas, and solve for missing dimensions. The materials further support facilitation through Math Chats and structured conversation routines that require students to explain strategies, compare approaches, justify reasoning, and critique mathematical thinking.

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 “Angle Relationships” scope, the “Procedure and Facilitation Points” section states that each student should complete the Quick Check independently, the Review either as 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 “Circles” scope, the Teacher Directions state that students should be divided into small groups of three or four students and to have “students work in their groups to match each pizza image with its appropriate circumference equations. Then have students use that information to calculate the circumference of each pizza and record it in Part II of their Student Journals.”

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 9” 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 for 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 “Circles” scope, the “Language Supports” section states that educators should emphasize “the meaning of the words radius and diameter while the students are exploring the pizza circumference cards. This can be done by modeling how to use the word. For example, say, ‘Yes, this is the radius. This is the diameter. The diameter is two times the radius.’ Students could also associate hand gestures with identifying the radius and diameter. For example, students could hold up one finger if the card has the radius shown and hold up two fingers if the card has the diameter shown. When answering the reflection questions, have students take turns saying their answers aloud to a partner, receiving feedback from their partner, and then writing out their response on the Student Journal. Students can make revisions as needed.”

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 “Circles” scope, the “Language Supports” section states, “Provide word walls and anchor charts depicting the words circumference, diameter, radius, and pi. Students may use these to self-monitor as they are responding to questions or talking with partners. Read the questions on the Student Journal aloud as students point to the words being read. Emphasize the terms circumference, radius, and diameter. Emphasize the meaning of the words radius and diameter while the students are exploring the pizza circumference cards. This can be done by modeling how to use the word. For example, say, ‘Yes, this is the radius. This is the diameter. The diameter is two times the radius.’ Students could also associate hand gestures with identifying the radius and diameter. For example, students could hold up one finger if the card has the radius shown and hold up two fingers if the card has the diameter shown. When answering the reflection questions, have students take turns saying their answers aloud to a partner, receiving feedback from their partner, and then writing out their response on the Student Journal. Students can make revisions as needed.”

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 “Real Numbers” scope’s Hook, students use a gardening scenario to investigate square roots and irrational numbers. By comparing square gardens with known and unknown side lengths, students approximate irrational values, connect area and side length, and apply square roots to solve real-world problems.

The Data Science activities in the “Elaborate” section of each scope provide practice opportunities that require students to demonstrate their understanding of grade-level concepts aligned with the TEKS through analysis, reasoning, and mathematical discussion. The educator facilitates a classroom investigation in which students analyze a visual dataset, identify angle relationships, and explain their reasoning using geometric concepts. For example, in the “Angle Relationships” scope’s Data Science activity, students determine the measures of labeled angles by applying relationships involving alternate interior angles, same-side interior angles, supplementary angles, exterior angles of triangles, and the triangle sum theorem. Students also justify why specific triangles are similar by citing shared angle measures and applying the angle-angle similarity criterion. The activity begins with open-ended questions that prompt students to interpret the dataset, identify patterns, classify angle relationships, and generate questions about the data before solving problems. The materials then extend student thinking through optional follow-up activities that require students to apply and explain their understanding in context. These practice opportunities engage students in analyzing, justifying, and applying geometric relationships while demonstrating conceptual understanding of grade-level content.

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 “Transformations” scope, students begin the unit in explore 1 by working with similarity within shapes. These skills are developed throughout the unit, culminating in explore 6, in which students explore the effects of transformations in a variety of contexts.

The Show What You Know 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 “Predictions with Probability” scope’s Show What You Know activity, the materials sequence questions and tasks so that students build from foundational probability concepts to more complex applications that require reasoning and problem-solving. In the first activity, students calculate theoretical and experimental probabilities, compare experimental results, and use these values to predict future outcomes. Students determine the theoretical probability of a coin landing on tails, calculate expected outcomes for 300 coin flips, determine experimental probability from collected data, and use those results to predict future frequencies. The materials then extend learning by requiring students to apply probability concepts in both qualitative and quantitative contexts. Students analyze a real-world scenario involving flower selections to determine the likelihood of selecting a rose or a tulip, justify reasoning, and then use percent data from customer purchases to create and solve a proportion to predict the number of Mother’s Day arrangements sold. This progression moves students from calculating probabilities and making predictions to explaining reasoning, modeling situations, and applying probability concepts to authentic contexts, which increases in both rigor and complexity and supports grade-level proficiency.

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

The Grade 7 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 7 Advanced STEMscopes Math is intentionally sequenced to build on students’ prior knowledge while extending their understanding of mathematical relationships, representations, and real-world applications. The progression emphasizes connections across number systems, algebraic reasoning, proportional thinking, geometry, and statistics to support a cohesive and rigorous mathematical experience that prepares students for increasingly abstract concepts in future mathematics courses.”

The Grade 7 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 show 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 “Similar Figures” scope, the Accessing Prior Knowledge activity has students complete a Two Truths and a Lie game to identify correct and incorrect mathematical statements, discuss their reasoning with peers, and explain their choices. The activity assesses prior knowledge and uncovers misconceptions about using proportions to solve for missing values in proportional relationships before beginning the lesson.

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 7.

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 “Volume” scope, the materials demonstrate coherence across grade levels by explicitly connecting students’ prior learning about area and volume to the current study of cylinders, cones, and spheres while also preparing students for future geometric concepts. The materials reference students’ earlier work determining the area of two-dimensional figures, finding the volume of rectangular prisms, and exploring relationships between prisms and pyramids in grade 7. The scope then explains how this learning extends into future mathematics, in which students analyze composite solids and investigate how changes in linear dimensions affect volume. These intentional connections help students understand how current concepts build on previous knowledge and support future 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 “Real Numbers” scope, the materials demonstrate lesson-level coherence through intentional connections between students’ prior knowledge of number sets, decimals, fractions, and integers, and new learning about the classification of real numbers. The lesson activates students’ existing understanding through discussion and guiding questions and then uses a Venn diagram to help students build connections among natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. Throughout the lesson, students apply previously learned concepts to classify numbers, justify their reasoning, and recognize the hierarchical relationships among number sets. Reflection questions, collaborative discussions, and instructional supports reinforce these connections and enable students to extend prior mathematical knowledge to develop a deeper understanding of real number classification.

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 “Equations and Inequalities” scope, the materials direct educators to help students connect defining a variable to creating an equation and explain how identifying an unknown quantity supports understanding of the scenario and corresponding equation. The materials also guide educators to review the order of operations when students need additional support so that students can understand which operations must be undone when solving equations. In addition, the materials encourage educators to use equation mats and model scales to reinforce students’ prior understanding of equality and balanced equations and to isolate variables. The materials further connect previously learned skills by having students check solutions by substituting into the original equation and by translating word-problem situations into algebraic expressions through step-by-step modeling. These instructional supports intentionally link established concepts and procedures to new learning, which helps students develop a coherent understanding of increasingly complex equation-solving processes.

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 “Real Numbers” scope, the materials provide multiple opportunities for students to retrieve and apply previously learned skills throughout the lesson. Students recall prior knowledge of whole numbers, integers, fractions, decimals, and number sets as they classify real numbers using a Venn diagram and justify their reasoning. The lesson reinforces previously learned concepts through guiding questions, collaborative classification tasks, reflection prompts, and an exit ticket, which allows students to repeatedly revisit and strengthen their understanding of number classifications while integrating new learning about rational and irrational numbers.

The materials provide spaced retrieval opportunities by revisiting previously learned skills and concepts related to proportional reasoning, rates, unit rates, graph interpretation, and the identification of independent and dependent variables through multiple Foundation Builder activities in the “Proportional and Non-Proportional Relationships” scope. Students first retrieve prior learning by analyzing real-world proportional situations involving constant rates, such as miles traveled per hour, books purchased per week, recipes made, and marathon pacing. Students then apply these concepts repeatedly across different representations, including verbal scenarios, graphs, and relationships among variables. The materials require students to identify independent and dependent variables, interpret proportional relationships from contextual situations, and determine values within those relationships before engaging in the unit’s grade-level learning. By revisiting foundational concepts through multiple examples and representations throughout the lesson sequence, the materials reinforce prior learning while preparing students for deeper work with proportional and non-proportional relationships.

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 within 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 the use 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 “Proportional and Non-Proportional Relationships” scope, students repeatedly analyze, compare, and apply concepts—such as unit rate, slope, constant of proportionality, y-intercept, tables, graphs, equations, and real-world situations—rather than practicing each skill in isolation. For example, students determine the y-intercept from a table, calculate the unit rate, and use both values to write an equation in slope-intercept form. Later, students apply the same concepts to graphs, tables, equations, and contextual scenarios involving proportional and non-proportional relationships.

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 1 in the “Represent and Interpret Data” scope engages students in tasks that require students to interpret, analyze, and evaluate multiple representations of three-dimensional figures, including nets and constructed models. Students must make connections between two-dimensional nets and three-dimensional figures, identify and justify attributes (faces, edges, and vertices), and explain their reasoning, thereby demonstrating a deep understanding of how models represent mathematical concepts.

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 allows students to use problem-solving methods, such as interpreting, analyzing, and evaluating solutions. For example, in the “Angle Relationships” scope, the “Skill Review and Practice Review” section allows students to interpret and analyze geometric diagrams and angle relationships, including exterior angles, transversals, and triangle similarity. Students evaluate relationships between multiple representations—such as diagrams, angle measures, and equations—and justify their reasoning when solving for unknown values or determining similarity, which demonstrates higher-level thinking 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 “Explore 1: Add and Subtract Rational Numbers, Show What You Know,” students use a horizontal number line and a real-world hiking scenario to model and analyze positive and negative fractions, decimals, and integers. In the Student Journal, students interpret a table of seven sequential elevation changes, beginning at an elevation of 0, and use a number line to determine each new elevation by applying the given positive and negative rational number changes. Students analyze how each elevation change affects the next segment, record and justify their work, evaluate whether the final elevation equals the total distance hiked, and explain their reasoning. Reflection questions further require students to compare addition and subtraction of rational numbers and analyze how students determined whether elevation increased or decreased during each segment. Educator facilitation supports these tasks through DOK-aligned questions that prompt students to interpret negative elevation changes, determine appropriate operations, and connect fractions and decimals before solving. Together, these opportunities require students to interpret, analyze, and evaluate mathematical representations and connect symbolic equations, number line models, and real-world contexts to develop conceptual understanding of rational number operations.

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 “Transformations” scope’s Mathematical Modeling Task, students model the airplane’s movement by graphing the translated image of a triangle, writing the corresponding translation rule in algebraic notation, and explaining how the image relates to the preimage. Students further analyze the properties of translations by explaining why orientation and congruence are preserved and by comparing translations with dilations. These tasks require students to use graphical and algebraic models to represent and explain a meaningful real-world scenario rather than simply perform a transformation procedurally.

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 “Volume” scope, the Choice Board provides students opportunities to create mathematical models that represent real-world situations involving volume. Students determine the dimensions of three-dimensional solids, construct physical and mathematical models with equivalent volumes, apply volume formulas to compare and analyze objects, and use these models to make decisions in authentic contexts, such as selecting containers and evaluating financial scenarios. These tasks require students to develop and apply mathematical representations to solve meaningful, real-world problems.

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 “Transformations” scope, the Mathematical Modeling Task provides students opportunities to apply their conceptual understanding of geometric transformations in a new, real-world context. Students transfer their knowledge of translations to model an airplane’s flight path by graphing the translated image, writing the translation rule in algebraic notation, and analyzing the relationship between the preimage and image. They extend their conceptual understanding by justifying why translations preserve orientation and congruence and by comparing the effects of a translation and a dilation, which demonstrates their ability to apply geometric concepts to solve and explain an authentic 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 “Volume” scope, the Choice Board provides students opportunities to apply their conceptual understanding of volume to new, meaningful contexts. Students use volume formulas to compare three-dimensional solids; determine equivalent volumes; analyze real-world objects, such as food containers; and apply geometric reasoning to financial, artistic, and career-related scenarios. These activities require students to transfer their understanding of volume to solve authentic problems and make informed decisions across a variety of contexts.

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 requiring students to repeatedly identify, classify, and justify angle relationships. The Two Truths and a Lie game in the “Engage” section of the “Angle Relationships” scope has students analyze multiple statements about complementary and adjacent angles, determine which statements are true or false, and explain their reasoning. This repeated retrieval and application of angle vocabulary and relationships helps students develop fluency with recognizing angle relationships and evaluating geometric claims. For example, students must determine that angles Y and Z are complementary because their measures sum to 90° (25° + 65°), identify that angles U and X are adjacent angles, and evaluate the false statement that angles U and V are complementary because their measures sum to 180°, which makes the angles supplementary rather than complementary. By repeatedly analyzing angle measures, classifying relationships, and justifying conclusions, students strengthen the automaticity needed for more complex geometry tasks involving angle relationships and geometric 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 opportunities to practice efficient, flexible, and accurate mathematical procedures by applying dilations on the coordinate plane. Students repeatedly apply scale factors to transform coordinates, use dilation rules with a variety of scale factors, and accurately calculate the resulting image coordinates. The sequence of tasks reinforces procedural fluency by requiring students to apply the same mathematical process across multiple figures and connects coordinate geometry, similarity, and proportional reasoning to a meaningful real-world context.

The materials provide opportunities for students to practice applying efficient, flexible, and accurate mathematical procedures in each Explore of every scope. For example, in explore 3 of the “Equations and Inequalities” scope, students write, model, and solve equations. Students analyze a real-world scenario, draw a model to represent the situation, explain how to solve the multistep equation, solve the equation, and show the algebraic steps. Students answer questions, including , “What do you notice about the steps using algebra tiles and the steps to solving the equation algebraically?” Later in the lesson, students choose a method to solve more complex multistep equations that have larger coefficients, fractions, and decimals. The materials prompt students to answer questions, such as, “When might you solve algebraically rather than using algebra tiles?” This activity allows students to practice applying efficient and flexible problem-solving strategies to complex equations.

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 “Rational Number Operations” scope, the Would You Rather activity provides students opportunities to evaluate mathematical procedures and solutions for efficiency, flexibility, and accuracy. Students write and compare equations representing two spending scenarios, analyze the resulting amounts of money remaining, and use mathematical evidence to justify which option students would choose. By comparing different solution paths, evaluating the accuracy of their calculations, and defending their reasoning, students engage in evaluating mathematical processes and solutions rather than simply computing an answer.

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 – Rate of Change and Slope” activity engages students in a partner-based Fix the Mistake activity in which students analyze provided solutions related to proportional and non-proportional relationships to determine whether the given slope and y-intercept values are correct. Students evaluate representations that include situations, tables, and graphs presented individually or in combination and determine whether the reasoning used to identify rate of change and initial value is accurate. When errors are identified, students determine where the mistake occurs in the process and compute the correct slope, y-intercept, or ratio based on the given information. Students also evaluate relationships between slopes of triangles on coordinate plane graphs to determine whether provided ratios are correct and correct the misrepresented relationship when necessary. Students record their evaluations on a student recording sheet and verify their responses using an answer key after completing all cards, which provides repeated opportunities to analyze and correct mathematical reasoning with a focus on accuracy in proportional relationships.

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

The Content Supports document 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 “Real Numbers” scope’s explore 1 activity, the lesson provides scaffolded guiding questions, a Venn diagram to illustrate relationships among number sets, collaborative card-sorting tasks, educator explanation cards to validate reasoning, and structured opportunities for students to compare and refine classification strategies. Embedded instructional supports address common misconceptions, recommend concrete models and visual representations, and include targeted differentiation, language supports, and discussion routines that help students progress from recognizing number classifications to efficiently and accurately applying the hierarchical relationships among real numbers.

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 “Equations and Inequalities” 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 equations and inequalities. 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 emphasize 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 “Circles” scope, the “Dissecting the Standard” section separates the TEKS into individual expectations by distinguishing conceptual understandings, such as describing π as the ratio of a circle’s circumference to its diameter, and connecting models to formulas from procedural expectations, such as determining the circumference and area of circles. The “Implications for Instruction” section further explains how instruction should progress from conceptual understanding to procedural application by emphasizing that students first develop an understanding of π through ratios and models before solving real-world problems involving circumference and area. For example, the materials state that students should use models to determine the approximate formulas for circumference and area, connect those models to the actual formulas, and solve contextual problems requiring students to determine the circumference, area, radius, or diameter using either exact values with π or approximations with 3.14 or 22/7. The “Vertical Alignment” section reinforces this progression by showing how prior work with ratios, area, and geometric formulas prepares students for grade-level circle concepts and supports future geometry standards involving circles.

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 to support conceptual understanding. For example, in the “Area and Surface Area” scope’s explore 2 activity, students physically construct three-dimensional figures from nets using pattern cards and manipulatives (concrete); analyze and match visual models and diagrams of nets and figures (pictorial); and record attributes, classify figures, and describe relationships using mathematical language (abstract). This intentional progression across representations aligns with the TEKS and supports students in making connections between models and symbolic reasoning.

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 “Pythagorean Theorem” scope’s “Skill Review and Practice Review” section, students use visual models, such as squares on triangle sides and diagrams of right triangles (pictorial), to represent relationships and apply the Pythagorean theorem using equations and numerical reasoning (abstract). This progression supports students in connecting representations and applying mathematical concepts as required by 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 solve equations and inequalities symbolically, write equations and inequalities from real-world contexts, graph solutions on a number line, and interpret algebra tile balance models. These tasks intentionally move students between concrete models, pictorial representations, and abstract representations to develop conceptual understanding alongside 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 “Area and Surface Area” scope, the explore 2 activity provides opportunities for students to build and manipulate nets to create three-dimensional figures, anal
yze how two-dimensional shapes form each face, and define and explain attributes, such as faces, edges, and vertices, using precise mathematical language. This progression helps students connect hands-on models and visual representations to abstract concepts and generalizations 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 for each scope, which help students connect, create, define, and explain representational models before transitioning to abstract mathematical concepts. For example, in the “Equations and Inequalities” scope, the Review begins with algebra tiles and an inequality mat to model two-step inequalities and then guides students to represent the same relationships symbolically, solve the inequality algebraically, write a solution statement, and graph the solution set on a number line. Students then transition from procedural models to symbolic algorithms through step-by-step explanations for solving equations with variables on both sides and equations with rational coefficients, and each procedure is connected to worked examples and mathematical justification. Additional tasks require students to move among real-world scenarios, symbolic equations and inequalities, algebra tile models, number line graphs, and written explanations, which reinforces the relationships among representations. Students also create real-world scenarios from symbolic inequalities and explain how variables, coefficients, constants, and comparison symbols relate to contextual situations, which supports the progression from representational models to abstract mathematical reasoning.

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 “Equations and Inequalities” scope, the Content Support materials use algebra tiles and number lines to help students solve equations and inequalities.

The Explore activities for each scope provide multiple opportunities for students to develop academic mathematical language through visuals, manipulatives, and structured activities. The materials reinforce students’ 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 “Real Numbers” scope’s explore 1 activity, students use a Venn diagram graphic organizer to help them classify real numbers.

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 “Circles” scope, a key vocabulary term is circumference. The materials provide the definition, “The distance around a circle.” The Picture Vocabulary pairs this definition with a visual of a circle, highlighting the circumference with a dotted line and arrow. 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 “Real Numbers” scope, the Teacher Directions for explore 1 include Math Chat questions, such as “How does the number of decimal places in a terminating decimal relate to its rationality or irrationality?” “Give an example of a terminating decimal. How would you determine whether it is rational or irrational?” and “How would you classify the sum of a rational and irrational number?”

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 “Real Numbers” scope’s Teacher Directions for explore 1, educators introduce and reinforce key mathematical vocabulary by using and discussing terms, such as real numbers, rational numbers, irrational numbers, integers, whole numbers, natural numbers, subsets, and Venn diagrams, and guide students to analyze the relationships among these classifications. Students work collaboratively to match classification names, definitions, and examples; justify their reasoning using the Venn diagram; and share their answers, justify their choices, ask each other questions, and make connections between classifications. Throughout the lesson, the materials provide educators numerous discussion prompts accompanied by exemplar responses that model precise mathematical language, such as explaining why “0.5 is rational because it can be written as a fraction” or why “the sum of a rational and irrational number would be irrational because you cannot write that sum as a fraction.” The lesson further strengthens mathematical discourse through a Math Chat, a structured conversation routine, and the language support activity “Convince Your Friend,” which provides sentence stems (e.g., “I know _____ is a rational number because . . .”) that allow students to hear, refine, and consistently use precise mathematical language while defending and revising their reasoning with peers over time.

The materials include embedded educator guidance to support students’ development and use of academic mathematical language through vocabulary, syntax, and discourse in the “Language Connections” section for each scope. For example, in the “Rational Number Operations” scope’s “Language Connections” section, the materials provide students tiered supports by proficiency level (beginner, intermediate, advanced), including vocabulary cards, picture vocabulary, and manipulatives, such as number lines, fraction circles, and place value models, to connect mathematical representations to language. Students use structured sentence frames, such as “Dog food will be _____ per bag” and “She will need to _____ the bags per month by the _____ months in a year,” to support mathematical syntax and to explain their reasoning. The Teacher Directions guide students to engage in partner and group discussions through echo reading, choral reading, and structured turn-taking routines, which ensures that students interact with mathematical language across listening, speaking, reading, and writing domains. The materials also prompt students to justify their thinking using visual models and real-world contexts through the final reflection page of the handout.

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

The Grade 7 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 weave the process standards into how students learn and demonstrate mathematical understanding.

The materials appropriately integrate the TEKS process standards throughout the “Ratios, Rates, and Percents” scope’s Mathematical Modeling Task in the “Evaluate” section by engaging students in an authentic decision-making scenario that requires proportional reasoning, percent calculations, and financial analysis. Students apply mathematics to everyday situations by determining the best purchasing option for a truck and accessories in a fixed budget. Students use a problem-solving model to analyze constraints, select strategies, perform multistep calculations involving discounts, rebates, taxes, and fees, and justify their final recommendation. Students select and use mathematical tools and representations to organize information from tables, compare purchasing scenarios, and record calculations. The task requires students to communicate mathematical ideas and create representations to organize and communicate mathematical thinking by showing their work and providing written justifications. Students analyze mathematical relationships by comparing how percentages, rebates, and fixed costs affect the total purchase price. Finally, students display, explain, and justify mathematical ideas using precise mathematical language when defending their purchasing decision. Educator guidance reinforces these process standards by encouraging the use of guiding questions rather than procedural directions, facilitating discussions of multiple solution methods, promoting mathematical justifications, incorporating structured mathematical conversations, and using rubrics to evaluate students’ 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 7 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 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 includes 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 to 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 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) within 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, which ensures 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 within daily instruction and student tasks.

The materials include a description for the unit of how the materials incorporate and connect the TEKS process standards throughout the unit. For example, the “Scope Overview” section for “Rational Number Operations” unit describes a coherent progression of learning across the entire scope and shows how students continuously apply the mathematical process standards through the engage, explore, explain, elaborate, evaluate, intervention, and acceleration components. The “Progression of Learning” organizes the essential learning pathway across multiple Explore lessons that develop adding, subtracting, multiplying, dividing, and mixed operations with rational numbers, while the “Additional Scope Resources” include Anchor Charts, Picture Vocabulary, Interactive Vocabulary, interactive notebooks, Language Connections, and six Show What You Know activities that reinforce mathematical communication and conceptual understanding throughout the unit. The “Scope Overview” also connects the process standards to ongoing fluency practice, interactive practice, PhET investigations, intervention resources, and multiple evaluation tools—including standards-based assessments, Skills Quizzes, Mathematical Modeling Tasks, technology-enhanced questions, and Heat Maps—which demonstrates how students apply problem-solving, reasoning, communication, and mathematical modeling throughout the entire unit rather than in a single lesson.

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

The Grade 7 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 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 “Rational Number Operations” scope’s explore 2 lesson explicitly identifies mathematical process standards (A, B, C, D, and G). The lesson integrates the process standards throughout instruction as students use number lines to multiply and divide positive and negative rational numbers in real-world contexts, such as scaling recipe batches in a school cafeteria and representing losses due to spills or errors. The lesson overview shows 7AM.1B embedded in a structured problem-solving model in which students analyze information from scenario cards, select strategies using number lines, determine solutions to multiplication and division of rational numbers, and justify whether answers are reasonable through estimation and comparison of expected values. Students engage in 7AM.1C and 7AM.1D when they use horizontal number lines, manipulatives, and symbolic reasoning to represent operations, analyze the effect of multiplying and dividing fractions, decimals, and integers, and communicate mathematical reasoning through guided discussion and Math Chat prompts. The lesson incorporates 7AM.1A through authentic, real-world contexts involving food preparation and workplace scenarios. At the same time, the lesson reinforces 7AM.1G as students explain and justify their reasoning using precise mathematical language during structured conversations and DoK Level 1 through DoK Level 3 questioning. Across the lesson, students continuously apply process standards through educator-guided facilitation, partner collaboration, and post-explore reflection activities, which demonstrates how the TEKS process standards are intentionally embedded at the lesson level.

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, supporting 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 “Transformations” scope’s Data Science activity, students analyze a coordinate-plane mural by identifying patterns, discussing scale factors and similarity, and applying dilations to determine the new coordinates of sea animals using multiple scale factors, such as (x,y)→(3x,3y), (2x,2y), and (0.75x,0.75y). This activity requires students to make sense of mathematical relationships, reason through coordinate transformations, justify their calculations, and persevere as they solve authentic, open-ended problems in context.

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 “Mean Absolute Deviation and Random Samples” scope’s “Mathematical Modeling Task: History Test” presents students data from a random sample of students’ history test and final exam scores and requires students to calculate the mean absolute deviation, determine whether the students in the activity made academic progress, and justify their conclusions using mathematical evidence. Students extend their reasoning by analyzing whether increasing every value in a dataset by a constant changes the mean absolute deviation, which requires students to apply conceptual understanding rather than procedural computation. The accompanying educator guidance encourages productive struggle by directing educators to use guiding questions instead of telling students what steps to take, facilitating discussions of multiple solution strategies, and providing 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 within 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 the “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 “Transformations” scope’s Mathematical Modeling Task, students graph the translated image of Triangle DEF, write the translation rule in algebraic notation (x,y)→(x+a,y+b), compare the preimage and image, and justify why a translation preserves orientation and congruence but a dilation with a scale factor of two does not. Because students explain and defend their reasoning using graphical, algebraic, and written representations, the activity reinforces that mathematical ideas can be represented and justified in multiple valid ways.

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 “Proportional and Non-Proportional Relationships” scope, “Show What You Know: Represent Proportional Relationships” requires students to represent the same proportional relationship in multiple forms, including tables, ratios, unit rates, and equations. Students complete missing values in proportional tables, determine and simplify ratios, explain the meaning of ratios and unit rates in the context of concert ticket prices, and develop an equation that represents each situation. The task extends these opportunities by having students compare online and box office ticket pricing scenarios, which requires students to apply the same mathematical concepts across different contexts and interpret each representation. These opportunities support students in making connections among multiple mathematical representations, explaining the meaning of each representation in context, and recognizing that proportional relationships can be represented and analyzed in more than one valid way.

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 their 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 “Transformations” scope’s Data Science activity, students solve coordinate-plane problems by calculating new coordinates for multiple sea animals using different scale factors, write their mathematical solutions, and discuss questions about scale factor, similarity, and the relationships between figures. The activity also begins with open-ended observation questions and includes a review of dilations, which provides multiple opportunities for 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 the “Rational Number Operations” scope’s “Explore 2: Multiply and Divide Rational Numbers” activity, students work collaboratively in pairs to solve real-world problems involving multiplication and division of positive and negative rational numbers using cooking challenge scenario cards, horizontal number lines, and the Student Journal. Students use number lines and written representations to model and solve problems, such as determining how many ingredients are needed when scaling recipes for different numbers of servings and representing losses caused by cooking mistakes using negative numbers. Students write about their mathematical thinking by recording solutions and strategies in the Student Journals and responding to reflection questions that require students to explain relationships among rational number operations, such as how multiplying by whole numbers differs from multiplying by fractions or decimals and how the factors in a multiplication problem affect whether the product is greater than or less than the original number. Students discuss mathematics with peers by sharing strategies, asking questions, making connections, and comparing approaches during the Math Chat, in which they explain how they determine whether solutions are reasonable and how multiplying or dividing by rational numbers can change the meaning of a situation, not just the answer.

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 them 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; and 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 within the Teacher Guide for each scope. For example, in the “Real Numbers” 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 the concept of categories and subsets is confusing for students, generate a Venn Diagram that represents different categories at your school,” and lists possible categories and phrasing to use with students. This targeted guidance provides educators a concrete visual model and exact phrasing to actively clarify student misconceptions during the lesson.