STEMscopes Texas Grade 8 Advanced Math, Algebra I

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

The Grade 8 Advanced Scope and Sequence clearly outlines the progression of concepts across the course, beginning with properties of numbers and ending with solving quadratics. 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 8 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 “Solve Equations” scope covers the standards 8AM.5.A and 8AM.12.F, connects with the standard 8AM.12.C, and connects with two major mathematical topics: linear functions, equations, and inequalities; and number and algebraic methods.

The Texas Math ELPS Alignment—Grade 8 in the “Essentials, Additional Texas Alignment” section outlines each scope and explores activities for both the 2007 and 2025 ELPS. For example, in the “Pairs of Linear Equations” scope, educators see that explore 1 aligns with the 2025 ELPS 1.CE 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 “Linear Functions and Models” scope, educators read about previous grade 7 student work on slope-intercept form and how this scope will expand on that knowledge and introduce function notation for the first time.

The Grade 8 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 8 Advanced STEMscopes Math is intentionally sequenced to deepen students’ understanding of functions, algebraic reasoning, and mathematical modeling while strengthening mathematical connections across multiple representations. The progression emphasizes moving from linear relationships to nonlinear and exponential relationships, culminating in a strong foundation for high school mathematics.”

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

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

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

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

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

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

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

The materials include a Content Support document for each scope that provides a comprehensive unit overview, including background knowledge, prior learning connections, and common misconceptions to support educators’ understanding of the content. The document also clearly defines key academic vocabulary and concepts that students will encounter, which ensures that educators are prepared to effectively introduce and develop the language and ideas within the unit. For example, in the scope “Linear Functions and Models,” educators read about previous grade 7 student work on slope-intercept form and how this scope will expand on that knowledge and introduce function notation 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 “Properties of Functions” scope, the take-home letter states, “In math class, your student is about to explore properties of functions. To master this skill, they will build on their knowledge of different representations, graphs and tables, to determine if a relationship is a function.” The letter is then followed by several examples and non-examples of functions, examples of how to find the domain and range of a given function, and a vocabulary section with definitions of new academic terms that are 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 “Properties of Functions” scope’s take-home letter, the “Math Outside the Classroom!” section begins by stating, “Functions are used all around our everyday lives. Chat about where you use functions in everyday life. Here are a few examples.” The letter then gives multiple examples of how functions are used in the real world and ideas of where to look for more functions.

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, 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 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 implement practice appropriately.

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 “Factors of Polynomials” scope, if a student is scoring in the 80–100 percentile mastery range for the standard 8.AM.10.D, the guide recommends that the student work on the Would You Rather activity and the Choice Board in the “Acceleration” section of the scope.

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

Each scope provides a Suggested Scope Calendar that includes a comprehensive range of instructional assessments at both the lesson and unit levels, such as diagnostic tools (e.g., Accessing Prior Knowledge), ongoing formative checks (e.g., exit tickets, Observation Checklists, Show What You Know activities), and summative measures (e.g., Skills Quizzes, standards-based assessments, 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 “Solve Equations” 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 within 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 “What Street is That?” 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 “Factors of Polynomials” scope, if a student is scoring in the 0–25 percentile (previous grade-level remediation) range, recommendations include the student working on the skill review and practice, the Fluency Builder activities, the Interactive Practice activity, the Guided Notes, and specific Skills Quiz questions. Additionally, each performance assessment, such as the Mathematical Modeling Task, 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, connecting each assessment item to specific TEKS and categorizing 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. It includes 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 “Bivariate Data” scope, an instructional support states, “If students need additional support in creating lines of best fit, show them several examples of lines that do not do a good job of modeling the data. Ask them to articulate why those models are less successful at fitting the data.”

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, visually identifying strengths and areas for growth through color-coded performance indicators (e.g., correct responses and error types). It 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 based on 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 “Factors of Polynomials” 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 Fluency Builder activity, the unit’s interactive skill review, 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 “Bivariate Data” scope, the “Instructional Supports” section states, “As students identify points on the scatterplot, encourage them to say aloud what the x- and y-coordinates each represent so the point has meaning within the context.”

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, educators are directed 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 “Quadratic Extensions” scope, the “Language Supports” section states, “Encourage students to notice and circle the verbs in the questions that let them know what to do, such as describe, graph, write, draw, etc.”

In the Teacher Directions of Explore lessons, the materials provide questions that allow students to access the task by discussing the scenario’s context. These directions allow educators to pre-teach necessary vocabulary and concepts. For example, in the “Bivariate Data” scope, task access questions include “Describe what you think is meant by the term outlier” and “Would an outlier be a good representation of the relationship between the variables? Explain.”

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 “Factors of Polynomials” scope, the materials recommend that students who are scoring in the 50 to 80 percentile mastery range work on the Picture Vocabulary, the Interactive Vocabulary, the Interactive Notebook, one of the Interactive Practice activities, the Data Science activity, 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 in 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 “Personal Financial Literacy” scope, the “Instructional Supports” section includes several guiding points for lesson instruction, such as “Students may need support with calculating percent values greater than 100. To help them with the process, ask them questions such as: (1) What is 120 as a fraction? (2) What would that represent in relation to the total budget? If students need additional support in setting up the solution process correctly, emphasize the use of visual models to help such students understand.”

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 “Arithmetic and Geometric Sequences” scope, the materials support educators in modeling and explaining recursive and explicit equations for arithmetic and geometric sequences. The lesson directs educators to introduce the concepts through real-world gardening scenarios and guide students as they analyze patterns, identify common differences and constant ratios, and construct equations. For example, educators ask questions, such as, “What does a common difference or constant ratio tell you about a set of data?” and “How can you use the completed data tables to create an explicit equation?” to model the reasoning required to move from patterns to equations. The materials also include sample explanations that help educators clarify key concepts, including the fact that recursive equations require the value of the previous term, whereas explicit equations do not. During the Math Chat, educators facilitate discussions using questions, such as “How can you use a recursive equation to create an explicit equation?” and guide students toward identifying the first term, common difference or ratio, and sequence type when constructing formulas.

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 in the Explore lessons guide effective lesson delivery using a variety of instructional approaches. The “Instructional Supports” section in the Teacher Directions offers additional options for educators to effectively meet the needs of their diverse classrooms. For example, in the “Instructional Supports” section of the “Quadratic Extensions” scope, the materials state, “If students need additional support with performing multiple transformations on a quadratic function, it may be helpful for them to create multiple graphs to show the steps of each successive transformation that they perform. To help students check that their equations for a transformed graph are correct, encourage them to substitute points from the graph into their equations.”

The “Procedure and Facilitation Points” section in the Teacher Directions of 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 “Linear Functions and Models” scope, the lesson launches with an authentic scenario in which students analyze body measurements and cartoon proportions, which helps educators connect linear regression and lines of best fit to meaningful contexts. Educators facilitate hands-on data collection by having students measure heights and wingspans, record class data, create scatterplots, and analyze patterns before formalizing the concept of a line of best fit. The materials support inquiry-based instruction by embedding DOK-aligned guiding questions that prompt students to predict relationships, identify trends, justify conclusions, and evaluate the reasonableness of linear models. Educators also incorporate technology by modeling how to use the Desmos graphing calculator and other graphing calculators to calculate lines of best fit and correlation coefficients, and the materials provide step-by-step instructions for each process. Throughout the lesson, students work collaboratively with partners to collect data, analyze multiple datasets, discuss correlations, and compare solution strategies. The lesson further strengthens facilitation through Math Chats and structured conversation routines that require students to explain reasoning, critique methods, and debate the accuracy of different approaches for creating linear models.

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 “Systems of Equations” 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 “Bivariate Data” scope, the Teacher Directions state that students should be divided into partners and that educators should explain “to students that they will analyze the scatterplot Absences vs. Test Scores and work with their groups to complete Principal Zed’s report. Monitor and talk with students as needed to check for understanding using the following guiding questions,” which is then followed by a list of DOK-aligned questions for students and sample exemplary responses.

The Suggested Scope Calendar supports multiple practice types: whole group, intervention, and collaborative. For example, in the Suggested Scope Calendar for the “Integer Operations” scope, the “Day 6” 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 “Bivariate Data” scope, the “Language Supports” section states that educators should create “sentence structures for the Student Journal to assist students in writing their responses: I notice _____. The relationship on the scatterplot could be _____ because _____. As students work and discuss ideas with their groups, summarize what you hear, and repeat key ideas and vocabulary you hear with intonation, slower speech, and visual cues: linear, nonlinear, no correlation, positive, negative, outlier, and cluster.”

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 “Bivariate Data” scope, the “Language Supports” section states, “Pair students, and instruct them to take turns explaining their descriptions of the relationships described on the scatterplot. Each time a student explains their work, their partner should rephrase what the student said and add their own thoughts. The following sentence structures can support students in this exchange of ideas: I heard you say _____. Is that correct? I heard you say _____. I agree because _____. I heard you say _____. I disagree because _____. Create sentence structures for the Student Journal to assist students in writing their responses: I notice _____. The relationship on the scatterplot could be _____ because _____. As students work and discuss ideas with their groups, summarize what you hear, and repeat key ideas and vocabulary you hear with intonation, slower speech, and visual cues: linear, nonlinear, no correlation, positive, negative, outlier, and cluster.”

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 “Solve Equations” scope’s Hook, students use a puzzle scenario to explore how to solve equations and verify solutions. The activity connects equation solving to a real-world context while promoting reasoning, discussion, and justification of mathematical thinking.

The Fluency Builder activity in the “Elaborate” section of each scope engages students in collaborative practice that requires them to demonstrate understanding of grade-level concepts aligned with the TEKS. For example, in the “Graphs of Quadratic Functions” scope’s Fluency Builder activity, the educator organizes students into pairs and facilitates a timed game in which students solve problems, explain their thinking, verify answers, and apply multiple quadratic concepts. Students write quadratic functions in standard form and factored form from given zeros; identify x-intercepts, y-intercepts, and vertices from graphs; determine maximum and minimum values; analyze the range of quadratic functions; identify roots of quadratic equations; compare characteristics of multiple functions; and interpret quadratic relationships in real-world contexts, such as projectile motion. Students analyze graphs, tables, equations, and verbal descriptions; connect multiple representations; justify solutions; and check answers with a partner. These practice opportunities engage students in applying concepts of quadratic functions and demonstrating conceptual understanding throughout the activity.

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 “Linear Functions and Models” scope, students begin the unit in explore 1 by identifying key features of functions. These skills are developed throughout the unit, culminating in explore 5, in which students identify and explain correlations and causation among a variety of functions.

The Show What You Know activity in the “Explain” section of each scope provides a progression of questions and tasks that increase in rigor and complexity and supports mastery of grade-level coordinate plane concepts. For example, in the “Inequalities and Systems of Inequalities” scope’s Show What You Know activity, the materials provide a coherent progression of questions and tasks that increase in rigor and complexity while maintaining alignment to the grade-level TEKS for inequalities and systems of inequalities. In the first activity, students demonstrate procedural fluency by solving and graphing one-variable inequalities, including those requiring the distributive property and variables on both sides, as well as real-world applications involving perimeter constraints, with mathematical justification of their solution strategies. Students then extend their understanding to graphing linear inequalities in two variables by writing inequalities from contextual situations, determining reasonable and unreasonable solutions, graphing solution regions, interpreting shading, and verifying solutions using ordered pairs. Next, students analyze graphs to determine intercepts, interpret real-world meanings, write inequalities from graphical representations, compare solution regions, and model situations using inequalities in multiple contexts. Finally, students apply their understanding to systems of inequalities by creating and graphing systems; interpreting feasible regions; evaluating constraints; verifying solutions; analyzing changing conditions; and solving multistep real-world optimization problems involving budgets, transportation limitations, and production constraints. Across the sequence, the tasks progress from procedural solving to graphical analysis, mathematical modeling, interpretation of solution regions, and application of systems of inequalities in increasingly sophisticated contexts, which builds toward 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 8 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 8 Advanced STEMscopes Math is intentionally sequenced to deepen students’ understanding of functions, algebraic reasoning, and mathematical modeling while strengthening mathematical connections across multiple representations. The progression emphasizes moving from linear relationships to nonlinear and exponential relationships, culminating in a strong foundation for high school mathematics.”

The Grade 8 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 “Bivariate Data” scope, the Accessing Prior Knowledge activity has students participate in a Four Corners discussion by selecting the scatterplot that correctly represents the relationship between study time and test scores. Students justify their choices with peers and discuss their reasoning as a class to assess prior knowledge and identify misconceptions about interpreting scatterplots and recognizing positive, negative, and no correlation.

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 8.

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 “Linear Functions and Models” scope, students build on previous experiences constructing linear models, interpreting scatterplots, and analyzing associations between variables. The materials then connect current Algebra I concepts to future Algebra II learning involving quadratic transformations, inverse functions, logarithmic and cube root functions, regression analysis, and statistical significance. These connections help students understand how mathematical concepts develop across courses and support a coherent progression of 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 “Properties of Functions” scope, the materials demonstrate lesson-level coherence that builds on students’ prior knowledge of tables, graphs, ordered pairs, coordinates, and input-output relationships to develop a conceptual understanding of functions. The lesson activates existing knowledge through introductory tasks and guiding questions, then has students apply familiar representations—including tables, graphs, mapping diagrams, and ordered pairs—to determine whether relationships are functions. Instructional supports encourage students to make connections among these representations, and collaborative discussions and reflection questions reinforce the defining characteristic of functions and deepen students’ understanding of how previously learned concepts extend to new mathematical learning.

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 “Solve Equations” scope, the materials recommend reviewing the order of operations and providing a reference sheet or having students create their own reference guides that identify each step and include examples. The materials also prompt educators to encourage students to continue defining variables, reinforcing a strategy students have previously used when solving equations, and extending that practice to more-complex situations involving multiple variables. Additionally, the materials direct educators to help students connect defining a variable with creating an equation so that students can better understand how unknown quantities in real-world situations translate into algebraic representations. The lesson further builds on students’ prior experiences with algebra tiles by encouraging students to label tiles and use those concrete representations to transition to more-abstract equations. These supports intentionally connect previously learned concepts and procedures to new mathematical understanding, which helps students build coherent and connected knowledge in the lesson.

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

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

The Teacher Directions for every Explore activity in each scope provide discussion prompts that activate students’ prior knowledge of preceding concepts as an access point for building new mathematical understanding. For example, in the “Properties of Functions” scope, the materials provide repeated opportunities for students to retrieve and apply previously learned skills related to tables, graphs, ordered pairs, coordinates, and input-output relationships as they develop an understanding of functions. Students revisit these concepts through multiple representations, including tables, graphs, mapping diagrams, and real-world scenarios, and the materials reinforce students’ understanding through guided questioning, collaborative discussions, reflection prompts, and an exit ticket. These recurring opportunities strengthen students’ retention of prior learning and support the development of new concepts about functions and nonfunctions.

The materials provide spaced retrieval opportunities for previously learned skills and concepts across lessons and units by incorporating Foundation Builder activities that require students to recall, represent, and solve equations and inequalities in multiple contexts before engaging in new learning in the “Inequalities and Systems of Inequalities” scope. The Foundation Builder Math Match Cards prompt students to retrieve prior knowledge by matching verbal scenarios to algebraic representations and solutions. For example, students solve one-variable equations represented by real-world situations, such as determining Ben’s age from the equation 2x + x = 30 and finding the cost of a ticket from the equation 2(t + 2) = 30. Students also revisit inequality concepts by interpreting and solving situations modeled by 2x + 6 ≤ 12, x + 683 ≤ 2,500, and 17x − 700 ≥ 1,000. These activities require students to retrieve previously learned procedures for writing, solving, and interpreting equations and inequalities before applying those skills to more-advanced work with inequalities and systems of inequalities, which provides intentional opportunities for spaced review across lessons and units.

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

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

The Daily Numeracy activity in the “Scopes” section provides opportunities for students to revisit previously learned concepts and select and use diverse strategies, which promotes 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 “Properties of Exponents and Radicals” scope, students first review the multiplication and division of exponents and then apply those skills alongside the power rules, rational exponents, radical expressions, square roots, and algebraic simplification. The materials require students to continually retrieve and apply previously learned exponent laws as they learn new concepts, such as using the product and quotient rules in power-of-a-power problems, applying exponent properties to geometric formulas, and connecting rational exponents to radical notation. This interleaving strengthens students’ ability to select appropriate strategies and recognize relationships among concepts rather than relying on isolated procedural practice.

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

The Explore activities in each scope offer a variety of tasks that require students to interpret, analyze, and evaluate models and mathematical representations. For example, explore 2 in the “Quadratic Extensions” scope asks students to interpret and analyze graphical and algebraic representations of quadratic functions and evaluate how transformations affect the graph. Students must connect equations to visual models, justify transformation choices, and compare multiple valid solutions, which demonstrates higher-level reasoning and evaluation of mathematical representations.

The “Skill Review and Practice Review” section in the “Intervention” section of each scope provides opportunities for students to work with different models and representations and allows students to use problem-solving methods, such as interpreting, analyzing, and evaluating solutions. For example, in the “Quadratic Extensions” scope, the “Skill Review and Practice Review” section engages students in tasks that require them to interpret, analyze, and evaluate multiple representations of linear relationships, including graphs, tables, equations, and verbal scenarios. Students must connect these representations to determine slope, write equations, and justify relationships, such as parallel and perpendicular lines, which demonstrates deeper reasoning about how mathematical models represent real-world and abstract situations.

The materials include questions and tasks in the Show What You Know activity of each scope that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. For example, in “Show What You Know—Part 1: Write, Model, and Solve Multistep Equations,” students independently apply their learning from the Explore lesson by interpreting and connecting multiple representations of equations. In the printable files, students match equations to balanced hanger models, write equations from models, create models from equations, analyze and compare two students’ solution strategies to determine which is more efficient, and justify their reasoning. Students also interpret a hanger model to identify the corresponding equation, solve the equation, verify the solution through substitution, and model equations with algebra tiles. Educator directions specify that students complete the activity independently, using manipulatives as needed, and that the task serves as a formative assessment to determine whether additional intervention is needed. These opportunities require students to analyze mathematical representations; evaluate solution methods; verify the reasonableness of solutions; and connect visual models, symbolic equations, and algebraic reasoning to solve multistep equations.

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 “Properties of Functions” scope’s Mathematical Modeling Task, students create mathematical models to represent a real-world business scenario. Students construct a graph of Isaac’s profit as a function of the number of golf balls sold, label axes, determine whether the model should be discrete or continuous, evaluate the function in context, and identify its domain. In Part III, students extend the modeling process by proposing additional data to collect, determining whether it forms a relation or function, identifying the domain, and explaining how the data could be used to make business decisions. These tasks require students to develop, interpret, and apply mathematical models to represent and analyze a realistic situation.

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 “Graphs of Quadratic Functions” scope, the Choice Board provides students opportunities to create mathematical models that represent real-world situations involving quadratic functions. Students develop quadratic models by creating and analyzing real-world scenarios, graphing parabolas, investigating projectile motion, and using the characteristics of quadratic functions to represent and interpret authentic contexts. These tasks require students to construct, apply, and communicate mathematical models to solve meaningful problems and demonstrate their understanding of quadratic relationships.

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 “Properties of Functions” scope, the Mathematical Modeling Task provides students opportunities to apply their conceptual understanding of functions, relations, graphs, and domains to a new, real-world business context. Students analyze and represent Isaac’s golf ball business by determining whether relationships are functions, graphing profit as a function of golf balls sold, interpreting function values in context, identifying whether the domain is discrete or continuous, and proposing additional data that could improve business decisions. These tasks require students to transfer their understanding of function concepts to solve authentic problems, justify their reasoning, and make data-driven recommendations.

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 “Graphs of Quadratic Functions” scope, the Choice Board provides students opportunities to apply their conceptual understanding of quadratic functions in new, meaningful contexts. Students transfer their knowledge of quadratic graphs and their characteristics to authentic situations by modeling a skateboarding jump, investigating the trajectory of a golf ball, creating artwork from parabolas, and connecting quadratic functions to engineering and historical applications. These activities require students to apply their understanding of quadratic relationships beyond routine exercises to solve problems in real-world and interdisciplinary 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 and.

The materials provide tasks designed to build the automaticity and fluency necessary to complete grade-level tasks by engaging students in repeated practice, identifying equivalent representations of linear relationships, and analyzing slope and rate of change. The Match Around the Room activity in the “Engage” section of the “Slope and Rate of Change” scope requires students to repeatedly connect equations in slope-intercept form to corresponding tables of values, which strengthens fluency with recognizing patterns, determining rates of change, and identifying y-intercepts. For example, students match the equation y = 3x + 5 with a table showing a constant increase of 3 in the y-values and an initial value of 5, and students must also distinguish the equation from similar representations with different rates of change and intercepts. This repeated comparison and matching process helps students develop automaticity with key linear function concepts that are foundational for later graphing, writing equations, and analyzing proportional and nonproportional relationships.

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 while solving and interpreting systems of inequalities in a real-world context. Students graph systems of inequalities, identify solution regions, interpret feasible solutions, and apply the model to make decisions about daily nutritional choices. Through repeated use of graphing procedures, inequality notation, and contextual reasoning, students build procedural fluency and apply mathematical concepts accurately to authentic scenarios.

The materials provide opportunities for students to practice applying efficient, flexible, and accurate mathematical procedures in each Explore activity in each scope. For example, in explore 2 of the “Solve Equations” scope, students analyze two strategies for solving a multistep problem. Students answer reflection questions, which ask, “What are the differences between the strategies used to solve?” “Which strategy is more efficient? Explain,” and “How many strategies are there for solving equations? How do you know which strategy is best?” Students then apply this flexible thinking to solve equations and choose the most effective strategy. Finally, students analyze a completed sample problem and identify the strategy used and how it is helpful. 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 within open-ended, discussion-based tasks. Students compare strategies, analyze outcomes, and justify which approach is most effective, which supports evaluation of efficiency, flexibility, and accuracy. For example, in the “Solving Quadratics” scope, the Would You Rather activity provides students opportunities to evaluate mathematical procedures, processes, and solutions for efficiency, flexibility, and accuracy. Students solve two quadratic equations to determine where each soccer kick lands, compare the resulting solutions in the context of the field layout, and evaluate which function provides the most advantageous outcome. Students justify their decision using mathematical evidence, which demonstrates their ability to assess the effectiveness and accuracy of different solution strategies in an authentic real-world scenario.

The materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout the unit. For example, the “Elaborate Fluency Builder – Rate of Change and Slope” engages students in a partner-based Fix the Mistake activity in which students analyze provided solutions involving slope and rate of change to determine whether the work is accurate. Students evaluate worked solutions represented in multiple forms, including graphs, situations, tables, and linear relationships, and determine whether the given slope or y-intercept is correctly identified. When inaccuracies are present, students identify where the error occurs in the reasoning or procedure and correct the solution based on their evaluations. Students also analyze relationships between slopes in graphical representations, including comparisons involving triangles on coordinate planes, to determine the correctness of reasoning. Students record their evaluations on a student recording sheet and verify responses using an answer key after all cards have been analyzed, which provides opportunities to evaluate and correct mathematical procedures and solutions with a focus on accuracy in the lesson.

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

The Content Supports document for each scope includes embedded supports—such as educator guidance, modeled strategies, and scaffolded representations—that help educators direct students toward more-efficient and more-effective problem-solving approaches. The resources provide 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 “Properties of Functions” scope’s explore 1 activity, the lesson includes scaffolded guiding questions, multiple representations (tables, graphs, mapping diagrams, ordered pairs, and written scenarios), collaborative discussions, and structured opportunities for students to compare strategies and justify their reasoning. Embedded instructional supports address common misconceptions, encourage students to transition among representations, and provide differentiation, language supports, and extension activities that help students refine their understanding and apply increasingly efficient and accurate methods for identifying functions.

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 “Slope and Rate of Change” 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 for slope and rate of change. 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,” “Implications for Instruction,” and “Vertical Alignment” sections in the Teacher Toolbox. For example, in the “Properties of Exponents and Radicals” scope, the “Dissecting the Standard” section identifies the procedural expectations by breaking the TEKS into specific skills, such as simplifying numerical and algebraic expressions involving integral and rational exponents and simplifying radical expressions, and by defining the key concepts and vocabulary students must understand, including the laws of exponents, rational exponents, radicals, and square roots. The “Implications for Instruction” section further explains the conceptual progression by stating that students should investigate exponent laws using numerical expressions before transitioning to algebraic expressions to bridge concrete and abstract thinking, recognize patterns in exponent rules, and connect rational exponents to radical notation. For example, the materials explicitly direct educators to have students explore exponent laws with numerical expressions first before applying those same relationships to algebraic expressions, which demonstrates how conceptual understanding supports procedural fluency. The “Vertical Alignment” section reinforces this emphasis by showing how prior learning in operations, exponents, and square roots leads to the grade-level expectations for simplifying radicals and expressions using the laws of exponents.

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, pictorial, and abstract representations throughout the Explore tasks to support conceptual understanding of how to solve equations. For example, in the “Solve Equations” scope’s explore 2 activity, students use algebra tiles to build and manipulate models (concrete), sketch and interpret visual representations of equations (pictorial), and connect these to symbolic equations and step-by-step algebraic procedures (abstract). This intentional progression across representations, supported by educator guidance and multiple solution strategies, aligns with the TEKS and strengthens students’ ability to connect models to 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 “Linear Functions and Models” scope’s “Skill Review and Practice Review” section, students interpret and analyze graphs, tables, and real-world scenarios (pictorial); connect these to equations, slope, and function notation (abstract); and use multiple forms, such as verbal descriptions, tables, and equations, to represent the same relationship. This integration of representations aligns with the TEKS and supports students in making connections across models and symbolic reasoning.

The materials incorporate concrete models, pictorial representations, and abstract representations throughout each scope’s Checkup section to reinforce students’ understanding of the concepts in the unit and the alignment with the TEKS. For example, in the “Solve Equations” scope’s Checkup, students solve symbolic equations, match equations to visual algebra tile models, complete hanger models, analyze balanced models, and verify solutions across multiple representations. For example, one question asks students to match symbolic equations to corresponding algebra tile models, and other questions require students to model equations using a hanger diagram, solve the equation algebraically, and check that the solution balances the model. These tasks intentionally engage students with concrete models (algebra tiles and hanger models), pictorial representations (diagrams and visual models), and abstract representations (symbolic equations), which aligns with the TEKS’s representational expectations.

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 “Solving Equations” scope, the explore 2 activity provides opportunities for students to build and manipulate algebra tiles, sketch visual models, and explain their thinking and justify their solutions using algebraic steps and mathematical language. This progression helps students connect hands-on and visual representations to symbolic procedures, which reinforces a deeper understanding 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” tab for each scope, which help students connect, create, define, and explain representational models before transitioning to abstract mathematical concepts. For example, in the “Slope” scope, the Review begins with visual models, such as similar right triangles on a coordinate plane, and guides students to connect the geometric representation to the abstract slope formula by comparing ratios, writing proportions, and explaining why the slopes are equivalent. Students then connect graphs, tables, and equations to the same mathematical idea, and there are explanations showing how the y-intercept and slope are represented differently across each representation. Throughout the Review, students transition among graphs, tables, ordered pairs, equations, proportions, and symbolic formulas while solving the same concepts, which reinforces the relationship between visual models and abstract procedures. In the “Direct Variation” section, students connect proportional situations, unit rates, equations, and proportions to demonstrate that these methods are equivalent for solving the same problem. These supports consistently help students create, interpret, and explain representational models before applying symbolic and algorithmic procedures.

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

The Content Support document for each scope provides structured opportunities for students to develop academic mathematical language through visuals, manipulatives, and multiple representations. Using the resources, students engage with concrete models (e.g., counters, algebra tiles), pictorial representations (e.g., number lines, graphs), and symbolic notation to build meaning for key concepts and vocabulary. These varied approaches help students make connections between mathematical ideas and the language used to describe them. For example, in the “Slope and Rate of Change” scope, the Content Support document uses graphs and tables as visual representations to help students calculate the slope from different situations.

The Explore activities for each scope provide multiple opportunities for students to develop academic mathematical language through visuals, manipulatives, and structured activities. Students reinforce vocabulary and conceptual understanding through hands-on activities and visual supports. Additionally, structured discussions and reflection questions encourage students to articulate their thinking using precise mathematical language. For example, in the “Properties of Functions” scope, the explore 1 activity asks students to use printed flash cards of different graphs and mappings to determine which relationships are functions and which are not.

The materials provide opportunities for students to develop academic mathematical language using visuals and language development strategies. Each scope has a Picture Vocabulary to introduce and reinforce key academic vocabulary. The materials provide definitions and visuals for each vocabulary word. For example, in the “Properties of Functions” scope, a key vocabulary word is discrete. The materials provide the definition, “Data that cannot contain the real number values between data points; data points are not connected.” The materials pair this definition with a visual of two graphs illustrating discrete data. 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 “Properties of Functions” scope, the Teacher Directions for explore 1 include Math Chat questions, such as “Do functions always have to be number values for their inputs or outputs?” “What is the significance of inputs when determining a function?” and “Which coordinate does the input represent? Which coordinate does the output represent?”

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 materials 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 “Properties of Functions” scope’s Teacher Directions for explore 1, educators consistently reinforce key vocabulary, including functions, nonfunctions, inputs, outputs, tables, mappings, graphs, coordinates, and relationships, and guide students to analyze multiple representations to determine whether a relationship is a function. Students work collaboratively to analyze tables, graphs, mapping diagrams, and written scenarios and discuss the different inputs and outputs and how they can be arranged to make functions, and the materials encourage students to share their strategies, ask each other questions, and make connections among representations. Throughout the lesson, the materials provide educators guiding questions and exemplar responses that model precise mathematical language, such as “If there are no repeating values in the input column, then the table is a function,” “Repeating outputs do not affect whether a relationship is a function,” and “each input has only one output.” The lesson further strengthens mathematical discourse through a Math Chat, a structured conversation routine, and language supports that require students to explain, restate, agree, or disagree using sentence stems, such as “I heard you say _____. I agree because _____” and to restate peers’ explanations using mathematical language, which provides repeated opportunities for students to hear, refine, justify, and consistently use precise mathematical vocabulary with peers over time.

The materials include embedded educator guidance to support the application of appropriate mathematical language, including vocabulary, syntax, and structured mathematical discourse, that enables students to hear, refine, and use math language with peers in the “Language Connections” section for each scope. For example, in the “Solve Equations” scope’s “Language Connections,” students engage in structured listening and speaking routines in which educators explicitly direct mathematical discourse using prompts, such as “Circle the step where we apply the distributive property” and “Put a box around the step where we do the inverse of addition,” which supports students in verbally and visually identifying key mathematical processes. Students use sentence stems, such as “An equation is literal if _____,” “The first step to solve would change because we would need to _____,” and “If we solved for W, our answer would be similar because _____,” to scaffold mathematical syntax and justify reasoning during partner discussions. Educator guidance supports structured discourse through turn-and-talk opportunities, think-pair-share interactions, and guided questioning sequences that prompt students to explain, compare, and refine solution steps across beginner, intermediate, and advanced proficiency levels. The materials further support students in reading and speaking activities through echo reading, choral reading, and partner discussion routines that require students to explain equations, interpret models, and justify responses using academic vocabulary, such as variable, inverse operations, distributive property, and literal equation. Writing supports extend mathematical language development by prompting students to explain solution steps using word banks, paraphrase peer explanations, and construct written justifications using structured academic sentence frames.

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

The Grade 8 Advanced Scope and Sequence shows how the materials intentionally integrate the TEKS process standards throughout the materials, as evidenced by the consistent inclusion of mathematical process standards in each scope. Additionally, the Scope and Sequence demonstrates that process standards are not taught in isolation but are systematically incorporated across all topics and learning experiences.

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

The “Factors of Polynomials” scope’s Mathematical Modeling Task in the “Evaluate” section integrates the TEKS process standards throughout an authentic real-world investigation rather than teaching content in isolation. Students apply mathematics to solve meaningful problems arising from everyday life by determining room dimensions from polynomial area expressions in the context of apartment layouts. They use a problem-solving model to analyze the situation, create and revise mathematical models, account for a support beam, and generalize conditions for square rooms. Students select and apply mathematical tools and representations by drawing area models, writing equations, and comparing visual and symbolic representations. They communicate mathematical ideas using multiple representations through written justifications, diagrams, equations, and generalized conclusions. The task requires students to create and use representations to organize, record, and communicate mathematical ideas by modeling room dimensions and representing changes to the area. Students analyze mathematical relationships to connect and communicate ideas when comparing polynomial factorizations, room dimensions, and area models. Finally, students display, explain, and justify mathematical ideas and arguments using precise mathematical language through written explanations, comparisons, and generalizations. Educator guidance further reinforces these process standards by encouraging the use of guiding questions rather than procedural directions, facilitating discussions of multiple solution strategies, requiring complete written justifications, and incorporating structured mathematical conversations and reflection.

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

The Grade 8 Advanced Scope and Sequence clearly describes how the materials integrate 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 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 TEKS process standards are incorporated and connected 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 into the materials.

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

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

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

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

The materials include a description for each unit of how the TEKS process standards are incorporated and connected throughout the unit. For example, the “Scope Overview” section for the “Solve Equations” unit describes a coherent progression of learning across the unit in which students continuously apply the TEKS process standards through the engage, explore, explain, elaborate, evaluate, intervention, and acceleration components as students move from writing and solving direct variation equations to solving multistep linear equations with variables on both sides and solving literal equations for a specified variable. The “Scope Overview” section and Explore activities emphasize consistent use of a structured problem-solving model in which students analyze real-world contexts (such as camp fees, bank vault combinations, and earnings scenarios), represent relationships using equations and multiple representations, determine solutions using appropriate strategies and tools (including algebra tiles and balanced hanger models), and justify and verify their reasoning through substitution and mathematical discussion. The “Additional Scope Resources,” including Anchor Charts, Interactive Notebooks, Language Connections, and Show What You Know activities, further reinforce the application of process standards by supporting students in communicating mathematical reasoning, using precise vocabulary, and applying representations across multiple forms. At the same time, assessment and intervention components, such as exit tickets, Skills Quizzes, and Mathematical Modeling Tasks, require students to independently apply problem-solving, reasoning, and communication skills throughout the unit.

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

The Grade 8 Advanced Scope and Sequence provides a clear overview of the TEKS process standards in each lesson by consistently including mathematical process standards in every Explore activity and scope. The Scope and Sequence explicitly lists the aligned process standards for each instructional component, which ensures that educators can easily identify how the materials embed these practices in daily instruction. This structure supports planning and reinforces the integration of the TEKS process standards across all lessons.

The Teacher Directions include an overview of the TEKS process standards for each lesson and explicitly list the mathematical process standards at the beginning. This section identifies the specific standards (e.g., problem-solving, use of tools, communication, justification) that will be emphasized during the lesson, which provides educators a clear instructional focus. By consistently presenting this overview in each Explore lesson, the materials ensure that process standards are intentionally incorporated into daily instruction. For example, the “Solve Equations” scope’s explore 2 lesson integrates mathematical process standards into a structured lesson in which students write, model, and solve multistep equations using algebra tiles and other representations while analyzing and comparing solution strategies for efficiency. The lesson explicitly embeds process standards through educator questioning and student discourse, such as using a problem-solving model to analyze given information and justify solutions; selecting tools, including algebra tiles and sketches, to represent equations; and communicating reasoning through structured Math Chats that require students to explain why different strategies (e.g., distributive property, combining like terms, isolating variables) produce equivalent solutions. The materials further support the Explore lesson through instructional supports and instructional decision points that prompt students to evaluate efficiency, verify solutions by substitution, and connect concrete models to abstract symbolic representations, which demonstrates consistent integration of reasoning, modeling, communication, and justification throughout the lesson.

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

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

The Data Science activities in the “Elaborate” section of each scope provide opportunities for students to think mathematically and persevere in problem-solving by engaging them in open-ended tasks that require interpreting data, making inferences, and applying concepts in real-world contexts. Students analyze datasets, consider multiple questions, and justify their conclusions, which supports sense-making and sustained problem solving. For example, in the “Inequalities and Systems of Inequalities” scope’s Data Science activity, students analyze a real-world nutrition dataset by interpreting a system of inequalities, graphing the solution region using solid and dashed boundary lines, and applying the graph to determine food choices that satisfy calorie guidelines for protein and carbohydrates. This activity requires students to make sense of mathematical relationships in context, reason through graphing and interpreting systems of inequalities, justify their solutions, and persevere as they apply mathematics to authentic decision-making scenarios.

The materials provide opportunities for students to think mathematically, persevere in solving problems, and make sense of mathematics through the Mathematical Modeling Tasks in the “Evaluate” section of each scope, which require reasoning, justification, and reflection. For example, the “Properties of Functions” scope’s “Mathematical Modeling Task: Golf Ball Gig” presents students with a multipart real-world scenario in which they analyze relationships, determine whether data represent a relation or a function, construct and interpret a graph of profit as a function, evaluate function values in context, identify an appropriate domain, and propose additional data that could improve a business model. Rather than following a prescribed procedure, students explain their reasoning, justify whether representations should be discrete or continuous, and apply mathematical concepts to new situations. The accompanying educator guidance encourages productive struggle by directing educators to use guiding questions rather than telling students what steps to take, to facilitate discussions of multiple solution strategies, and to have students share and justify their approaches. The Mathematical Modeling Task rubric further reinforces mathematical thinking by evaluating students’ understanding, strategy selection, reasoning, and use of mathematical language, emphasizing that students fully address all parts of the problem, employ appropriate strategies, support their reasoning with evidence, and communicate mathematical ideas clearly.

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

The materials support students in understanding that there are multiple ways to represent and solve problems by intentionally prompting them to compare strategies and discuss different solution paths in the Daily Numeracy activities. Guiding questions, such as “Is there a different strategy we could use?” and structured discussions help students explain and justify their reasoning while recognizing the validity of multiple approaches. For example, in 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 “Properties of Functions” scope’s Mathematical Modeling Task, students analyze a real-world scenario, determine whether the relationship between hours searched and golf balls found is a relation or a function, and explain their reasoning using evidence from the context. Because the task is open-ended and accepts multiple valid justifications, students demonstrate that mathematical ideas can be represented and supported through different reasoning strategies while defending their conclusions.

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 “Factors of Polynomials” scope, “Show What You Know: Factor Polynomials by Grouping” requires students to solve problems using multiple representations and compare different solution methods that produce equivalent results. Students explain how to determine an appropriate way to split the middle term when factoring a trinomial, compare two different groupings of the same polynomial to identify what remains consistent, and determine which student’s rewritten expression is equivalent before completing the factorization. Students also analyze an incorrectly grouped factorization, identify the error, and explain how to revise the work to produce matching factors. The task further reinforces multiple solution pathways by requiring students to factor the same polynomial using both two groups of three terms and three groups of two terms, which demonstrates that different representations and solution strategies produce the same result. These opportunities require students to justify their reasoning, compare approaches, analyze the validity of mathematical representations, and recognize that equivalent methods can be used to solve the same problem.

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 promote 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 “Inequalities and Systems of Inequalities” scope’s Data Science activity, students graph the solution region for a system of inequalities, apply the graph to determine meal choices that satisfy nutritional guidelines, and discuss questions about what the inequalities represent and how to graph the solution set. Students also explain how calorie recommendations may vary across individuals, which requires them to communicate and justify their mathematical reasoning to 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 each scope. For example, in the “Solve Equations Explore 2: Solve Multistep Equations,” students collaborate in groups to analyze real-world situations and create, model, and solve multistep equations representing Diego’s and Andrew’s earnings. Students use algebra tiles and symbolic representations to model equations, explain their reasoning in words, record algebraic steps, and interpret what their solutions mean in the context of the situation. Students write about their mathematical thinking in the Student Journal by analyzing different solution strategies, including comparing Diego’s and Andrew’s methods, identifying the properties used, determining which strategy is more efficient, and justifying their conclusions. Students further reflect on mathematical relationships by explaining how to determine whether an equation is true for all values of x, whether an equation has no solutions, why clearing fractions can be useful, and how to select an appropriate strategy for solving equations. Students discuss mathematics with peers by sharing strategies, asking questions, making connections, and comparing approaches during the Math Chat, in which students explain how different methods can yield the same solution and how to prove a solution is correct.

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. “Gallery Walk” and “Walk, Talk, Decide” provide opportunities for students to analyze classmates’ ideas, discuss problem-solving approaches, defend responses, and address misconceptions. These routines support educators in intentionally facilitating conversations in which students communicate mathematical reasoning, evaluate strategies, and justify their solutions.

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

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

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

The materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions in the Teacher Guide for each scope. For example, in the “Exponential Functions and Models” scope, the Teacher Guide provides in-depth guidance on educator facilitation for each lesson. The guide includes an “Identifying Misconceptions” section that outlines common student errors, which allows educators to anticipate and address them proactively. Additionally, facilitation tips embedded throughout the lesson outline key components, activity strategies, and potential misconceptions. Specifically, a facilitation tip during explore 1 states, “If students need additional support in understanding why some of the exponential functions do not have x-intercepts, have them substitute negative values into each equation and consider why they will never reach 0 or negative values.” This targeted framework equips educators with a precise instructional pivot to guide students past this potential misconception.