STEMscopes Texas Math - Grade 5 Spanish

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

The materials include a scope and sequence that clearly outline the Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and Mathematical Process Standards and a progression of learning showing how concepts build on each other over time. For example, in grade 5, the "Properties of Two-Dimensional Figures" scope begins with exploring symmetry and then moves to classify triangles, lines, and angles. This learning progression supports the teacher's planning of lessons to scaffold instruction and anticipate possible misconceptions. Materials include a year-long scope and sequence of concepts for instruction, showing how and when these concepts occur throughout the course. The materials include a scope and sequence that outlines the specific order of math TEKS and concepts taught throughout the course in the grade 5 curriculum section. The implementation guide for grade 5 includes a chart showing the scope of connections between major mathematical topics throughout the instructional year and the TEKS. The grade 5 "Implementation Guide" includes a comprehensive chart that aligns major mathematical topics with the TEKS throughout the instructional year. Within the "Curriculum Design" section, the "Scopes" tab features a link to the grade 5 "Scope and Sequence" document, which details the order of TEKS to be taught and demonstrates clear alignment to those standards. The grade 5 "Course Rationale," accessible through the "Scopes" tab, provides an overview of the TEKS addressed in the course. This document specifies key concepts, such as "Place Value of Whole Numbers," along with the corresponding TEKS codes (e.g., 5.2A, 5.2B). The "Teacher Toolbox" section offers an "Additional Texas Alignments" link, leading to a document that outlines TEKS alignment for each unit taught during the year, ensuring educators clearly understand the relationship between instructional content and state standards.

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 grade 5 materials include a clearly defined scope and sequence that provides teachers with an exact number of instructional days per lesson and per the Texas Essential Knowledge and Skills (TEKS), ensuring alignment with time allotments throughout the week. This structure supports purposeful instructional planning and pacing across the school year. For instance, the "Scope and Sequence" document assigns nine instructional days to the concept Problem Solve with the Four Operations. A comprehensive year-long pacing guide further supports instructional planning by offering a clear summary of the content standards addressed in each unit, along with the number of days recommended for instruction. The suggested "Scope Calendar" supplements this guide by including aligned planning resources, instructional pacing, opportunities for practice, and built-in assessments for each scope. These tools collectively ensure that teachers can implement the curriculum effectively while maintaining a steady progression through the required content. To support flexibility and adaptability across various instructional settings, the section "Various Instructional Calendar Options" provides guidance on how to adjust pacing for calendars with 165 or 180 instructional days, suggesting that activities may be added or removed as needed. This approach ensures that, while the materials follow a rigorous and structured design, they also accommodate the diverse scheduling needs of districts and campuses.

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.

The materials include a table that illustrates the learning progression. For example, grade 5 begins with a focus on multiplication and division algorithms. The materials explain the progression, outline the purpose of each unit, and clarify how the sequence supports connections to past and future learning. The "Teacher Toolbox" includes a course rationale, which outlines the focus areas of the materials, their sequencing, and their correlation with the TEKS. The grade 5 "Course Implementation Guide Rationale" includes a table depicting the progression within and across the major mathematical topics in grade 5. The "Grade 5 Course Rationale" includes a table outlining the major math topics for the grade level. For example, the information states, "Instructional time will be focused on four areas . . . the areas of focus emphasize the connections among the major mathematical topics throughout the instructional year." The "Grade 5 Course Rationale for Scope Order" explains how concepts will be learned and connected throughout the course. For example, "The Compare and Order Numbers scope builds on the concept of place value by teaching students to compare and sequence multi-digit whole numbers."

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

The grade 5 materials provide guidance to support vocabulary development and concept internalization. In whole-group discussions, students engage in academic conversations using mathematical terms such as producto and módulo. These opportunities encourage students to express reasoning, expand their vocabulary understanding, and apply terms in context. Each scope includes a "Content Support" section with key vocabulary, background knowledge, misconceptions, and process standards. For example, in the "Add and Subtract Fractions" unit, the "Content Support" section explains what students will learn and possible misconceptions. The "Content Unwrapped" section within each scope helps teachers preview unit objectives, vocabulary, and assessments. In the "Multiply Decimals" unit, the "Teacher Guide" includes a TEKS correlation, a lesson progression summary, and guidance for each instructional part. The suggested Scope Calendar supports planning by outlining daily lessons and pacing, ensuring instruction aligns with learning goals and supports mastery.

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

The grade 5 materials provide evidence of structured support for teachers to guide math instruction. In the "Curriculum Design" section, the "Implementation Guide" includes a section titled "Administration and Instructional Coaches Support" with tools such as Scope and Sequence, Planning Guides, and Teacher Preparation resources. These tools help align instruction with program goals. The "Implementation Guide" outlines best practices in the "Teacher Toolbox" section, which includes planning recommendations and instructional strategies. For example, the "Teacher Preparation and Planning Guide" sections in each unit offer support for lesson internalization. This guidance ensures teachers understand the content progression to deliver aligned lessons. The "Advocating Best Practices" section provides teachers with research-based strategies to support fluency and instructional consistency. By using real-time resources such as suggested calendars and scheduling tools, teachers ensure daily fluency routines are incorporated into the instruction.

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.

Each scope outlines essential background knowledge from previous years, helping teachers understand how learning builds on new learning. The material includes the academic vocabulary necessary to teach the unit concepts effectively. In grade 5, Scope 5.3a, students use the unit's "Terms to Know" sections to find the vocabulary and definitions of key concepts, such as compatible numbers, subtraction, sum, etc. Material includes a visual vocabulary with definitions to help students understand unit concepts and develop a deeper understanding of the academic vocabulary. In grade 5, the "Represent and Compare Decimals" picture vocabulary cards provide visual representations and definitions of key terms included in the unit, such as digit, expanded form, hundredths, etc. In the "Engage" section of each unit, materials provide an overview of previously taught concepts and strategies. For example, in grade 5, the "Engage" section of "Unit Conversions" includes a section for "Assessing Prior Knowledge." This part outlines an activity that describes the necessary materials, preparation, and procedures for teachers to assess students' background knowledge relevant to the topic covered within the unit. The "Explain" section of each unit contains materials designed for students to use their linguistic and cultural background knowledge to enhance their understanding of vocabulary and concepts. The grade 5 unit includes differentiated activities tailored to each language domain based on the students' proficiency levels: beginner, intermediate, and advanced. The grade 5 materials include evidence of comprehensive unit overviews that provide background content knowledge necessary to effectively teach concepts in the unit. For example, the "Content Support" section of the unit "Multiplication and Division Algorithms" describes background knowledge students should have before grade 5. The grade 5 materials include evidence of comprehensive unit overviews that provide the academic vocabulary necessary to effectively teach concepts in the unit. For example, the "Content Support" section of the unit "Multiplication and Division Algorithms" outlines Terms to Know with the vocabulary necessary for this unit.

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.

Each scope includes a "Take-Home Letter" with the concepts students are learning in class and offers a selection of activities to reinforce those concepts at home. In Scope 5.2ab, the "Take-Home Letter" gives an example of finding a decimal's position on a number line. It provides examples along with guidance on how to practice correctly at home. Materials include a list of academic vocabulary used in the unit for families to reinforce with their students at home. For example, in Scope 5.2ab, the take-home letter includes a list of concepts in Spanish, such as compare, decimal, and greater than, to facilitate families' understanding of the concepts from the classroom. In the "Home" section of each unit, materials include a section titled "Take-Home Letter" in English, which contains "[a] breakdown of the concepts the student is learning in class to practice the concepts at home." The unit "Multiply Decimals" includes a "Take-Home Letter" where students practice solving multiplication problems, including problems with money with products in the hundredth place, using concrete models and mathematical vocabulary. Each grade 5 unit's "Home" section includes a "Take-Home Letter" in Spanish. This letter explains the concepts the student is learning in class to facilitate practicing mathematical terms in Spanish at home. For example, in the "Balance a Budget" unit, students can practice terms like presupuesto, gasto, and ingreso with familial support. The grade 5 materials include evidence of support for families in English for each unit, with suggestions on supporting their students' progress. For example, the "Multiply Fractions" unit "Scopes" section includes a "Take-Home Letter" in English, which outlines information about the unit as well as activities to try at home to reinforce new learning. The grade 5 materials include evidence of support for families in Spanish for each unit, with suggestions on supporting their students' progress. For example, the "Multiply Fractions" unit "Scopes" section includes a "Take-Home Letter" in Spanish, which outlines information about the unit as well as activities to try at home to reinforce new learning.

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 "Instructional Builder" section provides all the necessary materials, background knowledge, and a hook to engage students, which is crucial for a practical and meaningful lesson. The slideshow has guiding questions attached to foster productive struggle within group discussion. Each scope includes a "Foundation Builder" within the "Engage" section. This section describes the corresponding unit, required materials, preparation steps, and procedures, listing both teacher and student materials necessary to deliver the lesson effectively. A scope calendar is provided for all units, such as "Multiplying Decimals." It includes daily manipulatives and materials for each lesson. The materials offer guidance and recommendations regarding the timing of lesson components, including the duration allocated for whole-group instruction, small-group activities, independent practice, and assessment options. The grade 5 materials demonstrate evidence of the teacher and student materials necessary to deliver the lesson effectively. In the "Numerical Expressions" unit, the "Explore" tab's activity, Grouping Symbols, lists materials needed for that lesson for students, as well as a "Preparation" section that supports the teacher in preparing the materials for the lesson. The materials include evidence of suggested timing for each lesson component. For the "Numerical Expressions" unit, the "Suggested Scope Calendar" has a breakdown of each day of the unit. Within that breakdown is a suggested lesson pacing, such as Day 1: 5–10 minutes for the "Warm-Up Options,1" 5 minutes for the "Whole Group, 3" 0–45 minutes for the "Small Group," and 15 minutes for the "Assessment Options."

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.

Each daily lesson includes a list of the materials the teacher needs to effectively teach each component and the materials the student needs to participate in the lesson. The suggested timing for each component of the lesson is outlined in the "Suggested Scope Calendar." Each scope includes a "Foundation Builder" within the "Engage" section, which describes the corresponding unit, required materials, preparation steps, and procedures, listing both teacher and student materials necessary to deliver the lesson effectively. A scope calendar is provided for all grade 5 units, such as "Multiplying Decimals." It includes daily manipulatives and materials for each lesson. The materials offer guidance and recommendations regarding the timing of lesson components, including the duration allocated for whole-group instruction, small-group activities, independent practice, and assessment options. The materials demonstrate evidence of teacher and student materials necessary to deliver the lesson effectively. In the "Numerical Expressions" unit's "Explore" section, the activity Grouping Symbols lists materials needed for that lesson for students, as well as a "Preparation" section to support the teacher in preparing the materials for the lesson. The grade 5 materials include evidence of suggested timing for each lesson component. For example, through the "Numerical Expressions" unit, the "Suggested Scope Calendar" has a breakdown of each day of the unit. Within that breakdown is a suggested lesson pacing, such as Day 1: 5–10 minutes for the "Warm-Up Options," 15 minutes for the "Whole Group," 30–45 minutes for the "Small Group," and 15 minutes for "Assessment Options."

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

Each scope contains an "Intervention" tab with activities and materials to support students requiring additional assistance. It also includes an "Acceleration" tab with activities and materials designed to deepen understanding for students who have mastered the content. The curriculum scopes include materials with an acceleration component to engage students in activities to deepen their understanding of the content and its applications. Each unit includes a Create Your Own Activity, an open-ended task that challenges students to utilize their newly acquired skills to create something. The scopes include materials with an elaboration component section ("Elaborate") designed to engage students in activities to deepen their understanding of the content and its applications. Each unit contains a "Fluency Builder," consisting of independent and partner games and other activities that allow students to practice the new concepts. In the materials, each unit includes a "Scaffolded Instruction Guide" that gives guidance on the effective use of lesson materials for extended practice. For example, the "Multiply Decimals" unit has information on what materials can be used based on student data and performance. For students who are at 80–100%, there are five different suggested activities for extension. Each unit also includes a section titled "Acceleration" that gives guidance on the effective use of lesson materials for extended practice. For example, the "Acceleration" tab in the "Multiply Decimals" unit includes several activities with descriptions for teachers that can be used as an extension of student learning in that unit.

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.

Grade 5 instructional materials integrate a variety of diagnostic, formative, and summative assessments aligned with the TEKS to monitor and support student learning. Each unit begins with the "Engage" tab, which includes the Assessing Prior Knowledge activity designed to gauge students’ conceptual readiness through tasks such as the Foundation Builder. These pre-assessments utilize tools like whiteboards and student discussion to reveal misconceptions and reinforce academic vocabulary. Within the "Evaluate" tab, each scope offers multiple assessment opportunities to determine mastery. For instance, Scope 5.5 features a Skills Quiz requiring students to organize polygons in a hierarchical flowchart and analyze their understanding using a "Heat Map." The "Evaluate" section also includes open-ended assessments such as "Decide and Defend," prompting students to justify their mathematical reasoning with representations and complete sentences. The "Suggested Scope Calendar" includes diagnostic checks in the "Multiplication and Division Algorithms" unit involving structured pre-assessment tools—problem-solving tasks and real-world questions—embedded across the "Foundation Builder" and "Hook" components. Formative assessments are ongoing and include observation checklists, varying levels of questioning, and day-specific assessment options outlined. Summative assessments at the unit and lesson level include standards-based quizzes and technology-enhanced items, ensuring students engage with multiple formats to demonstrate learning.

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

The grade 5 instructional materials align by integrating diagnostic, formative, and summative assessments within each unit to inform instruction and support student growth. Each scope includes a "Suggested Scope Calendar" that outlines daily assessment opportunities, defines each assessment type, and labels them as diagnostic, formative, or summative, guiding teachers in intentional planning. Formative assessments are embedded at the lesson level to provide ongoing insight into student understanding. The Exit Ticket, aligned to each lesson, delivers immediate data that allows teachers to adjust instruction responsively. Observation checklists, such as those in Scope 5.2C and 5.3AK, further support formative assessment by helping teachers monitor student learning and identify misconceptions in decimal operations, while also encouraging students to track their progress and set learning goals. Summative assessments provide evidence of mastery of the TEKS at the end of a unit. For example, the standards-based assessment in grade 5 is used to evaluate overall understanding after instruction and determine which students have met grade-level expectations. The "Evaluate" section of the "Divide Fractions" unit identifies the "Decide and Defend "task as a summative tool, requiring students to justify their reasoning using mathematical evidence, with clear labeling and purpose provided. Diagnostic assessments are clearly described within the "Scope Overview Teacher Guide" and "Evaluate" sections, which also explain the structure and purpose of each assessment type. In the "Evaluate" section of the "Represent and Compare Fractions" unit, materials offer definitions for standards-based skills quizzes and open-ended questions. The "Divide Fractions" unit further details the procedures and preparation needed to administer each assessment effectively, ensuring teachers apply them as intended and students engage meaningfully with the content.

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

The grade 5 instructional materials align with expectations by embedding diagnostic, formative, and summative assessments with structured teacher guidance to support accurate and consistent implementation. Diagnostic tools such as the "Fluency Builder," "Foundational Builder," "Daily Numeracy," and interactive practice offer opportunities to identify prior knowledge and readiness levels. Materials include structured discussions, facilitation questions, and observation checklists that help teachers determine whether students have mastered content or require additional support. For example, in Scope 5.3BC, guidance within diagnostic assessments directs the teacher to use responses to group students and provide targeted instruction. These materials provide comprehensive teacher support across assessment types, ensuring that the data collected is reliable, instruction remains responsive, and students are provided with the appropriate opportunities to demonstrate and build mastery. Formative assessments support ongoing instructional decisions through built-in tools and detailed teacher support. The Skills Quiz in Scope 5.3BC, under the "Evaluate" tab, includes a clear purpose, a materials list, preparation steps, and facilitation tips that guide the teacher in promoting deeper reasoning. It provides flexibility in administration—whether in small groups, independently, or one-on-one—ensuring adaptability to student needs. In the "Numerical Expressions" unit, Day 6 offers both the Skills Quiz and a small-group intervention checkup, each supported with a suggested timeframe and facilitation points, including the use of student data to inform the next steps using the "Scaffolded Instruction Guide." Summative assessments are structured for consistency and integrity across classrooms. The "Standards-Based Assessment" in Scope 5.3BC includes "Tips and Tricks" that clarify expectations, such as independent completion and options for peer review to address errors while allowing teacher monitoring. On Day 8 of the "Multiply Fractions" unit, the "Suggested Scope Calendar" links to both the "Decide and Defend" task and the standards-based assessment, each with clear procedural steps and facilitation points to ensure consistent administration.

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

The grade 5 instructional materials align with TEKS by embedding diagnostic, formative, and summative assessments that reflect the objectives of each unit, lesson, and the overall course. Each scope includes assessments intentionally developed to address specific standards, ensuring alignment and instructional coherence. Diagnostic assessments provide data on student readiness and prior knowledge through TEKS-aligned tasks. In Scope 5.3AED, the "Standards-Based Assessment" evaluates student estimation skills in real-world problems aligned with 5.3A, 5.3E, and 5.3D. The "True/False" card game in Scope 5.7A assesses students’ prior understanding of measurement conversions through collaborative reasoning and teacher-facilitated discussions aligned with 5.7A. In the "Divide Decimals" unit, an "Observation Checklist" on Day 2 supports early identification of student needs through targeted standards, with space for notes to guide instruction. Similarly, in the "Balance Budget" unit, the checklist highlights key concepts and skills for instructional alignment. Formative assessments support ongoing monitoring of student progress while reinforcing the learning objectives. In the "Division Models and Strategies" unit (5.3AFG), Day 5 includes an Exit Ticket aligned to the TEKS and daily objective, offering insight into student understanding to inform instructional adjustments. Summative assessments evaluate mastery of standards after instruction. In the "Numerical Expressions" unit (5.4E and 5.4F), the "Evaluate" section includes a "Standards-Based Assessment" aligned with both the TEKS and the unit objectives. Likewise, in the "Divide Decimals" unit, the summative task reflects mastery of 5.3AFG through rigorous, standards-aligned questions designed to measure student achievement at the end of the learning cycle. These assessments ensure that evaluation is consistent, purposeful, and directly connected to the intended instructional outcomes.

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

Grade 5 materials incorporate TEKS-aligned diagnostic, formative, and summative assessments that include multiple-choice, text-entry, and open-response formats. These are supported by an online assessment bank featuring technology-enhanced items such as inline choice, hotspot, drag-and-drop, and multi-select, allowing students to demonstrate understanding in varied ways. Through the "Assessments" tab, each unit provides pre-, mid-, and post-assessments, with items designed to measure student learning at different levels of complexity. For example, the "Texas Math Grade 5 Mid-Assessment" includes 23 multiple-choice, seven fill-in-the-blank, and three multiple-answer items. The post-assessment expands this structure with 23 multiple-choice, eight fill-in-the-blank, and four multiple-answer items, offering a comprehensive evaluation of TEKS mastery. The "Evaluate" section in units such as "Balance and Budget" includes instructional assessments using open-ended responses, multiple-response items, inline choices, and DOK-2 level tasks. Similarly, the "Numerical Expressions" unit features mid-assessment items aligned to both current and prior grade-level standards. In contrast, the "Multiply Decimals" unit presents diagnostic through summative assessments structured around varying item types and complexity levels to ensure alignment with TEKS and lesson objectives.

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

The grade 5 material provides detailed guidance for assessing and improving students' mathematical understanding, focusing on both content mastery and the reasoning processes behind it. For example, the teacher's "Observation Checklist" in Scope 5.3BC helps assess students' ability to apply, reason, and communicate key mathematical concepts, offering teachers an in-depth view of their students' thinking processes. This tool goes beyond content knowledge to evaluate how students approach problem-solving, and the "Notes and Feedback" section allows teachers to track behaviors, strategies, and misconceptions that can inform targeted interventions and instructional planning. In addition to observational assessments, the Scaffolded Instruction Guide offers a strategic framework for adjusting instruction based on assessment results. This guide, accessible in the "Home Guide" of any scope, helps teachers identify areas where students struggle or excel, and provides next-step recommendations for further support or enrichment. It also links to specific resources organized by standards and performance levels, ensuring that teachers can tailor instruction to meet the individual needs of their students. The guidance is further enhanced by scoring information that supports the interpretation of student performance, such as in the grade 5 "Multiply Decimals" unit, where a rubric helps teachers review student responses to determine mastery of key math concepts. The materials also feature tools that help teachers plan for further instruction based on students' assessment data. For example, in the grade 5 "Order Pairs" unit, teachers are provided with materials to interpret students' ability to explain the relationships between ordered pairs. The assessment includes scoring guidance that highlights areas of student strength or need, allowing teachers to make informed decisions about future instruction. Additionally, the "Scaffolded Instruction Guide" offers targeted resources based on student performance data, such as a table that identifies the level of support needed depending on students' scores in specific areas, ensuring that instructional decisions are aligned with students' current levels of understanding. The "Multiply Decimals" unit provides a "Scaffolded Instruction Guide" for teachers to "plan for the next steps based on student performance on the scope's assessments . . . an integrated tool that guides teachers to materials based on students' needs." Additionally, the "suggested materials are organized by standard . . . further sorted by the percentile range they best support." There is a table describing the percentages for instructional areas. For instance, in 5.3D, grades of 0–25 percent require previous grade level remediation and have several activities that can be used with students that fall within that range for that standard.

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 grade 5 materials integrate diagnostic and formative assessments to guide instruction and support student growth. "Assessing Prior Knowledge" in the "Engage" section functions as a diagnostic tool to identify gaps before instruction begins. In the "Multiply Fractions" unit, students respond to number line tasks. If they struggle, teachers are directed in the facilitation guide to implement the "Foundation Builder" to close knowledge gaps before progressing. The "Scope Overview Teacher Guide" for 5.3BC provides a post-assessment structure for grouping students by performance—acquiring, approaching, or mastering a concept—with aligned instructional supports. For instance, "Fluency Builder" and "Small-Group Intervention" target remediation, while "Problem-Based Tasks" extend learning for students showing mastery. This grouping enables precise differentiation based on assessment data. The "Scaffolded Instruction Guide" for 5.3A and 5.4B uses results from scope assessments or "MAP Growth" to organize resources by standard and percentile ranges, facilitating intentional planning. It promotes student engagement with core components such as Hook, Explore, and Skills Quiz, reinforcing essential standards through structured participation. In the "Numerical Expressions" unit, teachers evaluate prior understanding using procedure and facilitation notes, which guide instructional choices and direct the use of intervention tools when necessary. The "Add and Subtract Fractions" unit includes an "Evaluate-Decide-Defend" task, which functions as a formative, open-ended assessment prompting students to explain their reasoning and justify their mathematical choices using structured discussion strategies like those in the "Teacher Toolbox." The "Multiply Fractions" unit demonstrates how assessment-driven instruction informs the next steps using the "Scaffolded Instruction Guide." Activities are sorted by performance bands such as the 50–80 percent range for standard 5.3I, with explicit guidance on procedures and implementation. Across units, the materials link performance trends to targeted resources, ensuring instructional decisions are data-informed and responsive to student needs.

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 materials provide teachers and students with integrated tools to monitor learning progress and make informed instructional decisions. The "Heat Map" in Scope 5.3BC serves as a visual progress tracker, linking each quiz item to specific standards and using color-coded feedback to indicate levels of mastery. This structure enables teachers to quickly identify which concepts require remediation or extension and to adjust groupings and instructional pacing based on real-time data. Daily use of tools like Math Chats and Exit Tickets further supports responsive instruction by offering continuous insights into student understanding. Students take an active role in tracking their growth through embedded self-assessment tools. In Scope 5.3BC, the "Spanish Observation Checklist" includes a rubric that encourages students to reflect on their proficiency in multiplying and dividing multi-digit numbers using the standard algorithm. The rubric guides students to provide evidence of understanding, rate their confidence, and identify areas for improvement, helping them set personal goals and engage meaningfully with the content. Similarly, the "Graph in the First Quadrant" unit features a self-evaluation handout that prompts students to demonstrate their understanding and assess their confidence in applying key skills. Teachers further track progress using "Observation Checklists" across units, such as in "Represent and Divide Fractions," where a comprehensive handout allows for the documentation of student mastery on each standard. In the "Divide Fractions" unit, guidance in the "Procedure and Facilitation" section prompts students to reflect on their learning and assess their development in individual skills. These structured opportunities for reflection and feedback strengthen both instructional precision and student ownership, reinforcing a continuous cycle of assessment and growth throughout the year.

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 materials include teacher guidance that supports differentiated instruction. For example, the "Multiply Decimals" unit includes small group lessons where students use base-ten blocks and represent quotients using arrays, area models, the partial quotient strategy, and the standard algorithm to build understanding. The "Explore" section contains scaffolded lessons that serve as embedded formative assessments. For example, the lessons progress from "Classify Polygons" to "Classify Quadrilaterals" to "Classify Triangles." The materials reinforce learning through spiraled reviews and reteach opportunities embedded within the intervention and elaborate sections of units. For instance, the Scout’s Motto activity in the "Classify Two-Dimensional Figures" unit provides a review of previously taught materials. The "Numerical Expressions" unit includes a reteach activity for students who have not reached proficiency.

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).

In grade 5, the instructional materials provide frequent, structured opportunities for students to engage in academic discussions with peers, supporting concept development through activities. These collaborative conversations are embedded within lessons, introducing new concepts, allowing students to verbalize their thinking and clarify understanding through dialogue. For example, during Scope 5.3BC, students participate in the Picture Vocabulary activity focused on multiplication and division algorithms. This structured interaction not only reinforces content but also supports language acquisition, particularly for emergent bilingual (EB) students, by encouraging rephrasing, personal connections, and visual associations. The materials further strengthen vocabulary development through preteaching supports and embedded tools across all units. Visual strategies like anchor charts and vocabulary charts provide scaffolded learning experiences. For example, the Foundation Builder activity includes a "Possible Preconceptions" table, clarifying how common words might be misunderstood in mathematical contexts such as pie/pies. While students may associate it with body parts, in context, it refers to a unit of measurement (feet)—as used in "Dominique pateó el balón 12.5 pies." Vocabulary instruction is further supported through contextualized preteaching activities that address potential misunderstandings. In the "Engage" section of the "Numerical Expressions" unit, a vocabulary chart outlines student misconceptions and clarifies intended meanings for terms tied to multiplicative comparisons. The "Explain" section extends this support with a visual anchor chart highlighting grouping symbols and numerical expression structures. In the "Compare Fractions" unit, the "Foundation Builder" addresses confusion with the word pie/pies by explaining its mathematical meaning and providing contextual examples. These strategies ensure students develop accurate vocabulary knowledge while allowing teachers to assess understanding and address gaps in real time.

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 grade 5 materials include a range of assessment opportunities that support the application of mathematical understanding in authentic contexts. "Math Today" provides open-ended problems that require students to use grade-level skills to analyze real-world data. For example, in the "Represent and Interpret Data" unit, the African Penguins activity uses Associated Press media to help students interpret graphs and draw conclusions grounded in real-life situations. This type of task functions as a formative assessment by encouraging students to engage in mathematical content in meaningful ways while developing analytical thinking. For students who demonstrate proficiency, the materials include structured enrichment and extension activities designed to deepen learning. In Scope 5.5A, the" Acceleration" tab includes a Create Your Own project where students design an app to classify two-dimensional shapes by their attributes. This task pushes advanced learners to synthesize vocabulary, apply conceptual understanding, and present their thinking in a real-world format. The materials also provide teachers with specific guidance for differentiated instruction based on student proficiency levels. The "Suggested Scope Calendar" identifies which students should complete activities such as Math Today and the Create Your Own activity, which challenges students based on mastery of content. These activities integrate math with broader contexts. This consistent structure ensures all students are engaged in rigorous, purposeful tasks tailored to their learning needs.

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 grade 5 materials include guidance to support the teacher in modeling and explaining the concepts to be learned. The Explore 1 activity from the "Multiply Decimals" unit includes explicit dialogue for the teacher to use, such as, "Help students access the task by asking the following guiding questions: What do you already know about multiplication?" and "[D]emonstrate how you would like students to represent the starting amount of cake by shading in 8 tenths horizontally in rows." The guiding questions also have example student responses. The "Procedure and Facilitation Points" in the lessons offer explicit prompts to support the teacher in modeling and explaining the concept to be learned. For example, the Explore 4 activity requires students to estimate and calculate area using both whole numbers and decimals, then apply the standard algorithm. The materials include direct guidance for teachers to model and explain concepts, such as multiplying decimals using estimation and place value patterns. The teacher is supported with clear steps, sample explanations, and guiding questions to help model and explain the concepts. The "Multiply Decimals and Divide Decimals" unit includes "Procedure and Facilitation Points" that include guided questions and potential student responses to help the teacher connect new concepts to prior knowledge. In addition, the "Content Support" section of the unit presents potential misconceptions, visual aids for guidance, and exemplar models all support the teacher in modeling and explaining the concepts to be learned.

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

The grade 5 materials include detailed teacher guidance for delivering lessons using multiple instructional approaches. In Scope 5.7A, Explore 1, the "Procedure and Facilitation Points" guide teachers in leading hands-on measurement tasks, student discussion using "think and share," and group-based station rotations. The "Teacher Guide" provides teachers with the guidance and recommendations needed, providing clear instructional support and recommendations for effective lesson delivery and facilitation. It includes step-by-step guidance, facilitation prompts, and strategies to address misconceptions. The guide supports a variety of instructional approaches—whole group, small group, intervention, and acceleration—and offers both digital and print formats to meet diverse teaching needs. The "Instructional Supports" section includes strategies for using visual aids and real-world contexts to clarify measurement conversions for diverse learners and offers teachers multiple strategies to scaffold instruction. For example, it provides step-by-step procedures, visual tools, and real-world application tips that align with varied learner needs. Teachers receive guidance on how to integrate manipulatives, clarify measurement misconceptions, and adapt instruction for diverse student readiness levels.

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 "Teacher Guide" includes multiple types of practice for effective implementation by providing structured opportunities for multiple types of practice, including guided, independent, and collaborative learning. Each lesson includes clear teacher guidance on how to implement these practices within a variety of instructional settings, such as whole group, small group, and individual instruction. The guide outlines when and how to use different strategies, such as hands-on activities, digital tasks, and skill practice, ensuring students engage meaningfully with content. At the same time, teachers have the support needed for effective implementation. The "Suggested Scope Calendar" offers recommendations for lesson pacing, internalization, and grouping transitions, while also embedding "Daily Numeracy" routines for regular math practice. For example, lessons in the "Multiply and Divide Decimals" units include scaffolded activities that build procedural fluency and conceptual understanding. Instruction integrates teacher-guided, collaborative, and independent work to support differentiated instruction and ensure content is accessible to all learners. In the Explore 1 in the "Multiply Decimals" unit, students have opportunities to work with teacher guidance, collaboratively in groups using various supports, and there are independent activities included. Throughout the lesson, materials give the teacher guidance, such as prompts and guiding questions to support the implementation of the content.

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.

This guidance is not applicable because the Spanish program does not require guidance on providing linguistic accommodations.

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

The grade 5 instructional materials provide embedded implementation guidance to support teachers in bilingual/ESL programs. The "Scaffolded Instruction Guide" offers resources that outline key principles and strategies for language acquisition. Each lesson and unit includes interactive vocabulary and picture vocabulary, sentence frames, graphic organizers, and practical tips for scaffolding content and language development. In Scope 5.9ABC, "Language Connections" activities support students in using their native language and cultural knowledge to understand math concepts like data plots and decimals. The activities include visuals, manipulatives, and instruction across listening, speaking, reading, and writing. For example, in Scope 5.9ABC, Explore 3, Procedure and Facilitation Points, the activity includes oral and written tasks for language development and conceptual understanding. Teacher-guided questions, sentence frames, and collaborative discussions help students build academic vocabulary. The "Teacher Toolbox" offers comprehensive implementation guidance. It includes unit-specific TEKS, ELPS standards, and structured discourse activities with bilingual vocabulary and sentence stems. The materials available in both English and Spanish support teachers with implementation guidance through resources like the "Launch into Grade 5" unit and the "Language Connections" informational video. For example, the informational video states, "The intention of language connections is to keep the math content on grade level while adjusting the language used to communicate with an English Language Learner. The activity includes teacher-facing material and guidance—to meet the language needs of each student."

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.

The grade 5 instructional materials consistently embed teacher guidance to support EB students in developing academic vocabulary, improving comprehension, building background knowledge, and fostering cross-linguistic connections. For example, in the Explore 1 lesson of the "Perimeter, Area, and Volume" unit, the "Language Supports" section includes targeted strategies to meet the needs of students at varying proficiency levels. These strategies include identifying and discussing cognates such as área and perímetro (perimeter), helping students use background knowledge of their first language to access new mathematical vocabulary and concepts. This approach promotes both conceptual understanding and linguistic development. The instructional materials include structured opportunities for EB students to engage in oral and written discourse, supported by sentence stems, vocabulary scaffolds, and collaborative discussion routines. For example, in the "Divide Decimals" unit, the Explore 1 lesson provides sentence frames such as "The quotient is ___ because ___," which guide students to explain their reasoning. Students are encouraged to share verbal responses with a partner, revise their ideas based on feedback, and then record their thinking in writing. These supports allow students to build both content knowledge and academic language simultaneously. The materials offer guidance for leveraging students’ cultural and linguistic backgrounds to support language and concept development. The "Language Connections" section of the "Explain" section provides teachers with strategies to help students draw on their prior knowledge, including their home language and cultural experiences. For example, the tab directs teachers to use multilingual sentence stems and modify tasks by language domain (listening, speaking, reading, and writing) and proficiency level (beginner, intermediate, advanced). Differentiated handouts and discussion prompts support students in connecting new math concepts to familiar contexts, enhancing both language and content acquisition.

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.

Grade 5 materials embed TEKS-aligned instructional tasks and assessments throughout each unit to measure and support student mastery through varied opportunities that reflect the required depth of understanding. These embedded instructional assessments and practice opportunities provide ongoing data, allowing teachers to make informed decisions and tailor support aligned with the TEKS. In Scope 5.5A, the "Engage" section prompts students to compare two-dimensional figures based on attributes. Explores 1–3 progressively build geometric classification skills, culminating in students organizing figure categories and drawing annotated triangles in the "Explain" section. In the "Elaborate" section, the "Glass Art" activity engages students in applying geometric concepts by designing stained-glass windows and describing figure attributes. In the "Evaluate" portion, a Skills Quiz includes multiple item types to confirm mastery and guide further instruction. In the "Unit Conversions" scope, students deepen conceptual understanding by converting units of length using a visual chart in their journals. The "Divide Fractions" unit supports application by connecting division to real-world contexts, such as sharing pizzas, with an Exit Ticket in Explore 2 prompting justification of reasoning. In the "Income Taxes and Payment Methods" unit, a Skills Quiz evaluates fluency with financial concepts. These embedded instructional assessments and practice opportunities provide ongoing data, allowing teachers to make informed decisions and tailor support aligned with the TEKS.

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

Grade 5 materials present tasks that align with the TEKS and progressively increase in rigor, guiding students toward conceptual mastery and grade-level proficiency. In Scope 5.10EDF, students begin by interpreting profit statements and engaging in class discussions to explain reasoning. Then, they analyze financial records to track income and expenses. They determine if budgets are balanced and collaboratively solve open-ended budgeting challenges, like purchasing concert tickets, using evidence to justify their decisions. The "Explore" section supports financial literacy through hands-on tracking of income and expenses using real-world scenarios. In the same scope, students read budgeting-focused math stories, solve multistep problems, and apply mathematical reasoning in open-ended assessments tied to realistic financial decisions. The "Fluency Builder" in the "Perimeter, Area, and Volume" unit reinforces learning through paired games where students apply problem-solving strategies in real-life contexts. In the" Add and Subtract Fractions" unit, Explore 2 leads students from building fractions with manipulatives to representing and justifying their thinking in journals. In "Explore 5," students work through multistep problems involving fractions and decimals, responding to questions that progress from basic procedural understanding to deeper analytical thinking, and demonstrate mastery through Exit Tickets that require justification. Through these activities, students develop and apply mathematical reasoning with increasing complexity through structured practice and assessment.

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

The grade 5 materials demonstrate coherence across units by purposefully connecting mathematical concepts through recurring patterns and vertically aligned ideas. The "Content Unwrapped" section illustrates how foundational knowledge supports new learning, such as students using multiple strategies before applying the standard division algorithm. The "Course Rationale" outlines how concepts like operations with fractions and decimals, expressions, geometry, and data are interrelated; for example, volume connects multiplication to geometric reasoning, reinforcing operational fluency in new contexts. In Scope 5.2AB, the "Content Support" section builds on earlier understandings of place value and decimals from fourth grade, where students used base-ten blocks and number lines, and extends these tools through the thousandth place in grade 5. The "Multiply Fractions" scope identifies 5.3K as a connecting standard from the prior "Add and Subtract Fractions" scope, illustrating an intentional scope sequence to deepen conceptual understanding. The "Elapsed Time" unit uses geared clocks and number lines to connect time measurement with the four operations, helping students transfer prior skills to solve real-world problems. In the "Represent and Compare Decimals" scope, materials emphasize the importance of place value as foundational for subsequent work with operations and reasoning. The "Growth Measurement Pre-Assessment" supports diagnostic use by aligning questions to prior grade-level TEKS and using a "Heat Map" to connect student responses to standards. This structure ensures instruction builds meaningfully across units and grade levels, helping students apply knowledge flexibly across mathematical contexts.

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.

The grade 5 materials demonstrate coherence across units by intentionally connecting prior knowledge, current TEKS expectations, and future learning through organized, scaffolded support in both content and language. The Interactive Notebook serves as an ongoing, visual record of student understanding, linking new concepts with previously learned material through anchor charts, reference pages, and vocabulary that bridge past and upcoming content. Each scope’s "Teacher Guide" clearly outlines vertical alignment, as seen in Scope 5.3BC, where multiplication and division concepts build from fourth-grade models and place value knowledge, preparing students for sixth-grade applications such as negative numbers and the distributive property. The "Content Support" section of Scope 5.2AB reinforces coherence by deepening understanding of decimal concepts using consistent academic vocabulary from earlier grades—terms like compare, compose, and decompose—now applied to tenths, hundredths, and thousandths. The "Content Unwrapped" section of the "Unit Conversions" unit explicitly ties present instruction to past learning by referencing earlier use of tables for measurement conversions and aligning vocabulary accordingly. A vertical alignment chart within this section maps connections between prior, current, and future standards. The "Add and Subtract Fractions" unit supports coherence by the "What concrete words should students know?" section, which revisits foundational terms such as fraction, prime number, and composite number. The Implications for Instruction notes build on prior experiences with visual models and number lines, helping students transition to abstract reasoning. The "Coming Attractions" section projects future expectations, highlighting how fifth-grade fraction operations lay the groundwork for rational number problem-solving in seventh grade. This structure ensures students encounter familiar concepts in increasingly complex contexts, promoting cumulative understanding across the instructional year.

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 grade 5 materials demonstrate coherence at the lesson level by connecting prior knowledge of mathematical concepts and procedures to new learning through intentionally sequenced activities and embedded supports. The Skill Practice, Show What You Know, and the Strategy Work Mat activities begin with familiar tools such as partial products, virtual manipulatives, and an algorithm place mat, allowing students to build on what they know and apply it to new content. In the "Unit Conversions" section, students first practice multiplying and dividing by 10, 100, and 1,000 to prepare for more advanced conversion tasks. The "Multiply Decimals" unit's Explore 1 lesson reinforces coherence by prompting students to connect whole-number multiplication to decimal multiplication using previously learned strategies, such as repeated addition and base-ten blocks, guided by targeted facilitation questions. In the "Multiplication and Division Algorithms" unit, the Assessing Prior Knowledge activity asks students to analyze partially solved two-digit by two-digit multiplication problems using strategies learned in earlier grades, setting the stage for more complex tasks like three-digit by two-digit multiplication. Each "Engage" section intentionally links earlier concepts to current objectives. In Scope 5.5A, students revisit vocabulary words such as paralelo and ángulos to compare two-dimensional shapes, preparing them for deeper geometric reasoning. In another unit, students evaluate true or false equations involving time and length, drawing on earlier knowledge of measurement to transition smoothly into new content. In the "Divide Fractions" unit, students identify unit fractions and demonstrate composition strategies introduced in prior lessons, reinforcing connections between foundational knowledge and grade-level standards.

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

Grade 5 materials demonstrate coherence through consistent integration of spaced retrieval using spiraled reviews and Daily Numeracy routines that support multiple assessment types. In Scope 5.3BC, students begin solving two-step problems with multiplication and division using models and algorithms on Day 1, then reinforce their understanding on subsequent days by revisiting strategies such as the area model and partial products, deepening fluency through progressive applications. In Scope 5.3A, students extend those same strategies to solve multistep word problems with variables, connecting past learning to new problem-solving contexts. In Explore 2 of "Represent and Solve Multistep Problems," students apply the four operations and use equations with letters for unknowns. The instructional support notes encourage the use of diagrams from earlier lessons, promoting reflection and metacognitive growth. In the "Graph in the First Quadrant" unit, Explore 4 guides students to retrieve previous learning about generating tables and graphs to analyze relationships, supported by questions such as "¿Cómo encontraste la relación?" to prompt deeper connections. In the "Multiply Decimals" unit, Explore 1 builds on strategies from "Multiplication and Division Algorithms" by asking students to connect whole-number multiplication with decimal operations. Facilitation questions like "¿Cómo podemos usar nuestro conocimiento de la multiplicación como suma repetida para representar . . . ?" ensure that students revisit essential ideas across units, reinforcing retention through frequent, distributed practice.

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

The grade 5 materials embed interleaved practice across lessons and units by integrating varied assessment types and recurring engagement with previously learned content. In Scope 5.3BC, students solve multiplication and division problems using models and algorithms early in the unit, then reengage with those concepts using partial products and area models, reinforcing procedural fluency through multiple strategies. Scopes 5.4GH and 5.6AB further this by expanding on grade 4 perimeter and area knowledge to include volume, supporting concept connection across grade levels. "Interactive Notebooks" in the "Divide Decimals" unit serve as ongoing references during independent tasks and document student learning, while the spiraled review in the "Graph in the First Quadrant" unit, titled "Pentathlon," provides regular opportunities to revisit key concepts through warm-ups or homework. The "Choice Board" in the "Represent and Compare Decimals" unit prompts the application of earlier skills, such as comparing decimals and organizing data in real-world contexts, extending content through Strategy Choice Tasks and Accelerate activities. In the "Add and Subtract Fractions" unit, the "Elaborate" section’s spiraled review returns students to operations with decimals introduced in earlier scopes, using consistent reinforcement through practice aligned with the critical grade-level focus. Math Chats, Skill Quizzes, Reviews, and Intervention activities embedded throughout each unit further support retention by encouraging continuous interaction with both current and previously mastered concepts.

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

The grade 5 materials require students to analyze and justify solution strategies using a variety of models. In Scope 5.3AFG, "Explain" section, students compare grid models and base-ten blocks to model decimal division in a real-world scenario. For example, students solve a real-world division scenario by dividing 3.75 pounds of food into five portions. The task uses a grid model and mathematical expressions to help students link visual models with numeric reasoning. Students must compare base-ten blocks and grid models, then explain their efficiency for solving decimal problems. In the "Add and Subtract Decimals" unit, Explore 1, students use place value disks and a standard algorithm work mat to model and solve decimal operations. Explore 2 uses number lines for estimation and reasoning, and students reflect in journals using guiding questions to explain estimates. In the "Divide Fractions" unit, students manipulate paper pizza models to construct and deconstruct fractions and explain division situations. For example, the "Foundation Builder" includes paper pizza models that students manipulate to understand part-whole relationships, supporting comprehension of fraction division through physical modeling.

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

The grade 5 materials provide consistent opportunities for students to create models that represent mathematical situations. The Explore 1and Explore 3 Exit Tickets in Scope 5.3AFG have students create visual models, such as grid and area models, to solve decimal division problems. These tasks require students to write equations, estimate quotients, and justify their solutions, reinforcing the connection between visual representations and numerical reasoning in real-world contexts. The "Multiply Decimals" unit includes activities in both the "Explore" and "Elaborate" sections where students draw arrays and area models to represent multiplication of decimals. The "Student Handout" prompts students to model real-world problems, such as calculating the area of space, and to explain how their models guided their calculations. The Journal activity further supports this by requiring students to build physical or drawn representations and reflect on their use of modeling to find solutions. The "Elaborate" section of the "Multiply Decimals" unit includes a problem-based task titled Building a Business that asks students to analyze data from a table, model their production plan, and determine quantities needed to reach a profit goal. In the "Engage" section of the "Comparing Fractions" unit, the "Painting a Mural" task engages students in multiplying decimals through estimation and strategies rooted in place value and operations. These tasks make student thinking visible and help identify misconceptions, confirming that the materials align with the guidance to require models in problem-solving.

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

The grade 5 materials contain multiple examples of questions and tasks that provide students with opportunities to apply conceptual understanding to new problem situations and contexts. In Scope 5.2C and 5.3AK, the "Explain" task encourages students to check their work and explain their reasoning. For example, the section of Show What You Know Part 3 requires students to use their knowledge of decimal addition and subtraction in practical scenarios involving weights, comparisons, and estimation. In the "Elaborate" section of Scope 5.2C and 5.3AK, the "Problem-Based Task" presents a budgeting scenario where students must apply decimal operations to build custom sundaes within a spending limit. Students justify their decisions using mathematical reasoning, which confirms their ability to use previously learned skills in a realistic context. The Math Thoughts and Show What You Know components are designed to develop reasoning and connect math concepts across varying applications. The "Measurement" unit materials contain multiple examples of questions and tasks that provide students with opportunities to apply conceptual understanding to new problem situations and contexts. Some examples are in the Dairy Farm interactive practice, where students solve problems involving unit conversions related to volume and capacity. In Explore 1, Convert Units of Length, students address multistep real-world problems using customary and metric systems. In the "Problem Solve with the Four Operations unit, the Explore 2 activity engages students in using a strip diagram and equation model to solve multi-step problems, as seen in the Exit Ticket structure. In the "Divide Decimals" unit, the "Explain" section prompts students to model scenarios, write equations, and complete solution statements, showing that students consistently apply mathematical concepts in new contexts.

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

The grade 5 materials support the development of academic vocabulary and automaticity through structured instructional tools. "Content Unwrapped" and "Structured Conversations" build fluency by embedding mathematical language into problem-solving tasks. Students engage in activities that require the use of operations, reinforcing vocabulary and computation skills. In the "Elaborate" tab, the spiraled review provides targeted practice with operations such as comparing fractions, reading data, and solving problems involving time and place value. For example, materials include mini-lessons through structured practice with multi-digit numbers. For example, activities such as Guess the Number and Solve It reinforce place value understanding and operation fluency, while progress trackers support student growth over time. The "Fact Fluency" sections for both the "Addition and Subtraction" unit and the "Multiplication and Division" unit, provide tasks to build speed, accuracy, and confidence, enabling students to solve with greater ease and precision. For example, in "Fact Fluency Station 1" for "Multiplication and Division," students use linking cubes to explore related facts within 20.

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 grade 5 "Engage" sections at the beginning of each scope help students practice the efficient and flexible application of mathematical procedures. They focus on helping students connect prior knowledge to new procedures through meaningful experiences. For example, in the "Decimal Operations" unit, students use base-ten blocks to model decimal multiplication and discuss how shifting place values impact results. This approach supports accuracy and builds procedural fluency. The "Fluency Builder" provides students with repeated opportunities to practice efficient, flexible, and accurate mathematical procedures throughout each unit. The activities consistently practice procedural skills with an emphasis on efficiency and adaptability. In the "Decimal Addition and Subtraction" unit, the "Fluency Builder" supports students in aligning place values and applying standard algorithms to problems with tenths and hundredths, promoting accurate and efficient computation. The "Teacher Toolbox" and lesson components offer daily opportunities to apply mathematical procedures with efficiency and flexibility. For example, the Daily Numeracy activities, such as pattern creation and extension, support number sense and reasoning. In the "Divide Decimals" unit, students use arrays and area models in journals and exit tickets to apply strategies in varied formats. The "Problem Solve with the Four Operations" unit provides structured opportunities to solve real-world problems using chosen methods, with support for modeling, estimation, and accurate solution reporting.

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 grade 5 materials include teacher prompts that guide student evaluation of area and partial models, promoting strategy refinement based on efficiency and mathematical confidence. Lessons connect previous learning to multiplication algorithms, encouraging students to adapt and apply appropriate strategies for accuracy and fluency. Tasks support the use of reasoning, model-building, and algorithm application to solve problems involving place value and decimals across units. Scope 5.3ADE materials have embedded mathematical procedural strategies across lessons that engage students in exploring multiplication concepts through place value analysis, repeated addition, and model-based reasoning. In measurement activities, students use base-ten blocks to represent dimensions and area, building procedural understanding of decimal operations. Guided questions and collaborative modeling prompt students to justify their reasoning and adjust methods based on accuracy and efficiency. "Perimeter, Area, and Volume," "Unit Conversions," "Multiply Decimals," and "Add and Subtract Decimals" units offer targeted prompts to help students assess solution strategies and support the evaluation of mathematical processes across lessons and units. Instructional questions encourage students to reflect on formulas, estimation, and algorithm use. Tasks embed evaluation of efficiency, flexibility, and accuracy within lessons, providing procedural fluency across mathematical content.

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

The grade 5 materials in Scope 5.3AJL provide embedded teacher support that promotes increasingly efficient problem-solving approaches. For example, the "Procedure and Facilitation Points" section directs teachers to use real-world models, such as dividing paper pizzas, to build students' understanding of dividing whole numbers by unit fractions. Students represent their thinking through equations, drawings, and labels, while the teacher provides structured support that transitions students from hands-on models to abstract reasoning. Explore 1 materials offer embedded supports designed to foster efficiency. It provides step-by-step guidance using relatable contexts and visual tools like fraction tiles and number lines. Teachers use prompts to move students from concrete to abstract representations, helping them identify patterns and adopt efficient, strategy-based methods. For example, in the "Measurement" unit, Explore 1 further supports this guidance by encouraging teachers to lead students in analyzing equivalent measurements within the same system, promoting reasoning that supports procedural efficiency. Explore 1 provides embedded support that fosters strategic thinking to increase efficiency. For example, in the "Add and Subtract Decimals" unit, students round values using number lines and real-time data, while teachers monitor understanding using targeted questions. The "Add and Subtract Fractions" unit’s "Scope Summary" emphasizes using benchmark fractions and number sense to estimate and evaluate solutions. The "Number Patterns" unit provides guiding questions to direct students to rewrite expressions and simplify fractions, reinforcing the use of efficient methods grounded in reasoning and structure.

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

The grade 5 materials demonstrate how the conceptual and procedural emphasis of the TEKS is addressed through structured activities. For example, the "Content Unwrapped" and "Assessing Prior Knowledge" sections show the connection between expanded form and expanded notation, addressing both conceptual understanding and procedural steps. The "Implications for Instruction" and "Explore" activities help students move from conceptual understanding to procedural fluency by applying real-world scenarios and progress from basic methods to the standard algorithm. Materials include clear teacher guidance on supporting both processes and concepts. For example, Scope 5.3BC in grade 5 outlines a sequence from area models and partial quotients to the standard division algorithm. This sequence is supported by instructional guidance helping teachers implement TEKS-aligned lessons that build conceptual understanding and procedural accuracy. The "Place Value of Whole Numbers" unit and the "Area and Perimeter" unit materials outline the progression from conceptual models to procedural applications by using concrete objects to teach area and perimeter before moving to formulas. The materials also ensure that students connect physical models with abstract representations, reinforcing that procedural skills are grounded in conceptual understanding.

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 grade 5 materials provide structured opportunities for students to move from concrete to abstract representations. For example, in the "Multiply and Divide Whole Numbers" unit, the "Content Unwrapped" and "Dissecting the Standard" sections include key conceptual vocabulary and progression, guiding students to understand the process of division through arrays, area models, and standard algorithms. The "Implications for Instruction" section explains how students build prior knowledge of basic multiplication and division facts to solve multi-digit problems using concrete models (such as base-ten blocks or counters), pictorial representations (such as area and strip diagrams), and then move toward the abstract use of equations. The "Operations with Decimals" unit asks students to use place value charts and base-ten models to represent decimal numbers and operations. The "How to Use STEMscopes Texas Math" video reinforces this approach, showing that students first manipulate concrete representations of decimals, then draw visual models, and finally apply standard notation and algorithms.

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.

Grade 5 instructional materials explicitly support students' connections between concrete and representational models. For example, in Explore 3, students use concrete and representational models such as base ten blocks and dry-erase boards to create physical arrays and area models in their journals. Then, they write equations and use expanded form, place value, and algorithmic strategies such as partial quotients to explain abstract concepts. The materials in Explore 2 use real-world objects such as water bottles and dot stickers to collect and organize data. They record and interpret this data using dot plots, number lines, tables, and written reflections. Similarly, in the "Represent and Compare Decimals" unit, the "Explore" section engages students with base ten blocks and "Decimal Work Mats" to investigate decimal place value. The "Multiply Fractions" unit includes targeted instructional support to help students create and explain models that represent fraction multiplication. For example, in the "Explore" section, students use two-color counters to model fractional parts, draw the models in their journals, and write corresponding solution statements. The "Explain" section continues this progression by incorporating manipulatives and written models.

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

The grade 5 materials provide structured opportunities for students to develop academic mathematical language through the use of manipulatives, visuals, and targeted language development strategies. In Scope 5.3AHK and 5.4A, Explore 2, students use fraction tiles to explore equivalence and operations. The lesson includes guided questions and collaborative tasks that prompt students to express reasoning using accurate vocabulary in both oral and written forms. The "Explore" activities in Scope 5.3AHK and 5.4A include manipulatives and visuals that strengthen vocabulary and conceptual understanding. "Explore" presents real-world contexts such as games and family events to support students in adding and subtracting fractions. For example, in Explore 3, students engage with scenarios like games and family events to practice adding and subtracting fractions. They use visual fraction models and hands-on tools to represent their thinking while participating in structured math discussions. These activities encourage students to use precise mathematical vocabulary, reinforcing language acquisition and conceptual understanding through collaborative problem-solving and teacher-facilitated dialogue. Language development support appears across multiple features throughout the materials. For example, in Explore 2 of the "Graph in the First Quadrant" unit, the Math Chat section includes Structured Conversation routines and Depth of Knowledge questions to promote academic dialogue. The "Explain" section provides anchor charts that illustrate numerical patterns and key vocabulary. For example, students record key vocabulary and mathematical ideas directly onto the anchor chart. This visual aid reinforces conceptual understanding through repeated exposure to mathematical language. The "Teacher Toolbox" includes resources for multilingual learners, such as visual glossaries, sentence stems, and manipulatives to support vocabulary development. In the "Multiply Fractions Unit," Explore 3, students use grid paper and counters alongside language supports to communicate their reasoning with clarity.

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

The grade 5 materials in Scope 5.3AHK and 5.4A include embedded teacher guidance to support and extend student use of academic vocabulary in mathematical discussions. For example, in Explore 1, teachers use scripted prompts and visual models to scaffold vocabulary like arrays and factors in group settings. Depth of Knowledge questions guide peer interaction using specific language to justify reasoning. Explore 2 materials in Scope 5.3AHK and 5.4A prompts students to use vocabulary such as common denominator and equivalent fractions when explaining strategies. Teachers ask structured questions to reinforce connections between vocabulary and mathematical processes. Sample responses model appropriate syntax, supporting students in refining and expanding their mathematical language. In the "Divide Fractions" unit, the "Explore" lessons integrate sentence stems and example responses within the "Language Support" section. Students engage in peer conversations using frames such as "¿Qué significa que la tierra esté dividida?" ("What does the land is divided mean?") and respond with modeled academic vocabulary. "Anchor Chart" activities in the "Explain" section guide vocabulary support, allowing students to articulate definitions and relationships during teacher-led discourse.

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 grade 5 materials provide embedded teacher guidance that supports the application of mathematical vocabulary, syntax, and discourse. The "Interactive Notebook," "Procedure and Facilitation Points," and "Student Handout" (Choose Operation and Solve) supply strategies to enhance classroom conversations using structured language and mathematical vocabulary. For example, these tools equip teachers to scaffold discussions and help students organize their mathematical thinking using complete sentence structures and accurate terminology. The "Teacher Toolbox" includes the "Communicate Math" section, which outlines expectations for math discourse, emphasizing academic vocabulary and organized student responses shared in pairs, small groups, and whole-class settings. For example, teachers are guided to ensure student participation through organized, vocabulary-rich dialogue in pairs, small groups, and whole-class discussions. Guidance includes using sentence stems, structuring student explanations, and modeling academic precision. In Scope 5.3AHK and 5.4A, the materials provide repeated opportunities for students to use, refine, and internalize mathematical language with peers. For example, in "Explain," the My Math Thoughts activity, students are prompted to express their thinking in peer discussions using appropriate academic language, strengthening their understanding over time. For example, in Scope 5.2C and 5.3AK, the teacher-guided prompts and reflection tasks in the Explore 1 activities help students explain mathematical relationships, using appropriate academic vocabulary in syntax, and provide example responses as students practice rounding decimals. These structured supports help students articulate reasoning with correct terms and complete sentence structures. In the "Launch" unit, "Vocabulary Strategies" such as "Speak Up" engage students in connecting new vocabulary to key mathematical concepts through games and peer interaction. The strategy involves students defining terms, using them in sentences, drawing representations, or explaining through analogies. This practice is supported by teacher facilitation through the "Procedure and Facilitation Points." The "Profit, Income, Taxes, and Payment Methods" unit provides embedded guidance for developing a language toolkit through real-world mathematical discussion. For example, in Explore 1, the Types of Taxes activity guides students to define and classify terms like payroll tax and income tax using a visual glossary. The "Language Support" section provides teacher guidance to clarify unfamiliar words and prompt students to share real-life connections. In the "Represent and Compare Decimals" unit, the "Explore" lessons provide guided questions with exemplar student responses, modeling precise use of academic mathematical language. These structured supports help students build fluency in using and understanding mathematical language in meaningful contexts. For example, when exploring decimal notation, a model response states, "Sabemos que nuestra expresión representará el número de bloques en ese lugar multiplicado por el valor de ese bloque." ("We know that our expression will represent the number of blocks in that location multiplied by the value of that block.") This guidance provides students with accurate language models and helps teachers reinforce correct mathematical syntax during discourse.

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

The grade 5 materials in Scope 4.3ABC integrate TEKS process standards through structured activities that promote mathematical reasoning and flexible problem-solving. For example, in Explore 1, students interpret data using dot plots and stem-and-leaf plots while justifying their reasoning. The use of the "Strategy Work Mat"—with multiple representations—strengthens students’ ability to select appropriate methods in unfamiliar contexts, supporting critical thinking and analysis. The "Unit Conversions" and "Numerical Expressions" units include instructional features that align with TEKS process standards. The "Content Unwrapped" section in the "Unit Conversions" unit guides students in using operations to convert measurement units, emphasizing reasoning through vocabulary roots and reference tools. For example, in the "Numerical Expressions" unit, Problem Tents and journal prompts require students to create, simplify, and explain expressions, while the Show What You Know activities include teacher facilitation points that promote tool use, model selection, and written justification, ensuring process standards are embedded throughout instruction. In the "Division Strategies" unit, the materials apply process standards through real-world application and conceptual connections. For example, in Explore 2, students work through division problems using area models and partial quotients in a collaborative setting. For example, the "Three in a Row" game board allows students to transfer their learning across tasks and apply knowledge in new scenarios, reinforcing strategy selection and connection-making between mathematical ideas.

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

The grade 5 "Explore" materials incorporate and connect TEKS process standards throughout the course. In the "Numerical Expressions" unit, students apply mathematics to real-world problems and represent their reasoning in the Student Journal. For example, the "What Might That Look Like" section provides examples specific to grade 5, such as graphing ordered pairs, where students analyze coordinate placement. These components demonstrate that the materials intentionally connect process standards across units, supporting deep, transferable learning. The "Teacher Toolbox" contains a "Process Standards" tab that explains the instructional role of each standard. For example, in the "Analyze Relationships to Communicate Ideas" section, teachers are advised to connect new concepts to prior knowledge and guide students in monitoring their own thinking. The "Communicate Mathematical Ideas and Their Implications" section highlights how discussion, writing, and collaborative reasoning strengthen understanding, ensuring consistent application of process standards across the curriculum. The "Add and Subtract Decimals" unit includes a clear description of how the TEKS process standards are incorporated and connected throughout the course. For example, student expectations align with process standards by key concepts that focus on rounding, estimation, and fluency in operations, reinforcing reasoning and application in real-world scenarios to develop mathematical fluency and critical thinking over time.

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

The grade 5 materials include a section titled "Content Unwrapped" that identifies where each TEKS process standard is addressed in the lesson. This structure supports intentional instructional planning and ensures consistent integration of process standards throughout the curriculum. For example, each unit and lesson begins with a summary of the applicable process standards and describes how students will engage with these standards through problem-solving and reasoning. The "Teacher Toolbox" provides unit-level explanations of how TEKS process standards are integrated across instructional content. For example, in Scope 5.3BC, the materials outline student expectations such as applying mathematics to real-world problems, using appropriate tools, and communicating ideas. The "Display," "Explain," and "Justify Mathematical Ideas" sections offer teachers strategies and examples that promote mathematical discourse and justification aligned with grade-level expectations. The "Multiply Decimals and Numerical Expressions" unit explicitly describes how process standards such as 5.3D, 5.3E, and 5.1F are applied. Definitions of verbs and nouns clarify student actions and concepts, while instructional notes emphasize critical thinking over procedural fluency. In the "Analyze Relationships to Communicate Ideas" section, the materials guide teachers to help students connect new concepts with prior knowledge and apply reasoning in tasks such as graphing ordered pairs or simplifying expressions, ensuring coherence and alignment with TEKS process standards.

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

Grade 5 materials include a consistent and structured presentation of the TEKS mathematical process standards. Each unit begins with a summary of the process skills, and each lesson highlights the relevant standards. For example, Scope 5.3BC, Explore 1 and Scope 5.3A, 5.4B, Explore 1 explicitly list the mathematical process standards addressed. This structure ensures that the standards are visible and clearly integrated into the instructional sequence of every lesson. The "Represent and Interpret Data Unit "in grade 5 further demonstrates how the process standards are applied in context. The "Scopes Overview Materials" outline how students engage with Standard 5.1A by using frequency tables, dot plots, stem-and-leaf plots, and scatterplots to solve real-world problems. Lessons incorporate relatable activities such as coin tosses, bottle-flipping contests, and classroom measurement challenges to reinforce the practical application of data representation and analysis. The "Teacher Toolbox" enhances this by offering unit-level guidance and tools like "Putting Standards into Action" to support teacher understanding and delivery of the standards. Student-facing materials also show strong alignment with TEKS process standards. For example, in the "Numerical Expressions" Unit, students solve real-world problems and document solutions in their "Student Journals," supporting Standard 5.1A. In the "Divide Decimals" unit, students demonstrate Standard 5.1B by using models and written equations to communicate mathematical ideas clearly. These examples confirm that it integrates TEKS process standards into both teaching and learning throughout the grade 5 curriculum.

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

The grade 5 materials provide teacher guidance that supports mathematical thinking, student perseverance, and conceptual understanding. Lessons such as Show What You Know Part 2: Division Algorithm encourage the development of strategies for working through complex problems. In the "Fluency Builder" game "Division Problem Solving with Multi-Digit Divisors," students build long-term understanding by reasoning through division rather than relying on rote memorization. These resources help students persist through challenges and engage actively with mathematical content. In "Explore," students calculate the area of buildings by using area models and partial products, label their responses, and compare total areas to justify conclusions, offering real-world contexts and structured problem-solving tasks that provide opportunities for deep thinking and logical reasoning. For example, in Explore 2, students apply skip counting, repeated subtraction, estimation, and modeling to divide large numbers. Partner discussions and guiding questions reinforce math vocabulary and encourage persistence and step-by-step reasoning throughout the problem-solving process. Also in "Explore," students determine whether sample budgets are balanced and suggest realistic adjustments to correct imbalances by combining financial literacy tasks that require mathematical reasoning and reflection. In the "Future Planning" unit, the "Small Group Intervention" section, students work to develop financial record-keeping systems and consider strategies for modifying expenses when they exceed income. Additionally, in the "Divide Decimals" unit, students use base ten blocks to model and solve decimal division problems, responding to reflection questions such as, "¿Por qué es útil comprender el valor de posición al representar y resolver expresiones de división decimal?" These reflect consistent alignment by fostering student thinking, perseverance, and mathematical understanding across varied contexts.

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 grade 5 materials support students in understanding, explaining, and justifying that mathematical problems can be represented and solved in multiple ways. The "Explore" activities promote conceptual understanding by encouraging students to compare and explain various strategies, mirroring similar expectations. For example, in Explore 1, students create diagrams, label parts of real-world scenarios, and write equations to match their models. In Explore 2, students work collaboratively to build and revise visual models, examine different equations, and justify why each method works. In the "Add and Subtract" unit, the instructional materials provide tools that promote discourse and flexible problem-solving. In the "Explore" activities, students use place value disks, visual diagrams, and algorithms to solve real-world problems presented in scenario cards. For example, students record multiple representations in the "Student Journal" and reflect using questions, such as, "Al sumar o restar decimales, ¿cómo puedes determinar si tu solución es razonable y precisa?" ("When adding or subtracting decimals, how can you determine if your solution is reasonable and accurate?") In the "Elaborate" lesson of the "Income, Taxes, and Payment Methods" unit, "Problem-Based Task: Carley’s Budget," students apply skills collaboratively to solve open-ended budgeting challenges. The materials integrate real-world tasks that allow for multiple solution paths. For example, in the Choice Board activity, students complete tasks using varied representations, such as measuring parachute flight times, recording data, and modifying variables, reinforcing that problems can be approached and solved using different strategies, with clear justification and mathematical reasoning.

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 grade 5 materials provide multiple opportunities for students to make sense of mathematics through active problem-solving, collaboration, writing, and discussion. In Scope 6.8A in Explore 2, students use protractors, triangle cards, and rulers to measure angles and record their strategies and conclusions in journals. Students discuss their measurements with peers during Math Chats and respond to teacher-guided questions. In Explore 3, students construct and classify triangles using tools like geoboards, explain their reasoning through writing, and participate in group discussions, reinforcing comprehension through peer collaboration and reflection. The grade 5 materials support students in making sense of mathematics by offering opportunities to do, write about, and discuss mathematical ideas. In Scope 5.5A in Explore 2, students collaborate to sort and classify shapes, record their thinking in journals, and share ideas in classroom discussions. In Explore 3, students use hands-on materials to classify triangles by sides and angles to promote mathematical discourse and reflection through peer collaboration and teacher-guided questions. The Explore 4 activities in the "Divide Decimals" unit allow students to use their knowledge of place value and the standard algorithm to divide decimals in real-world contexts. The materials promote deep conceptual understanding through problem-solving and written explanation. The Student Journal activity asks students to determine the size of candy pieces by applying strategies and writing about their reasoning. In the "Numerical Expression" unit, in the Explain: Show What You Know Part 2 activity, students examine tables, write and solve equations, and draw visual models to represent mathematical scenarios, strengthening their ability to connect mathematical operations to written and visual representations. In the "Divide Decimals" unit in the Explore 1 lesson, students use base ten blocks and models to divide decimals with peers. Reflection questions in the "Student Journal" encourage both written and verbal reasoning: "¿Por qué es útil comprender el valor de posición al representar y resolver expresiones de división decimal?" ("Why is it useful To understand place value when representing and solving decimal division expressions?") The "Small Group Intervention" lesson extends this work by guiding students through decimal division using manipulatives and prompting reflection with questions to demonstrate understanding in the "Checkup" by integrating multiple opportunities to engage, write, and talk about mathematics: "¿Qué valor posicional esperarías tener como valor mayor en tu cociente?" ("What positional value would you expect to have as the largest value in your quotient?")

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 grade 5 materials provide structured support for teachers to guide students in sharing and reflecting on their problem-solving strategies, with a focus on reasoning, justification, and critical thinking. In Scope 5.3AHK, 5.4A in the Explore 3 activity, students use visual models to solve fraction problems and engage in partner discussions to explain their thinking. Teacher-guided questions prompt students to justify their methods, evaluate accuracy, and compare problem-solving approaches, allowing students to deepen their understanding through discourse. The Explore 4 section, in the "Multiply Decimals" unit, provides teacher guidance that supports student discussions around regrouping, equivalent fractions, and estimation. For example, the Explore 4 has structured reflection questions that encourage students to articulate their mathematical reasoning and justify their process during whole-class and partner discussions, and explain how area models and partial products connect to multiplication strategies. The "Divide Decimals and Numerical Expressions" unit reinforces student reflection through guided routines and prompts. The "Teacher Toolbox" includes "Structured Conversations" and sentence stems in "Structures for Intentional Discourse (Spanish)," such as the "Pair, Square, Share" routine, which supports discussion and exploration of diverse problem-solving methods. For example, students work collaboratively to write mathematical expressions, then share and reflect using teacher-guided questions to reinforce justification through contextual reasoning: "¿Qué crees que significan los paréntesis?" and "¿Cómo sabes qué operación completar primero?" ("What do you think the parentheses mean?" and "How do you know which operation to complete first?").

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

The grade 5 materials provide teachers with targeted support to deliver explanatory feedback by identifying student misconceptions and offering instructional strategies to address them. In Scope 5.AHK, 5.4A the "Content Support,""Misconceptions and Obstacles" materials identify common errors, such as confusing factors with multiples. Suggested strategies include using number lines, grid paper, and hands-on models to clarify student understanding. The "Engage," "Foundation Builder," "Possible Preconceptions" section adds further support by offering definitions, examples, and corrective guidance for vocabulary and concepts that students may misinterpret. These elements help teachers move beyond surface-level corrections and target the root of students’ misunderstandings. The materials provide teachers with specific tools to address student misconceptions and offer explanatory feedback in real time. For example, in Scope 5.3AHK, the "Multiplication Algorithm" fact fluency activities are embedded to help teachers correct misunderstandings as they occur. These opportunities promote accurate reasoning and support a growth mindset by treating mistakes as learning opportunities rather than failures. In the "Divide Decimals" unit, the "Scaffolded Instruction Guide" provides a structured plan based on student assessment data, directing teachers to relevant resources for intervention or enrichment. In the "Represent and Compare Decimals" unit, the "Teacher’s Guide" includes anticipated student responses and facilitation tips, such as addressing place value errors with visual models like base ten blocks and place value charts. These resources provide teachers with proactive feedback strategies that improve conceptual understanding through thoughtful, tailored support.