InsightMath Texas, Grade 5

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

The program includes a scope and sequence outlining the Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and course concepts. The scope and sequence establishes a clear order of instruction that helps educators pace learning effectively. It maps out a comprehensive yearlong instructional plan that shows when and how students learn each concept. The grade 5 scope and sequence also organizes instruction into units and clusters, providing consistency, coherence, and completeness throughout the program.

The materials incorporate the TEKS and ELPS taught in the course. Within the Grade 5 Overview, the “Standards” tab outlines the TEKS and ELPS addressed in each unit and lesson. The scope and sequence includes TEKS and ELPS alignment for the course, showing how and when these concepts occur throughout the grade level.

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 suggested pacing to support effective implementation of the program. The “Pacing Details” outline the concepts and the suggested number of days allotted for each unit. Additionally, the units are organized into clusters and lessons, further clarifying the pacing needed for effective program implementation.

The materials provide pacing for various instructional calendars. For example, the “Texas Program Overview Guides” web page provides pacing suggestions for a range of school-year lengths, including suggestions for 180-day and 165-day calendars. The two suggested calendars, organized into units, are accompanied by a recommended range of instructional days necessary to effectively implement the program. The “Grade 5 Pacing Guide” within the InsightMath Program Overview Guide, Grade 5 provides a clear overview of the content standards addressed throughout the year and the time allotted to units and lessons with the material.

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 grade 5 instructional materials include a rationale for unit order. For example, the “Big Ideas and Course Organization” section provides the rationale of unit order and how concepts to be learned connect throughout the course. The material provides a graphic illustrating the progression of learning, outlining the units, big ideas, and connections across domains and clusters. The materials explain how and why units are ordered and contribute to overarching learning goals.

Additionally, the “Balanced Instruction” section explains the logic underlying unit progressions about conceptual understanding, procedural skills, fluency, and application. The “Coherence” section within each unit specifically outlines for educators the connections among prior learning, the current unit, and future learning. The materials describe the intentional purpose of each unit and its sequence, explaining how concepts connect to future and prior learning.

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

Located in the Help Center, “Understanding the Structure of InsightMath” provides protocols for educators on internalizing the overall unit, cluster, and lesson structures of the materials. The article also provides guidance on effectively connecting content across lessons and highlighting the cluster and unit-level “Essential Understandings” and big ideas. Additionally, “Setting Up Your Planning Routine” provides guidance for educators on using the recommended protocols to internalize units and lessons in the program.

The Digital Planning Guide for each unit contains guidance to support educators in previewing the unit, understanding intended outcomes, and internalizing the sequence of learning within the unit and each lesson. For example, lessons include key information such as lesson timing, lesson overview, objectives, vocabulary, and brief activity descriptions. By expanding the individual sections, educators gather specific information about lesson delivery and student support, deepening their understanding of the overall lesson. Together, the structures provide support as educators gain an overall sense of the lesson and internalize its main aspects.

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

Materials include resources for instructional leaders to support educators in implementing the materials as designed. “Support for School-Level Leaders” in the Help Center contains resources for supporting schools through the first year of program implementation, such as suggestions for laying the foundation of the program: creating a shared vision, planning professional learning, and establishing implementation expectations. Furthermore, “Implementation Success Indicators” provide school-level leaders to address classroom environment, instructional practice, assessment, and data collection measures to equip instructional leaders throughout the implementation process, addressing challenges and providing solutions.

Materials include guidance for instructional leaders to support educators in implementing the materials as designed. The Help Center’s “School Implementation Timeline and Checklist” is a comprehensive list of monthly action steps to help instructional leaders support educators in implementing the program effectively. Additionally, “Supporting Data-Driven Leadership for School-Level Leaders” establishes a systematic approach to collecting, analyzing, and acting on information to maximize instructional leaders’ coaching of the program.

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

The grade 5 materials include comprehensive unit overviews that provide the background content knowledge necessary to effectively teach the concepts in the unit. A “Schema Building” section in each unit introduction provides background knowledge regarding the growth and development of content within the unit and how students’ schemas will grow and change relative to unit content. Additionally, each unit contains a “Math” tab that describes how math knowledge is balanced and connected to previous and future content, providing background for the educator on the extent of the content within each unit. Furthermore, “At a Glance” within each cluster of learning outlines the “Essential Understandings,” “Schema Building,” and cluster outcomes necessary for mastery of the material. The materials provide educator guidance to support concept development by outlining the background knowledge educators need to teach each lesson effectively.

Comprehensive unit overviews in the materials provide the academic vocabulary necessary to teach unit concepts effectively. Within the Grade 5 Overview, the “At a Glance” page summarizes the big idea driving each distinct unit of instruction. The materials review previously taught concepts at the beginning of each unit and describe connections students will build throughout the clusters and lessons. Furthermore, the materials include a glossary defining mathematical terms, accompanied by the grade level at which each is introduced and used in instruction. Listed vocabulary terms also appear at cluster and lesson levels of each 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.

The materials provide Spanish- and English-language resources that help families reinforce mathematics learning at home throughout each unit. For example, the “Family Guides – Texas” page contains links to support for families in English and Spanish, organized by grade and unit, with suggestions for supporting the growth of their student. The “Family Guide Grade 5” PDF outlines key math ideas, tips for home support, and suggestions for at-home practice of skills and concepts. The at-home activities support students’ understanding of unit concepts while encouraging families to use mathematical vocabulary during learning.

The materials organize family resources so educators can access and share Spanish- and English-language supports throughout the materials. For example, each unit’s “Resources” section contains a link to the “Family Guides – Texas” in English and Spanish, enabling educators to review, print, or digitally share the guides with families. The guide extends classroom learning by providing families with structured activities and strategies that reinforce concepts introduced during instruction.

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 materials organize daily instruction into a consistent sequence that supports effective teaching and learning. Each detailed lesson plan includes daily objectives, questions, tasks, materials, and formative instructional assessments required to meet the content and language standards of the lesson. In addition, the “Discourse Questions” and “Look-Fors” have an integral role in assisting educators to ensure that both content and language objectives are met by each student.

The grade 5 materials provide educators with the instructional components needed to implement each lesson from beginning to end. Lessons introductions include lesson and language objectives, key lesson questions, and aligned vocabulary needed for mastery of the content. Additionally, clusters integrate materials and formative instructional assessments into lessons to meet the content and language requirements for each lesson.

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

The instructional materials prepare educators with the materials and planning information needed before instruction begins. For example, “Preparing for This Lesson” lists the educator and student materials necessary to deliver each lesson, including prep notes, tools, and templates, and “Practice Pages” provide a comprehensive list and description of student and educator materials.

The grade 5 materials include the suggested timing for each lesson component in the program. The article “Understanding the Structure of InsightMath” in the Help Center outlines a consistent four-part lesson structure, including allotted time and guidance for “Launch,” “Explore,” “Reflect and Connect,” and “Workshop” activities.

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

The materials include guidance on providing opportunities for students to extend and reinforce learning beyond the core lesson. Within each lesson’s “Differentiation” section, details for “Extension” challenges support educators in collecting evidence of progress toward mastery. Additionally, within each lesson, “Workshop Time” contains game assignments that give students opportunities to investigate and practice a unit concept.

The educator resources explain how to implement extended learning opportunities within the lesson structure. For example, the grade 5 materials include the article “Understanding the Structure of Insight Math,” which provides specific guidance for educators on the use of the activities in the “Workshop Time” section of the lesson. “Workshop Time” offers strategies for additional practice activities that may be completed simultaneously, independently, or in small groups for extension, enrichment, or homework opportunities.

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.

The assessment resources measure student understanding at key points throughout each unit using a range of question formats and mathematical tasks. For example, each unit contains a diagnostic assessment to use at the beginning of the unit to identify prerequisite areas where students may need additional support, and a summative assessment at the end of the unit to assess unit content. These assessments contain a wide variety of question types, such as problem-solving tasks, concrete models, representational models, fill-in-the-blank, written response, true/false, multi-select, and real-world application, supporting educators in understanding students’ thinking and providing students many ways to show understanding.

Additionally, lesson-level assessment opportunities measure student understanding through multiple task formats and question types. For example, formative assessments appear within each cluster, indicating where educators should implement them. These embedded assessment opportunities incorporate diverse task formats and question types, enabling educators to monitor student progress during instruction and collect evidence of learning through various assessment experiences.

Lastly, the materials include a variety of instructional assessments at the lesson level, including formative assessments that vary in types of tasks/questions. For example, formative assessment opportunities are highlighted within each cluster and identified at the point where they occur within the lessons. Because of the embedded nature of these activities, the formats and question types used within these activities are especially diverse.

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

The grade 5 materials explain how each instructional assessment supports teaching and learning throughout the program. Each unit of study contains an “Assessment” tab with detailed descriptions of the purpose of the diagnostic, formative, and summative assessments provided. The program defines formative assessments as useful for “observing, eliciting, and analyzing evidence of student thinking.” Diagnostic assessments are “an opportunity for students to show the foundational skills previously mastered and to reveal areas in which they may need additional support.” Finally, each summative assessment “provides an opportunity for students to demonstrate they have met the key learning objectives of the unit.”

The article “Making Assessments Accessible for All Students” describes formative assessments as “especially productive moments where students show their thinking on paper, on screen, through conversation with peers, and in whole-class discussions within the context of daily lessons.” The article explains diagnostic and summative assessments as “intended for students to take independently to demonstrate their understanding of prerequisites before the unit and mastery of content and skills learned from the unit.” The program’s materials and resources give clear definitions and purposes of the types of assessments to support educators with planning, delivering instruction, and using assessment data to monitor student progress.

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

The materials provide structured administration procedures that support consistent implementation across classrooms. The diagnostic “Assessment Guide” section for each unit includes explicit implementation instruction, materials, an item map aligned with the TEKS, and suggestions for supporting students. The materials provide a script to ensure the administration of assessments is standard across examiners.

In addition, “Making Assessments Accessible for All Students” provides guidance for educators in determining how to accommodate students with special needs during assessments while ensuring the content and rigor of an assessment remain the same. The article outlines considerations to support all students during formative, diagnostic, and summative assessments, and the recommendations support accurate and reliable results for diverse students.

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

The materials’ formative assessments are aligned to the TEKS and objectives of the course, unit, or lesson. Within each cluster, formative assessments at the lesson level align to the TEKS and lesson objectives. The TEKS content and lesson objectives are clearly labeled. “Look-Fors” and “Discourse Questions” in the “Explore” block of each lesson contain activities, prompts, and questions aligned to the lesson objectives and the TEKS.

Additionally, the diagnostic assessments identify students’ prerequisite knowledge before instruction begins and help educators plan targeted support. For example, the section of the “Assessment Guide” on diagnostic assessments correlates each item number with the relevant TEKS, suggesting activities to help students build prerequisite skills and providing notes for educators to monitor emerging skills that will develop over the course of the unit.

Finally, the summative assessments measure student learning at the conclusion of each unit by evaluating mastery of unit objectives. For example, “Assessment Guide” entries for each summative assessment include an item map containing specific information on each item’s alignment to the TEKS.

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

The materials’ instructional assessments measure student understanding through multiple question formats and response types. For example, item types within the diagnostic and summative assessments vary in format and include matching, multi-select, fill-in, and open response. The TEKS-aligned instructional assessments within the program include two or more question types, providing a comprehensive view of student growth and learning.

Instructional assessments engage students in mathematical thinking across a range of cognitive demands. For example, assessment items vary in difficulty and ask students to create a model, choose a problem-solving strategy, write an equation, calculate, and solve real-world problems. The summative assessment section of the “Assessment Guide” provides information on each item’s alignment to Webb’s Depth of Knowledge (DOK) levels, indicating the level of complexity of the cognitive processes used within each item.

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

The grade 5 formative assessment resources help educators analyze student understanding and determine appropriate instructional next steps. For example, each formative assessment guides educators in interpreting student performance, noting specific student actions and misconceptions to notice, look for, or listen for to determine student mastery. Suggestions for supporting students and occasional extensions follow. Lastly, the materials offer the “Formative Assessment Recording Log” for recording student performance.

The “Assessment Guide” provides scoring support to help educators evaluate student responses consistently, such as scoring information and guidance for interpreting student performance via detailed examples of student responses, particularly when there is more than one possible answer. For instance, the diagnostic “Assessment Guide” section for unit 3 includes the following guidance: “(4 × 7) + 3 = 31. Students may also answer (5 × 3) + 16 = 31 or (4 × 4) + 15 = 31, and they may write the factors in any order, such as (7 × 4) + 3 = 31.” Unit 1 includes the following guidance: “Accept all answers that make the inequalities true,” and “Students may also estimate 6.4, 6.5, 6 1/2, 7, or other amounts between 6 and 7” as additional information following sample answers.”

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 diagnostic assessment resources connect student results to targeted instructional supports. For example, each unit in the “Assessment Guide” provides diagnostic assessment guidance on supporting students with emerging skills for each item aligned to the TEKS.

The assessment resources include instructional recommendations that help educators address patterns in student learning. For example, the grade 5 materials contain educator guidance to support students whose summative assessment performance indicates “Areas of Struggle.” The accompanying “Ways to Address” suggestions are designed to be used to respond to the needs of individual students or groups of students according to trends in the assessment data.

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

The assessment resources provide documentation tools that help educators monitor student learning throughout each unit. For example, each cluster level within every unit offers formative assessment opportunities. The “Formative Assessment Recording Log” is available for educators to track student growth during the unit by documenting observations and planning next steps. The log has an area for each student’s name, whether the cluster objective was met, anecdotal notes, and if support was needed or provided.

The lesson resources incorporate structured reflection opportunities that encourage students to monitor their own learning throughout the year. Students have multiple opportunities throughout a unit to assess their learning of the unit’s content in “My Thinking Path,” and their development of math process strengths in “My Goal” activities. A Thinking Path activity appears midway through and at the end of each unit, and there are Goal activities at the beginning, middle, and end of each unit. Because students work on the same strengths in “My Goal” activities throughout the year, they have opportunities throughout the course to reflect on their growth relative to the strength, tracking their progress and growth throughout the school year. For example, “I do not give up, even when a problem is challenging” appears in units 1, 5, and 9. “I choose representations to help me solve problems and to record and share my thinking” appears in units 1, 3, and 8.

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 provide targeted supports to help educators address unfinished learning and strengthen grade-level understanding. For example, the “After this Unit” page in each unit offers ways to support students who have yet to reach proficiency on grade-level content and skills. When students struggle to divide whole numbers to get a decimal quotient in unit 7, the program prompts educators to “Highlight the strategy of adding a trailing 0 to the end of the dividend as a way to continue dividing when a remainder exists, and encourage students to explain why this works rather than simply applying it.”

Furthermore, each grade 5 lesson includes a “Differentiation” section that provides educators with guidance on adjusting activities to support all students in meeting grade‑level proficiency. For example, in unit 6, lesson 4, the “Differentiation” component of the lesson suggests covering parts of the screen with sticky notes so that only one expression is visible; offering specific visual cues for lesson vocabulary; and providing sentence frames to support students in meeting the grade-level standard of discovering patterns involving fractions multiplied by whole numbers.

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

The materials provide instructional supports that help students understand unfamiliar language encountered during instruction. For example, within the “Differentiation” section of each lesson, the “Supporting Language” suggestions provide educator guidance, such as including sentence frames and key lesson vocabulary support. Additionally, this section contains support for in-text references that may need additional explanation, such as figurative language, idioms, and words with mathematical meanings that differ from colloquial meanings.

Furthermore, “Addressing the Needs of Special Populations in Texas” offers guidance for educators to support emergent bilingual (EB) students. For example, the article encourages educators to show central concepts multimodally by using different types of sensory inputs: acting out scenarios or inviting students to do so; showing videos or images; using gestures, and discussing the context of what is happening.

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 opportunities to deepen and extend learning beyond grade-level expectations with lessons containing an “Extension” challenge within the “Differentiation” phase. For example, in unit 4, lesson 3 suggests, “Challenge students to find patterns and determine faster or more organized ways to determine if a number is prime or composite (e.g., all even numbers are composite).” The “Teaching Guide” also suggests providing activities and tasks, including higher-order thinking, open-ended questions, and real-world applications.

Additionally, the grade 5 lesson “Analyzing Correlations of Real-World Scatterplots” includes an “Extension” activity in which students predict what they think data about the library’s Summer Reading Program will look like.

The materials include educator guidance for differentiated instruction, enrichment, and extensions to support students who have demonstrated proficiency in grade-level content and skills. For example, formative assessments for each lesson include a specific enrichment challenge activity for students. The educator guidance for differentiation and extension is evident. However, no educator guidance for enrichment is explicitly labeled.

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 lesson resources provide a structured framework that helps educators introduce and develop new mathematical concepts. Each activity within a lesson includes detailed steps and prompts to guide educators in modeling and explaining key concepts. For example, the “Explore” component of each lesson contains scripted explanations, details, and questions, emphasizing key learning moments, understanding, and vocabulary necessary for concept mastery.

The materials support effective instructional delivery through structured questioning and examples that build student understanding. For example, lesson activities include educator “Discourse Questions” for modeling and explaining concepts. Additionally, the “Look-Fors” provide student exemplars to support students in consolidating their understanding and restating it in clear mathematical language. Each phase of the lesson plan is summarized concisely, offering models and clear explanations for conveying key concepts.

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 prepare educators to facilitate instruction through a range of instructional routines for use throughout the program. Unit 0 introduces various instructional approaches for lessons and provides guidance on facilitating related activities, preparing educators for the types of learning interactions they will facilitate throughout the year. For example, unit 0, lesson 3 presents “Puzzle Talk,” an instructional approach in which students engage in a whole-class discussion, sharing strategies and analyzing feedback.

Additionally, the materials incorporate instructional routines such as virtual manipulatives, “Discourse Questions,” writing to justify answers, puzzles, and “Practice Pages” that support student engagement and mathematical understanding. For example, unit 1, lesson 8 uses puzzles, collaborative exploration, small-group and class discussion, Playbook assignments, and open-ended writing to teach adding and subtracting decimals with place value.

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 materials engage students in learning through a balance of instructional experiences designed to build understanding and reinforce new concepts. For example, lessons include a combination of guided, collaborative, and independent learning opportunities with detailed steps to implement those activities and facilitate discussions about the underlying mathematics.

The grade 5 materials organize instruction using flexible grouping formats that support various learning experiences throughout each lesson. Within each lesson’s “Workshop Time,” activities vary in structure and include a game or a “Practice Page” completed independently to provide students an opportunity to extend practice at their own pace. “Explore” activities within lessons are suggested for implementation in a small-group setting. Lastly, the “Reflect and Connect” phase of each lesson involves individual reflection followed by whole-group discussions, during which students share their written responses and hear multiple ways to justify an answer.

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

The materials include instructional guidance to support language development for EB students. “Addressing the Needs of Special Populations in Texas” includes educator guidance on providing linguistic accommodations for various levels of language proficiency. The article offers a list of universal language supports that are not called out within the “Differentiation” section for specific lessons and provides essential information for educators about the language supports within the “Differentiation” section. However, the educator guidance does not directly reference the ELPS proficiency levels to support EB students.

The materials do not contain differentiated linguistic accommodations for an additional language proficiency level. While supports such as sentence frames, visual cues, and vocabulary guidance are provided, there are no accommodations for multiple proficiency levels as defined by the ELPS.

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

The materials explain how to adapt and implement the program to meet the needs of EB and ESL classrooms. For example, “Addressing the Needs of Special Populations in Texas” includes implementation guidance and detailed instructions to support educators in effectively using and integrating the materials in state-approved bilingual/ESL programs. 

The Universal Design for Learning (UDL) offers further guidance on how to implement lessons to reach all students, including EB students. The UDL identifies the design elements that make the program especially accessible to EB students, providing explanatory details and a rationale for recommended use.

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 materials incorporate embedded language supports that help teachers strengthen students’ academic language and content understanding during instruction. Each lesson includes embedded guidance for educators to support EB students through “Supporting Language” in the “Differentiation” section. However, cross-linguistic oral and written connections are not present in the materials.

The materials encourage mathematical discussion that strengthens academic language and conceptual understanding. For example, the grade 5 lessons provide opportunities for oral discourse via “Discourse Questions” that develop academic vocabulary, increase comprehension, and build background knowledge.

The materials include embedded guidance for educators to support EB students in developing academic vocabulary, increasing comprehension, and building background knowledge through written discourse. Multiple lessons in each unit also provide opportunities for students to use written discourse to develop academic vocabulary, increase comprehension, build background knowledge, and make cross-linguistic connections.

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.

Practice opportunities throughout lessons require students to apply their learning in ways that demonstrate understanding of the grade-level TEKS. For example, in lesson 2, students use open area models and partial products to multiply multi-digit numbers, connect both strategies to the distributive property, estimate products, and explain how place value supports each method. Students discuss connections among area models, partial products, and equations before reflecting on how place value contributed to finding the product.

The materials include instructional assessments that allow students to demonstrate their understanding of grade-level mathematical concepts and skills aligned to the TEKS. For example, formative assessments embedded throughout each unit require students to represent multiplication and division concepts using multi-digit multiplication, fractional quotients, and division with multi-digit numbers. Additionally, the unit summative assessment requires students to apply these understandings to solve problems and demonstrate mathematical reasoning. These assessments require students to demonstrate depth of understanding aligned to the TEKS.

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

In lesson 1, students move from solving equations with a single unknown to recognizing that variables can represent multiple values, then create tables and graphs to compare additive and multiplicative relationships. In lessons 2 and 3, students use function machines to generate rules, tables, and graphs, explaining characteristics of additive relationships before extending their understanding to multiplicative patterns. In lessons 4–6, students represent and interpret real-world additive and multiplicative situations; identify distinguishing characteristics across tables, graphs, and equations; and write equations and create graphs from written scenarios, demonstrating increasingly complex application of the TEKS.

The materials sequence learning experiences to build students’ mathematical understanding from concrete to increasingly complex applications of grade-level concepts. Across unit 10, students progress from exploring variables with concrete examples to representing additive and multiplicative relationships with tables, graphs, and equations before independently applying these concepts to real-world situations.

Furthermore, “Discourse Questions” progressively increase in rigor and complexity by requiring students to analyze and compare multiple solution strategies for multi-digit multiplication. Students first identify the strategy used, then justify their reasoning and evaluate the effectiveness of different approaches by explaining which strategy they prefer and why. These questions increase cognitive demand and support grade-level proficiency aligned to the TEKS.

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

The materials establish clear connections among mathematical concepts throughout the course, reinforcing important patterns and relationships as students progress from unit to unit. The materials demonstrate coherence across units by connecting students’ prior understanding of place value and decimal fractions from grade 4 to decimal operations in grade 5. The “Schema Building” section explains that students extend their understanding of multiplicative relationships between adjacent place values and apply this understanding to multiplying and dividing by powers of 10. These connections reinforce the base 10 system as a unified structure and highlight relationships among place value, decimals, and operations.

The grade 5 materials demonstrate consistency and clarity across units by connecting patterns, big ideas, and relationships. The “Course Organization” article for each grade level explicitly details how patterns, big ideas, and relationships among mathematical concepts connect throughout the grade level. For example, students use their knowledge of multi-digit multiplication from unit 2 to help them calculate the volume of rectangular prisms in unit 4.

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.

Grade 5 materials connect content and academic language learned in previous grade levels to current grade-level learning. The “Schema Building” section explicitly states that students enter grade 5 with an understanding that decimals extend the place value system and that multiplicative relationships exist between adjacent place values. Students build on previously learned concepts and vocabulary, including place value, decimal fractions, multiplication, division, and powers of 10, to develop an understanding of decimal operations and the base 10 system.

The materials build on students’ prior mathematical language by reinforcing familiar vocabulary while introducing new terminology in context. For example, in unit 10, students use the coordinate plane and the use of a variable to represent an unknown quantity to represent how two quantities change in relation to each other. The understanding students build here—that equations, tables, and graphs represent the same relationship—is fundamental for grade 6 work with proportional relationships, rates, and using variables to represent two quantities that change in relation to one another.

Finally, the materials connect current grade-level learning to future grade-level learning through “Coherence” sections, which draw direct connections among students’ prior, current, and future learning with regard to big ideas, patterns, and conceptual relationships.

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 materials connect previously learned and current mathematical concepts to new content, enabling students to build on existing knowledge as they develop deeper mathematical understanding. The grade 5 materials organize lessons into clusters that develop a shared mathematical understanding. Just as the clusters within each unit build the unit’s big idea, the lessons within each cluster build the cluster’s “Essential Understanding.” For example, in unit 1, cluster 2, the “Big Idea” section states, “Place value is the foundation for understanding how decimals are written, ordered, and rounded.” Throughout the lessons in this cluster, the materials connect concepts and procedures across the current grade level to deepen students’ understanding of place value with decimals.

The materials connect mathematical procedures from current and previous grade levels to new learning, supporting students as they apply and extend procedural knowledge in increasingly complex situations. At the beginning of each lesson, the Digital Planning Guide includes lesson descriptions that situate the lesson’s content in relation to students’ previous learning and preview the concepts they will develop in future lessons. “Discourse Questions” within each lesson prompt students to connect prior knowledge to new mathematical skills. Lessons within and across units follow a coherent learning progression that intentionally builds on previously developed concepts. For example, in unit 1, lesson 1, students apply their prior understanding of factors while exploring how factor pairs create rectangles. In unit 1, lesson 4, students extend that understanding by exploring multiples and discussing that multiples continue infinitely.

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

Units and clusters conclude with one or more lessons featuring mixed review of content from across the unit. This cumulative review prompts students to determine which operations or strategies best fit each task while identifying the distinguishing features that guide their mathematical decisions. For example, in the final three lessons of unit 6, students review addition, subtraction, multiplication, and division skills from units 1–3, helping them recognize key characteristics of each situation and select appropriate operations and solution strategies based on the context and the numbers involved.

The lesson resources integrate ongoing review into daily instruction to strengthen students’ recall of previously learned concepts. Each lesson includes a student “Practice Page” with spaced spiral review problems. For example, in the unit 3, lesson 6 “Practice Page,” students review “shapes with perpendicular sides,” a concept from grade 4, “identifying multiples,” a concept from earlier in grade 5, and finally solve multistep problems from the current lesson.

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

The materials reinforce previously taught skills by integrating review opportunities into daily instruction. Each lesson includes a student “Practice Page” with spaced spiral review problems to interleave with the targeted practice aligned to the day’s focus and word problems. In the unit 3, lesson 6 “Practice Page,” students review a concept from grade 4, “shapes with perpendicular sides,” and “identifying multiples,” a concept from earlier in the grade, before solving multistep problems from the current lesson.

The materials revisit mathematical concepts throughout the course to strengthen connections across lessons and units. For example, unit 6 develops students’ understanding of multiplying and dividing fractions. Unit 7 then extends those concepts by combining fraction multiplication and division with whole-number computation strategies and the place-value structure of Additionally, in the unit 3, lesson 6 “Practice Page” students review “shapes with perpendicular sides,” a grade 4 concept, and “identifying multiples,” a concept introduced earlier in grade 5, before solving multistep problems from the current lesson.

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

The questions and tasks require students to interpret models and representations for mathematical concepts and situations. Across a cluster, unit, or group of related units, students begin by making sense of concepts through manipulatives and visual models, then progress toward flexibly using numerical or symbolic representations and strategies. Students interpret, analyze, and evaluate a range of models and make connections between various models and strategies. For example, in unit 6, lesson 1, “Discourse Questions” such as “How does each equation match its picture?”, “What is the same or different between these two equations?”, “Where do you see equal groups in the pictures?”, and “Where do you see equal groups in the equation?” require students to interpret mathematical representations and analyze the relationship between models and equations. In activity L2, students continue this work by comparing multiple equations and representations through questions such as “How are the equations the same or different?”, “Where do you see how many sea stars there are in each equation?”, and “How do both equations show equal groups?”, requiring students to analyze and evaluate how different representations model the same mathematical concept.

The questions and tasks require students to analyze models and representations for mathematical concepts and situations. For example, students interpret, analyze, and evaluate strip diagrams to discuss how they represent multiplicative and additive relationships. In unit 6, lesson 1, “Students explore various ways to demonstrate how repeated addition of unit fractions relates to multiplication, and they examine visual models and write equations to replicate the models. Through discussion, students begin to see the relationship between the numerator of the product and the whole-number multiplier.”

The questions and tasks require students to evaluate models and representations for mathematical concepts and situations. In the “Explore” section of unit 3, lesson 7, students interpret real-world situations from word problems regarding fundraiser sales. They must evaluate how to translate the scenarios into a mathematical representation, a multistep equation, to solve for an unknown total. During the strategy-sharing phase, students analyze their peers’ mathematical models, evaluating and explaining why they chose particular operations, and justifying why their chosen solution path is mathematically efficient.

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

The materials contain questions and tasks in which students construct mathematical models to represent and communicate real-world and mathematical situations. For example, in unit 6, lesson 9, students construct, compare, interpret, and connect mathematical representations—including visual models, equations, and contextual situations—to solve multiplication problems involving fractions and whole numbers, explain relationships among representations, and justify their mathematical reasoning.

Additionally, the tasks require students to create models representing mathematical situations. Across a cluster, unit, or group of related units, students begin by exploring and demonstrating understanding of concepts through manipulatives and visual models, then progress toward flexibly using numerical or symbolic representations and strategies. Students create a range of models and make connections among various models and strategies. In unit 6, lesson 5, students create and use fraction models in a game and on paper to represent multiplying whole numbers by fractions in mathematical and real-world contexts.

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

The materials include questions and tasks that encourage students to extend their mathematical understanding by applying previously learned concepts to unfamiliar situations and meaningful contexts. Within and across lessons, students learn concepts through simple examples, then transfer and reinforce their understanding through additional tasks with less scaffolding and/or greater challenge. In unit 6, lesson 9, students progress from drawing and analyzing visual models to explain why taking a fraction of a whole number uses multiplication, to connecting this to the commutative property and to whole-number division, then to multiplying fractions by whole numbers without visual support. At each stage, students first learn the concept, apply it to a new and similar task with less scaffolding, and finally apply it to a more complex situation as their schemas grow.

Additionally, the culminating lesson for unit 6 provides students with opportunities to apply conceptual understanding by connecting visual models, equations, and real-world contexts involving fractions. Students analyze and match fraction models to multiplication and division equations, explain relationships among equivalent representations, and justify their reasoning. They then apply this understanding to solve contextual problems involving recipes, measurements, and bead designs using dot plots, fractional measurements, and equations. Students generate their own questions, write corresponding equations, and use multiple representations to communicate mathematical thinking. These tasks require students to transfer prior learning about fractions, operations, and measurement to new situations while explaining and defending their mathematical reasoning.

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

The materials reinforce the student automaticity necessary to complete grade-level tasks, such as targeted lessons that support developing grade 5 fluency with adding and subtracting positive rational numbers (fractions and decimals) fluently. In unit 1, students practice adding and subtracting decimals, first with conceptual supports of place-value tokens and place-value charts, then using the standard algorithm in lesson 8, and finally using strategies of their choice with contextual problems in lesson 9.

The materials include tasks that promote fluent use of mathematical strategies and procedures to solve grade-level problems accurately and efficiently. Unit 1, lesson 8 provides multiple opportunities for students to develop computational fluency with decimal addition and subtraction. Students estimate before solving, use place-value representations, solve computations accurately, analyze the reasonableness of solutions, identify and correct errors in regrouping, complete missing-digit problems, and engage in independent practice. These repeated opportunities promote accuracy, efficiency, and flexible use of computational strategies while reinforcing conceptual understanding.

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 materials provide opportunities for students to strengthen efficient problem-solving by applying mathematical procedures throughout lessons and across the unit. For example, in lesson 13, students apply procedures for finding differences between mixed numbers and fractions using visual models and equivalent fractions. Students solve partner tasks, complete independent practice, compare and justify different solution models, and explain their reasoning using mathematical language. The lesson culminates with a “Practice Page” that requires students to independently solve subtraction problems involving fractions and mixed numbers, reinforcing procedural efficiency through repeated practice, comparison of strategies, and mathematical justification.

The materials include opportunities for students to use and compare flexible solution strategies and to apply mathematical procedures throughout instruction. Students practice flexible strategies through a specific focus on individual skills and immediate practice and reinforcement. For example, unit 5, lesson 2 introduces students to three efficient strategies for adding and subtracting mixed numbers (consecutive strategies, regrouping, and converting mixed numbers to fractions), then solve practice problems with a choice of the three strategies. They end by discussing which strategies they would use for different numeric situations that do and do not require regrouping wholes.

Additionally, students reinforce procedural accuracy through repeated application of mathematical procedures within lessons and across the unit. For example, as students solve two-step word problems involving mixed numbers in unit 5, lesson 13, the shared strategy discussion focuses on a key method choice: deciding when to solve using mixed numbers versus converting to fractions greater than one. This gives students direct practice in selecting the most efficient and accurate way to calculate based on the structure of the numbers in the problem.

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.

Students evaluate procedures, processes, and solutions for efficiency within the lessons and throughout the units. For example, in unit 5, lesson 5, students notice that in some circumstances they can add or subtract fractions with different denominators by finding equivalent fractions that have a lesser denominator—that is, by dividing the numerator and denominator by the same number instead of multiplying. Students compare the efficiency of different strategies for creating common denominators and notice when it is possible to use lesser denominators.

Lessons throughout the units offer opportunities for students to evaluate procedures, processes, and solutions for flexibility. For example, in unit 2, lesson 7, students demonstrate procedural fluency by estimating, selecting appropriate procedures, and accurately solving contextual problems involving mixed numbers and fractions. They apply fraction addition and subtraction procedures to real-world situations, use estimation to assess the reasonableness of solutions, compare distances, and justify decisions based on their calculations. The lesson reinforces procedural accuracy while encouraging strategic application of efficient methods in meaningful mathematical contexts.

Students evaluate procedures, processes, and solutions for accuracy within the lessons and throughout the units. In unit 5, lesson 7, for instance, students “continue to build their schema for adding and subtracting with related denominators as they start to select strategies more flexibly. They consider which fraction should be reexpressed to solve most efficiently. Students will build upon this thinking in future lessons when they consider the ways both denominators can be reexpressed in cases of unrelated denominators.” The lesson structure enables students to evaluate processes and solutions for efficiency and flexibility throughout the lesson.

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

In many lessons, the “Details,” “Look-Fors,” and “Discourse Questions” support the educator in guiding students toward a more efficient strategy in a learning trajectory that progresses across each cluster, unit, or group of related units. For example, the unit 5, lesson 10 “Discourse Questions” and “Look-Fors” support educators in guiding students to notice efficient strategies for finding common denominators, ending by discussing the advantages and disadvantages of each method.

Furthermore, many activities contain student exemplars called “Argumenteers.” Often, these Argumenteers steer students toward key strategies for efficiency. The “Details” section explains how to use the Argumenteers to enhance classroom discussion while guiding students toward increasingly efficient approaches. For example, Argumenteers in unit 5, lesson 6 show efficient strategies for adding and subtracting mixed numbers with different denominators, as well as ways that students could notate them. Students begin by using their own solving strategies, then progress toward using a more efficient strategy in the next similar task and across the unit. After students have seen several examples with the new strategy, they practice without this support, adding and subtracting with additional word problems and new types of visual models.

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

The program directly addresses the conceptual and procedural emphases of the TEKS at the unit level. Each unit includes a “Coherence” section that explains the relevant content that students learned in prior grades and units, the progression of concepts and skills that build across the unit, and how these will support students in future grades and units. For example, in unit 5, the “Conceptual Understanding” section states, “Students develop understanding of fraction addition and subtraction by recognizing that fractions can only be combined when they represent the same-sized parts. Building on their grade 4 work with equivalent fractions, students now explore how to create same-sized parts through common denominators, recognizing that when one denominator is a factor or multiple of another (related denominators), only one fraction needs rewriting, while unrelated denominators require both fractions to be rewritten.”

The materials communicate how students develop procedural knowledge and apply the mathematical skills required by the grade-level TEKS. A section within each unit explains the conceptual and procedural focus of the unit. In the unit on “Exploring Two- and Three-Dimensional Space,” students’ understanding of volume progresses from defining volume in terms of cubic units to recognizing how layers of area build (conceptual emphasis) to create volume (V = Bh). Students progress from counting individual unit cubes to using the formulas V = Bh and V = lwh efficiently when calculating volumes of rectangular prisms (procedural emphasis).

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.

Throughout grade 5, questions and tasks include the use of concrete models and manipulatives, pictorial representations, and abstract representations. In many lessons, units, and clusters, students begin with more concrete representations and models, then transition to more abstract representations. For example, in unit 7, lesson 1, students use virtual or physical base 10 blocks to represent making equal groups of decimal amounts and associating this with multiplication expressions. Students then represent multiplication expressions with hops of decimal amounts on the number line.

In addition, students build upon knowledge of pictorial representations in unit 7, lesson 6 through the computer game Fraction Area Multiplying Tenths. Students move blocks on their screens to divide grids into smaller sections, which builds a visual understanding of how decimal multiplication works. Students examine a visual area model to understand decimal multiplication using whole numbers before shifting to decimals. They partition the drawing and discuss why a solution works. Then they use the area model to explain why multiplying tenths by tenths results in an abstract product written in hundredths.

The questions and tasks include the use of abstract representations. Unit 7, lesson 6 develops conceptual understanding of decimal multiplication through concrete and pictorial representations before moving to abstract notation. Students construct area models, represent decimal factors using hundred grids, interpret completed models, connect visual representations to multiplication equations, and solve decimal multiplication problems independently. The lesson intentionally progresses from modeling to symbolic reasoning, demonstrating multiple mathematical representations that deepen conceptual understanding.

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.

As students define, create, explain, and connect concrete and representational models to abstract concepts, “Differentiation” sections of many lessons provide educator guidance to support students in connecting these representations. For example, in unit 7, lesson 11, the activities on the slides and the “Discourse Questions” prompt students to use, create, and explain how unit square models represent dividing whole numbers by whole numbers to get a fractional quotient. The “Differentiation” section provides additional strategies to support students in connecting models to abstract representations.

The materials include supports that guide students in constructing and creating concrete and representational models to demonstrate and communicate abstract mathematical concepts. In unit 7, lesson 11, the activities on the slides and the “Discourse Questions” prompt students to use, create, and explain how unit square models represent dividing whole numbers by whole numbers to get a fractional quotient.

Lastly, the materials include supports that encourage students to define and explain abstract mathematical concepts by using concrete and representational models to justify their mathematical thinking. The “After This Unit” suggestions in unit 6 offer support for students who are struggling to represent a fraction as a product of unit fractions. The guidance advises educators to “Encourage students to represent a fraction with bar models that show unit fraction and write all three forms side by side. Continue to use bar models that make each unit fraction visible as a separate piece. Ask students to describe what the whole number and the unit fraction each tell them before making their calculation.”

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

The materials support mathematical communication by connecting visual models to academic vocabulary and conceptual understanding. Students engage with new mathematical language by using manipulatives. In unit 4, lesson 6, for example, students use linking cubes to build figures. During a discussion of the figure, students learn new vocabulary terms, including unit cube and cubic unit, which further develop their understanding of volume. This concrete manipulative helps students visualize the mathematical terms they are learning.

The materials encourage collaborative mathematical discussions in which students listen to, build on, and strengthen their use of mathematical language through ongoing peer interactions. For example, through unit 9, lesson 6, students develop academic mathematical language while investigating the coordinate plane through visual models, structured discourse, and vocabulary instruction. Students initially explain directions using their own language, then refine their explanations as the educator introduces academic vocabulary, including coordinate plane, x-axis, origin, ordered pair, horizontal number line, and vertical number line. Educator guidance intentionally supports language development by prompting students to discuss, revise, and justify their reasoning through partner conversations, whole-class discussions, “Look-Fors,” and “Discourse Questions.” Students use precise mathematical language to describe movement, explain locations on the coordinate plane, identify ordered pairs, and justify why particular points or shapes satisfy given conditions. Visual coordinate plane representations provide contextual support while students transition from informal language to precise mathematical terminology.

The materials promote the development of mathematical vocabulary through structured opportunities to discuss, explain, read, and write about mathematical ideas.

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

The materials explain how the mathematical process standards support instruction across lessons and learning experiences throughout the course. During a unit 9 lesson on representing polygons on the coordinate plane, for example, the educator guidance scaffolds new vocabulary by giving students a set of ordered pairs for which they must determine what shape can be made. This activity prompts the comparison of an unlabeled grid to a labeled grid. Through the discourse that follows, the educator asks, “How does having labels on the grid change how we know where to place the points?” and “Why do we need a standard starting point?” These questions establish the need for a coordinate grid and the axes, enabling students to realize that without a clear, labeled system, positioning is random. The educator then attaches the formal name coordinate grid to the tool that solves this problem.

Embedded educator prompts and instructional routines in the materials encourage students to develop and apply precise mathematical terminology within mathematical contexts. Within the “Differentiation” section of each lesson, “Supportive Language” suggestions provide sentence frames, additional important language, and other strategies to support expressive and receptive mathematical language and scaffold language development to meet each student’s needs. In unit 9, lesson 1, sentence frames such as “The [color] triangle belongs in the [category name] group. The [color] triangle belongs in the [category name] group because ____. I can sort and categorize triangles by ____”, serve as embedded instructor support to scaffold vocabulary development as students internalize triangle attributes.

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 materials include embedded educator guidance that intentionally develops students’ mathematical language through vocabulary instruction, structured syntax, meaningful discourse, and opportunities for collaborative mathematical conversations. After students analyze equal groups and repeated addition, educators introduce and reinforce the academic vocabulary multiply and multiplication, explicitly defining multiplication as “finding the total of equal groups or equal parts.” The materials direct educators to model appropriate mathematical syntax by reading equations aloud using precise language, such as “3 multiplied by 5 equals 15” and “3 times as much as 5 is 15.” These language models provide students with examples of how multiplication equations should be communicated using accurate mathematical terminology. The materials further support mathematical discourse prompts that require students to explain and justify reasoning, including “How does the repeated addition/multiplication equation represent the number of shoes?” “How are the equations the same and different?” “Could you write a multiplication equation for 10 + 2 + 5 = 17? Why or why not?” These questions encourage students to compare representations, analyze mathematical structure, justify their reasoning, and communicate using academic language. Embedded “Look-Fors” identify the mathematical language and reasoning educators should expect to hear, such as students explaining that multiplication represents equal groups, identifying what each number in the equation represents, and correctly using the terms multiply and multiplication in their explanations. Educators also identify the common misconception that unequal groups can be represented with multiplication, allowing them to facilitate productive mathematical discussions that clarify understanding.

The materials encourage collaborative mathematical discussions in which students listen to, build on, and strengthen their use of mathematical language through ongoing peer interactions. During the unit 10 lesson on identifying independent and dependent variables, the materials direct the educator to anchor the concept by asking the open-ended contextual question “What does it mean for something to depend on something else?” Once students ground themselves in the concept, the materials provide explicit scripting to introduce the definitions: “After students have used their own language to explain their thinking, introduce the vocabulary terms dependent variable (a variable that depends on the independent variable) and independent variable (a variable that does not depend on any other variable).” The educator then uses the “Look-Fors” and “Discourse Questions” to expand student thinking and keep mathematical conversations focused on the relationship between the two variables.

The materials provide educators with exemplar responses that illustrate expected mathematical thinking and support effective questioning and feedback during instruction. Each cluster of study within a unit contains a “Common Errors and Misconceptions” support section for educators. In unit 7, for example, the educator guidance addresses ways to correct misunderstandings about decimal multiplication. Embedded exemplars such as “When asked why the decimal point is placed in a particular position, students say, ‘Because that is the rule’ without reference to place value” provide educator scaffolding and support.

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

Grade 5 instructional materials integrate the TEKS mathematical process standards throughout instruction by embedding mathematical practices within the content lessons. In unit 1, for example, the materials explicitly identify the applicable TEKS mathematical process standards and describe how students apply mathematics to authentic situations involving money, measurement, consumer decisions, and decimal operations. Students engage in structured problem-solving by analyzing information, formulating solution strategies, determining and justifying solutions, evaluating the reasonableness of answers, and reflecting on their mathematical reasoning. The materials identify the lessons in which each process standard is addressed, demonstrating intentional integration of the TEKS mathematical process standards throughout instruction.

The materials embed the mathematical process standards within lessons and activities, allowing students to apply reasoning, problem-solving, communication, and representation while learning grade-level mathematics. The unit 10, lesson 10 activity on analyzing data in stem-and-leaf plots and dot plots provides students with an opportunity to engage with TEKS 5.1F. Students analyze data representations to identify the number of data points that meet the given criteria and explain the steps they take to relate this value as the numerator of the fraction and the total number of data points as the fraction’s denominator, such as “I know the fraction of skateboarders who practiced less than 3 hours is 10/25 because there are 10 dots for 1/2 hour through 2 1/2 hours and there are 25 total dots in the dot plot.”

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

The materials explain how the mathematical process standards support instruction across lessons and learning experiences throughout the course. Grade 5, lesson 3 identifies process standards 5.1E and 5.1F alongside the content TEKS and describes how students create representations, organize and communicate mathematical ideas, and analyze relationships between partial products and the standard algorithm. The lesson-level implementation demonstrates how the program integrates process standards across lessons and units.

The materials describe the relationships among the mathematical process standards and their continuity across the course. The materials include a clear, intentional design that integrates process standards throughout the lessons, reinforcing lesson concepts throughout the unit to build mathematical fluency and strong math habits. Rather than isolating a skill to one lesson, multiple process standards coalesce in a single activity, ensuring that a data-analysis activity is never just about plotting a point or reading a graph, for example. Students select an equation or a graphing tool, figure out how the independent and dependent variables relate, and explain the real-world story or correlation to their classmates using precise math language. This overlapping design helps the process standards become everyday math habits across the course.

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

The materials explain how the mathematical process standards support instruction and learning experiences within each unit. Several learning experiences incorporate process standard 5.1B. For example, in unit 10 lessons 8, 9, and 11, “Students use a structured problem-solving approach throughout the unit as they work with scatterplots, data tables, frequency tables, bar graphs, stem-and-leaf plots, and dot plots. They begin by identifying what is known and what they need to find, and then they select appropriate representations and operations to reach a solution. Students justify their solutions by referencing specific data points or graph features (e.g., explaining why a line through the origin signals a multiplicative relationship) and evaluate the reasonableness of their answers by checking them against the data or a different representation. This cycle of analysis, strategy, solution, and reflection runs through every cluster of the unit.”

Furthermore, the materials describe the relationships among the mathematical process standards and their continuity throughout each unit, including in the article “InsightMath Texas—Connecting the Process Standards.” InsightMath Texas intentionally incorporates the seven TEKS mathematical process standards throughout its curriculum using a progressive system of student strengths that build in complexity across grade levels. Instead of treating these standards as isolated skills, the curriculum combines multiple process standards within the same lesson, which ultimately continues throughout the course.

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

The materials identify the mathematical process standards addressed within individual lessons to support instructional planning and implementation. The lesson 2 overview notes that the TEKS mathematical process standard 5.1D is incorporated into the lesson, explaining how students communicate mathematical reasoning by connecting equations, input–output tables, and graphs, interpreting multiple representations, and explaining the relationships among them. The overview clearly describes how the process standard is integrated into lesson instruction.

The materials provide lesson-level information identifying the mathematical process standards associated with the instruction, including educator guidance for each mathematical process standard that is incorporated into a lesson. For example, unit 10, lesson 10 states that the mathematical process standard 5.1.C is addressed as “Students use pencil and paper to create tools such as stem-and-leaf plots and dot plots to represent data, and they select which tool they prefer to use to answer questions comparing data points. They also use mental math and number sense techniques (e.g., visually comparing the number of dots on a dot plot to determine the difference between two scores) to solve one- and two-step problems that involve comparing values and finding differences.”

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

In grade 5, unit 0, students complete activities focused on developing mathematical thinking, perseverance through problem-solving, and making sense of mathematics. These activities provide students and educators with the language needed to explicitly use, build, and discuss these skills throughout the grade level. In addition to the activities themselves, the math process standards highlight these skills within each lesson in unit 0 and throughout the course. The lessons in the first unit introduce students to open-ended, creative mathematical challenges with low floors and high ceilings while developing the mathematical mindsets, language, and skills students need to engage in creative mathematical thinking throughout the year.

The materials require students to persevere through problem-solving. For example, in unit 2, lesson 13, students think mathematically as they analyze relationships among customary units of capacity, predict outcomes, select appropriate operations, and compare multiple solution strategies. Students persevere through problem-solving as they independently analyze conversion situations, discuss their reasoning with partners, evaluate feedback, compare multiple puzzles, and determine when multiplication or division is appropriate. The materials support students in making sense of mathematics as they explain unit relationships, justify operational choices, compare representations, and communicate their mathematical reasoning through structured discourse.

Students make sense of mathematics throughout the program. In the unit 2, lesson 13 “Launch,” students do more than calculate answers. They analyze a visual puzzle to evaluate why a conversion strategy works. The discussion questions “What does the key tell you?” and “Which unit of measurement is larger? How do you know?” encourage students to focus on the relationship between units, such as pints and cups, rather than rely on a procedural strategy. Students think critically about the relative sizes of units to determine the mathematical operation needed to solve the problem.

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

The materials guide students to understand, explain, and justify multiple ways to represent and solve problems. In the unit 2, lesson 1 ST Math video game, students use base 10 blocks to model products, connect concrete models to symbolic representations, and reason about place value, factors, and the distributive property. Students analyze the Critter’s strategy, solve multiplication problems by factoring numbers in different ways, compare multiple solution strategies, and explain why different representations produce the same product. Educator guidance, including “Look-Fors” and “Discourse Questions” such as “What strategy did you use?” and “Do you think of this problem the same way as the Critter? Why or why not?”, prompts students to explain why three groups of 300 equal 900; describe how 300 can be factored as 3 × 100; justify why multiplying the nonzero digits and then applying powers of 10 produces the same product; and compare, defend, and evaluate multiple solution strategies using precise mathematical vocabulary.

Students explain multiple ways to represent and complete tasks through numerous opportunities for mathematical reasoning. In the unit 2, lesson 2 “Explore” section, students use an open area model and a partial-products algorithm to multiply two-digit numbers. As students share their thinking, they identify connections between the two strategies by comparing their similarities and differences. Educator prompts such as “What is the same [or different] about each strategy?”, “How do the values inside the area model relate to the partial products?”, and “What is the sum of the values inside the area model? Where else do you see this sum?” encourage students to explain and justify how the representations connect and demonstrate the same multiplication process.

Students must justify their thinking in representing and solving mathematical problems. In unit 2, lesson 5, students solve problems and complete tasks using tools, models, and strategies of their own choosing. Some activities in this lesson include Argumenteers showing different methods for solving the same problem and enhance discourse by encouraging students to explain and justify that multiple approaches can solve problems and complete tasks. Argumenteers support students as they understand, explain, and justify multiple approaches or strategies by placing effective target strategies alongside students’ strategies. In this lesson, slides E1b, E2b, E3a, and E3b include Argumenteers that demonstrate how students can use different strategies to divide whole numbers and obtain fractional quotients.

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.

Students have multiple opportunities to make sense of mathematics through collaboration with their educator and peers. Each unit includes two lessons with a “My Thinking Path” activity for “Workshop Time.” For example, in unit 2, lesson 7, students reflect on and make sense of the mathematics they have explored throughout the cluster by writing about their thinking and discussing their ideas with their educator and peers.

Students do, write, and discuss mathematics while developing their understanding through interactions with educators and peers. For example, in unit 2, lesson 7, students complete math journal entries about the unit’s big ideas in their Playbooks, share their thinking with a partner, contribute to whole-class discussions and class charts, and represent their thinking through writing or drawings. Students ask questions about classmates’ reasoning; make connections between ideas; reflect on how their understanding has changed; and monitor their mathematical growth by setting goals, evaluating their progress, and identifying next steps. Educator “Discourse Questions” prompt students to explain and justify their reasoning, compare their thinking before and after instruction, and describe strategies for continued improvement as mathematicians.

Discussion activities require students to make sense of mathematics. Each lesson requires students to make sense of mathematics by exploring, writing, and discussing ideas with their educator and peers. In unit 2, lesson 1, students first explore and discuss patterns in the number of zeros when multiplying single digits by multiples of powers of 10 through visual models. Students then explain a sample strategy for multiplying by factoring out powers of 10, solve a similar problem independently, and discuss how they chose to factor and multiply to find the product. Students continue to multiply using area models—and by factoring, discussing the approaches they selected, and writing about the patterns they observe, consolidate and share their understanding of multiplying by powers of 10. The “Details,” “Look-Fors”, and “Discourse Questions” prompt students to show their thinking using models, equations, and words, and then discuss their strategies and reasoning with peers.

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 program supports educators in encouraging students to share explanations, arguments, and justifications. The lesson notes provide educators with “Details,” “Look-Fors,” and “Discourse Questions” to guide students in sharing and reflecting on their problem-solving approaches by analyzing different strategies and justifying why one strategy may be preferred over another. In unit 7, lesson 9, for example, students solve word problems involving decimal multiplication. Students reflect on their problem-solving choices and justify their decisions to their peers by explaining why they used a factoring strategy or a partial-products strategy with an open area model.

The materials provide educator guidance to support student reflection on problem-solving through explanations, arguments, and justifications. In unit 7, lesson 9, students estimate decimal products, explain their reasoning, solve problems using a strategy of their choice, and compare approaches such as factoring and partial products with an open area model. Students use Argumenteers to analyze multiple solution strategies and discuss the mathematical reasoning behind each method. “Look-Fors” and “Discourse Questions” prompt students to explain their estimates, justify why a strategy is effective, describe how the open area model represents multiplication, explain metric conversions such as kilometers to meters, and compare the efficiency of different solution strategies.

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

The materials include prompts that support educator feedback based on student responses and anticipated misconceptions. For example, in unit 1, lesson 1, the educator prompts students to verbalize that each place to the left represents 10 times as much and each place to the right represents one-tenth as much. Educators ask questions such as “What do you notice about how many flats are in the cube?”, “Do you see this same relationship between any other base 10 blocks?”, “How many of each base 10 block are needed to make a cube?”, “What do you notice about how many of them are needed?”, and “How did using the cube to represent the ones place impact what base 10 blocks you used to represent the other place values?” This line of questioning helps ensure that students recognize the patterns connecting decimal place value to whole-number place value, preventing a common error.

Additionally, for each unit and cluster, educators receive guidance on providing explanatory feedback based on student responses and anticipated misconceptions. The “Common Errors and Misconceptions” guidance for unit 5, cluster 1 provides suggestions for preventing students from adding or subtracting denominators in fractions instead of recognizing that denominators represent the size of the parts and should remain the same. When students correctly add numerators but incorrectly change denominators, the materials provide several supports and prompts. To address these misconceptions, educators may encourage students to estimate before computing and check their results. Educators may also ask students to draw heavier lines around each whole and use dashed lines between related bar models to show that the wholes are the same size.