Imagine+ Math ™ Texas, Grade 4

Evaluation for 1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.

The materials include an Alignment Guide that outlines the Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and the mathematical concepts covered at each grade level. For each module, the guide identifies the specific TEKS and ELPS standards addressed and describes the concepts covered, such as decomposing numbers, building fluency with operations, and working with fractions and proportional reasoning. This structure is consistent across all modules at every grade level, helping educators clearly see which standards and concepts are addressed in each learning experience.

The Imagine+ Math K–6 Rationale for Learning Paths document provides a rationale for learning paths both across and within grade levels. For vertical alignment, it describes how foundational concepts introduced in earlier grades are intentionally extended and applied in later grades, moving from concrete understanding of numbers and quantities to more abstract reasoning with operations, fractions, measurement, and data. For horizontal alignment within a grade level, it describes how the Math Builder pathway supports students who are two or more grade levels below through targeted foundational remediation, while the Math Mastery pathway supports grade-level-ready students in deepening conceptual understanding of the same grade-level TEKS concepts.

Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, such as just-in-time supports, advanced learning, or as a course.

The Implementation Guide identifies two distinct models for how educators can deploy the program across various classroom structures and learning environments. The Scheduled Class Time model describes structured learning periods during which all students work on their individual learning paths, with options for a Rotation Model or a Whole-Class Model. The Flexible Learning Time model provides four contexts for student engagement outside structured class periods—Homework/At-Home Practice, Independent Study, After-School Programs, and Tutoring or 1:1 Instruction—allowing students to apply and extend what they learn in core instruction beyond the scheduled class period.

The Teacher Guide includes a “Usage Recommendations” table that sets consistent usage as the standard to ensure steady progress and skill development throughout the school year. The table provides grade-differentiated time allotments—a minimum of 45 minutes per week for grades K–2 and a minimum of 60 minutes per week for grades 3 and up—reflecting the program’s recognition that instructional needs vary across grade bands. Across all grades, the lesson completion expectation is 1–2 lessons per week, with a school-year goal of 30 lessons completed. These recommendations apply regardless of the implementation model the educator selects, establishing a consistent usage floor across both Scheduled Class Time and Flexible Learning contexts.

Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.

The Assessment and Placement options document explains how embedded Mastery Checks generate diagnostic data that the program uses to determine each student’s skill entry point. Based on Mastery Check performance, students are placed in either the Math Mastery or Math Builder pathway, with entry points determined by demonstrated readiness in TEKS-aligned instructional domains. This data-driven placement ensures that students begin instruction at the point most appropriate to their current level of understanding, rather than by grade level alone. Educators can manually review and adjust placement at any time.

The materials include a TEKS correlation guide titled Crosswalk: NWEA Diagnostic Domains with Imagine+ Math Lesson Domains. This document maps each NWEA MAP® Growth™ assessment domain to the corresponding TEKS-aligned lesson domains in the materials, linking diagnostic results to recommended skill entry points. When NWEA MAP® Growth™ data is integrated, the program uses domain-level RIT scores to determine an appropriate starting point within each TEKS-aligned instructional domain. The accompanying RIT score range table specifies the score ranges for each grade level, supporting instructional placement decisions. Students begin at an entry level aligned with their performance in each domain. They progress through increasingly complex TEKS-aligned content as they demonstrate mastery.

The materials include an Alignment Guide that correlates digital lessons in both the Math Mastery and Math Builder pathways to specific TEKS, including content and mathematical process standards. This guide serves as a TEKS correlation tool by identifying which standards each lesson addresses, enabling educators to connect diagnostic assessment results to targeted skill entry points within the program’s instructional sequence. Together with the NWEA Crosswalk and the embedded Mastery Check system, this Alignment Guide helps educators determine where individual students should enter the instructional pathway based on their demonstrated performance.

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

In the program, the Teacher Guide clearly explains the unit and lesson internalization protocols. These protocols provide logistical support and guidance for successful program implementation and help educators plan instruction and make informed decisions about student pathways, learning needs, and instructional adjustments.

The materials include two instructional protocols that guide educators through unit and lesson internalization. For unit internalization, both protocols direct educators to review unit overviews to internalize TEKS-aligned concepts, mathematical vocabulary, and suggested instructional activities. For lesson internalization, the protocols guide educators to preview lesson objectives and TEKS alignment in the Assignment Builder and to use embedded Teacher Supports to prepare individualized support and anticipate student misconceptions.

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

The Imagine+ Math Instructional Leader Guide provides a clear roadmap for launching and sustaining a digital supplemental math program. The guide outlines practical steps for building educator capacity, establishing schoolwide systems, monitoring usage and effectiveness, and ensuring strong student outcomes. Organized by implementation phases, it offers action items and tips that leaders can use as a checklist. The guide also supports distributed leadership by showing how math campus coordinators, specialists, coaches, and grade-level leaders can assist with implementation. Together, these features equip instructional leaders to plan, monitor, and sustain the program across a campus.

The “First 30/60/90 Days for Administrators” section provides instructional leaders with a sequence of resources and guidance to support educators throughout implementation. The learning path organizes administrator actions into three phases, each building on the previous one to sustain program fidelity over time. During the 90-day phase, administrators access step-by-step Help Center articles to monitor progress and track student growth. Resources include guides for viewing the “Student Progress,” “Mastery,” and “Benchmark” reports, as well as instructions for exporting student data and managing benchmark assessments. Together, these tools help instructional leaders use data to guide educator practice and ensure the program is implemented as designed.

Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

This guidance is not applicable because the program is not designed to be static.

This guidance is not applicable to the program.

Evaluation for 1.2b
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

Each lesson preview page includes a detailed overview listing the lesson objective, aligned domain, and TEKS. For example, a lesson preview lists the objective “Compute quotients of fractions within and without context” under the “Overview” heading, identifies Number and Operations under the “Domain” heading, and displays the aligned TEKS standard under the “Standards” heading. The “English Language Support” section within the Teacher Support identifies the aligned ELPS for each lesson and provides educators with language support guidance alongside TEKS-aligned content objectives.

The Teacher Guide provides unit overviews, suggested lesson time frames, and additional information on lesson components to support implementation. The TEKS and ELPS are embedded in the lessons and Mastery Checks, which serve as the program’s assessments throughout the instructional materials.

Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).

The Teacher Guide includes a home support checklist in both English and Spanish, organized by grade level and unit. For each unit, families receive activity suggestions that reinforce classroom learning with everyday materials at home. These activities connect grade-level math skills to everyday life, and families use the checklist to track completed activities with their child. Together, the English and Spanish versions ensure that all families can access unit-level guidance to support their student’s progress.

The materials provide families with unit-by-unit activity suggestions in both English and Spanish. These suggestions are explicitly aligned with the TEKS. Each activity reinforces classroom learning with everyday materials and equips families with practical tips for supporting their student, such as keeping practice sessions to 10–15 minutes and connecting math to real-life situations.

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

The Implementation Guide defines Mastery Checks as instructional assessments that provide timely feedback and determine next steps for students, rather than as summative assessments for grading. In the grades 3–6 Mastery pathway, each lesson includes two seven-item Mastery Checks—one at the start and one at the end—that adjust pacing based on student performance. Students who score 85 percent or higher on the first Mastery Check advance to the next lesson, while those who score below 85 percent receive Guided Learning and Practice before completing the second Mastery Check. Educators review Mastery Check results in reports to monitor student progress and identify when students may need additional support.

The Teacher Guide defines Mastery Checks as instructional assessments that serve as both diagnostic and formative measures. It explicitly states that they are not used for summative evaluation or grading. Educators use Mastery Check data in the “Reports” section to monitor student progress, determine student readiness to move forward, and guide targeted reteaching, intervention, or enrichment. Educators also preview Mastery Checks in the Assignment Builder to align instruction with assessment expectations and review answer rationales to understand the reasoning behind correct and incorrect student responses. This guidance supports educators in lesson planning, delivering instruction, and making data-driven instructional decisions throughout the school year.

The Teacher Guide defines diagnostic assessments and describes their purpose as identifying students’ prior knowledge, misconceptions, and areas needing additional support before instruction or independent practice begins. When administered at the start of a lesson, Mastery Checks serve this diagnostic function by establishing baseline data on a student’s foundational knowledge and proficiency. Educators use this data to preview content, anticipate potential misconceptions, and adjust instruction before introducing new material.

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

The Teacher Guide includes a “Monitoring Progress with Mastery Checks” section that offers clear guidance for the consistent, accurate administration of instructional assessments. The section explains how educators preview Mastery Checks in the Assignment Builder, review key skills and concepts, and anticipate potential misconceptions to adjust instruction before the assessment begins. Educators also review answer rationales for each Mastery Check item to understand the reasoning behind correct and incorrect responses, supporting consistent interpretation of results across classrooms.

The materials include an Assessment and Placement options guide that supports consistent administration of instructional assessments across the Mastery and Builder pathways. The Implementation Guide explains how the program uses student data to adjust lesson sequencing, pacing, and skill progression. In the “Reports” section, it outlines clear expectations for educators to monitor and review student results to ensure instruction remains aligned with student needs.

Evaluation for 2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.

In the grades 3–6 Math Mastery pathway, digital assessments include printable versions that educators can access to support individual students, including Mastery Checks printed from the Assignment Builder. The materials provide text-to-speech in Mastery Check assessments; however, they do not provide embedded calculators or language supports that educators can enable or disable.

Through student profile settings, educators can enable and disable text-to-speech for individual students needing the accommodation. However, the materials do not include content and language supporst that educators can enable or disable, nor do they include an embedded calculator accommodation.

Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

Diagnostic assessments include more than two distinct interactive item types, such as drag-and-drop, multiple-choice, text-entry, and matching tasks, that are aligned with the TEKS. In one grade 4 Mastery Check, students drag an equation to match a fraction model that represents decomposing fractions.

The materials include diagnostic assessments with TEKS-aligned tasks and questions designed to address more than two levels of complexity. Questions range from basic recall to the application of skills and concepts and extend to higher-order thinking, such as analysis, synthesis, and strategic thinking.

Evaluation for 2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The materials include formative assessments with TEKS-aligned tasks and questions designed to address more than two levels of complexity. Questions range from basic recall to the application of skills and concepts and extend to higher-order thinking, such as analysis, synthesis, and strategic thinking.

Formative assessments include more than two distinct interactive item types, such as drag-and-drop, multiple-choice, text-entry, and multi-select tasks, that are aligned with the TEKS. Students engage with these item types across varying levels of complexity, from conceptual understanding and procedural fluency to application and higher-order thinking.

Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.

The Implementation Guide provides scoring information and guidance for interpreting student performance using lesson scores and standards proficiency categories. Educators use the “Class Summary” and “Cumulative Standards Proficiency” reports to monitor achievement and identify students who may need support. The guide defines three performance levels—meeting the goal, approaching the goal, and below the goal—and offers suggested instructional actions for each level to guide targeted follow-up instruction and practice.

The Implementation Guide includes an “Answer Rationales” section that explains the reasoning behind correct and incorrect Mastery Check responses. For correct responses, the rationales explain the reasoning used to reach the solution. For incorrect responses, the rationales describe likely student thinking, identify associated misconceptions, and explain how to solve the problem correctly. Educators access answer rationales through the “Student Progress” report or by previewing Mastery Check items in the Assignment Builder.

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 Implementation Guide provides guidance on using the included tasks and activities to respond to student performance trends on assessments. Educators use Mastery Check results to determine next instructional moves, such as implementing Teacher Support for students who do not consistently demonstrate mastery, selecting an activity from the “Enrichment and Extension” section for students who consistently perform well, or reviewing answer rationales to identify misconceptions among students who perform poorly on a Mastery Check.

The Teacher Guide includes instructional decision-making protocols that provide cadence-based guidance for reviewing assessment data and making instructional decisions about student placement, support needs, and pathway adjustments. Weekly, educators review the “Usage” and “Class Summary” reports to identify students who may need support or reteaching. Biweekly, educators use the “Student Progress” and “Class Progress” reports to check performance patterns across Mastery Checks and identify clusters of students struggling with similar skills. Monthly, educators use the “Cumulative Standards Proficiency” report to analyze TEKS-level evidence and plan short- and long-term instruction to support coherence between the TEKS concepts and skills.

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 Implementation Guide includes reporting tools that help educators monitor student progress and growth across domains and learning pathways. Educators use the “Class Summary” report to identify students who need support and lessons for reteaching; the “Class Progress” report to track progress across lessons and domains and pinpoint class-wide trends; the “Student Progress” report to view individual student lesson activity and performance; and the “Cumulative Standards Proficiency” report to monitor TEKS proficiency at the class and student levels and plan reteaching and practice.

The Implementation Guide includes student-facing progress-monitoring tools that help students track their learning path progress and growth over time. The “My Progress” page shows students their active time and lesson progress for the current week and provides a printable school-year view of completed lessons, including completion dates and scores. Additionally, printable Lesson Trackers help students set weekly usage goals, reflect on their effort, and notice growth over time, while progress charts give students a visual way to recognize milestones and maintain momentum across weeks.

Evaluation for 2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.

This guidance is not applicable because the program is not designed to be static.

This guidance is not applicable to the program.

Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.

The materials include adaptive Mastery Checks embedded at key points throughout lessons in both the Mastery and the Builder pathways to frequently monitor student understanding. Mastery Check results provide immediate feedback and automatically adjust lesson progression, supports, and next steps based on student performance.

In the Mastery pathway, students complete two seven-item Mastery Checks at the beginning and end of each lesson. Students who meet the mastery threshold on the first Mastery Check advance to the next lesson, while students who score below the threshold receive Guided Learning and Practice before completing the second Mastery Check. In the Builder pathway, students encounter up to three Mastery Checks within each lesson—at the start, mid-lesson, and end. Students who do not pass receive Instruction, Supported Practice, or Independent Practice activities tailored to their needs before moving forward.

Evaluation for 3.1a
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.

The materials include explicit educator guidance for scaffolded support through the “Support for Struggling Students” component in each lesson. The materials direct educators to use pre-teaching activities to strengthen prerequisite understanding before grade-level tasks. Reteaching supports include step-by-step educator directions and examples that help educators address misconceptions and build the conceptual understanding students need for more complex concepts. These scaffolded supports are embedded within lesson guidance to move students toward grade-level proficiency.

Educators assign graphic organizers based on students’ specific math needs. Students who need additional support use the graphic organizer and reference it as a guide during practice, while more advanced students use a similar organizer to analyze and solve complex problems.

Evaluation for 3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.

The materials include explicit educator guidance for language supports within the “Support for Struggling Students” component during lessons. The materials direct educators to pre-teach academic vocabulary related to concepts using representations and educator-guided examples to build understanding before grade-level instruction. Embedded supports within reteaching activities provide educator directions and examples that reinforce mathematical language, help educators address misconceptions, and strengthen conceptual understanding.

The materials guide educators to introduce mathematical vocabulary using student-friendly definitions, visual representations, real-world examples, and sentence frames that help students connect new terms to mathematical concepts. These embedded supports develop academic language and increase students’ ability to engage in mathematical discussions and problem-solving activities.

Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.

The materials include explicit educator guidance for enrichment and extension within the Teacher Guide under the “Enrichment and Extension” section. This section provides educator-directed guidance for extending student learning through activities that deepen understanding and challenge students who have demonstrated proficiency in grade-level concepts and skills. The guide includes multiple opportunities to enrich instruction and extend mathematical thinking, supporting educators in providing learning experiences beyond initial mastery.

Educators use student performance data to identify learners ready for more advanced work and to access activities that deepen understanding and promote higher-level thinking. Additionally, the Assignment Builder allows educators to customize and assign enrichment tasks that encourage students to apply mathematical concepts in more complex, meaningful ways.

Evaluation for 3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.

The materials include guidance in the Implementation Guide’s “Assistive Technology” section on enabling and disabling text-to-speech as an accessibility feature for students. The guide provides specific instructions for educators on using text-to-speech to support language accessibility during instruction. The materials also note that calculators are available only when intentionally embedded in an activity and that students who need a calculator as an accommodation must receive a physical calculator. However, the materials do not include guidance for educators on enabling or disabling calculator accommodations for individual students within the digital platform. Additionally, available supports such as interactive hints, visual supports, and clickable vocabulary definitions are accessible to all students and cannot be toggled for individuals. The materials reference language translation rather than content and language supports as defined by the indicator.

The program includes text-to-speech that educators can enable or disable to support individual students. The materials also include interactive hints; visual supports such as diagrams, models, and manipulatives; simplified language options; and clickable definitions for key math vocabulary. However, these content and language supports are available to all students, and educators cannot enable or disable them for individual students.

Evaluation for 3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.

The materials include educator guidance in the Teacher Guide and the Implementation Guide to support students in demonstrating understanding of mathematical concepts in multiple ways. The Teacher Guide provides guidance on using a problem-solving graphic organizer that helps students make sense of mathematical concepts through a structured problem-solving process. It encourages students to explain their thinking, persevere through challenges, and represent their understanding in an organized format. Additionally, the Implementation Guide, under “Universal Design for Learning,” explains how students engage with mathematical concepts through multiple means of representation, action and expression, and engagement. Students may perform, express, and represent mathematical thinking in varied ways to deepen their understanding and support access to learning.

Math Journaling resources provide educators with reflection prompts, graphic organizers, problem-solving reflections, and end-of-lesson organizers to help students explain strategies, justify solutions, and reflect on their learning. The “Demonstrating Understanding” section also offers alternative ways for students to demonstrate mastery, such as using movement to model concepts on a number line, creating visual representations, and participating in mathematical discussions with peers.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.

The materials include educator guidance within lessons in the “Building Foundations” section to activate prior knowledge and anchor big ideas by connecting to prerequisite skills and using educator-directed instructional strategies. This section supports educators in helping students build foundational understanding before new learning.

The program equips educators with explicit prompts and guidance to build knowledge by activating prior knowledge and anchoring big ideas. Grade 4 Unit Overviews establish this framework by linking prerequisite understanding to new mathematical concepts. Each unit opens with an overview that anchors the unit’s big idea—for example, unit 2, “Algebraic Reasoning,” frames the shift from arithmetic to symbolic reasoning as students write and solve equations in which a letter represents an unknown number—followed by Vocabulary Development that distinguishes new grade-level terms from previously introduced ones. Within each lesson, “Building the Foundation” provides targeted scaffolds for prerequisite concepts and skills for students who need additional help before or after instruction, and “Coherence and Connections” highlights connections between prior knowledge and current grade-level concepts. “Practice for Long-Term Learning” further activates prior knowledge through brief, spiraled retrieval prompts that revisit previously taught standards throughout the year.

The program highlights and connects key patterns, features, and relationships through multiple means of representation. In unit 1, “Number and Operations,” the “Fraction Line” fluency activity connects the relationship between equivalent fractions across three representations. Students place symbolic fraction cards on a number line, generate matching equivalent fraction cards (such as 2/4 for 1/2), and justify orally why the two fractions are equivalent before extending their reasoning to a real-world word problem. In unit 2, “Algebraic Reasoning,” the “What’s the Rule?” fluency activity connects a numeric pattern across multiple representations: Students apply a symbolic rule card (such as “× 3” or “+ 5”) to an input number spoken aloud, share the resulting output orally, and record their work in a pre-drawn input-output table, then create and test their own rules with a partner. In unit 3, “Geometry and Measurement,” the “Angle Detectives” fluency activity connects the defining feature of angle type across multiple representations: Students predict whether a pictured angle is acute, right, or obtuse; use a protractor to measure and confirm or revise their prediction; and then search the classroom for real-life objects with matching angles.

Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.

This guidance is not applicable because the program is not designed to be static.

This guidance is not applicable to the program.

Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.

The materials provide multiple types of practice opportunities, including guided practice through educator questioning, intervention supports, and scaffolded instruction, as well as independent practice through lesson activities and problem-solving tasks. The materials also include multiple instructional structures, including whole-group instruction, small-group intervention, and individualized support for students who need additional assistance. Additionally, the materials provide explicit educator guidance for implementation through educator tips, intervention recommendations, support for struggling students, common misconception alerts, and monitoring suggestions, supporting educators in effectively implementing multitiered intervention methods.

The materials include collaborative practice opportunities through structured partner and small-group activities, such as Fluency Activities and Problem-Solving Activities, in which students work together to solve problems, compare strategies, and justify their reasoning with peers.

Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.

The materials include enrichment and extension methods that support multiple forms of engagement, including independent work, collaborative learning, choice boards, creative problem-solving, reflection, discussion, and peer sharing. Additionally, the Teacher Guide provides explicit educator guidance for implementation through a structured sequence of steps that explain how to select activities, prepare materials, establish expectations, determine instructional settings, facilitate participation, and provide feedback throughout the enrichment process.

Educators access “Enrichment and Extension” activities through the Teacher Support section of the Assignment Builder to deepen student understanding and increase engagement. These methods support differentiated instruction by fostering critical thinking, encouraging curiosity, and challenging students through deeper learning experiences.

Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.

The materials include educator guidance within the Teacher Guide under “Justifying Solution Strategies” to support timely feedback during instruction. This section provides educator question stems that prompt educators to check for understanding, gauge student thinking, and provide immediate feedback during lesson delivery. These formative prompts help educators monitor student understanding, identify misconceptions or areas for improvement, and adjust instruction or reteach when necessary to support student progress.

The STEM-Focused Applications Task guide provides introductory questions and prompts that encourage students to explain and justify their thinking. During instruction, educators use “Class Summary,” “Student Progress,” and “Assignment Summary” reports to monitor student responses, scores, and lesson progress. The materials also prompt educators to provide immediate support through guided questions, clarification, small-group instruction, and reteaching opportunities using Teacher Support within the Assignment Builder.

Evaluation for 3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all 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 program is not designed to be static.

This guidance is not applicable to the program.

Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all 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 “Instructional Tools and Strategies” section supports linguistic accommodations by providing word walls, math language journals, the Frayer model, visual representations, cross-linguistic connections, and collaborative discourse routines. These recurring supports help students build, practice, and extend academic mathematical vocabulary, moving from foundational understanding, such as defining a term with visuals and real-life examples, toward more complex application, such as justifying strategies and comparing vocabulary words in discussion. Together, these tools give educators explicit guidance for engaging students in increasingly sophisticated mathematical language use across instruction.

The materials also provide differentiated linguistic accommodations based on a student’s bilingual program model and language proficiency trajectory. The Teacher Guide outlines distinct guidance for Transitional Bilingual Early Exit, Transitional Bilingual Late Exit, Dual-Language One-Way, and Dual-Language Two-Way programs, specifying how to adjust the use of Spanish- and English-language lessons, sentence frames, and written response expectations as a student’s English proficiency increases. This progression, from primarily Spanish-language support with structured scaffolds toward increasing English-language production, engages students in using increasingly complex academic mathematical language as their proficiency develops.

The program includes embedded linguistic accommodations designed to support students at varying levels of English language proficiency, aligned with the ELPS. Each lesson includes embedded English Language Support, used during instruction to scaffold understanding and use of academic language through sentence frames, such as “The number ____ represents ____ objects,” and modeled responses that help students explain their mathematical thinking. The Problem-Solving graphic organizer, available in both English and Spanish, extends this accommodation by giving students bilingual access to the same problem-solving structure, allowing them to engage with mathematical content in their language of instruction while building toward academic English.

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

The materials include guidance within the Implementation Guide for supporting language access and implementation for emergent bilingual students. The guide provides explicit educator guidance on enabling and using built-in language supports, including translation features that support over 60 languages and provide translation into 45 languages. Step-by-step instructions help educators activate these supports and increase access to instruction for emergent bilingual students. Additionally, the guide includes a dedicated section for bilingual and ESL programs that outlines how to implement the language-support features in those instructional settings.

The program includes implementation guidance to support educators in using the materials within state-approved bilingual and ESL programs. For example, the program offers Spanish versions of grade K–6 lessons and the student interface, along with on-screen translations in more than 60 languages and audio translations in 45 languages. These language-support features help emergent bilingual students access the instructional materials.

Evaluation for 3.3d
Materials include embedded guidance 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 include structured language supports within the Teacher Guide under “Facilitating Discourse with Mathematical Vocabulary.” This section provides educator and student question stems to support both oral and written discourse around mathematics. The question stems offer structured opportunities for students to discuss, explain, and justify their reasoning in meaningful ways, helping reduce language barriers while strengthening conceptual understanding. Additionally, the materials provide educators with practical tools to support student language development while maintaining a focus on content understanding and mathematical proficiency.

Educators use Frayer models, sentence stems, writing frames, math journals, and graphic organizers to help students connect mathematical vocabulary to prior knowledge and explain their reasoning through both speaking and writing. The materials also support cross-linguistic connections by allowing students to express their understanding in Spanish and transition to English through guided writing activities, strengthening academic language while communicating mathematical thinking.

Evaluation for 3.3e
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.

This guidance is not applicable to the program.

Evaluation for 4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The materials provide instructional assessments that require students to demonstrate depth of understanding aligned to the TEKS, giving educators accurate data on students’ grade-level proficiency to inform instructional decisions. For example, students demonstrate understanding through interactive, technology-enhanced questions in the Mastery Check, which aligns to the full intent of the TEKS by requiring students to show conceptual understanding, procedural fluency, and application.

The instructional design progresses students through Guided Learning, Practice, and Mastery Check experiences that support conceptual understanding, procedural fluency, and application of mathematical knowledge at increasing levels of rigor. For example, within the “Measuring Obtuse Angles” learning pathway, students begin with Guided Learning, exploring the characteristics of obtuse angles and the proper use of a protractor to measure angles greater than 90 degrees and less than 180 degrees. Students then engage in Practice activities that require them to measure, compare, and classify angles in a variety of contexts, with tasks that increase in complexity and require applying angle measurement to solve mathematical problems. The pathway culminates in a Mastery Check, where students demonstrate their understanding through tasks requiring accurate measurement, mathematical reasoning, and application of concepts aligned to the TEKS.

Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.

Students experience rigor through tasks that promote critical thinking, problem-solving, and real-world application, using concrete, representational, and abstract models that connect concepts across learning pathways. Educators receive detailed, lesson-specific enrichment and extension strategies that increase in rigor and complexity, including a STEM-focused, project-based learning experience that enables students to extend and apply their understanding beyond grade-level TEKS expectations.

The program uses assessment-based recommendations and adaptive learning pathways so students engage with appropriately challenging content. Based on domain-level performance data, students receive personalized learning experiences that target areas of need while continuing to engage with grade-level content in domains where they demonstrate proficiency. Mastery Checks guide progression by allowing students to move beyond content they have mastered. Additionally, educators use the Assignment Builder to create customized assignments from the TEKS-aligned content library, selecting lessons, STEM-focused application tasks, and practice activities that extend learning beyond a student’s assigned pathway. For example, in a grade 4 enrichment activity, students apply their knowledge of adding and subtracting fractions by creating a fraction art project, using different shapes and colors to represent fractional parts of the whole artwork.

Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.

The grade 4 “Horizontal Concept Map” shows how students’ understanding of rational numbers begins with representing, comparing, and ordering positive and negative numbers on a number line, then extends as students perform operations with integers and multiply and divide positive rational numbers. Students apply these same rational number skills within the “Proportionality” lesson, solving problems involving ratios, rates, percentages, and measurement conversions; using ratio reasoning to analyze relationships between quantities; and solving real-world problems involving unit rates and pricing.

The grade 4 “Expressions, Equations, and Relationships” unit guides educators in helping students transition from arithmetic reasoning to algebraic thinking. Students build on their prior understanding of operations with whole numbers, fractions, and decimals as they learn to write, interpret, and evaluate algebraic expressions, applying the order of operations and properties such as the distributive, associative, and commutative properties to generate equivalent expressions. Students then solve one-step equations and inequalities using models, algebra tiles, and symbolic representations, such as in the Equation Mystery Match activity, reinforcing the relationship between concrete models and abstract algebraic reasoning.

Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.

A well-structured progression of mathematical concepts across grade levels allows students to build a strong foundation, reinforcing prior knowledge while introducing new, developmentally appropriate skills. The materials include a “Vertical Concept Map” that identifies explicit connections to prior knowledge and future mathematical concepts, supporting vertical coherence across grade levels aligned to the TEKS.

In grade 4, the materials demonstrate vertical coherence by connecting algebraic reasoning across grade levels through a progression of increasingly complex concepts and representations. Students write and solve equations where a letter represents an unknown number, making the transition from arithmetic to symbolic reasoning while building on prior experiences with the four operations. Students use strip diagrams, number lines, and equations to represent problem situations. Students explore relationships between numbers through input-output tables, identifying and applying rules to generate numeric patterns. The Teacher Guide includes reflection questions such as how a problem connects to prior learning and why the problem matters in mathematics, prompting students to make connections across their developing understanding.

Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.

The “Lesson Coherence Map” explicitly connects prior learning from grade 3 to current grade 4 concepts and future grade 5 expectations. Students build on grade 3 place value concepts, including expanding and rounding whole numbers, to engage in grade 4 lessons such as writing and expanding numbers to 1,000,000, place-value concepts up to 1,000,000,000, and rounding whole numbers, which prepare them for grade 5 work with decimal place value and rounding decimals. Similarly, students extend their understanding of equivalent fractions from grade 3 through grade 4 lessons on finding equivalent fractions, comparing and ordering fractions, and adding and subtracting fractions, establishing the foundation for grade 5 fraction operations involving unlike denominators and fraction representation on number lines.

Before students begin a grade 4 lesson on finding the area and perimeter of rectangles, the materials provide educators with strategies to activate and assess prerequisite knowledge, ensuring students have the foundational understanding needed to access grade-level content. Students review basic multiplication and division and practice identifying the length and width of rectangles, preparing them to compute area and perimeter and solve related problems at the current grade level. This intentional sequencing ensures that new concepts build directly on what students already know, supporting coherent mathematical understanding within and across lessons.

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

The materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways, allowing for continuous assessment of student progress so educators can adjust teaching strategies as needed. Every unit includes spaced retrieval opportunities with previously learned skills and concepts, and educators also receive home activities to support students in retaining previously learned skills and concepts.

The materials strengthen long-term retention by sequencing practice so students actively retrieve information from memory across multiple opportunities over time, rather than reviewing content once and moving on. For example, before a grade 4 lesson on classifying two-dimensional figures by their lines and angles, students complete a “What You Know” task that prompts them to recall previously learned content on parallel and perpendicular lines, as well as acute, obtuse, and right angles. This activates prior knowledge and prepares students for the current lesson on classifying two-dimensional shapes using angles and lines.

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

The materials require students to apply a variety of skills and concepts within the same learning sequence rather than practicing a single skill in isolation. For example, students engage in practice tasks that combine prior mathematical understandings with newly introduced concepts, requiring them to select appropriate strategies and justify their thinking. Educator-facing supports also guide educators in monitoring student understanding through reflection prompts, mathematical discussions, and analysis of student work, along with instructional guidance and worked examples that support effective implementation.

The materials enhance students’ problem-solving abilities and promote flexible thinking by requiring students to switch between different types of problems and strategies within the same activity, improving retention and helping students integrate knowledge and skills over time. For example, grade 4 students complete "Interleaved Practice 1," a printable practice with problems involving comparing whole numbers, addition and subtraction of decimals, multiplication and division, perimeter and area, multistep problems, expanded notation, classifying shapes, and data tables. As students work through these problems, they draw on previously learned concepts and skills to choose the most effective strategy for solving each one.

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

The online materials display base 10 block models representing both whole numbers and decimals. Students interpret the same model in multiple ways, analyze how a single set of base 10 blocks can represent 42 as well as 4.2 depending on the value assigned to each block, and evaluate the validity of different interpretations by completing mathematical statements using place-value understanding.

In a lesson on multiplying decimal numbers, students analyze models such as 7.8 × 5.2, 7.8 × 0.52, and 7.8 × 52 to evaluate how changes in place value affect the product. Students also interpret real-world problems such as calculating distance using speed and time, evaluating whether their solutions are reasonable by comparing estimates to exact answers.

Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.

In the grade 4 Interleaved Practice section, students create a frequency table from a data set, identify the mode, write an equation to represent a real-world situation involving a health club membership fee, and use a protractor to draw and label a 120-degree angle.

Students use an area model to divide by a one-digit number, creating both pictorial and concrete representations to demonstrate their understanding of the division process.

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

In the “Angles 0°–180°” lesson, students apply their understanding of angle measurement to classify, compare, and solve problems involving acute, right, obtuse, and straight angles in real-world and mathematical contexts. Rather than identifying angle types in isolation, students use protractors, interpret angle models, and apply angle benchmarks to estimate and verify measurements in unfamiliar contexts.

Students extend their understanding of division by evaluating real-world situations involving glue bottles in an art class, applying division strategies to solve problems in unfamiliar contexts.

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

The materials provide students and educators with five fluency activities that reinforce skills such as fraction lines, input/output tables, classifying angles, and stem-and-leaf plots, building accuracy, efficiency, and flexibility in mathematical thinking. The materials also include interleaved practice that revisits previously learned skills alongside new content, strengthening retention and fluency across varied contexts.

The materials provide educators with a step-by-step fluency activity for each unit of study that reinforces TEKS-aligned content related to number sense, operations, and automaticity through focused practice. These fluency activities help students develop the accuracy and efficiency needed to engage with grade-level content and focus on critical thinking and problem-solving without pausing for basic computation.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.

Interleaved Practice activities integrate previously learned skills with new content, enabling students to apply mathematical procedures accurately, efficiently, and flexibly across multiple contexts.

Students engage in real-world activities that involve calculating the area and perimeter of rectangles, applying mathematical procedures accurately, selecting efficient strategies, and verifying calculations. Students also represent data in bar graphs, dot plots, and stem-and-leaf plots using whole numbers and fractions. Students decompose fractions in multiple ways using visual models and fraction strips, demonstrating flexibility in mathematical thinking.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.

In grade 4, students decompose fractions and justify multiple ways to represent fractions such as 8/6, demonstrating flexibility in mathematical thinking. Students also use a protractor to measure angles and evaluate a peer’s worked example to determine whether the steps used to find the angle measure are correct, analyzing representations and assessing the efficiency and accuracy of another student’s approach.

In grade 4, students use a problem-solving reflection sheet to evaluate their mathematical representations, models, strategies, and solutions. They reflect on the strategy used to solve the problem, explain their thinking to others, and consider how their reasoning ensures accuracy.

Evaluation for 5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.

The materials provide educator guidance in selecting efficient strategies and approaches to solving problems, helping students become adaptable and strategic problem solvers.

The materials provide educators with suggested prompts and guidance to support students in choosing efficient approaches to solving problems.

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

The Imagine+ Math K–6 Rationale for Learning Paths, used alongside the Alignment Guide, identifies the TEKS addressed in each domain and explains the mathematical concepts and skills emphasized in the Teacher Guide. The rationale outlines the progression of learning across grade levels by showing how concepts in number and operations, algebraic reasoning, geometry and measurement, data analysis, and personal financial literacy develop over time. It also explains how units within a grade are sequenced to reinforce prior learning and prepare students for subsequent content. The document also identifies prerequisite skills and extension opportunities that support progression into Algebra I, Geometry, and Algebra II.

In the grade 4 lesson “Decomposing Fractions,” students use fraction models to explore how a fraction can be represented as the sum of smaller fractions with the same denominator, building conceptual understanding of why the procedure works. As students progress through the Guided Learning Practice Problems, they apply procedures by writing equations that decompose fractions in multiple ways and demonstrate fluency with fraction notation. The lesson also provides immediate feedback and instructional support when students answer incorrectly, reinforcing conceptual understanding and helping students correct procedural errors.

Evaluation for 5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.

Students represent fractional situations using visual fraction models and connect these representations to addition equations when solving problems. The materials incorporate concrete models within instructional videos to demonstrate mathematical concepts and support conceptual understanding. Although physical manipulatives are not provided, students are encouraged to use physical objects or drawings to represent mathematical situations and reinforce their understanding. Through Interleaved Practice and worksheets, students apply these representations to solve problems and connect concrete and pictorial models to symbolic notation. These opportunities support students in developing conceptual understanding and strengthening problem-solving skills through multiple representations.

The materials support the use of pictorial and abstract models to develop mathematical understanding in grade 4. For example, students use area models to represent division by a one-digit divisor and then apply numerical equations to solve related problems. These tasks reinforce connections between visual representations and abstract reasoning.

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.

Instructional supports help students move from hands-on and visual models to symbolic and numeric representations. For example, students use instructional videos and practice tasks to connect and explain concrete and representational models when writing decimals as fractions, thereby supporting transitions from visual models to symbolic notation.

The materials support students in creating and explaining representational models and connecting those models to abstract procedures. Lessons prompt students to define visual representations and explain how those models relate to symbolic forms, strengthening conceptual understanding before applying algorithms.

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

In the grade 4 Guided Learning lesson “Area and Perimeter of Rectangles,” the “Developing Vocabulary” Teacher Support pre-teaches the term area using grid paper visuals to count square units, paired with the sentence frame “The area of the rectangle is ____ square units.” Educators also embed support for the term perimeter by displaying a rectangle visual and highlighting its outline, using the sentence frame “The perimeter of the rectangle is ____ units.” Educators clarify the term rectangle through examples and non-examples paired with the sentence frame “A rectangle has sides of length ____ and ____.”

In the grade 4 lesson “Classify 2-D Shapes (Lines and Angles),” the “Developing Vocabulary” Teacher Support pre-teaches the term parallel lines using visuals of railroad tracks, paired with the sentence frame “Parallel lines are lines that ____.” Educators also embed support for the term perpendicular lines using a plus-sign visual to show a right-angle intersection, and introduce the term acute angle using a slice-of-pizza visual. Each term has its own sentence frame.

Evaluation for 5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.

In the grade 4 Teacher Guide, the “Scaffolding Mathematical Vocabulary” section provides embedded guidance for educators to model academic language through the Frayer model, using sentence frames such as “The definition of ____ is . . . ” and “An example of ____ is . . . ” and posing clarifying questions such as “Why does this example represent ____?” Educators also facilitate partner discussions in which students explain a section of their Frayer model to a peer and restate a peer’s explanation using the vocabulary word.

In the grade 4 Teacher Guide, the “Extending Academic Vocabulary” section offers embedded guidance for educators to extend students’ use of a vocabulary word after they have demonstrated understanding. This includes comparing two vocabulary words using Frayer models, creating original word problems that require correct use of the term, and justifying thinking during discussions with prompts such as “Explain how ____ helps you solve this problem.” Educators also encourage students to respond to peers’ ideas using academic language, agreeing or disagreeing with evidence.

Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.

In the grade 4 Teacher Guide, the “Facilitating Discourse with Mathematical Vocabulary” section offers question prompts that help students apply academic vocabulary during oral discourse, such as “Can you use this word in a sentence about math?” and “Turn to your partner and use this word to describe a problem you worked on.” These prompts help students explain, describe examples and non-examples, and connect vocabulary to prior learning using precise mathematical language.

Beyond oral discourse, the “Writing with Mathematical Vocabulary” section of the grade 4 Teacher Guide directs educators to provide students with structured opportunities to apply academic vocabulary in written explanations, including sentence stems such as “The word ____ means . . .” and “This example shows ____ because . . .” It also prompts students to revise written responses using precise mathematical language after peer or educator feedback.

Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.

In the grade 4 Teacher Guide, the “Supporting Collaborative Problem Solving and Discourse” section offers embedded guidance for educators to facilitate partner or small-group work in which students solve problems together, particularly during word problems. Educators prompt students to explain their strategies to peers using precise mathematical language, and students hear one another’s reasoning as they compare approaches and ask clarifying questions. The materials note that this collaborative structure strengthens students’ language development alongside their reasoning skills, giving students repeated opportunities to listen to and process the range of strategies and vocabulary peers use during shared problem-solving.

In the grade 4 Teacher Guide, the “Justifying Solution Strategies” section provides embedded guidance for educators to facilitate discussions in which students refine and use academic vocabulary by explaining the reasoning behind their approach and connecting their strategy to models, equations, or representations. Educators pose questions such as “Did anyone solve this in a different way?” and “Which strategy was most efficient, and why?” to prompt students to respond to peers’ strategies, agreeing or disagreeing with justification, using sentence stems such as “I agree/disagree with this strategy because . . .” and “This model shows . . .” The Practice Peer Review step of the “Journaling Lesson Plan” reinforces this refinement by having students trade revised journal entries with a peer to compare differing strategies and representations. The student rubric asks students to be “prepared to explain my work to my teacher or a classmate using mathematical and academic language from the lesson.”

Evaluation for 5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.

In the grade 4 Teacher Guide, the “Mastery Check Answer Rationales” section provides educators with anticipated correct and incorrect answer choices for each digital Mastery Check item. For correct answers, the rationale outlines the steps used to reach the exemplar solution, modeling clear mathematical reasoning and academic language that educators can reference when assessing student understanding.

In the grade 4 lesson “Classify 2-D Shapes (Lines and Angles),” the “Support for Struggling Students” section provides a reteaching strategy for students who have not yet mastered classifying shapes by their lines and angles. Educators use an interactive whiteboard or digital tool to create a classification chart with categories such as “Shapes with Parallel Lines,” “Shapes with Perpendicular Lines,” and “Shapes with Acute Angles,” and guide students to drag and drop shapes such as a square, rectangle, and triangle into the correct category to redirect inaccurate classifications.

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

The grade 4 Teacher Guide explains that lessons offer targeted opportunities for students to practice and apply TEKS-aligned skills through tasks that emphasize the mathematical process standards, including problem solving, reasoning, representation, communication, and precision. In the “Angle Relationships and Polygons” module of the Alignment Guide, lessons on measuring and classifying angles integrate these standards by requiring students to apply mathematics to real-world problems, use a problem-solving model to measure angles accurately, select tools such as protractors, and communicate their findings with diagrams and precise language.

In the “Two- and Three-Dimensional Shapes” module of the Alignment Guide, lessons on classifying shapes by their lines and angles integrate the TEKS process standards by requiring students to use problem-solving strategies to categorize shapes by attributes, communicate their reasoning with diagrams and precise language, and analyze relationships among lines, angles, and polygons to connect and deepen their understanding.

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

The Imagine+ Math K–6 Rationale for Learning Paths explains that the mathematical process standards are embedded in both the Math Builder and Math Mastery pathways used in grade 4, rather than taught in isolation. Students apply these standards directly as they explore concepts, solve problems, represent their thinking, and explain their reasoning in instructional lessons and practice activities throughout the program.

In the Alignment Guide, the same core process standards recur across grade 4 modules that cover different content. For example, 4.1.A (applying mathematics to real-world problems), 4.1.B (using a problem-solving model), and 4.1.D and 4.1.E (communicating through representations) appear in the “Perimeter/Area/Volume/Surface Area,” “Angle Relationships and Polygons,” and “Two- and Three-Dimensional Shapes” modules. This recurring integration connects the process standards across the grade 4 learning pathway rather than isolating them within a single unit.

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

In the “Representation/Interpretation of Data” module of the grade 4 Alignment Guide, the lesson list identifies which TEKS process standards apply to lessons such as “Representing Data” and “Solving Problems Using Data,” noting that students apply mathematics to real-world scenarios, communicate ideas through graphs and plots, and analyze relationships to identify patterns and trends.

The Imagine+ Math K–6 Rationale for Learning Paths illustrates the same process-standards integration in the lesson “Data Representation,” where students identify the most appropriate data display for different situations and explain and justify their reasoning as part of the “Explaining and Justifying Reasoning” process standard.

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

The materials engage grade 4 students in mathematical tasks that require sustained effort and build meaning around mathematical concepts. Students explain their reasoning, justify their solution strategies, and describe why their approach works during problem-solving tasks. In Supported Practice activities, such as “Writing Decimals as Fractions,” students receive immediate feedback when an answer is incorrect and can revise their response before moving on, which encourages them to keep working through a problem rather than stopping at a wrong answer. The Teacher Guide’s Promoting Self-Efficacy strategies further support this persistence by encouraging students to monitor their understanding and adjust their approach when they encounter difficulty.

The Problem-Solving graphic organizer walks students through identifying important information, visualizing the problem, solving it, and checking that their answer makes sense, building both mathematical thinking and perseverance through each step. Interleaved Practice pushes this process further by mixing previously learned skills with new ones in a single session; the Teacher Guide notes that this approach is designed to align with the TEKS framework by fostering conceptual understanding, reasoning, and problem-solving perseverance. As students work through varied problem types, they explain which strategy they chose for each one and why, reinforcing that different approaches can lead to a correct solution.

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

The program gives educators a structured routine for helping students discover that a problem can be solved in more than one valid way. Educators introduce a problem and set the expectation up front that there may be multiple correct paths to a solution, then let students work independently or in pairs using a strategy of their choosing. Once students finish, educators invite several students to share how they solved the problem, ask follow-up questions that prompt students to justify why their strategy works, and lead a discussion comparing the different approaches for similarities, differences, and efficiency. In the recurring Problem-Solving activity found throughout each unit, this same idea appears in the Justifying Multiple Solutions prompts, which ask students whether another approach could also work and how they know their answer is correct.

The materials provide students with language supports to explain and defend their chosen strategy. Educators can offer sentence stems such as “My strategy works because . . . ” and “Another way to solve this is . . . and it works because . . . ” to help students articulate their reasoning, whether they agree or disagree with a classmate’s strategy. The Problem-Solving graphic organizer reinforces this support from the start of a problem: its stated purpose is to help students recognize that there are multiple approaches to solving a problem and to encourage them to explore different strategies before justifying their reasoning and solution. Together, these supports build students’ confidence in explaining why their approach works and in evaluating a peer’s approach as equally valid.

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/or educators.

The Problem-Solving graphic organizer guides students through a problem step by step, then sets aside time to discuss their work and solution with peers. Writing to Explain Mathematical Thinking provides educators with sentence frames, such as “I used ____ because ____,” that help students articulate their strategy and reasoning. Supporting Collaborative Problem Solving and Discourse has students solve problems together in pairs or small groups, ask each other clarifying questions, and justify their thinking through oral or written discourse. Together, these routines move students from solving a problem to writing about it to defending their thinking with classmates.

After solving a problem with the Learning Organizer, students turn to the Problem-Solving Reflection page in their Math Journal to describe their strategy, what worked well, and what they might try next time. At the end of the lesson, the End Lesson Organizer prompts students to capture new vocabulary and reflect on their learning process. From there, the Supporting Collaborative Problem-Solving and Discourse routine brings students back together in small groups to compare strategies, ask each other questions, and justify their thinking out loud. Across a single lesson, a student moves from solving independently to writing about the process in a journal to talking it through with classmates.

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

The Teacher Guide gives educators concrete ways to help students share and reflect on how they solved a problem. In “Supporting Multiple Solution Strategies,” educators invite several students to explain how they solved a problem, then ask follow-up questions that require them to justify why their strategy works and compare it to a classmate’s approach. “Justifying Solution Strategies” adds sentence stems, such as “My strategy works because . . . ” and “I agree/disagree with this strategy because . . . ” that give students language for building an argument around their thinking. The Problem-Solving graphic organizer reinforces this process after a problem is solved: Its Confirm step prompts students to reflect on their thinking, which the guide notes builds their ability to explain, argue, and justify solutions.

In a grade 4 Problem-Solving activity, an educator poses one word problem and walks students through it using a set of guiding questions. Under “Understanding & Explanation,” the educator asks a student what strategy they used and why they chose it. Under “Justifying Multiple Solutions,” the educator asks whether another approach could also work and how the student knows the answer is correct, prompting the student to defend their thinking. Under “Writing & Discussing Math,” the student describes their thinking to a classmate. Finally, under “Reflection & Growth,” the student looks back at what was most challenging and what they learned from any mistakes. This recurring structure gives every grade 4 unit a consistent way for students to share their reasoning and reflect on it afterward.

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

The materials include a “Common Misconceptions” Teacher Support for each grade 4 lesson, identifying likely student errors and providing educators with specific feedback to address each one. In the “Classify 2-D Shapes (Lines and Angles)” lesson, for example, the support alerts educators that students may think all triangles have at least one right angle or that all quadrilaterals have two pairs of parallel sides. For each misconception, it offers educators a way to respond: showing examples of triangles with acute, obtuse, and right angles, or using a trapezoid to show a quadrilateral with only one pair of parallel sides. This support helps educators anticipate where students are likely to go wrong before instruction even begins and respond with feedback targeted to the specific misunderstanding rather than a simple right-or-wrong response.

The materials provide explanatory feedback based on what a student actually answers, not just on what they are expected to struggle with. Every Mastery Check item includes an answer rationale that explains the reasoning behind each answer choice: For a correct response, it walks through the steps that lead to the right answer; for an incorrect response, it describes the likely thinking that led the student there and explains how to solve the problem correctly. Educators can review a student’s specific responses alongside these rationales in the Assignment Builder, then choose a matching Teacher Support, such as “Common Misconceptions” or “Building the Foundation,” to work with that student individually or in a small group. This structure ties explanatory feedback directly to each student’s work on a given item, rather than relying only on anticipated errors.