Imagine+ Math ™ Texas, Grade 2

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 mathematical concepts covered at every grade level. For each module, the guide identifies the specific TEKS and ELPS addressed and describes the concepts covered, such as decomposing numbers, building fluency with operations, and working with fractions and proportional reasoning. This structure repeats across every module and grade level, helping educators clearly see which standards and concepts each learning experience addresses.

The Imagine+ Math K–6 Rationale for Learning Paths provides a rationale for learning paths both across and within grade levels. For vertical alignment, the document 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, the document describes how the Math Builder pathway supports students two or more grade levels below through targeted foundational remediation, while the Math Mastery pathway supports grade-level-ready students in deepening their 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 are learning in core instruction beyond the scheduled class periods.

The Teacher Guide includes a "Usage Recommendations" table that frames consistent usage as the standard for ensuring 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+—reflecting the program’s recognition that instructional needs differ across grade bands. Across all grades, the lesson completion expectation is one to two lessons per week, with a school year goal of 30 lessons passed. These recommendations apply regardless of which implementation model the educator selects, establishing a consistent usage floor across both the structured 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 describe how embedded Mastery Checks generate the diagnostic data that the program uses to determine each student’s skill entry point. According to a student’s Mastery Check performance, the student is 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 students begin instruction at the most appropriate point for their current level of understanding, rather than by grade level alone. Educators retain the ability to 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 Imagine+ Math, establishing the connection between diagnostic results and recommended skill entry points. When NWEA MAP® Growth™ data is integrated, the program uses domain-level RIT scores to determine an appropriate starting point in each TEKS-aligned instructional domain. The accompanying RIT score range table specifies the score range associated with each grade level, supporting instructional placement decisions. Students begin at an entry level matched to their performance in each domain and 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 both content standards and mathematical process standards. This guide serves as a TEKS correlation guide by identifying which standards each lesson addresses, allowing educators to connect diagnostic assessment results with targeted skill entry points in the program’s instructional sequence. Together with the NWEA Crosswalk and the embedded Mastery Check system, this Alignment Guide helps educators identify 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.

The materials include a Teacher Guide that clearly explains the unit and lesson internalization protocols. These protocols provide logistical support and guidance for successful program implementation and help educators make instructional plans and informed decisions related to 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, both protocols guide educators to preview lesson objectives and TEKS alignment in the Assignment Builder and to use the embedded educator 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 road map 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. The guide is organized by implementation phases and offers action items and tips that leaders can use as a checklist. The guide also supports distributed leadership by identifying 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” document provides instructional leaders with sequenced resources and guidance for supporting educators throughout implementation. The learning path organizes administrator actions across three phases, with each phase building on the previous one to sustain program fidelity over time. In 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 directions for exporting student data and managing benchmark assessments. Together, these tools support instructional leaders in using data to guide educator practice and ensure that educators implement the program 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 with the lesson objective, aligned domain, and the 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 under the “Standards” heading. The “English Language Support” section in educator supports identifies the aligned ELPS for each lesson and provides educators with language support guidance and TEKS-aligned content objectives.

The Teacher Guide provides unit overviews, suggested lesson time frames, and additional lesson component information 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 broken down by unit. For each unit, families receive activity suggestions designed to reinforce classroom learning using everyday materials at home. Activities connect grade-level math skills to everyday life, and families use the checklist to track completed activities with their children. Together, the English and Spanish versions ensure that all families can access unit-level guidance to support their children’s progress.

The materials provide families with unit-by-unit activity suggestions in both English and Spanish that are explicitly aligned to the TEKS. Each activity reinforces classroom learning using everyday materials, and the suggestions equip families with practical tips for supporting their children, 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 designed to provide timely feedback and determine next steps for students rather than serve as summative assessments for grading. In the K–2 Mastery pathway, Mastery Checks appear before related practice to identify what students already know and to determine whether they continue to additional lessons or move ahead in their learning paths. Students who score 90 percent or higher on a Mastery Check move past related content, but students who score below 90 percent receive a “Review” or “Remediation” lesson before continuing. Educators review Mastery Check results in reports to monitor student progress and identify when students might need additional support.

The Teacher Guide defines Mastery Checks as instructional assessments designed to function as both diagnostic and formative measures, explicitly noting that they are not used for summative evaluation or grading. Educators use Mastery Check data to monitor student progress in the “Reports” section, determine student readiness to move forward, and guide targeted reteaching, intervention, or enrichment. Furthermore, educators 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 teachers with 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 diagnostic 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 provides clear guidance for consistent and accurate administration of instructional assessments. The section outlines how educators preview Mastery Checks in the Assignment Builder before students take them, review key skills and concepts in advance, 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 both the Math Mastery and Math Builder pathways. The Implementation Guide explains how the program uses student data to adjust lesson sequencing, pacing, and skill progression, and it outlines clear expectations for how educators monitor and review student results in the “Reports” section 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 K–2 Mastery pathway, digital assessments include printable supplemental worksheets that educators can access to support individual students. However, the materials do not provide embedded digital assessment accommodations, such as text-to-speech, content and language supports, and calculators, that educators can enable or disable to meet individual student needs.

The materials demonstrate printable versions of digital assessments and text-to-speech through TextHelp SpeechStream integration but do not demonstrate content and language supports that educators can enable or disable to support individual students in digital assessments, and the materials do not 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 unique interactive item types, such as drag-and-drop, multiple-choice, text-entry, and matching tasks, that are aligned to the TEKS. For example, in a Mastery Check, students select from four answer choices to identify the length of a crayon using a ruler.

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

Formative assessments include more than two unique interactive item types, such as drag-and-drop, multiple-choice, text-entry, and multi-select tasks, that are aligned to 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 through lesson score and standards proficiency status categories. Educators use the “Class Summary” report and “Cumulative Standards Proficiency” report 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 provides 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 both correct and incorrect Mastery Check responses. For correct responses, rationales describe the reasoning used to reach the solution. For incorrect responses, 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 for using the included tasks and activities to respond to student trends in performance on assessments. Educators use the Mastery Check results to determine next instructional moves, such as implementing a Teacher Support for students who do not consistently demonstrate mastery, selecting an Enrichment and Extension activity for students who consistently perform well, and reviewing answer rationales to identify misconceptions for students who demonstrate low performance on Mastery Checks.

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 might 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-term and long-term instruction to support coherence between 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 allow educators to monitor student progress and growth across domains and learning pathways. Educators use the “Class Summary” report to identify students who need support and lessons to reteach, the “Class Progress” report to monitor progress across lessons and domains and to 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 to plan reteaching and practice.

The Implementation Guide includes student-facing progress-monitoring tools that allow students to track their own 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 lessons completed, including completion dates and scores. Additionally, printable Lesson Trackers help students set weekly usage goals, reflect on their efforts, and notice growth over time, and progress charts provide a visual way for students 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 that are embedded at key points throughout lessons in both the Math Mastery and Math Builder pathways to frequently monitor student understanding. Mastery Check results provide immediate feedback and automatically adjust lesson progression, supports, and next steps according to student performance.

In the Math 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, but 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 in 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 worked examples that help educators address misconceptions and build the conceptual understanding students need for more-complex concepts. These scaffolded supports are embedded in lesson guidance to help students move toward grade-level proficiency.

The materials include explicit educator guidance for lessons and activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. For example, educators assign graphic organizers according to students’ specific math needs. Students who need additional support use the graphic organizers as a guide during practice, and more-advanced students use similar graphic organizers 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 in 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 in reteaching activities provide educator directions and worked examples that reinforce mathematical language, help educators address misconceptions, and strengthen conceptual understanding.

The materials include explicit educator guidance for using embedded language supports to develop academic vocabulary and address unfamiliar references in text. For example, 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 Teacher Guide includes an “Enrichment and Extension” section that 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 Teacher Guide includes multiple opportunities to enrich instruction and extend mathematical thinking, supporting educators in providing learning experiences beyond initial mastery.

The materials include explicit educator guidance for extending learning opportunities for students who have demonstrated mastery of grade-level content and skills. Educators use student performance data to identify students ready for more advanced work and 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 and 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 “Assistive Technology” section of the Implementation Guide for enabling and disabling text-to-speech as an accessibility feature for students. The Implementation Guide provides specific educator instructions for 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 state that a student who needs 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 in 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 also reference language translation rather than content and language supports.

The materials include a text-to-speech accommodation 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 Implementation Guide for supporting students in demonstrating understanding of mathematical concepts in multiple ways. The Teacher Guide provides guidance for using problem-solving graphic organizers that help students make sense of mathematical concepts through a structured problem-solving process, encouraging them to explain their thinking, persevere through challenges, and represent their understanding in an organized format. Additionally, the “Universal Design for Learning” section of the Implementation Guide explains how students engage with mathematical concepts through multiple means of representation, action and expression, and engagement, allowing students to perform, express, and represent mathematical thinking in varied ways to deepen their understanding and to support access to learning.

The materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, including performing, expressing, and representing their thinking. Math Journaling resources provide educators with reflection prompts, graphic organizers, problem-solving reflections, and end-of-lesson organizers that help students explain strategies, justify solutions, and reflect on their learning. Furthermore, the “Demonstrating Understanding” section offers alternative methods for students to show 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 in the “Building Foundations” section of each lesson to activate prior knowledge and anchor big ideas through connections to prerequisite skills and 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. Unit overviews establish this framework by connecting prerequisite understanding to new mathematical concepts. Each unit opens with an overview that anchors the unit’s big idea. For example, unit 2 frames repeated addition, equal groups, and arrays as the foundation for understanding the relationships among addition, subtraction, multiplication, and division, followed by a “Vocabulary Development” section that distinguishes new grade-level terms from previously introduced ones. In each lesson, the “Building the Foundation” section gives educators targeted scaffolds to address prerequisite concepts and skills for students who need additional help before or after instruction, and the “Coherence and Connections” section highlights connections between prior knowledge and current grade-level concepts. The “Practice for Long-Term Learning” section 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 representations. In unit 2, the “Array Build” fluency activity connects both a numeric pattern and the relationship between repeated addition and multiplication across multiple representations. Students build an array with counters or on grid paper after hearing a fact, such as “3 groups of 4,” and write two equations to match the array—an addition equation (4 + 4 + 4 = 12) and a multiplication equation (3 × 4 = 12)—with the repeated addition equation revealing the skip-counting pattern of adding 4 each time as groups increase, before comparing and extending with a partner who calls out a new group. In unit 3, the “Measurement Match-Up” fluency activity connects the feature of an object’s length across multiple representations. Students measure the same object with two different tools, record both measurements, discuss and decide which unit is more reasonable, and sort the object into the correct category.

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 include multiple types of practice opportunities, including guided practice through educator questioning, intervention supports, and scaffolded instruction, and 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 include 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 multi-tiered intervention methods.

The materials include collaborative practice opportunities through structured partner and small-group activities, such as fluency 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, such as independent work, collaborative learning, choice boards, creative problem-solving, reflection, discussion, and peer-sharing. Additionally, the Teacher Guide provides explicit 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.

The materials include enrichment and extension methods that support various forms of engagement and guidance for educators to support effective implementation. For example, educators access enrichment and extension activities through the “Teacher Supports” 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 in the “Justifying Solution Strategies” section of the Teacher Guide 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 the “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 by using the “Teacher Supports” section of 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 include differentiated linguistic accommodations according to a student’s bilingual program model and language proficiency trajectory. The Teacher Guide outlines distinct guidance for the 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 lesson-level “English Language Support” section organizes educator guidance by proficiency level, from pre-production through advanced, with scaffolds that progressively increase language demands. The pre-production and beginning levels incorporate visual aids, modeled academic language with gestures, peer-buddy practice, word banks, and sentence frames. Intermediate levels expand student language through reasoning sentence frames and comparison word problems, and high intermediate levels build on this by having students write and solve their own comparison word problems and explain their reasoning. Advanced levels engage students in small-group discussions in which they compare, explain, and justify their thinking using more-complex sentence frames and multistep word problems.

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 in the Implementation Guide for supporting language access and implementation for emergent bilingual students. The guide provides explicit educator guidance on how to enable and use built-in language supports, including translation features that support more than 60 languages and provide translations into 45 languages. Step-by-step instructions help educators activate these supports and increase access to instruction for emergent bilingual students. Additionally, the Implementation Guide contains a dedicated section for bilingual and English as a Second Language (ESL) programs that outlines how the language-support features can be implemented in those instructional settings.

The materials include implementation guidance to support educators in using the materials in state-approved bilingual and ESL programs. For example, the program offers Spanish versions of grades K–6 lessons and the student interface, and the program provides 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 in the “Facilitating Discourse with Mathematical Vocabulary” section of the Teacher Guide. This section provides educators and students with question stems to support oral and written discourse about mathematics. The question stems offer structured opportunities for students to discuss, explain, and justify their reasoning in meaningful ways, helping reduce language barriers and strengthen 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.

The materials also help students build background knowledge and make cross-linguistic connections through oral and written discourse. For example, 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 and 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 lesson “Partition into Equal Shares II” provides practice opportunities that require students to demonstrate depth of understanding of partitioning shapes into equal shares, which is aligned with the TEKS. Students analyze visual models to distinguish between equal and unequal partitions, reconstruct whole shapes using fractional pieces, and reason about the relative size of shares in shapes divided into halves, thirds, and eighths. Through interactive sorting, modeling, and reasoning tasks, students apply their understanding of equal shares and the relationship between the number of parts and the size of each share. These activities move beyond recall and require students to demonstrate conceptual understanding using visual representations.

The lesson “Adding up to Four 2-Digit Numbers” includes an instructional assessment that requires students to demonstrate depth of understanding of addition concepts, which is aligned with the TEKS. Students solve real-world problems involving the addition of up to four two-digit numbers and apply strategic thinking to determine efficient solution methods. Assessment items require students to analyze number relationships, such as identifying which addends to combine first based on place-value reasoning, rather than simply performing computations. The variety of contextualized problems and higher-order questions provides evidence of students’ conceptual understanding and ability to apply addition strategies beyond basic calculation.

In the Imagine+ Math Interleaved Practice, “Interleaved Practice #1” offers students opportunities to demonstrate mastery of multiple previously taught mathematical skills and concepts in a single activity. Students compare two-digit numbers, write numbers in word form, solve addition and subtraction problems, interpret picture data, identify geometric attributes, analyze a graph, tell time on an analog clock, distinguish between a.m. and p.m., and solve a multistep word problem. The activity requires students to independently apply previously learned concepts and generate responses through written answers, visual representations, data interpretation, and problem-solving strategies. By integrating content from multiple domains, the materials provide assessment opportunities that measure student understanding across a variety of skills and concepts rather than assessing a single isolated skill.

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.

The “Even and Odd Numbers” lesson includes lesson-specific enrichment and extension activities that increase in rigor and complexity. The “Odd and Even Scavenger Hunt” and “Even Number Art” activities build grade-level proficiency aligned with TEKS 2.7A by requiring students to identify, classify, count, and represent even numbers as sums of two equal addends. The “Real-World Even and Odd” activity extends learning by having students identify even and odd numbers in authentic contexts, explain their reasoning, and share their findings. This progression from identifying and representing even numbers to applying concepts in real-world situations demonstrates increasing rigor and complexity that supports both grade-level and above grade-level proficiency in the mathematics TEKS.

In “Interleaved Practice #1,” students engage with multiple mathematical concepts in a single activity, including number comparison, two-digit addition, place value, data interpretation, geometry, telling time, and multistep word problems. The activity provides a balanced collection of questions that address multiple TEKS expectations and require students to apply skills across content strands. Tasks progress from procedural work, such as comparing numbers and solving computation problems, to application tasks that require students to interpret data, analyze representations, and solve real-world problems. By requiring students to move among different representations and mathematical concepts in the same activity, the materials support grade-level proficiency and extend students’ ability to connect and apply mathematical understanding across content areas.

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

The “Horizontal Concept Map” demonstrates coherence across grade-level concepts by linking big ideas in number and operations, geometry and measurement, algebraic reasoning, data analysis, and personal financial literacy. For example, the map connects shape partitioning to addition and links area modeling to multiplication as repeated addition, highlighting relationships among mathematical concepts across strands. These connections help students recognize patterns and understand how concepts build on and support one another rather than being taught in isolation. By making these relationships explicit, the materials demonstrate horizontal coherence aligned with the TEKS.

In the Teacher Guide, the unit 1 overview demonstrates horizontal coherence by connecting place value concepts, addition and subtraction strategies, and money as related mathematical ideas in a single learning progression. The overview explains how students use their understanding of place value and number relationships to support computation and problem-solving, highlighting connections among grade-level concepts. The overview also notes that these understandings prepare students for future multiplication and division concepts, showing how current learning is built on interconnected ideas. The vocabulary section further reinforces coherence by distinguishing previously introduced terms from new vocabulary, helping educators see how mathematical concepts develop and connect throughout the grade.

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.

The K–6 “Vertical Concept Map” illustrates how algebraic reasoning concepts build on prior learning and prepare students for future mathematical understanding. The algebraic reasoning strand shows how students extend their abilities to recognize patterns, represent mathematical relationships, and solve problems involving unknown quantities while building on foundational concepts introduced in earlier grades. The progression also shows how these understandings support future learning in grade 3 and beyond, where students apply algebraic reasoning to multiplication, division, and increasingly complex problem-solving situations. By explicitly connecting patterns, relationships, and mathematical structures across grade levels, the concept map supports vertical coherence and helps students develop algebraic thinking as a connected progression of learning.

The materials include a “Lesson Coherence Map” that demonstrates vertical coherence by showing how mathematical concepts develop across grade levels through explicit connections among prior learning, current instruction, and future expectations. For example, regrouping lessons build on earlier addition and subtraction strategies and prepare students for future multi-digit computation. Throughout the map, concepts related to place value, addition, subtraction, mental math, fractions, and problem-solving are linked through prior-current-future lesson progressions, illustrating how mathematical understanding develops over time. These connections help educators see how current learning builds on previous knowledge and supports future mathematics success.

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” organizes lessons to show how mathematical concepts connect across domains and build over time. The map demonstrates how conceptual and procedural knowledge from grade 1 supports grade 2 learning and prepares students for grade 3 concepts. By linking prior learning to current and future grade-level mathematics, the materials demonstrate coherence across lessons and activities.

The Teacher Guide demonstrates coherence by explicitly connecting students’ prior knowledge of concepts and procedures to grade 2 learning and future mathematical development. For example, the unit 1 overview explains how students extend their understanding of whole numbers and place value developed in grade 1 and notes that understanding place value and number relationships prepares students for future multiplication and division concepts. Additionally, each unit’s vocabulary section distinguishes between previously introduced words and new words to the grade level, highlighting connections among prior learning and new content. These unit-level connections show how the materials intentionally link prior, current, and future mathematical learning throughout grade 2.

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

The Teacher Guide includes “Practice for Long-Term Learning” sections that provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways. In these activities, students revisit place-value understanding by discussing the value of digits in different positions; adding groups of tens to numbers; explaining numbers in standard, expanded, and word form; connecting repeated addition to multiplication; and interpreting unknown quantities in equations. These recurring prompts require students to recall and apply prior learning in new contexts, supporting retention and reinforcing connections among mathematical concepts over time.

In “Interleaved Practice #1,” students engage in spaced retrieval by revisiting previously learned skills and concepts from multiple mathematical domains in a single activity. Students recall and apply concepts related to number comparison, addition and subtraction, place value, data interpretation, geometry, telling time, and problem-solving. Tasks require students to compare numbers, solve computation problems, write numbers in word form, interpret a graph, identify polygons, tell time, and solve word problems. By requiring students to retrieve and apply concepts and procedures from earlier lessons in a variety of contexts, the activity reinforces learning over time and supports long-term retention of skills and concepts.

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

The Interleaved Practice materials provide eight student-facing practice sets that require students to apply previously learned skills and concepts in the same activity rather than practicing a single strategy in isolation. Each practice set includes a variety of problem types from multiple mathematical domains, requiring students to determine which skill, concept, or strategy is appropriate for each problem. By mixing content and encouraging students to switch between different types of mathematical thinking, the materials provide interleaved practice opportunities with both skills and concepts across learning pathways.

The Teacher Guide includes a “Connecting Mathematical Concepts with Interleaved Practice” section that provides guidance for using interleaved practice to reinforce previously learned skills and concepts. The guidance directs educators to have students explain strategy choices, to address misconceptions as they arise, and to use student responses to determine whether reinforcement or extension is needed. By supporting the implementation of mixed practice that revisits prior learning, the materials provide interleaved practice opportunities across learning pathways.

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

In the K–2 Problem-Solving Organizer, students draw a picture to represent a mathematical situation, solve the problem using that representation, and then revisit their work in the “Did I Get It Right?” section. Students interpret their models to understand the problem, analyze the relationship between their models and solutions, and evaluate whether their answers are reasonable by explaining how they know their answers make sense.

In “Interleaved Practice #1,” students work with multiple mathematical representations, including picture graphs, analog clocks, geometric models, and visual data displays, to answer questions and solve problems. Students interpret these representations by reading information from graphs to determine quantities and examining clock models to identify the correct time. They analyze the information presented to compare data, identify relationships, solve mathematical situations using the visual models, and evaluate their conclusions by selecting and justifying answers using evidence from the representations.

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

In the K–2 Problem-Solving Organizer, the “Show It With a Picture” section requires students to create a pictorial representation of the mathematical situation. Students draw objects, shapes, dots, or other visual models to represent the quantities, relationships, and actions described in the problem before solving it. Rather than simply recording a numerical answer, students create their own representations to communicate their mathematical thinking and model the problem situation.

In the “Lesson Coherence Map,” the lesson “Three-Digit Numbers” asks students to model three-digit numbers using base 10 blocks and place value cards before reading, writing, ordering, comparing numbers, and adding or subtracting hundreds. This lesson requires students to build and manipulate concrete place-value models to represent three-digit numbers and demonstrate mathematical relationships among hundreds, tens, and ones. Students use these tangible models to represent mathematical situations and develop conceptual understanding before applying symbolic notation and computation.

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

In the “Using Data to Solve Problems” lesson, the Mastery Check presents a different pictograph and real-world scenario in the items, such as determining how many students chose carrots or beans from a vegetable survey, comparing how many more friends prefer beef tacos to chicken tacos, and identifying which statement is true using class lunch data. As students progress through the Mastery Check, the data sets, key values, and question types change, requiring students to interpret the graphs and apply addition, subtraction, and comparison strategies rather than rely on memorized procedures.

In the “Adding up to Four 2-Digit Numbers” Mastery Check (questions 1–15), students apply their understanding of place value and addition strategies to problems involving shopping purchases, collected items, distances, grouped objects, and other contextual situations that require finding the total of four two-digit numbers. Rather than repeating a single computation format, students must determine an efficient strategy for combining multiple addends by using place-value reasoning and composing numbers. The problems are presented through word problems, tables, and numerical representations, requiring students to transfer their understanding of addition concepts to unfamiliar situations and select appropriate solution strategies.

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

In the fluency activities, the “Place Value Scoop” activity asks students to scoop a handful of labeled sticks, sort them by place value, and quickly record the resulting number in standard, word, and expanded form, strengthening automaticity with three-digit place value concepts. Additional activities, including “Array Build” and “Graphing Group Data,” provide purposeful, repeated practice with equal groups, measurement, and data analysis, helping students develop increasing accuracy, efficiency, and confidence across multiple mathematical concepts.

“Interleaved Practice Set 4” integrates nine problems aligned with the TEKS in a single practice set, having students move among comparing three-digit numbers, solving addition and subtraction problems within 100, identifying fourths, recalling coin values, and applying other concepts rather than practicing one skill in isolation. Because the practice set intentionally combines previously learned skills with current grade-level content, students repeatedly recall and apply multiple strategies with increasing accuracy, efficiency, and flexibility.

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

In the Interleaved Practice materials, students solve a variety of problem types in each practice set, engaging with place value, addition and subtraction, time, geometry, data interpretation, and word problems. Students compare numbers, perform computations, interpret mathematical representations, and apply reasoning across multiple concepts. Because the problem types vary throughout each practice set, students must determine the most appropriate procedure for each task, transition efficiently between strategies, and solve problems accurately rather than rely on a single method.

In the Teacher Guide, the “Developing Mathematical Fluency” section explains how fluency activities serve as brief, focused practice opportunities that strengthen foundational mathematical skills through quick recall, mental math strategies, and visual models. The guidance also recommends using these activities as warm-ups, formative check-ins, or small-group rotations, providing students repeated opportunities to apply mathematical procedures in a variety of instructional settings.

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 the “Decomposing to Get Ten” worksheet, students use 10-frame models and numerical representations to decompose numbers before solving subtraction problems. Students analyze how breaking apart a quantity to make 10 supports the subtraction process, compare the 10-frame model to the corresponding numerical procedure, and determine how the representation leads to a correct solution. As students connect the visual model to the subtraction strategy, they evaluate why decomposing to make 10 is an efficient approach, apply the strategy flexibly across different subtraction problems, and verify the accuracy of their solutions.

In the “Describing Multiplication Situations” worksheet, students interpret multiplication equations and compare quantities using multiple representations and analyzing arrays, diagrams, and multiplication equations across a variety of scenarios. The worksheet concludes by asking students to explain, “How do you compare the numbers 2, 5, and 10 using a multiplication equation?” This reflective prompt requires students to evaluate how multiplication equations represent relationships among quantities, justify their reasoning, and determine the most appropriate representation for the situation.

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

In the Interleaved Practice materials, the educator guidance directs educators to encourage students to determine the most appropriate strategy for each problem, explain their reasoning to a partner, and reflect on their problem-solving process. The guidance also includes follow-up questions, such as “How did you know which strategy to use for this problem?” that prompt students to evaluate their strategy selection and consider whether a different approach might be more effective.

In the Teacher Guide, the “Justifying Solution Strategies” section includes discussion prompts, such as “Which strategy was most efficient and why?” and sentence stems, such as “I chose this strategy because . . . ” to help students explain, compare, and justify their mathematical approaches. The guidance encourages educators to facilitate discussions that prompt students to reflect on the effectiveness of different solution strategies, consider alternative approaches, and explain why one method might be more efficient than another.

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

The materials explicitly explain how the TEKS' conceptual and procedural emphases are addressed throughout the Math Builder and Math Mastery pathways. In the Imagine+ Math K–6 Rationale for Learning Paths, the conceptual emphasis describes how students develop mathematical understanding through instruction, supported practice, and independent practice using visual models, multiple representations, and real-world contexts, explaining how lessons build conceptual understanding before students apply mathematical procedures. The procedural emphasis explains how TEKS-aligned practice activities reinforce procedural fluency and skill application through repeated opportunities to practice and apply mathematical procedures.

In the “Vertical Concept Map,” the grade-level descriptions explain how students develop conceptual understanding of number relationships, place value, operations, fractions, and mathematical reasoning and apply those concepts through activities, such as counting, comparing quantities, composing and decomposing numbers, solving addition and subtraction problems, and representing mathematical ideas in multiple ways. The descriptions consistently identify the mathematical understandings that students are expected to develop and the procedures they practice and apply.

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.

In the Interleaved Practice sets, students interpret shape models, balloon collections, analog clocks, and visual data displays as pictorial representations and solve problems using numerical computations, number comparisons, symbolic notation, and written responses as abstract models. Students connect visual information to mathematical procedures by interpreting representations, applying mathematical reasoning, and expressing their solutions using numbers and mathematical symbols.

In the “Place Value Scoop” fluency activity in unit 1 of the Teacher Guide, students scoop a handful of ice pop sticks labeled as ones, tens, and hundreds; sort them onto a place value mat; and use the physical materials to build and represent numbers. After organizing the concrete model, students count the value represented and record it in standard form, word form, and expanded form, which connects the hands-on model to abstract numerical representations.

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.

In the “Write and Expand Three-Digit Numbers Worksheet,” students use pictorial place-value models to represent hundreds, tens, and ones that are directly connected to standard, expanded, and word form in the “Review and Try It” sections. Worked examples and instructional prompts explain how each visual representation corresponds to symbolic notation before students create their own models and record the matching abstract representations.

In the “Place Value Scoop” fluency activity in unit 1 of the Teacher Guide, students scoop ice pop sticks labeled as ones, tens, and hundreds; sort them onto a place-value mat; and use the concrete materials to build numbers. Students then count the value represented and record the number in standard, word, and expanded form, which connects the physical model directly to symbolic notation.

In the “Describing Multiplication Situations Worksheet,” students interpret arrays and diagrams, connect each representation to a corresponding multiplication equation, and apply the equations in multiple problem situations. The lesson extends students’ thinking by asking them to explain how the numbers 2, 5, and 10 can be compared using a multiplication equation, which requires students to justify how the visual models relate to symbolic notation and multiplication relationships.

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

In the Teacher Supports document for the “Tell and Write Time to the 5 Minutes” activity, the “Developing Vocabulary” section uses visuals and structured language supports to introduce students to the terms analog clock, digital clock, hour hand, minute hand, a.m., and p.m. Students encounter these terms through labeled clock visuals, an anchor chart, real-world morning and afternoon examples, and sentence frames, such as, “The hour hand is pointing to ____ and the minute hand is pointing to ____.” By pairing clock vocabulary with visuals, real-world context, and sentence frames, the section gives students repeated opportunities to build and use academic mathematical language.

The “Developing Academic Mathematical Language and Discourse” section of the Teacher Guide offers strategies for building academic mathematical language through visuals and structured language supports. The section guides educators to scaffold, reinforce, and extend vocabulary using pictures; real-world objects, such as base 10 blocks; real-life connections; and sentence stems. By combining visual supports with structured language routines, educators give students repeated opportunities to build, practice, and confidently use academic mathematical vocabulary during instruction and mathematical discussions.

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 Teacher Guide, the “Scaffolding Mathematical Vocabulary” and “Extending Academic Vocabulary” sections guide educators through structured routines for introducing and building on academic mathematical vocabulary during peer and educator discussions. Educators demonstrate the Frayer model, provide sentence frames, facilitate partner discussions, and use clarifying prompts that require students to explain vocabulary in context. To extend learning, students compare vocabulary terms using Frayer models, create word problems, justify their reasoning, and respond to peers using academic mathematical language, moving from supported practice to independent mathematical discourse.

The “Developing Vocabulary” section of the “Guided Learning Teacher Supports” for the “Introduction to Hundreds” lesson guides educators in introducing and building academic mathematical vocabulary during mathematical discussions. Educators introduce the term hundreds using base 10 blocks, a hundreds chart, and sentence frames, such as “The number ____ is a multiple of 100,” to support students in communicating mathematical relationships with precise vocabulary. Educators then extend vocabulary development by introducing the term numerals, modeling standard form representations, and engaging students in oral explanations that connect place-value concepts, representations, and academic vocabulary as they communicate with peers and the educator.

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

In the Teacher Guide, the “Facilitating Discourse with Mathematical Vocabulary” and “Writing with Mathematical Vocabulary” sections guide educators in supporting students’ oral and written use of academic mathematical language. Educators use categorized discussion prompts that require students to explain vocabulary in their own words, communicate with a partner, and reflect on the students’ mathematical thinking. Students also use sentence stems, such as “The word ____ means . . . ” and “This example shows ____ because . . . ” to explain, justify, restate, and revise their mathematical thinking using precise academic vocabulary after peer or educator feedback.

The “Developing Vocabulary” section of the “Guided Learning Teacher Supports” for the “Introduction to Hundreds” lesson gives students structured opportunities to apply academic mathematical language while discussing place value. Using base 10 blocks, a hundred chart, visual models, and sentence frames, students explain hundreds, multiples of one hundred, numerals, and standard form using precise mathematical vocabulary. These supports require students to apply academic language, explain place-value relationships. and discuss mathematical representations with peers and the educator.

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 lesson “Tell/Write Time to Nearest Minute,” the “English Language Supports” section structures peer conversations by proficiency level as students practice describing time. At the beginning proficiency level, students work with a buddy to practice saying times aloud, allowing students to hear mathematical language from a peer. At the high intermediate level, students ask and answer questions about time and explain their reasoning during peer discussions, which provides opportunities to refine and use academic mathematical language in conversation.

In the “English Language Support” section for “Identify and Compare Round Numbers,” students use sentence frames and visual supports to compare round numbers with a partner, justify why one number is greater than or less than another, and explain place-value reasoning during the discussion. Educator prompts encourage students to refine their mathematical explanations and apply lesson vocabulary in collaborative conversations and written responses.

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 lesson “Using Data to Solve Problems,” the “Common Misconceptions” educator support section identifies specific errors students are likely to make when interpreting pictographs, bar graphs, and addition and subtraction word problems. For each misconception, the materials offer explicit guidance for educators, such as prompting students to check the pictograph key and highlight relevant bars before solving. These lesson-specific supports help educators recognize misconceptions and provide targeted feedback to strengthen students’ mathematical reasoning.

In the Teacher Guide, the Mastery Check’s answer rationales model the reasoning behind both correct and incorrect student responses for each item. For correct answers, the rationales outline the steps to reach the solution and provide exemplar responses for educators and students. For incorrect answers, the rationales identify likely misconceptions and explain the correct solution path, equipping educators with lesson-specific guidance to recognize and address inaccurate thinking.

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

The “Mathematical Process Standards” overview in the Imagine+ Math Texas Alignment Guide aligns specific process standards with grade-level content across mathematical strands. The guidance explains how students solve problems using multiple representations, communicate and justify their mathematical reasoning, analyze relationships, and connect mathematical ideas while engaging with grade-level content. This overview shows that the materials embed the process standards throughout instruction across all mathematical strands rather than teaching them in isolation.

In the lesson “Using Data to Write Word Problems,” students use pictographs and bar graphs to interpret data, answer questions, write and solve word problems, and explain the information shown in graphs. These tasks require students to analyze representations, connect data to mathematical situations, select appropriate operations, and communicate their mathematical reasoning, demonstrating that the materials embed the process standards within content instruction rather than teaching them separately.

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 and the Alignment Guide show how the TEKS mathematical process standards appear in the lessons and connect to the grade-level content taught in each instructional module. The Rationale for Learning Paths explains how the materials embed the process standards in lessons and provide students with opportunities to solve real-world problems, apply mathematical reasoning, and communicate their thinking throughout instruction. The Alignment Guide further shows how the process standards connect to grade-level TEKS in each instructional module, demonstrating that the materials integrate the process standards with content standards and reinforce them across the learning pathway rather than teaching them in isolation.

The “Horizontal Concept Map” traces how mathematical concepts build across the year, embedding the TEKS mathematical process standards at each stage of the learning pathway. As students progress through grade-level content, they continue to apply reasoning, communication, representation, and problem-solving practices and connect new learning to prior understanding. This progression shows that the materials integrate the process standards throughout instruction and reinforce them across increasingly complex mathematical concepts rather than teaching the process standards in isolation.

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

The Imagine+ Math K–6 Rationale for Learning Paths identifies which TEKS mathematical process standards apply to each lesson in the sequence. The introductory paragraph explains that the materials embed the process standards throughout the Math Builder and Math Mastery pathways, which ensures that students consistently apply mathematical reasoning, problem-solving, and communication during instruction. The guide further reinforces this overview through lesson-specific examples, including “As Many As, More, and Less,” “Evaluating Costs and Benefits,” “Partition into Equal Shares I,” and “Money II,” by identifying the process standards applied in each lesson and describing how students use mathematical tools, representations, and reasoning to meet lesson objectives.

The “Horizontal Concept Map” illustrates how mathematical concepts progress and connect across lessons as students build conceptual understanding. Students continue to apply mathematical reasoning, communication, representation, and problem-solving practices across connected learning experiences as they advance through the sequence. This progression shows the materials consistently embedding the process standards throughout the curriculum rather than teaching them in isolation.

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

In the Teacher Guide, the “Promoting Self-Efficacy” section encourages educators to build students’ confidence by having them predict answers, model think-aloud strategies when difficulties arise, and apply successful strategies to new problems, thereby promoting productive perseverance. The guide’s “Demonstrating Understanding” section offers students multiple ways to express their thinking through actions, verbal explanations, and visual representations, helping them communicate their reasoning and develop a deeper conceptual understanding of mathematics.

The Teacher Guide provides structured opportunities for students to think mathematically and make sense of mathematics as they solve problems. The guide’s “Communicating Mathematical Thinking” and “Supporting Multiple Solution Strategies” sections outline a routine in which students solve problems independently or with a partner, share their thinking using words, models, numbers, or diagrams, and reflect on the strategy they selected and why it was effective. Sentence stems, such as “My strategy works because . . . ” and “Another way to solve this is . . . ” support students in explaining and justifying their reasoning, which helps them make sense of their own mathematical thinking and that of their classmates.

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 Interleaved Practice set is built on the idea that a math problem can be solved in more than one valid way. The set’s directions ask educators to explain that the purpose of the practice is to apply different strategies and skills, not rely on a single method. As students work through each problem, they decide which strategy fits best and explain their reasoning to the educator and peers, either orally or in writing. Guiding questions, such as “How did you know which strategy to use for this problem?” push students to justify their thinking and recognize that more than one approach can lead to a correct answer.

The Teacher Guide gives students structured practice in explaining and defending a chosen strategy. The guide’s “Communicating Mathematical Thinking” and “Supporting Multiple Solution Strategies” sections walk educators through a process in which students select a strategy, share their approach with peers, explain their reasoning, and justify why their strategy works while considering other methods that might also work. The sentence stem “Another way to solve this is . . . and it works because . . . ” scaffolds students as they put these explanations and justifications into words, which reinforces that more than one strategy can lead to a correct solution.

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 fluency activities give students multiple opportunities to do mathematics collaboratively with peers and the educator through hands-on tasks. Across activities such as “Place Value Scoop,” “Array Build,” “Measurement Match-Up,” “Graphing Group Data,” and “Savings Goal Jar,” students build arrays, compare measurement strategies, collect and graph data, and discuss mathematical ideas in whole-class and small-group settings. These activities engage students in active mathematical thinking and verbal discussion with others, which strengthens their ability to communicate their reasoning to peers and the educator.

The Teacher Guide provides structured opportunities for students to write about and discuss mathematics with peers and the educator through a recurring “Problem-Solving” activity in each unit. This activity has students share their solutions, respond to guiding questions, and explain their mathematical thinking during classroom discussions. The guide’s “Writing & Discussing Math prompts,” including such questions as “Can you write a sentence explaining your solution?” and “How would you describe your thinking to a classmate?” ask students to communicate their reasoning through both written and oral responses. These embedded routines help students make sense of mathematics by explaining, discussing, and reflecting on the students’ thinking.

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

In the Teacher Guide, the “Supporting Multiple Solution Strategies” and “Justifying Solution Strategies” sections outline a 10-step instructional framework in which students explain their reasoning, compare solution strategies, justify why their approaches work, and reflect on how another strategy might also be effective. These sections also provide educators with follow-up questions and sentence stems, such as “My strategy works because . . .” and “I agree/disagree with this strategy because . . .,” to scaffold mathematical discussions, evidence-based arguments, and student reflection.

The Implementation Guide provides educators with guidance for helping students share and reflect on their problem-solving approaches through explanations, arguments, and justifications. The guide’s “Academic Discourse” section describes supports embedded in both the Math Mastery and Math Builder pathways. In the Math Mastery pathway, students respond to problem-solving tasks that prompt them to compare strategies and explain why a method works; the pathway includes reflection questions that ask students to self-assess and explain their understanding. In the Builder pathway, downloadable worksheets include discussion questions with flexible oral and written response formats that give students multiple ways to explain and justify their thinking. Together, these supports give educators structured ways to facilitate mathematical discourse and guide students in sharing and reflecting on their problem-solving approaches.

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

The Teacher Guide provides educators with prompts and guidance for delivering explanatory feedback according to student responses and anticipated misconceptions. Throughout the guide, each unit’s “Common Misconceptions or Errors” feature identifies a likely student misunderstanding in that domain and pairs it with Teacher Tips that guide educators in addressing it. Each unit also includes an “Open-Ended Questions” section that educators use to probe student thinking and extend the discussion. Together, these paired supports give educators both guidance and prompts to address anticipated misconceptions, respond to student thinking, and deepen students’ conceptual understanding and mathematical reasoning.

The Implementation Guide provides educators with prompts and guidance for delivering explanatory feedback according to student responses and anticipated misconceptions. The guide’s “Teacher Supports” section names the “Common Misconceptions” sections as one of several supports available in every lesson across both the Math Mastery and Math Builder pathways. The guide’s decision chart directs educators to use this support when students demonstrate confusion or make repeated errors, describing it as a way to surface student thinking and address a likely misunderstanding through clear, targeted feedback.