Imagine+ Math ™ Texas, Kindergarten

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 standards addressed along with a description of the concepts covered, such as decomposing numbers, building fluency with operations, or working with fractions and proportional reasoning. This structure repeats across every module at every grade level, helping educators clearly see which standards and concepts are addressed within 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 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 of structured class periods—Homework/At-Home Practice, Independent Study, After-School Programs, and Tutoring or one-on-one Instruction—allowing students to apply and extend what they are learning in core instruction beyond the scheduled class period.

The Teacher Guide includes the “Usage Recommendations” table, which 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 1–2 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 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 in Imagine+ Math describes 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 within the 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 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 within each TEKS-aligned instructional domain. The accompanying RIT Score Range table specifies the score ranges 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 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 supports educators in identifying 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 Teacher Guide clearly explains the unit and lesson internalization protocols, which provide logistical support for successful program implementation while also helping 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 explore unit overviews to internalize TEKS-aligned concepts, mathematical vocabulary, and suggested instructional activities. For lesson internalization, educators are guided to preview lesson objectives and TEKS alignment in the Assignment Builder and use 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. It is organized by implementation phase 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 their campus.

The “First 30/60/90 Days for Administrators” 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 “Student Progress,” “Mastery,” and “Benchmark” reports as well as directions for exporting student data and managing benchmark assessments. Together, these tools help instructional leaders use data to guide educator practice and ensure that 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 does not apply 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 standard under the “Standards” heading. The “English Language Support” section within Educator Supports identifies aligned ELPS for each lesson and provides educators with language support guidance alongside the TEKS-aligned content objectives.

The Teacher Guide provides unit overviews, suggested lesson timeframes, and additional information on lesson components to support implementation. The TEKS and ELPS are embedded within 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 daily life, and families use the checklist to track activities they complete with their child. Together, the English and Spanish versions ensure that all families can access unit-level guidance to support student progress.

The materials provide families with unit-by-unit activity suggestions (in English and Spanish) that are explicitly aligned with the TEKS. Each activity reinforces classroom learning using everyday materials, and the materials equip families with practical tips for supporting their child, 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 determine whether they will continue on to additional lessons or move ahead in their learning path. Students who score 90 percent or higher on a Mastery Check move past related content, while 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 may need additional support.

The Teacher Guide defines Mastery Checks as instructional assessments designed to function as both diagnostic and formative measures, explicitly noting they are not used for summative evaluation or grading. Educators use Mastery Check data to monitor student progress in the “Reports” section, determine whether a student is ready 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 helps educators to plan lessons, deliver instruction, and make 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 beginning instruction or independent practice. 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 in advance, 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 clearly outlines how to consistently and accurately administer instructional assessments. The section describes how educators preview Mastery Checks in the Assignment Builder before students complete them, review key skills and concepts in advance, and anticipate potential misconceptions to adjust instruction before starting the assessment. 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 the Assessment and Placement Options guide, which supports consistent administration of instructional assessments across both the Mastery and Builder pathways. The Implementation Guide explains how the program uses student data to adjust lesson sequencing, pacing, and skill progression, and outlines clear expectations for how educators monitor and review student results in the “Reports” section to ensure that 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, or calculators that educators can enable or disable to meet individual student needs.

The materials include 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 help individual students during 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. In a grade K Mastery Check, students drag beads into a box to count out the number of objects.

The materials include diagnostic assessments with 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.

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 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 help for interpreting student performance based on categories that cover the lesson score and standards proficiency status. 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 suggests instructional actions for each level to guide targeted follow-up instruction and practice.

The Implementation Guide includes the “Answer Rationales” section, which 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” reports 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 included tasks and activities to respond to student trends in performance on assessments. Educators use Mastery Check results to determine their next instructional moves, such as implementing an Educator Support for students who do not consistently show mastery, selecting an enrichment and extension activity for students who consistently perform well, or reviewing answer rationales to identify misconceptions for students who perform below the expected level on a Mastery Check.

The Teacher Guide includes instructional decision-making protocols that explain when and how often to review assessment data and make instructional decisions about student placement, support needs, and pathway adjustments. On a weekly basis, educators review the “Usage” and “Class Summary” reports to identify students who may need help or reteaching. On a biweekly basis, 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. On a monthly basis, educators use the “Cumulative Standards Proficiency” report to analyze TEKS-level evidence and plan short- as well as 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 for reteaching, the “Class Progress” report to monitor progress across lessons and domains as well as pinpoint class-wide trends, the “Student Progress” report to view individual students’ lesson activity and performance, and the “Cumulative Standards Proficiency” report to monitor TEKS proficiency at the class and student levels as well as plan for 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 effort, and notice growth over time, while 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 does not apply 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 the lessons in both the Mastery and 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.

The materials include adaptive Mastery Checks embedded at key points throughout the lessons in both the Mastery and 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 instruction 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 directions and worked examples that help educators address misconceptions and build the conceptual understanding students need for more complex concepts. Such scaffolded instruction is embedded within lesson guidance to help students move toward grade-level proficiency.

The program includes 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 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 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 educators with directions and worked examples that reinforce mathematical language, help educators address misconceptions, and strengthen conceptual understanding.

The program includes explicit guidance for embedded language supports for developing academic vocabulary and addressing 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 help students develop their academic language and increase their 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 guidance for enrichment and extension within the Teacher Guide under the “Enrichment and Extension” section. This section helps educators extend student learning through activities that deepen understanding and challenge students who have shown 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.

The program clearly explains how educators can extend learning opportunities for students who have demonstrated mastery of grade-level content and skills. Educators use student performance data to identify learners who are ready for more advanced work as well as access activities that deepen students’ 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 instructions within the Implementation Guide under the “Assistive Technology” section for enabling and disabling text-to-speech as an accessibility feature for students. The guide clearly explains to educators how they can use text-to-speech to support language accessibility during instruction. The materials also note that calculators are only available when they are intentionally embedded in an activity and state that students who need a calculator as an accommodation must receive a physical calculator. However, the materials do not instruct educators how to enable or disable 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. Furthermore, 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 help 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.

Within the Teacher Guide and Implementation Guide, the materials explain how to support students in demonstrating understanding of mathematical concepts in multiple ways. The Teacher Guide describes how to use a problem-solving graphic organizer that helps 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 Implementation Guide, under “Universal Design for Learning,” clarifies how students engage with mathematical concepts through multiple means of representation, action and expression, and engagement, allowing them to perform, express, and represent mathematical thinking in varied ways to deepen their understanding and support access to learning.

The program guides educators on how to offer students options and supports to show they understand 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 demonstrate mastery, such as using movement to model concepts on a number line, creating visual representations, and participating in mathematical discussions with their 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.

In the “Building Foundations” section, the materials explain to educators how, within lessons, they can help students 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 learning something new.

The program equips educators with explicit prompts and guidance to build knowledge by activating prior knowledge and anchoring big ideas. “Kindergarten Unit” overviews establish this framework by connecting prerequisite understanding to new mathematical concepts. Each unit begins with an overview that anchors the unit’s big idea. For example, unit 2, “Algebraic Reasoning,” frames recognizing and creating patterns as well as understanding part-whole relationships as the foundation for flexible thinking about how numbers can be put together and taken apart. This is followed by Vocabulary Development, which distinguishes new grade-level terms from previously introduced ones. Within each lesson, “Building the Foundation” gives educators targeted scaffolds to address prerequisite concepts and skills for students who need additional help before or after instruction. Furthermore, Coherence and Connections highlights links 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.

Imagine+ Math highlights and connects key patterns, features, and relationships through multiple means of representation. In unit 2, “Algebraic Reasoning,” the Pattern Clap fluency activity connects a repeating pattern across multiple representations: Students clap or tap a simple sound pattern (such as clap-clap-pat), repeat it together, predict and extend what comes next, and then transform the same pattern into a visual or object format using colors or shapes. In unit 3, “Geometry and Measurement,” the Shape Hunt fluency activity connects the defining features of two- and three-dimensional shapes across multiple representations: Students learn a shape from a card, find a real classroom object with the same shape, describe the object using attribute vocabulary (such as “It has straight sides”), and sort and compare objects by shape or size as a group. In unit 4, “Data Analysis,” the Favorite Fruit Graph fluency activity helps students understand the relationship between data categories across multiple representations: Students place a picture card into a category on a class chart, answer comparison questions (such as “How many more students like apples than bananas?”), and then physically line up by preference to represent the data with their bodies.

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 does not apply 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 such as whole-group instruction, small-group intervention, and individualized support for students who need additional assistance. Additionally, the materials provide explicit implementation guidance through educator tips, intervention recommendations, support for struggling students, common misconception alerts, and monitoring suggestions, helping educators implement multi-tiered intervention methods effectively.

The materials also 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 their 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 promote multiple forms of engagement, including independent work, collaborative learning, choice boards, creative problem-solving, reflection, discussion, and peer sharing. Additionally, the Teacher Guide clearly describes how educators can implement the program 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 program includes enrichment and extension methods that promote various forms of engagement, along with 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 strengthen students’ understanding and increase engagement. These methods support differentiated instruction, allowing educators to foster critical thinking, encourage curiosity, and challenge students through deeper learning experiences.

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

Within the Teacher Guide, the materials include strategies 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 reteaching when necessary to support student progress.

The program includes prompts and guidance to help educators provide timely feedback during lesson delivery. For example, the STEM-Focused Applications Task Guide contains 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 offer immediate support through guided questions, clarification, small-group instruction, and reteaching opportunities using Educator Supports 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 does not apply 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 their 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 use of mathematical language 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 steps 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 Imagine+ Math program includes embedded linguistic accommodations for all levels of English language proficiency, as defined by the ELPS, and engages students in increasingly academic language throughout instruction. Lesson-level English Language Support 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. The Intermediate levels expand student language through reasoning sentence frames and comparison word problems; the High Intermediate levels build on this by having students write and solve their own comparison word problems while explaining their reasoning. The Advanced levels engage students in small-group discussions where they compare, explain, and justify their thinking using more complex sentence frames and multi-step 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 suggestions in the Implementation Guide to support language access and implementation for emergent bilingual students. The guide provides explicit instructions on how to enable and use built-in language supports, including translation features that support over 60 languages and provide translation into 45 languages. Step-by-step directions are included to help educators activate these supports and increase access to instruction for emergent bilingual students. Additionally, the guide contains a dedicated section for emergent bilingual programs that outlines how the language-support features can be implemented within those instructional settings.

The program includes implementation guidance to support educators in using the materials within state-approved emergent bilingual programs. For example, the program offers Spanish versions of grade K–6 lessons and the student interface, along with on-screen translations in 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 question stems for both educators and students to support 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 students’ language development while maintaining a focus on content understanding and mathematical proficiency.

The materials include embedded guidance to support emergent bilingual students in developing academic vocabulary and increasing comprehension. 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 link mathematical vocabulary with 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 does not apply because the program is not designed for dual language immersion (DLI) programs.

This guidance does not apply 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.

In the grade K digital lesson “Count Out a Number of Objects,” students engage in guided practice by counting a specified number of objects and matching quantities to numerals. Students interact with visual representations while applying counting strategies and one-to-one correspondence to demonstrate understanding of number concepts.

In the grade K digital lesson “Decomposing 10,” students independently demonstrate their understanding of composing and decomposing numbers by identifying combinations that make 10 and solving assessment items aligned to the lesson objective. Students apply previously learned concepts and show mastery of the skill through a series of Mastery Check questions.

The grade K Teacher Guide identifies Supported Practice as the lesson component where students apply newly learned TEKS-aligned skills through interactive, guided problems with embedded supports, providing structured opportunities to practice mathematical concepts throughout the learning pathway. The guide also defines Mastery Checks as instructional assessments embedded within lessons that function as diagnostic and formative measures to evaluate student understanding and determine the next instructional steps. The guide directs educators to review Mastery Check results on day 5 and use the data to form small groups or provide one-on-one support, demonstrating how assessment is integrated into the learning pathway to inform instruction.

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.

In grade K, the materials include lesson-specific enrichment and extension activities for the digital lesson “Measurement I,” found in the Teacher Support section. The “Measuring with Body Parts” activity builds grade-level proficiency with TEKS K.7B by having students measure, compare, and record object lengths using non-standard units. The Outdoor Measurement Hunt increases rigor and complexity by requiring students to apply measurement concepts to real-world objects and use rulers and measuring tapes. Because these standard measurement tools are formally introduced in grade 1 TEKS 1.7D, the activity extends learning beyond grade-level expectations. The progression from measuring with body parts to using standard measurement tools demonstrates increasing rigor and complexity that supports both grade-level and above-grade-level proficiency in the mathematics TEKS.

In the Imagine+ Math grade K “Interleaved Practice #1,” students engage with multiple mathematical concepts within a single activity, including counting objects, composing and decomposing numbers, comparing quantities, identifying shapes, measuring length, and interpreting picture data. Tasks progress from foundational skills (such as counting and shape recognition) to application tasks that require students to compare quantities, analyze representations, and solve problems using previously learned concepts. By connecting multiple mathematical ideas within one practice set, the materials support grade-level proficiency while encouraging students to apply and transfer learning 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 Imagine+ Math grade K “Horizontal Concept Map” demonstrates coherence across concepts within the grade level by connecting patterns, big ideas, and relationships among Number and Operations, Geometry and Measurement, Algebraic Reasoning, Data Analysis, and Personal Financial Literacy. For example, the map connects counting, grouping by tens and ones, and composing and decomposing numbers within Number and Operations, while Algebraic Reasoning builds on this understanding through number relationships, visual representations, and problem-solving strategies. By illustrating how concepts support and reinforce one another across domains, the materials help students recognize mathematics as an interconnected set of ideas rather than isolated skills, demonstrating horizontal coherence within the grade K level.

In the Teacher Guide, the unit 1 Number and Operations overview demonstrates horizontal coherence by connecting foundational number sense, composing and decomposing numbers, place value concepts, and addition and subtraction within a single learning progression. The overview explains how students build understanding of numbers, group quantities into tens and ones, and apply this knowledge to describe and solve real-world problems, highlighting explicit connections among mathematical concepts within the grade level. The vocabulary section further supports these connections by distinguishing newly introduced terms from previously learned vocabulary, reinforcing the development of related concepts across the unit.

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 Imagine+ Math K–6 “Vertical Concept Map” provides a strand-organized progression that explicitly connects mathematical concepts across grade K–6. The Number and Operations strand displays grade-level columns that illustrate how foundational number concepts introduced in grade K develop into increasingly sophisticated operations and numerical reasoning in later grades. By showing how mathematical ideas build from one grade level to the next, this resource highlights patterns, big ideas, and relationships across the K–6 continuum, helping educators understand how current learning connects to both prior knowledge and future mathematical expectations. This vertical progression supports coherent instruction and reinforces mathematics as an interconnected body of knowledge rather than a collection of isolated skills.

The materials include a grade K “Lesson Coherence Map” that demonstrates vertical coherence by explicitly identifying prior-, current-, and future-grade lessons for each mathematical concept. For example, the concept Understanding Tens builds on prior learning from “Writing Numbers 0–10” and progresses to future learning in “Reading and Writing Numbers to 100.” Throughout the map, concepts related to number sense, operations, counting, comparison, measurement, and money are linked across grade levels, illustrating how mathematical understanding develops over time. These explicit connections help educators see how current learning builds on prior knowledge and prepares students for future mathematics.

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.

This guidance statement does not apply to the program because grade K does not have a preceding course with prior knowledge to connect to the current grade level or future grade levels.

This guidance does not apply to the program.

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

The Teacher Guide includes a “Practice for Long-Term Learning” section in each of the five units that intentionally revisits previously learned skills and concepts, giving students opportunities for spaced retrieval across learning pathways. By embedding distributed practice throughout the year rather than limiting review to recently taught content, the materials support ongoing recall and reinforcement of prior learning. Including this feature in every unit demonstrates a consistent design for strengthening retention and promoting long-term mathematical understanding.

In the Imagine+ Math "Interleaved Practice #1" for grade K, students engage in spaced retrieval by revisiting previously learned skills and concepts throughout a single practice activity. Students recall and apply counting, addition, graphing, geometry, comparison, measurement, and financial literacy concepts that are introduced earlier in the learning pathway. Tasks include counting objects, solving an addition equation, reading a picture graph, identifying shapes, comparing groups and lengths, and distinguishing between needs and wants. By requiring students to retrieve and apply previously learned concepts across multiple mathematical domains, 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 Imagine+ Math Interleaved Practice for grade K provides eight student-facing practice sets that require students to apply a variety of previously learned skills and concepts within a single practice session, rather than focusing on one skill at a time. For example, "Interleaved Practice #1" combines tasks from multiple mathematical domains, including number sense, measurement, geometry, and data. By integrating previously learned content from different domains within the same activity, the materials provide interleaved opportunities for practice with both skills and concepts across learning pathways.

The Teacher Guide includes a “Connecting Mathematical Concepts with Interleaved Practice” section that explains how interleaved practice combines previously learned skills and concepts from multiple mathematical domains within a single activity. The guide directs educators to have students explain strategy choices, identify strengths and misconceptions across content areas, and use results to provide reinforcement, targeted support, or extension. This guidance enables interleaved practice 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.

Imagine+ Math provides tasks that require students to interpret, analyze, and evaluate mathematical models and representations. 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 own model to understand the problem, analyze the relationship between the model and their solution, and determine whether their answer is reasonable by explaining how they know it makes sense.

The materials provide tasks that require students to interpret, analyze, and evaluate mathematical models and representations. In "Interleaved Practice #1" for grade K, students engage with multiple visual representations (including ten-frames, picture graphs, counters, and groups of objects) to solve mathematical tasks. Students interpret a ten-frame to determine the quantity of counters shown, analyze groups of objects to compare sets and identify which group has more or less, and examine visual representations to make sense of mathematical situations. As students use information from the models to answer questions and justify comparisons, they evaluate the accuracy of their conclusions based on the evidence provided in the representation.

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

Imagine+ Math provides opportunities for students to create pictorial representations of mathematical situations. In the K–2 Problem-Solving Organizer, a designated “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 representation to communicate their mathematical thinking and model the problem situation.

The materials provide opportunities for students to create and use concrete models to represent mathematical situations. In the grade K digital lesson “Decomposing 10,” the Independent Practice activity has students use ten-frame models with colored counters to represent different ways to decompose 10. Students select concrete representations such as 5 and 5, 6 and 4, or 8 and 2. They also model part-whole relationships and demonstrate their understanding of decomposing 10 through tangible representations rather than abstract numbers alone.

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

Imagine+ Math provides opportunities for students to apply their conceptual understanding to new problem situations and contexts. In the grade K “Draw Conclusions from Picture Graphs” digital lesson, the Mastery Check presents a different graph and real-world scenario on each item, such as determining how many ladybugs Russ finds, how many sunny days are shown on a weather graph, or how many crabs Kalia sees at the beach. Because each item presents a new data set and context, students must transfer their understanding of how picture graphs represent quantities and part-to-whole relationships, rather than repeating the same example.

The materials provide opportunities for students to apply their conceptual understanding to new problem situations and contexts beyond those presented in the lesson. In the Imagine+ Math “Enrichment and Extension” section's Draw Conclusions from Picture Graphs activities, students collect data from their own environment, organize and represent it with picture graphs, and use the graphs to answer questions, generate their own questions, and create story problems through activities such as Create Your Own Graph, Graph Scavenger Hunt, and Story Problems with Graphs. Because students work with self-generated data and authentic contexts, they must transfer their understanding of picture graphs to unfamiliar situations, rather than rely on provided examples.

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

Imagine+ Math provides repeated, structured activities designed to build the automaticity and fluency needed for grade-level mathematical tasks. In the grade K fluency activities, the Dot Flash activity has students briefly view a flashcard displaying one to five dots for two to three seconds and quickly identify the quantity, strengthening automaticity with subitizing and number recognition without relying on one-to-one counting. Additional activities, including Pattern Clap and Shape Hunt, provide repeated, purposeful practice with patterns, shapes, and data concepts, helping students develop increasing accuracy, efficiency, and confidence.

In the grade K Interleaved Practice, “Practice Set 3” integrates nine TEKS-aligned problems into a single practice set. Students move among counting objects, writing the number of stars shown, completing a ten-frame, counting by tens, and distinguishing circles from other shapes rather than practicing a single skill in isolation. This mixed-skill format requires students to repeatedly recall and apply foundational number sense and geometry concepts with increasing accuracy and efficiency.

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

Imagine+ Math provides opportunities for students to apply efficient, flexible, and accurate mathematical procedures throughout the learning pathway. In the grade K Interleaved Practice, each practice set intentionally combines counting, comparing, number recognition, early addition and subtraction, geometry, and other grade K concepts rather than isolating a single skill. Because problem types vary within each session, students must determine the most appropriate mathematical procedure for each item, apply it accurately, and transition efficiently among strategies as they solve the problems.

The materials include opportunities for students to apply efficient, flexible, and accurate mathematical procedures. In the grade K enrichment and extension activities, students interpret graphs and solve various questions based on represented data. They compare quantities, determine differences, analyze information displayed in graphs, and use the data to answer questions and solve problems presented in different contexts. Because the activities require students to select the appropriate procedure for each task rather than rely on a single strategy, they develop flexibility in applying mathematical concepts across multiple problem types.

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.

Imagine+ Math provides opportunities for students to evaluate mathematical representations and models for efficiency, flexibility, and accuracy. On the grade K “Making Shape Models” worksheet, students examine shape models and everyday objects, compare their defining attributes, and determine which geometric representation most accurately matches each object. As they distinguish among multiple shape models, students evaluate the accuracy of each representation, consider flexible ways to identify shapes based on their attributes rather than appearance alone, and select the most appropriate model to represent the object.

The materials include a grade K “Teacher Supports for Making Shape Models” enrichment and extension activity (the Shape Construction Challenge), which asks students to build a three-dimensional model using sticks and clay and explain the design process and the shapes they used. The educator guidance encourages students to describe how 2-D shapes combine to form 3-D structures, supporting mathematical communication and conceptual understanding.

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

Imagine+ Math contains guidance to support students in selecting increasingly efficient approaches to solving mathematics problems. The grade K Interleaved Practice directs educators to engage students in discussions about how they solved each problem, why they selected a particular strategy, and whether another approach might also work. Reflection questions and educator observations encourage students to explain their reasoning, compare strategies, and refine their mathematical decision-making as they work through varied problem types. The guidance also explains that the eight Interleaved Practice sets can be implemented before or after a lesson, as warm-up activities, exit tickets, learning center tasks, or additional practice, providing repeated opportunities for educators to help students move toward increasingly efficient problem-solving strategies.

The materials contain guidance to support students in selecting increasingly efficient approaches to solving mathematics problems. In the grade K “Adding with Objects” lesson, the “Supports for Struggling Students” section includes pre-teaching and reteaching strategies to help educators identify student misconceptions, scaffold conceptual understanding, and introduce alternative problem-solving approaches when needed. The guidance equips educators with instructional actions that help students progress from foundational strategies to more efficient methods.

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

Imagine+ Math explicitly explains how both the conceptual and procedural emphasis of the TEKS are addressed throughout the Math Builder and Math Mastery learning pathways. In the 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, and explains 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 those procedures.

The materials clearly describe how lessons balance the conceptual understanding and procedural fluency highlighted by the grade K TEKS across each mathematical strand. In the Level K Alignment Guide, the “Mathematical Process Standards” section provides educators with explicit explanations of how each mathematical strand integrates both emphases. For example, one strand shows that the module focuses on applying mathematics to real-world problems (Process Standard A) as students solve addition and subtraction word problems, reinforcing foundational number sense while developing fluency with addition and subtraction procedures.

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.

Imagine+ Math gives students opportunities to use pictorial representations and abstract models to develop conceptual understanding and procedural fluency. The grade K digital lesson “Two-Digit Numbers above 20, III” presents pictures of objects (such as buttons and shells) that students cross out to model subtraction before recording the result as a number sentence. On the accompanying Subtraction Number Sentences worksheet, students continue by crossing out pictures to determine the difference and then circle the matching subtraction equation (such as 9 − 4 = 5), connecting their pictorial work to symbolic notation.

In the grade K "Count Out a Number of Objects" Mastery Check (questions 11–15), students count collections of real-world objects displayed on the screen, using them as concrete representations of quantities, before organizing and counting visual sets as pictorial models. Students then connect their counting to abstract number symbols by selecting or recording the numeral that matches the quantity shown.

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 grade K digital lesson “Add and Subtract within 10,” Activity 4, students represent a group of blue and red monsters by coloring circles to match the quantities shown, identify the corresponding addition equation, and use number tiles and operation symbols to construct the matching number sentence.

On the grade K Counting Objects up to 20 worksheet, students examine towers of stacked blocks and learn that each block represents one object before counting the blocks and writing the corresponding numeral. Students then apply the same process independently by counting collections of objects and recording the matching number.

The materials include explicit support for students to define and explain how representational models connect to abstract mathematical concepts as required by the TEKS. In the grade K digital lesson “Ordinals and Operations within 20,” the Addition Number Sentences worksheet guides students through examining a pictorial model of five blue cubes and three green cubes while explaining the purpose of the addition and equal signs before presenting the equation 5 + 3 = 8. Students then match additional pictorial models and word problems to their corresponding number sentences.

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 K digital instruction lesson “Identifying Shapes and Solids,” the materials help students develop academic mathematical language using visuals, real-world objects, and explicit vocabulary instruction. Characters introduce students to the terms flat shape and solid shape using familiar objects such as a soccer ball, stamp, ice cube, and door, modeling and demonstrating the differences by rotating the objects. Labeled visuals and narration introduce additional vocabulary, including circle, square, rectangle, triangle, sphere, cube, cylinder, and cone. Students strengthen their understanding by matching shape names to images, comparing shapes, and identifying real-world examples. The combination of visual representations, repeated vocabulary exposure, real-world connections, and interactive practice provides meaningful opportunities for students to develop and apply academic mathematical language.

In the grade K “English Language Support” document for “Identify Coin Names and Values,” the materials provide opportunities for students to develop academic mathematical language through visuals and structured language supports. Students use leveled sentence frames such as “This coin is called a ____. It is worth ____ cents” alongside labeled visuals of coins, pronunciation modeling, and graphic organizers that categorize coins by name and value. The materials differentiate these supports across proficiency levels from Pre-Production through Advanced, giving students repeated opportunities to hear, practice, and apply mathematical vocabulary while connecting coin names and values to visual representations. By pairing coin vocabulary with visuals, pronunciation modeling, and graphic organizers, the materials give students repeated concrete opportunities to build and use academic mathematical language.

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 provide embedded guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary during discussions with peers and the educator. Educators demonstrate how to use the Frayer model with student-friendly definitions, visuals, sentence frames, examples, and non-examples before students apply the organizer independently. Students explain vocabulary through partner discussions, restate a partner’s thinking, and respond to educator prompts using academic vocabulary in context. To extend learning, educators guide students to compare vocabulary terms, justify their reasoning, create original word problems and real-world examples, and support their ideas with mathematical evidence, helping students move from supported practice to independent mathematical discourse.

In the grade K Guided Learning Teacher Supports for “Identify and Compare Round Numbers,” the “Developing Vocabulary” section provides embedded guidance to support students’ use of academic mathematical vocabulary. Educators pre-teach the terms decompose, round numbers, and compare using base 10 blocks, a highlighted number line, real-world contexts, and sentence frames such as “The number ___ is a round number because it ends in ___.” These supports help students explain mathematical ideas and compare numbers using academic vocabulary during discussions 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 grade K Teacher Guide, the “Facilitating Discourse with Mathematical Vocabulary” and “Writing with Mathematical Vocabulary” sections provide embedded guidance to support students’ application of academic mathematical language in both oral and written discourse. Educators use categorized discussion prompts that require students to explain vocabulary in their own words, communicate with a partner, and reflect on their 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 receiving feedback from their peers or the educator.

In the grade K Guided Learning Teacher Supports for “Identify and Compare Round Numbers,” the “Developing Vocabulary” section provides embedded guidance for students to apply academic mathematical language during discourse. Using base 10 blocks, visual models, and sentence frames, students explain why a number is a round number, decompose numbers into groups of ten, and compare quantities using mathematical vocabulary in discussions with their peers and the educator. These structured supports promote the application of appropriate mathematical language while communicating mathematical ideas.

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 K digital lesson “Comparing Numbers up to 20,” the English Language Supports provide embedded guidance to facilitate mathematical conversations with peers. At the Beginning proficiency level, students work with a buddy to practice using comparison symbols. This allows them to hear mathematical language from a peer. At the High Intermediate level, educators facilitate small-group discussions in which students compare numbers using academic vocabulary and create their own comparison statements, providing opportunities to refine and use mathematical language with their peers.

In the grade K digital lesson “Compare Two Groups of Objects,” embedded guidance directs educators to structure peer conversations as students count and compare groups of animals using the terms compare, more, less, greater, fewer, and same. The lesson connects related vocabulary (e.g., greater = more and fewer = less) and includes discussion prompts (such as “How do you know when two groups are the same?”) that encourage students to explain their reasoning and apply comparison vocabulary during peer discussions.

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 K digital lesson “Comparing Flats and Solids,” the materials anticipate a variety of student answers by engaging students in comparing shapes using attributes such as sides, corners, edges, same, different, size, and color. Students explain how shapes are alike and different, identify shapes that belong to a group, and describe multiple ways to compare shapes. These tasks provide educators with insight into students’ thinking and common misconceptions (such as confusing sides, corners, and edges or comparing shapes by color rather than mathematical attributes), allowing educators to anticipate a range of responses during instruction.

In the grade K digital lesson “Add and Subtract within 10,” the “Support for Struggling Students” section walks educators through a scaffolded progression that begins with counting using number lines and concrete objects before introducing addition and subtraction with manipulatives. Students then transition from modeling “put together” and “take apart” situations with concrete materials to drawing visual representations. Educators learn explicit strategies to address misconceptions and build conceptual understanding before students move on to abstract problem-solving.

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

In the grade K Teacher Guide, the “Support for Struggling Students” and “Open-Ended Questions” sections embed the TEKS Mathematical Process Standards throughout lesson instruction. For example, students count objects arranged in different configurations to build one-to-one correspondence (K.1C) and respond to an open-ended question about counting to ten using their fingers to explain their thinking (K.1F). This integration continues across the remaining unit lessons, demonstrating that the materials embed the process standards within daily instruction and connect them to grade-level mathematical content, rather than teaching them in isolation.

In the grade K digital lesson “Compare Two Groups of Objects,” the “Mastery Check” asks students to use visual representations to count, compare, and analyze groups of elephants, snakes, and shapes to determine which group has more, fewer, or greater quantities. These tasks require students to reason about quantities, analyze visual models, and justify their selections using mathematical evidence rather than relying on rote counting. The lesson also includes Answer Rationales that reinforce mathematical reasoning and support instructional follow-up.

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 document how the TEKS Mathematical Process Standards appear across grade-level lessons and link to specific content within each instructional module. The Rationale for Learning Paths explains how the materials embed the process standards across grade K–6 lessons, providing opportunities for students to solve real-world problems, apply mathematical reasoning, and communicate their thinking throughout instruction. The Alignment Guide further demonstrates how the process standards connect to grade-level content within each instructional module, showing that the materials integrate the process standards with the TEKS content standards and reinforce them across the learning pathway rather than teaching them in isolation.

The grade K “Horizontal Concept Map” traces how mathematical concepts build on each other across the year, embedding the TEKS Mathematical Process Standards at each stage of the learning pathway. As students progress through the instructional sequence, they repeatedly engage in reasoning, problem-solving, representation, and mathematical communication while connecting new learning to prior understanding. This organization illustrates that the materials integrate the process standards with conceptual development and reinforce them across increasingly complex mathematical ideas, rather than teaching them 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 across the grade K–6 sequence. The introductory paragraph explains that the materials embed the process standards throughout the Math Builder and Math Mastery pathways, ensuring 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.” The guide identifies the process standards applied within each lesson and describes how students use mathematical tools, representations, and reasoning to meet lesson objectives.

The grade K “Horizontal Concept Map” illustrates how mathematical concepts connect across related lessons as students move through the instructional sequence. Students repeatedly engage in reasoning, representation, communication, and problem-solving while building on prior learning as they progress through the pathway. This progression shows how the materials embed the process standards across lessons and support the development of increasingly complex mathematical understanding.

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

The Imagine+ Math grade K Teacher Guide suggests ways that educators can help students think mathematically, persevere through challenging tasks, and make sense of mathematics. The “Promoting Self-Efficacy” section encourages educators to build confidence by having students predict answers, model think-aloud strategies when difficulties arise, and apply successful strategies to new problems, promoting productive perseverance. The “Demonstrating Understanding” section gives 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 grade K Interleaved Practice set mixes different problem types within a single practice session, rather than focusing on one skill at a time. In “Interleaved Practice 1,” for example, students solve tasks that involve addition, measurement comparison, and number relationships using directions that simply say to solve each problem and show their work, without a prescribed method. Students select their own strategies to count, draw, compare, and solve each problem, requiring them to reason through different mathematical concepts, persist across a sequence of tasks, and demonstrate their understanding through their chosen approach.

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 around the idea that a math problem can be solved in more than one valid way. The 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 they work through each problem, students decide which strategy fits best and explain their reasoning to the educator and their 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 while recognizing 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 “Communicating Mathematical Thinking” and “Supporting Multiple Solution Strategies” sections walk educators through a process in which students select a strategy, share their approach with their 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 . . . ” supports students as they put these explanations and justifications into words, reinforcing the idea 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 grade K fluency activities give students multiple opportunities to do mathematics collaboratively with their peers and the educator through hands-on tasks. Across activities such as Dot Flash, Pattern Clap, Shape Hunt, Favorite Fruit Graph, and Wants vs. Needs Sort, students solve problems, compare ideas, and discuss mathematical concepts in whole-class and small-group settings. These activities engage students in active mathematical thinking and verbal discussion, strengthening 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 their peers and the educator through a recurring Problem-Solving activity found in each unit, during which students share their solutions, respond to guiding questions, and explain their mathematical thinking during classroom discussions. The Writing & Discussing Math prompts—including questions such 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 their 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 describe their reasoning, compare solution strategies, justify why their approach works, and reflect on how another strategy might also be effective. These sections also give teachers 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.

In the Implementation Guide, the “Academic Discourse” section describes supports embedded in both the Mastery and Builder pathways. In the Mastery pathway, students respond to problem-solving tasks that prompt them to compare strategies and explain why a method works, along with reflection questions that ask them to self-assess and clarify their understanding. In the Builder pathway, downloadable worksheets include discussion questions with flexible formats for oral and written responses, giving students multiple ways to show 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.

Throughout the grade K Teacher Guide, each unit’s Common Misconceptions or Errors feature identifies a likely student misunderstanding within that domain and pairs it with Teacher Tips that help educators to address it. Each unit also includes open-ended questions (such as “How can you count to 10 using your fingers?”) that teachers can use to probe students’ thinking and extend the discussion. Together, these paired supports help educators address misconceptions, deepen conceptual understanding, and strengthen students’ mathematical reasoning.

In the Implementation Guide, the “Teacher Supports” section names Common Misconceptions as one of several supports available in every lesson across both the Mastery and Builder pathways. The guide’s decision chart directs educators to use this support when students appear confused or make repeated errors, describing it as a way to help students share their thinking and address a likely misunderstanding with clear, targeted feedback.